Session UP11: Poster Session VIII: Non-Neutral, Antimatter and Strongly Coupled Plasmas; Waves; Conventional and Spherical Tokamaks; Magneto-Inertial Fusion

First Experiments with ${e^{-}} \mathord{\left/ {\vphantom {{e^{-}} {H^{-}}}} \right. \kern-\nulldelimiterspace} {H^{-}}$ Plasmas: Enhanced Mode Damping and Transport

Negative Hydrogen ions are produced and confined in a room-temperature electron plasma, causing enhanced mode damping and particle transport effects. We accumulate an $H^{-}$ charge fraction ${n_{H^{-}} } \mathord{\left/ {\vphantom {{n_{H^{-}} } {n_{e} \sim 20\% }}} \right. \kern-\nulldelimiterspace} {n_{e} \sim 20\% }$ in about 200 seconds, as externally excited $H_{2} $ molecules undergo dissociative electron attachment in the plasma. The accumulated $H^{-}$ fraction causes a novel \textit{algebraic} damping of diocotron mode amplitude $A(t)$, and the damping is coincident with an \textit{enhanced} outward drift $\upsilon_{r} $ of the $H^{-}$ ions. That is, ${dA} \mathord{\left/ {\vphantom {{dA} {dt=-\alpha }}} \right. \kern-\nulldelimiterspace} {dt=-\alpha }$, with $\alpha \propto n_{H^{-}} \ast \upsilon_{r} $. We observe that heating the ${e^{-}} \mathord{\left/ {\vphantom {{e^{-}} {H^{-}}}} \right. \kern-\nulldelimiterspace} {H^{-}}$ plasma terminates the enhanced damping and enhanced centrifugal separation, both of which resume when plasma re-cools by cyclotron radiation at $B=$1.2T. Other interesting observations include: (1) enhanced $e^{\mathrm{-\thinspace }}$cooling from collisions with $H^{-}$ cooled by neutrals; (2) enhanced damping of plasma waves due to ${e^{-}} \mathord{\left/ {\vphantom {{e^{-}} {H^{-}}}} \right. \kern-\nulldelimiterspace} {H^{-}}$ collisional drag; (3) strong exponential damping of diocotron modes in a ``floppy'' nearly-pure $H^{-}$ plasma, created by rapid axial ejection of the electrons. Additional novel drift modes and instabilities are predicted theoretically in such a plasma [1]. [1] D.H.E. Dubin, Phys. Plasmas 17, 112115 (2010).   

Novel Kinetic Trapped-Particle Mechanism for Modulational Instability in Nonlinear Plasma Waves

Modulational instabilities, in which a longer-wavelength wave grows on a shorter-wavelength nonlinear wave-train, are endemic in plasmas. This poster discusses a new instability mechanism caused by a small fraction $f$ of particles trapped in the potential wells of the wave-train. This mechanism describes a recently-observed modulational/parametric decay instability in Trivelpiece-Gould waves$^{\mathrm{2}}$, and could also be active in a broad range of nearly-collisionless nonlinear plasma waves. In the instability, adjacent peaks of the wave-train approach one-another (and therefore recede from the next peaks). This adiabatically heats particles trapped between the approaching peaks, and cools trapped particles between receding peaks. This heating and cooling would normally produce a pressure restoring force that stabilizes the motion of the peaks. However, some trapped particles are heated enough to become untrapped, and these particles are then retrapped and cooled between receding peaks. The net effect of this detrapping and retrapping is to change the sign of the pressure force, producing a trapped particle pressure that amplifies the modulations with a growth rate scaling as$_{\mathrm{\thinspace }}\surd f$. Expressions for the instability growth rate will be presented and compared with experiments and simulations. $^{\mathrm{2}}$See adjacent poster   

Long-Range Collisions : Overview and Open Questions

Wide-ranging theory and experiments at UCSD have broadly characterized the enhanced transport of particles, momentum, and energy from "long-range" collisions. These are drift-kinetic collisions with impact parameters in the range r$_{\mathrm{c}}$\textless $\rho $\textless $\lambda_{\mathrm{D\thinspace }}$, distinguished from "classical" velocity-scattering collisions with $\rho $\textless r$_{\mathrm{c}}$ . These long-range interactions are dominant in non-neutral plasmas, and can enhance the electron channel heat transport and particle transport in neutral plasmas. Some observed characteristics are: (-a-) Cross-field thermal diffusivity is \textit{independent }of magnetic field, and is observed up to 10\textasciicircum 6 times classical in electron plasmas at B$=$12.kG. (-b-) Cross-field particle diffusion and viscosity are strongly enhanced, but \textit{reduced by plasma drift-flow shear, }with B-scalings dependent on the shear and on the axial plasma length. Viscosity up to 10\textasciicircum 8 times classical is observed in short electron plasmas. (-c-) Individual particle slowing rates are substantially enhanced at low emperatures, exhibiting the novel effects of "velocity caging" and multiple simultaneous collisions. Recent experiments observe 10x enhanced collisional plasma wave damping in cold ion plasmas.[2] (-d-) Open questions remain concerning the transition from the 3D drift-kinetic regime to the 2D drift-only regime, especially with regard to the subtleties of shear viscosity. [2] M.Affolter et al, Phys.Rev.Lett \textbf{117}, 155001 (2016) and other references at NNP.ucsd.edu .   

Finite-Length Diocotron Modes in a Non-neutral Plasma Column

Diocotron modes are 2D distortions of a non-neutral plasma column that propagate azimuthally via $E\times B$ drifts. While the infinite-length theory of diocotron modes is well-understood for arbitrary azimuthal mode number $\ell$, the finite-length mode frequency is less developed (with some exceptions\footnote{T. J. Hilsabeck and T. M. O'Neil, Phys. Plasmas \textbf{8}, 407 (2001).} \footnote{K. S. Fine and C. F. Driscoll, Phys. Plasmas \textbf{5}, 601 (1998).\label{f2}}), and is naturally of relevance to experiments. In this poster, we present an approach to address finite length effects, such as temperature dependence of the mode frequency. We use a bounce-averaged solution to the Vlasov Equation, in which the Vlasov Equation is solved using action-angle variables of the unperturbed Hamiltonian. We write the distribution function as a Fourier series in the bounce-angle variable $\psi$, keeping only the bounce-averaged term. We demonstrate a numerical solution to this equation for a realistic plasma with a finite Debye Length, compare to the existing $\ell=1$ theory, and discuss possible extensions of the existing theory to $\ell\neq1$.   

Measurement of Correlation-Enhanced Collision Rates in the Mildly Correlated Regime ($\Gamma \quad \sim $\textbf{1)}

We have recently measured correlation-enhanced perpendicular-to-parallel collision rates $\nu_{\bot //} $ in cryogenic, strongly magnetized ion plasmas in the mildly correlated regime. The enhancement of $\nu_{\bot //} $ is directly analogous [1] to the correlation-enhancement of fusion collisions in hot dense stellar plasma, as first analyzed by Salpeter [2]. The enhancement occurs because plasma screening reduces the repulsive Coulomb potential between charges, allowing closer collisions for a given relative energy. The correlations are parameterized by $\Gamma =e^{2}/aT$which is the ratio of the nearest neighbor potential energy to the ion thermal energy. Our prior measurements [3] over the range $0<\Gamma <15$ observed enhancement up to 10$^{\mathrm{7}}$x, in broad agreement with Salpeter ``equilibrium screening'' theory. However recent ``dynamical screening'' theories [4] predict negligible enhancement for $\Gamma \sim 1$. In our magnesium ion plasmas, we obtain $\Gamma \sim 1$ at densities $n=2\times 10^{7}\mbox{cm}^{-3}$and temperatures$T\cong 5\times 10^{-5}\mbox{eV}$. Recent improvements in our cooling and diagnostic lasers provide better long-term stability in $T$, enabling more accurate measurements of the enhancements. Our new results rule out the dynamical screening theories. [1] D.H.E. Dubin, Phys. Plasmas \textbf{15}, 055705, (2008) [2] E.E. Salpeter, Austr. J. Phys., 7, 373, (1954) [3] F. Anderegg et.al., Phys. Rev. Lett. \textbf{102}, 185001, (2009) [4] W. D\"{a}ppen and K. Mussack Contrib. Plasma Phys. 52, 149, (2012).   

The Influence of Trapped Particles on the Parametric Decay Instability of Near-Acoustic Waves

We present quantitative measurements of a decay instability to lower frequencies of near-acoustic waves. These experiments are conducted on pure ion plasmas confined in a cylindrical Penning-Malmberg trap. The axisymmetric, standing plasma waves have near-acoustic dispersion, discretized by the axial wave number $k_{z} = m_{z}(\pi/L_{p})$. The nonlinear coupling rates are measured between large amplitude $m_{z} = 2$ (pump) waves and small amplitude $m_{z} = 1$ (daughter) waves, which have a small frequency detuning $\Delta\omega = 2\omega_{1} - \omega_{2}$. Classical 3-wave parametric coupling rates are proportional to pump wave amplitude as $\Gamma \propto (\delta n_{2}/n_{0})$, with oscillatory energy exchange for $\Gamma < \Delta\omega/2$ and decay instability for $\Gamma > \Delta\omega/2$. Experiments on cold plasmas agree quantitatively for oscillatory energy exchange, and agree within a factor-of-two for decay instability rates. However, nascent theory suggest that this latter agreement is merely fortuitous, and that the instability mechanism is trapped particles. Experiments at higher temperatures show that trapped particles reduce the instability threshold below classical 3-wave theory predictions.   

Simulating the experimental detectability of axisymmetric Bernstein modes in a finite-length non-neutral plasma

We use a 2-D PIC code to model high-frequency axisymmetric oscillations in a finite-length pure-ion plasma. These modes are not detectable in the surface charge on the walls of infinite-length plasmas because of axisymmetry and lack of z-dependence. This is not true in a finite-length plasma, because the perturbed density has to have nodes a short distance beyond the ends of the plasma. This gives the modes a $\cos(k_z z)$ or $\sin(k_z z)$ dependence, with a $k_z$ such that an integral number (approximately) of half-wavelengths fit into the plasma. This $z$-dependence makes the mode detectable in the surface charge on the walls. There are two effects that contribute to the size of the signal induced on the wall. For the bulk of the plasma the change in the total charge underneath a section of the wall is proportional to the density perturbation $\delta$n, and is due to $\nabla \cdot v$. The other contributor is the movement of the end of the plasma column due to the $v_z$ of the mode. This is proportional to $v_z\partial n_0/\partial z$ and is therefore confined to the ends of the plasma. The relative size of these effects depends on the aspect ratio of the plasma. We will quantify what size of density perturbation is necessary to produce experimentally measurable signals.   

Dynamics and stability of electron plasma vortices under external strain

The behavior of an initially axisymmetric 2D ideal vortex under an externally imposed strain flow is studied experimentally [1]. The experiments are carried out using pure electron plasmas confined in a Penning-Malmberg trap; here, the dynamics of the plasma density transverse to the field are directly analogous to the dynamics of vorticity in a 2D ideal fluid. An external strain flow is applied using boundary conditions in a way that is consistent with 2D fluid dynamics. Primarily, elliptical distortions of the vortex core are studied, including dynamical orbits, equilibria, and stability properties. In the case of a quasi-flat vorticity profile, the results are in good agreement with a simple theory of a piecewise elliptical vorticity distribution [2]. For smooth vorticity profiles, deviations from this theory are discussed. Results for time-dependent strain and tests of adiabatic behavior will also be discussed. These experiments may be relevant to many types of quasi-2D fluid behavior, including the dynamics of geophysical fluids, other types of strongly magnetized plasma, and various astrophysical scenarios. [1] N. C. Hurst, et. al., Phys. Rev. Lett. 117, 235001 (2016). [2] S. Kida, J. Phys. Soc. Japan 50, 3517 (1981).   

Electron Plasma Heating due to Collisional Separatrix Crossings

We observe heating of a pure electron plasma as it undergoes forced sloshing through an electrostatic squeeze potential. Our preliminary measurements show that separatrix induced heating is much larger than bulk viscous heating in the low collisionality regime and the scaling of the heating rate is consistent with theoretical predictions. The cylindrical plasma column is confined in a Penning-Malmberg trap where a $\theta $-symmetric squeeze is applied to the axial midplane of the column. This squeeze creates a velocity separatrix that divides the phase space into regions of trapped and passing particles. Oscillating the confinement end potentials of the trap forces the plasma a distance, $\delta $L, through the squeeze potential. During the compression and expansion of the trapped particle orbits there is collisional separatrix heating, which is caused by particle diffusion across the separatrix, as well as bulk viscous heating. The heating rate is measured via changes in frequency of the m$_{\mathrm{\theta }}=$ 1 Diocotron mode. We use sloshing frequencies, f$_{\mathrm{sl}}$, that are greater than the collision rate, $\nu_{\mathrm{c\thinspace }}$, and smaller than the axial bounce frequency in order to minimize bulk viscous heating. For the low collisionality regime, the heating rate due to collisional separatrix crossings is predicted to scale as dT/dt $\propto $ T($\delta $L/L)$^{\mathrm{2}}$ (f$_{\mathrm{sl}}\nu _{\mathrm{c}})^{\mathrm{1/2}}$ which is in agreement with our results as well as results from recent experiments in pure ion plasmas (F. Anderegg, et al., BAPS.2016.DPPP.P10.114)   

Discoveries and developments in support of electron/positron pair plasmas.

Novel techniques being developed by the APEX/PAX (A Positron Electron eXperiment/ Positron Accumulation Experiment) project are presented. These are crucial steps ib enabling the creation and confinement of an electron-positron pair plasma in the magnetic field of a levitated dipole. A high flux ($~10^8$/s) of low-energy positrons ($<20$ eV) has been produced and characterized at the NEPOMUC positron source at FRM-II in Munich, leading to nearly $100\%$ injection of positrons into a dipole magnetic field. Luminescent responses to positrons and electrons have been measured for several phosphors, increasing their utility for both positron beam and plasma diagnostics. Compared to other levitated dipoles, APEX will be much smaller, requiring the solution to a complex optimization problem. Proof-of-principle tests are in progress to verify both the levitation feedback system and cold-head cooling. Finally, several future projects with linear positron traps will be discussed. One extends the capabilities of NEPOMUC by efficient generation of pulsed beams; another seeks to accumulate record numbers of positrons.   

Positron experiments in a supported dipole trap.

A new levitated dipole trap is being designed to experimentally study the unique physics of electron-positron pair plasmas. In parallel with the design process, a number of key questions have been investigated in a supported dipole trap. This includes the use of $E\times B$ drift injection, the manipulation of positron spatial distribution in the trap by external electrostatic potentials, and studies of the positron confinement time in a system with asymmetric perturbations. In particular, $E\times B$ drift injection has been shown to be a viable and robust means of injecting positrons from the NEPOMUC (NEutron-induced POsitron source MUniCh) beam line, across the separatrix, and into the confinement region of the dipole. Nearly 100\% injection of the beam has been demonstrated for a large region of parameter space. Once in the trap, positrons can be moved deeper into the confinement region by means of either static or oscillating potentials applied strategically to the segmented outer wall of the trap. Finally, once the injection potentials are switched off, experiments have demonstrated a long-lived component of the trapped positrons lasting for hundreds of milliseconds.   

Plasma diagnostic development and UHV testing for the ALPHA collaboration at Marquette University

At Marquette, we are developing the next generation of nonneutral plasma diagnostics for the ALPHA experiment at CERN. ALPHA is building a new vertical experiment to test the gravitational interaction of antihydrogen with Earth. This expansion requires significant changes to the design of our plasma diagnostic suites: the next generation of tools must be able to measure plasmas from two directions, and must be capable of operating in a horizontal position. The diagnostic suite includes measurements of plasma density, shape, and temperature. The hardware used includes a MicroChannel Plate (MCP), a Faraday Cup, and an electron gun. In addition, we are building a vacuum chamber to test the viability of 3-d printed components for UHV compatibility, with target pressures of 10$^{\mathrm{-10}}$ mbar.   

Non-Neutral Plasma Innovations for Antihydrogen Production

In the ALPHA collaboration in 2016, we succeeded in major improvements in the non-neutral plasma manipulations involved in creating antihydrogen. ALPHA uses plasmas of antiprotons, positrons, and electrons in Penning-Malmberg traps at cryogenic temperatures and 1-3T magnetic fields. the first development was SDREVC, a combination of the strong drive regime with EVC which stabilizes particle numbers and densities allowing us to have repeatable and tunable plasma conditions. After establishing SDREVC, we took advantage of our new stability and changed our antihydrogen mixing procedure from autoresonance excitation of antiprotons to "smerge," where we slowly lower the potential barrier between the antiproton and positron plasmas. Using smerge, we achieved a ten-fold increase in the average trapping rate. With a higher trapping rate, we then proceeded to develop a method to send electron and positron plasmas through trapped antihydrogen atoms in order to trap additional sets of antihydrogen atoms which allowed us to trap dozens of antiatoms. With these plasma developments that lead to much higher numbers of antihydrogen atoms, we are able to do some measurements more efficiently and additional measurements previously impossible.   

Integral Transport Analysis Results for Ions Flowing Through Neutral Gas

Results of a computational model for the flow of energetic ions and neutrals through a background neutral gas will be presented. The method models reactions as creating a new source of ions or neutrals if the energy or charge state of the resulting particle is changed. For a given source boundary condition, the creation and annihilation of the various species is formulated as a 1-D Volterra integral equation [1] that can quickly be solved numerically by finite differences. The present work focuses on multiple-pass, 1-D ion flow through neutral gas and a nearly transparent, concentric anode and cathode pair in spherical, cylindrical, or linear geometry. This has been implemented as a computer code for atomic (3He, 3He$+$, 3He$++)$ and molecular (D, D2, D-, D$+$, D2$+$, D3$+)$ ion and neutral species, and applied to modeling inertial-electrostatic conÞnement (IEC) devices. The code yields detailed energy spectra of the various ions and energetic neutral species. Calculations for several University of Wisconsin IEC and ion implantation devices will be presented. [1] G.A. Emmert and J.F. Santarius, ``Atomic and Molecular Effects on Spherically Convergent Ion Flow I: Single Atomic Species {\&} II: Multiple Molecular Species'', Phys. Plasmas 17, 013502 {\&} 013503 (2010).   

An investigation into the role of metastable states on excited populations of weakly ionized argon plasmas, with applications for optical diagnostics.

Low temperature plasmas ($T_e < 10 \ eV$) are ubiquitous in the medical, industrial, basic, and dusty plasma communities, and offer an opportunity for researchers to gain a better understanding of atomic processes in plasmas. Here, we report on a new atomic dataset for neutral and low charge states of argon, from which rate coefficients and cross-sections for the electron-impact excitation of neutral argon are determined. We benchmark by comparing with electron impact excitation cross-sections available in the literature, with very good agreement. We have used the Atomic Data and Analysis Structure (ADAS) code suite to calculate a level-resolved, generalized collisional-radiative (GCR) model for line emission in low temperature argon plasmas. By combining our theoretical model with experimental electron temperature, density, and spectral measurements from the Auburn Linear eXperiment for Instability Studies (ALEXIS), we have developed diagnostic techniques to measure metastable fraction, electron temperature, and electron density. In the future we hope to refine our methods, and extend our model to plasmas other than ALEXIS.   

Diffusion of Magnetized Binary Ionic Mixtures at Ultracold Plasma Conditions

Ultracold plasma experiments offer an accessible means to test transport theories for strongly coupled systems. Application of an external magnetic field might further increase their utility by inhibiting heating mechanisms of ions and electrons and increasing the temperature at which strong coupling effects are observed. We present results focused on developing and validating a transport theory to describe binary ionic mixtures across a wide range of coupling and magnetization strengths relevant to ultracold plasma experiments. The transport theory is an extension of the Effective Potential Theory (EPT), which has been shown to accurately model correlation effects at these conditions, to include magnetization. We focus on diffusion as it can be measured in ultracold plasma experiments. Using EPT within the framework of the Chapman-Enskog expansion, the parallel and perpendicular self and interdiffusion coefficients for binary ionic mixtures with varying mass ratios are calculated and are compared to molecular dynamics simulations. The theory is found to accurately extend Braginskii-like transport to stronger coupling, but to break down when the magnetization strength becomes large enough that the typical gyroradius is smaller than the interaction scale length.   

Effects of Coulomb Coupling on the Stopping Power of Plasmas

Stopping power of charged particles in plasma is important for a detailed understanding of particle and energy transport in plasmas, such as those found in fusion applications. Although stopping power is rather well understood for weakly coupled plasmas, this is less the case for strongly coupled plasmas. In order to shed light on the effects of strong Coulomb coupling, we have conducted detailed molecular dynamics simulations of the stopping power of a One-Component Plasma (OCP) across a wide range of conditions. The OCP allows first-principle computations that are not possible with more complex models, enabling rigorous tests of analytical theories. The molecular dynamics simulations were compared to two analytical theories that attempt to extend traditional weakly-coupled theories into the strong coupling regime. The first is based on the binary approximation, which accounts for strong coupling via an effective scattering cross section derived from the effective potential theory. The second is based on the dielectric function formulation with the inclusion of a local field corrections.   

Transport Regimes Spanning Magnetization-Coupling Phase Space

The manner in which transport properties vary over the entire parameter-space of coupling and magnetization strength is explored. Four regimes are identified based on the relative size of the gyroradius compared to other fundamental length scales: the collision mean free path, Debye length, distance of closest approach and interparticle spacing. Molecular dynamics simulations of self-diffusion and temperature anisotropy relaxation spanning the parameter space are found to agree well with the predicted boundaries. Comparison with existing theories reveals regimes where they succeed, where they fail, and where no theory has yet been developed. The results suggest that magnetic fields may be used to assist ultracold neutral plasma experiments to reach regimes of stronger electron coupling by reducing heating of electrons in the direction perpendicular to the magnetic field.. By constraining electron motion along the direction of the magnetic field, the overall electron temperature is reduced nearly by a factor of three. A large temperature anisotropy develops as a result, which can be maintained for a long time in the regime of high electron magnetization.   

Cooling expansion in an inhomogeneous ultracold plasma created by using space shaped laser pulses.

The ultracold neutral plasmas (UCNP) are created by photoionizing the laser cooled atoms. Here, our main goal is to enhance the coupling strength of UCNP and also try to mitigate the disorder induced heating (DIH). For this, we considered an inhomogeneous UCNP which has been created by using the space shaped laser pulses. An adiabatic expansion of this UCNP from higher dense regions to lower dense regions have been studied. $\backslash $pardA particle based approach has been employed to explore the dynamical evolution of UCNP. The lighter electron density is presumed to follow the Boltzman relation while the heavy ions interact through a Yukawa potential. The spatial average properties (central moments) like density, velocity and temperature have been studied. In the preliminary results, it is observed that as the ions undergo expansion, ion temperature gets lower in higher density regions and vice versa. Several cases of ion flow configuration have been considered for this study.   

Measurement of strong coupling influences on the electron-ion collision rate in an ultracold plasma

We have experimentally measured electron oscillation damping rates in ultracold plasmas formed with a minimal (less than 10 $\mu$eV) initial kinetic energy. Under our conditions, the oscillation damping rate is predicted to be dominated by electron-ion collisions and so the measuring the damping rate provides a measure of the electron-ion collision rate. Strong coupling effects are expected to be relevant for these conditions, and indeed we observe a damping rate over a factor of 3 larger than the rate obtained assuming weak coupling. We compare our measurements with theoretical predictions derived from other theories that extend processes such as electron-ion temperature equilibration and stopping power to parameters with significant strong coupling. Simple extensions of these theories do not match our measurements, with implications for the applicability of standard collision approximations that are often used.   

The ion cyclotron turbulence generated by a low frequency kinetic Alfven wave, and the related turbulent heating of ions

The ion cyclotron instability driven by the strong kinetic Alfven wave is investigated as a possible source of the anisotropic heating of ions in the coronal holes and solar wind. We present a novel model of a plasma with coupled inhomogeneous current and the sheared flow, which follows from the studies of the particles motion in the electric field of the kinetic Alfven wave of the finite wavelength. The investigation is performed employing the non-modal kinetic theory grounded on the shearing modes approach. The solution of the governing linear integral equation for the perturbed potential displays that the flow velocity shear, which for the corona conditions may be above the growth rate of the ion cyclotron instability in plasma with steady current, changes the exponential growth of the ion cyclotron potential on the power function of time, that impedes the growth of the unstable ion cyclotron wave and reduces the turbulent heating rate of ions across the magnetic field.   

Tertiary instability of zonal flows within the Wigner--Moyal formulation of drift turbulence

The stability of zonal flows (ZFs) is analyzed within the generalized-Hasegawa--Mima model. The necessary and sufficient condition for a ZF instability, which is also known as the tertiary instability, is identified. The qualitative physics behind the tertiary instability is explained using the recently developed Wigner--Moyal formulation [1] and the corresponding wave kinetic equation (WKE) in the geometrical-optics (GO) limit. By analyzing the drifton phase space trajectories, we find that the corrections proposed in Ref.~[1] to the WKE are critical for capturing the spatial scales characteristic for the tertiary instability. That said, we also find that this instability itself cannot be adequately described within a GO formulation in principle. Using the Wigner--Moyal equations, which capture diffraction, we analytically derive the tertiary-instability growth rate and compare it with numerical simulations. \\ $[1]$ D.~E. Ruiz, J.~B. Parker, E.~L. Shi, and I.~Y. Dodin, {\it Zonal-flow dynamics from a phase-space perspective}, Phys. Plasmas {\bf 23}, 122304 (2016).   

Parametric decay of plasma waves near the upper-hybrid resonance

An intense X wave propagating perpendicularly to dc magnetic field is unstable with respect to a parametric decay into an electron Bernstein wave and a lower-hybrid wave. A modified theory of this effect is proposed that extends to the high-intensity regime, where the instability rate $\gamma$ ceases to be a linear function of the incident-wave amplitude [1]. An explicit formula for $\gamma$ is derived and expressed in terms of cold-plasma parameters. Theory predictions are in reasonable agreement with the results of the particle-in-cell simulations reported in Ref.~[2].\\{[1]} I.~Y. Dodin and A.~V. Arefiev, Phys. Plasmas {\bf 24}, 032119 (2017).\\{[2]} A.~V. Arefiev, I.~Y. Dodin, A. K\"ohn, E.~J. Du Toit, E. Holzhauer, V.~F. Shevchenko, R.~G.~L. Vann, arXiv:1612.07860, to appear in Nucl. Fusion.   

Hall-Driven Effects in Electron-Magnetohydrodynamic Z-Pinch--Like Implosions

In previous work,\footnote{A. S. Richardson, et al., Physics of Plasmas, 23(5), 2016} it has been shown that density gradients give rise to Hall-driven magnetic field penetration in electron-magnetohydrodynamics (EMHD). Here, we examine the effect of geometry on this Hall-driven penetration. It is found that in z-pinch--like geometries, the implosion velocity of a Hall-driven magnetic pinch depends on its distance from the axis, moving faster as it approaches the axis. We compare analytical and numerical results for the z-pinch geometry to previous results for a rectangular slab geometry. Similar effects are found in both geometries, including electron-inertia driven nonlinearities, a Kelvin-Helmoltz like instability, and the generation of vortices. The electric field in the vortices is also examined, to determine how much charge separation occurs. If the electric field becomes large enough, it could accelerate the background ions to very high energies.   

Ion-Acoustic Wave-Particle Energy Flow Rates

We present an experimental characterization of the energy flow rates for ion acoustic waves. The experiment is performed in a cylindrical, magnetized, singly-ionized Argon, inductively-coupled gas discharge plasma that is weakly collisional with typical conditions: n\textasciitilde 10$^{\mathrm{9}}$cm$^{\mathrm{-3}}$ T$_{\mathrm{e}}$\textasciitilde 9 eV and B\textasciitilde 660 kG. A 4 ring antenna with diameter similar to the plasma diameter is used for launching the waves. A survey of the zeroth and first order ion velocity distribution functions (IVDF) is done using Laser-Induced Fluorescence (LIF) as the main diagnostics method. Using these IVDFs along with Vlasov's equation the different energy rates are measured for different values of ion velocity and separation from the antenna.   

Interaction of Kelvin-Helmholtz and drift wave instabilities in IMPED

The unique control features of Inverse Mirror Plasma Experimental Device (IMPED) enables production of magnetized plasmas with variable radial density, potential and electron temperature profiles over a wide range. The radial density and potential profiles are tailored to simultaneously excite Kelvin-Helmholtz and drift wave instability. The instabilities are identified by measuring the wavelength, amplitude of density and potential fluctuations and radial profiles of density and plasma potential. These instabilities are observed to interact nonlinearly with each other leading to the formation of side bands. Bispectral analysis has been used to confirm the nonlinear coupling. The side bands are usually asymmetric in nature. However, the extent of asymmetry, i.e. the ratio of the power of the left to the right side band is controlled experimentally, which occasionally leads to symmetric side bands. The method of excitation and control of these instabilities and the probable mechanism of power distribution in side bands is presented.   

Nonlinear saturation of Weibel-type instabilities

Weibel-type instabilities, which grow in plasmas with anisotropic velocity distribution, have been studied for many years and drawn recent interest due to their broad applicability spanning from laboratory laser plasmas to origins of intergalactic magnetic fields in astrophysical plasmas. Magnetic particle trapping has been considered as the main mechanism of the nonlinear saturation of these instabilities. However, novel continuum kinetic and two-fluid five moment simulations show that there are additional effects -- the transverse flow introduced by the magnetic field creates a secondary electrostatic two-stream instability which alters the saturation and is responsible for a quasi-periodic behavior in the nonlinear phase.   

Zonal-flow dynamics from a phase-space perspective

The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in the studies of zonal flows (ZFs) emerging from DW turbulence. However, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics (GO) limit. Here we present a new theory that captures both of these effects, while still treating DW quanta (``driftons") as particles in phase space [Ruiz {\it et~al.}, Phys. Plasmas {\bf 23}, 122304 (2016)]. In this theory, the drifton dynamics is described by an equation of the Wigner--Moyal type, which is analogous to the phase-space formulation of quantum mechanics. The ``Hamiltonian" and the ``dissipative" parts of the DW--ZF interactions are clearly identified. Moreover, this theory can be interpreted as a phase-space representation of the second-order cumulant expansion (CE2). In the GO limit, this formulation features additional terms missing in the traditional WKE that ensure conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the traditional WKE. Numerical simulations are presented to illustrate the importance of these additional terms.   

Studies of Plasma Instabilities using Unstructured Discontinuous Galerkin Method with the Two-Fluid Plasma Model

The discontinuous Galerkin (DG) method has the advantage of resolving shocks and sharp gradients that occur in neutral fluids and plasmas. An unstructured DG code has been developed in this work to study plasma instabilities using the two-fluid plasma model. Unstructured meshes are known to produce small and randomized grid errors compared to traditional structured meshes. Computational tests for Rayleigh-Taylor instabilities in radially-converging flows are performed using the MHD model. Choice of grid geometry is not obvious for simulations of instabilities in these circular configurations. Comparisons of the effects for different grids are made. A 2D magnetic nozzle simulation using the two-fluid plasma model is also performed. A vacuum boundary condition technique is applied to accurately solve the Riemann problem on the edge of the plume.   

Study of Beta-induced Alfvén Eigenmodes with RMP system in J-TEXT Tokamak

The feature of Beta-induced Alfvén eigenmodes (BAE) are studied by two sets of external applied resonant magnetic perturbations (RMPs) system with different magnetic field component in J-TEXT Ohmic plasmas. The experimental results show that with moderate amplitude of RMP, a 3/1 magnetic oscillation emerges, which is regarded as BAE and has standing wave structure with its frequency in the gap triggered by kinetic thermal ion effect in the Alfvén continuum. The strength of BAEs becomes stronger with increasing RMPs coil current. With strong enough RMP, m/n=2/1 field penetration is triggered. The structure of BAE transits from 3/1 surface to 2/1 while frequency increase about 10kHz which agree with the theoretical dispersion relation of BAE.In the meantime, another magnetic oscillation with higher frequency of 70 kHz is driven, which is defined as MiAE that as nonlinear interaction with magnetic island, i.e. frequency is modulated by width of magnetic island mainly. When we change the RMP component to generate a magnetic island on 3/1 surface, MiAE is triggered only. By measuring the width of magnetic island experimentally, we verified the theoretical dispersion relation of MiAE is agree with experimental value for the first time.   

Subcritical bifurcation detected in an unstable magnetized plasma column.

The study of the transition to turbulence is of major importance in nonlinear dynamics research. We studied the bifurcations in a magnetized plasma when the plasma is rotating (1). When the angular velocity of the plasma column is reduced, the azimuthal modes are evolving from m$=$3 to m$=$1. This situation has been revisited checking the existence of a hysteresis near each bifurcation points, determining if the bifurcations are of supercritical or subcritical. A subcritical transition displays hysteresis. This situation has already been investigated theoretically for drift wave in magnetized plasmas (2). The experiment is conducted choosing the same parameters as in (1). The control parameter is the potential of the anode that controls the rotation of the plasma. The control parameter is varied near each bifurcation points in two cases: at first increasing the control parameter and then decreasing the control parameter. Starting from a m$=$2 mode, the negative anode potential is increased until the m$=$1 mode is established. Then the anode potential is decreased to get a transition toward an m$=$2 mode. The results indicate that a hysteresis is present, though a rather high dispersion of the critical value is recorded. The results are more conclusive in the case of the transition from m$=$1 mode to the turbulent state. A theoretical model is under preparation to get a more precise description of the bifurcations. 1- T. Klinger et al., Phys. Rev. Lett. 79,3913,1997. 2- K. He, and A. Salat, Plasma Phys. Contr. Fusion, 31, 123--141, 1989.   

Axisymmetric Global Alfven Eigenmodes (GAEs) within the ellipticity-induced frequency gap in the Joint European Torus

Alfven eigenmodes with toroidal mode number $n=0$ (i.e. axisymmetric) have been observed in the ellipticity-induced frequency range in JET. The $n=0$ modes are of interest because they may be used to diagnose fast particle energy distributions at the mode location. The modes were identified as Global Alfven Eigenmodes (GAEs), with the ellipticity of the plasma cross-section preventing strong continuum damping of the modes. The MHD codes CSCAS, MISHKA and AEGIS were used to compute the $n=0$ Alfven continuum, eigenmode structure and continuum damping. Finite ellipticity splits the Alfven continuum branch into two branches, producing a frequency gap, and splits the single GAE into two modes. One mode has dominant poloidal harmonics $m=\pm 1$ with the same polarity and exists below the minimum of the top branch. The frequency of this mode coincides with the experimentally observed frequency. The other mode is found below the lower branch with opposite polarity of the poloidal harmonics, and is not observed experimentally. Analytical theory for the $n=0$ continuum and GAE mode structure in an elliptical cylinder agree with the numerical modelling. Mode drive and damping calculations will also be presented.   

Laser and Plasma Parameters for Laser Pulse Amplification by Stimulated Brillouin Backscattering in the Strong Coupling Regime

In the ongoing quest for novel techniques to obtain ever higher laser powers, plasma amplification has drawn much attention, benefiting from the fact that a plasma can sustain much higher energy densities than a solid state amplifier. As a plasma process, Stimulated Brillouin Backscattering in the strong coupling regime (sc-SBS) can be used to transfer energy from one laser pulse (pump) to another (seed), by a nonlinear ion oscillation forced by the pump laser. Here, we report on experimental results on amplification by sc-SBS using the ARCTURUS Ti:Sapphire multi-beam laser system at the University of Duesseldorf, Germany. Counter-propagating in a supersonic Hydrogen gas jet target, an ultrashort seed pulse with a pulse duration between 30 and 160 fs and an energy between 1 and 12 mJ was amplified by a high-energy pump pulse (1.7 ps, 700 mJ). For some of the measurements, the gas was pre-ionized with a separate laser pulse (780 fs, 460 mJ). Preliminary analysis shows that the amplification was larger for the longer seed pulses, consistent with theoretical predictions.   

Hamiltonian Single Wave Models to Investigate the Nonlinear Self-Consistent Interaction of Whistler Waves and Electrons

We investigate the nonlinear evolution of a self-consistent Hamiltonian model for the interaction of resonant electrons with whistler waves. We find that in the parallel propagating case there are two classes of solutions. The first class has properties similar to previously derived single wave models and involves a perfectly resonant electron beam. We show that test-particle models in the modulated wave-field indicate that the particles are trapped in a first-order island that tracks the location of the majority of particles. We develop a macro-particle model which explains the small frequency and amplitude oscillations. The second class of solutions involves a slightly off-resonant interaction which leads to an amplitude modulation of the wave that resembles the sub-packet structure observed in both chorus and recent laboratory experiments. In the second class, we show that test-particle models demonstrate that instead of being trapped in the primary resonance, particles get trapped in a second-order island chain. The location of the second-order island chain in phase space tracks the location of the majority of electrons. We develop a two macro-particle model which reproduces the amplitude modulation and sub-packet structure of the full model.   

Investigating parasitic current formation in MITLs through high-order continuum kinetic simulations

The Z pulsed power facility is designed to deliver more than 20 MA of current to a load through magnetically insulated transmission lines (MITLs), which prevent high voltage arcs. Experimental results show that as much as 10\% of the current can be lost due to the unintended formation of low-density plasmas in the MITLs. The configuration of the electric and magnetic fields within the MITL, where the plasma is born, creates conditions in which drift and kinetic instabilities can lead to the formation of parasitic currents. To understand the plasma dynamics that lead to current loss, the MITL configuration is investigated using a high-order continuum kinetic Vlasov-Poisson solver in two spatial and two velocity dimensions. The simulations capture the effects of varying magnetization and yield insights into plasma behavior over the course of current rise and corresponding magnetic field generation. The effects of plasma formation at the cathode versus at the anode are explored in detail.   

Generalized Case–Van Kampen theory for electromagnetic oscillations in a magnetized plasma

The Case-Van Kampen theory [1,2] is set up to describe electrostatic oscillations in an unmagnetized plasma. Our generalization to electromagnetic oscillations in magnetized plasma is formulated in the relativistic position-momentum phase space of the particles. The relativistic Vlasov equation includes the ambient, homogeneous, magnetic field, and space-time dependent electromagnetic fields that satisfy Maxwell’s equations. The standard linearization technique leads to an equation for the perturbed distribution function in terms of the electromagnetic fields. The eigenvalues and eigenfunctions are obtained from three integrals – each integral being over two different components of the momentum vector. Results connecting phase velocity, frequency, and wave vector will be presented. [1] N. G. Van Kampen, \textit{Physica} \textbf{21}, 949 (1955). [2] K. M. Case, \textit{Annals of Physics} \textbf{7}, 349 (1959).   

Exploring the Alfv\'en-wave acceleration of auroral electrons in the laboratory

Inertial Alfv\'en waves likely contribute to the acceleration of auroral electrons. However, a definitive test of Alfv\'enic electron acceleration is lacking. The Large Plasma Device (LAPD) at UCLA provides a controlled environment to study this wave-particle interaction that may be responsible for a significant fraction of auroras. Inertial Alfv\'en waves were produced in the LAPD while simultaneously measuring the suprathermal tails of the electron distribution function using resonant whistler mode wave absorption. During a burst of inertial Alfv\'en waves, the measured portion of the distribution function oscillates at the Alfv\'en wave frequency. The phase space response of the electrons is well-described by a solution to the linearized Boltzmann equation. Experiments have been repeated using electrostatic and inductive Alfv\'en wave antennas. The oscillation of the distribution function is described by a purely Alfv\'enic model when the Alfv\'en wave is produced by the inductive antenna. However, when the electrostatic antenna is used, measured oscillations of the distribution function are described by a model combining Alfv\'enic and non-Alfv\'enic effects. Indications of a nonlinear interaction between electrons and inertial Alfv\'en waves are present in recent data.   

Nonlinear plasma wave models in 3D fluid simulations of laser-plasma interaction

Simulations of laser-plasma interaction (LPI) in inertial confinement fusion (ICF) conditions require multi-mm spatial scales due to the typical laser beam size and durations of order 100 ps in order for numerical laser reflectivities to converge. To be computationally achievable, these scales necessitate a fluid-like treatment of light and plasma waves with a spatial grid size on the order of the light wave length. Plasma waves experience many nonlinear phenomena not naturally described by a fluid treatment, such as frequency shifts induced by trapping, a nonlinear (typically suppressed) Landau damping, and mode couplings leading to instabilities that can cause the plasma wave to decay rapidly. These processes affect the onset and saturation of stimulated Raman and Brillouin scattering, and are of direct interest to the modeling and prediction of deleterious LPI in ICF. It is not currently computationally feasible to simulate these Debye length-scale phenomena in 3D across experimental scales. Analytically-derived and/or numerically benchmarked models of processes occurring at scales finer than the fluid simulation grid offer a path forward. We demonstrate the impact of a range of kinetic processes on plasma reflectivity via models included in the LPI simulation code pF3D.   

Landau damping of sound waves in kinetic magnetohydrodynamics

The Landau damping of slow sound waves propagating parallel to the magnetic field in a homogeneous, collisionless and quasineutral plasma is investigated using the kinetic magnetohydrodynamics formulation of J.J. Ramos, J. Plasma Phys., 905810325 (2015), 905820607 (2016). In this approach, the electric field is eliminated from a closed, hybrid fluid-kinetic system that ensures automatically the fulfillment of the quasineutrality condition. Considering the time evolution of a parallel-propagating sound wave spatial Fourier mode, this can be cast as a standard, second-order self-adjoint problem, with a continuum spectrum of real and positive squared frequencies. Therefore, a standard resolution of the identity with a single continuum basis of singular normal modes is guaranteed, which simplifies significantly a Van Kampen-like treatment of the Landau damping. The explicit form of such singular normal modes is obtained and they are used to derive the damped time evolution of the fluid moments of a wave packet of distribution functions in an initial value problem. As mentioned, the electric field is not used in the treatment of this problem, but it is calculated from its solution after it has been obtained.   

Towards a better understanding of high-energy electron pitch-angle scattering by electromagnetic ion cyclotron waves.

Shear Alfven waves are a fundamental mode in magnetized plasmas. Propagating near the ion cyclotron frequency, these waves are often termed electromagnetic ion cyclotron (EMIC) waves and can involve multiple ion species. Near the earth, for example, the wave may interact resonantly with oxygen ions at altitudes ranging from 1000 to 2000 km. The waves may either propagate from space towards the earth (possibly involving mode conversion), or be generated by RF transmitters on the ground. These preliminary experiments are motivated by theoretical predictions [1] that such waves can pitch-angle scatter relativistic electrons trapped in the earth's dipole field. EMIC waves are launched in the Large Plasma Device at UCLA's Basic Plasma Science Facility in plasmas with single and multiple ion species into magnetic field gradients where ion cyclotron resonance is satisfied. We report here on the frequency and k-spectra in the critical layer and how they compare with theoretical predictions in computing an effective diffusion coefficient for high-energy electrons. [1] B. Eliasson and K. Papadopoulos (in submission)   

Laboratory experiments on Alfven and kink modes in an arched magnetized plasma

In a recently upgraded laboratory plasma experiment, dynamics of an arched magnetized plasma has been explored with a particular focus on Alfven and global kink modes that exist in solar prominences and coronal loops. The arched plasma ($\beta \approx 10^{-3}$, Lundquist number $\approx 10^2$-$10^5$, plasma radius/ion-gyroradius $\approx$ 20, B = 1 kGauss at footpoints, Length $>$ 0.8 m) was created using a lanthanum hexaboride (LaB6) plasma source. It evolved in an ambient magnetoplasma produced by another LaB6 source. The experiment runs continuously with a 0.5 Hz repetition rate. Plasma parameters are recorded with excellent resolution using movable Langmuir and three-axis magnetic-loop probes. Images of the plasma are recorded using a fast-CCD camera. The kink-mode oscillations were observed as transverse oscillations across the symmetry plane of the arched plasma. The relative magnitudes of parameters of the arched and ambient plasma were varied to simulate varieties of conditions relevant to the sun. We examine the relevance of theoretical models of kink-modes and study the dispersion of Alfvén waves in the presence of an electrical current. References: (1) Tripathi and Gekelman, Phys. Rev. Lett. 105, 075005 (2010) (2) Tripathi and Gekelman, Solar Phys. 286, 479 (2013)   

Low frequency waves behavior in presence of strongly emissive cathodes in the VKP experiment

Low frequency plasma parameters fluctuations are known to be the cause of strong perpendicular transport in hot plasma devices. These instabilities also appear in smaller linear devices where their excitation and mitigation have been studied using different setups such as polarized cold grids, electro-magnetic drive or concentric annular cold electrodes. We study the behavior of these fluctuations in the Von-K\`arm\`an Plasma experiment (VKP) and its modification under the injection of electrons from strongly emissive cathodes and the induced shaping of the plasma potential. VKP is a cylindrical, low pressure, high density plasma experiment with an axial confinement field. The rotation profile of the plasma is controlled using hot emissive cathodes biased relatively to the experiment wall or to cold anodes. Current emission from biased cathodes dramatically changes the radial gradients of plasma density and plasma potential, which therefore modifies the plasma rotation. We report on the influence of this controlled rotation and plasma parameters shaping over the dynamics of low frequency fluctuations in the plasma.   

Singl/multiple Global Geodesic Acoustic Modes

Both experiments and simulations reveal that there exist single/multiple global geodesic acoustic modes that have constant frequencies over radial extension in the tokamak plasmas. In the framework of ideal MHD, the global structure of the mode emerges as the requirement the momenta associated with the second poloidal harmonics inside the coupling between the magnetic (geodesic) curvature and the leading pressure perturbations be balanced by the Alfven perturbations, which involve the the plasma displacements of higher order: the normal displacement and the second poloidal harmonic component of the geodesic displacement. The analytical and numerical solutions to the eigen-mode equation will be presented for typical q and temperature profiles. This theory is extended to the case where single local GAM splits into multiple branches as a result of plasma rotations. The rotation also induces richer poloidal harmonic structures and it eventually leads to two coupled ODEs of 2nd order. Multiple global GAMs occur naturally as the solutions of this eigen-value problem.   

The temporal evolution of the resistive pressure-gradient-driven turbulence and anomalous transport in shear flow across the magnetic field

The temporal evolution of the resistive pressure-gradient-driven mode in the sheared flow is investigated by employing the shearing modes approach. It reveals an essential difference in the processes, which occur in the case of the flows with velocity shearing rate less than the growth rate of the instability in the steady plasmas, and in the case of the flows with velocity shear larger than the instability growth rate in steady plasmas. It displays the physical content of the empirical ”quench rule” which predicts the suppression of the turbulence in the sheared flows when the velocity shearing rate becomes larger than the maximum growth rate of the possible instability. We found that the distortion of the perturbations by the sheared flow with such velocity shear introduces the time dependencies into the governing equations, which prohibits the application of the eigenmodes formalism and requires the solution of the initial value problem.   

Instabilities and transport in ExB plasma discharges

We present a nonlinear fluid model describing fluctuations and instabilities in partially magnetized plasma discharge supported by the ExB electron current. This model describes several fundamental modes of partially magnetized plasma: ion sound mode, lower-hybrid mode and anti-drift mode due to plasma density gradient. Density and magnetic field gradients and the electron current result in complex coupling of various modes destabilized by the interplay of ExB drift, ion beam velocity, density and magnetic field gradients, collisions and ionization. The nonlinear simulations have been performed to investigate the nonlinear saturation of the instabilities and resulting nonlinear transport. The simulations demonstrate highly intermittent electron current with magnitudes generally consistent with typical experimental parameters. It is shown that while the most unstable are small scale modes, the dominant contribution to the anomalous transport is provided by the large scale modes. The nonlinear energy transfer to large scale modes is demonstrated in nonlinear simulations. Effects of the parallel electron dynamics and sheath boundary conditions is studied. The role of electron cyclotron instabilities detected in PIC simulations is also discussed.   

Slow rotating mode detection using magnetic probes on passive plate in KSTAR

Since 2015 experimental campaign, to detect a low rotating or fixed non-axisymmetric plasma disturbance, 20 magnetic probes (MPs) which can catch the parallel component of magnetic field have been installed on the passive plate with different toroidal/poloidal positions in KSTAR. To identify n(toroidal mode number) =1 or 2 plasma instability, the Fourier decomposition method is applied and some preliminary results show its effectiveness when the external fields by the in-vessel coils are properly compensated. This identification method has been implemented in the KSTAR plasma control system to avoid the mode locking and the RWM(Resistive Wall Mode) in the future.   

Transport and stability analyses supporting disruption prediction in high beta KSTAR plasmas*

KSTAR plasmas have reached high stability parameters in dedicated experiments, with normalized beta $\beta_{\mathrm{N}}$ exceeding 4.3 at relatively low plasma internal inductance l$_{\mathrm{i}}$ ($\beta _{\mathrm{N}}$/l$_{\mathrm{i}}$\textgreater 6) [1]. Transport and stability analyses have begun on these plasmas to best understand a disruption-free path toward the design target of $\beta_{\mathrm{N}}=$5 while aiming to maximize the non-inductive fraction of these plasmas. Initial analysis using the TRANSP code indicates that the non-inductive current fraction in these plasmas has exceeded 50 percent. The advent of KSTAR kinetic equilibrium reconstructions now allows more accurate computation of the MHD stability of these plasmas. Attention is placed on code validation of mode stability using the PEST-3 and resistive DCON codes. Initial evaluation of these analyses for disruption prediction is made using the disruption event characterization and forecasting (DECAF) code [2] The present global mode kinetic stability model in DECAF developed for low aspect ratio plasmas is evaluated to determine modifications required for successful disruption prediction of KSTAR plasmas. [1] Y.S. Park, S.A. Sabbagh, W.H. Ko et al., Phys. Plasmas \textbf{24} (2017) 012512 [2] J.W. Berkery et al., Phys. Plasmas \textbf{24} (2017) 506103 *Work supported by U.S. DoE under contract DE-SC0016614   

Measurement of vertical stability metrics in KSTAR

The paper summarizes results of multi-year ITPA experiments regarding measurement of the vertical stabilization capability of KSTAR discharges, including most recent measurements at the highest achievable elongation ($\kappa \sim 2.0-2.1$). The measurements of the open-loop growth rate of VDE ($\gamma_z$) and the maximum controllable vertical displacement ($\Delta Z_{max}$) are done by the release-and-catch method. The dynamics of the vertical movement of the plasma is verified by both relevant magnetic reconstructions and non-magnetic diagnostics. The measurements of $\gamma_z$ and $\Delta Z_{max}$ were done for different plasma currents, $\beta_p$, internal inductances, elongations and different configurations of the vessel conductors that surround the plasma as the first wall. Effects of control design choice and diagnostics noise are discussed, and comparison with the axisymmetric plasma response model is given for partial accounting for the measured control capability.   

Automated Identification of MHD Mode Bifurcation and Locking in Tokamaks*

Disruption avoidance is critical in reactor-scale tokamaks such as ITER to maintain steady plasma operation and avoid damage to device components. A key physical event chain that leads to disruptions is the appearance of rotating MHD modes, their slowing by resonant field drag mechanisms, and their locking. An algorithm has been developed that automatically detects bifurcation of the mode toroidal rotation frequency due to loss of torque balance under resonant braking, and mode locking for a set of shots using spectral decomposition. The present research examines data from NSTX, NSTX-U and KSTAR plasmas which differ significantly in aspect ratio (ranging from A $=$ 1.3~-~3.5). The research aims to examine and compare the effectiveness of different algorithms for toroidal mode number discrimination, such as phase matching and singular value decomposition approaches, and to examine potential differences related to machine aspect ratio (e.g. mode eigenfunction shape variation). Simple theoretical models will be compared to the dynamics found. Main goals are to detect or potentially forecast the event chain early during a discharge. This would serve as a cue to engage active mode control or a controlled plasma shutdown. $^{\mathrm{\ast }}$Supported by US DOE Contracts DE-SC0016614 and DE-AC02-09CH11466.   

LH Transition and rotation studies under non-axisymmetric magnetic fields in KSTAR

A thorough study of LH transition under the influence of non-axisymmetric field (NF) has been conducted in KSTAR. It shows that LH power threshold depends on the resonant NFs and the line-averaged density-LH power threshold curve agrees well with the power law scaling [Martin, JOP(2008)] as the resonant NF ($\delta $B/B$^{\mathrm{n=1}})$ applied up to 2.7x10$^{\mathrm{-4\thinspace }}$in KSTAR which has a low intrinsic error field. However, LH power threshold is independent of non-resonant NFs with n$=$1 and n$=$2 which reduced only toroidal rotation by 30{\%} in L-mode The rotation pedestal during LH transition with both co- and counter-NBI heating appears saturated at a critical level of edge rotation [Ko, NF (2015)] which is dependent of LH power threshold However, the core rotation increased with the stored energy in the co-NBI with and without NFs while it is saturated in counter-NBI plasma. In co-NBI heated H-mode, the pedestal width of rotation is 5 cm with wide that of ion temperature (2 cm). On the other hand, in counter-NBI heated H-mode, the rotation pedestal width (2 cm) appeared as similar as that of ion temperature. The newly diagnosed results of rotation in KSTAR seemingly pose a variety of physics questions.   

MHD stability analysis and global mode identification preparing for high beta operation in KSTAR

H-mode plasma operation in KSTAR has surpassed the computed $n=$1 ideal no-wall stability limit in discharges exceeding several seconds in duration. The achieved high normalized beta plasmas are presently limited by resistive tearing instabilities rather than global kink/ballooning or RWMs. The ideal and resistive stability of these plasmas is examined by using different physics models. The observed $m$/$n=$2/1 tearing stability is computed by using the M3D-C$^{\mathrm{1}}$ code, and by the resistive DCON code. The global MHD stability modified by kinetic effects is examined using the MISK code. Results from the analysis explain the stabilization of the plasma above the ideal MHD no-wall limit. Equilibrium reconstructions used include the measured kinetic profiles and MSE data. In preparation for plasma operation at higher beta utilizing the planned second NBI system, three sets of 3D magnetic field sensors have been installed and will be used for RWM active feedback control. To accurately determine the dominant $n$-component produced by low frequency unstable RWMs, an algorithm has been developed that includes magnetic sensor compensation of the prompt applied field and the field from the induced current on the passive conductors.   

Kinetic equilibrium reconstruction of KSTAR plasmas including internal pitch angle profile measurement

High fidelity kinetic equilibrium reconstructions are an essential requirement for accurate stability and disruption prediction analyses to support continuous operation of high beta KSTAR tokamak plasmas. The present work significantly expands our past magnetics-only equilibrium reconstruction capability. [1] The present kinetic equilibrium reconstructions include Thomson scattering (TS) data, charge exchange spectroscopy (CES) data, and allowance for fast particle pressure in addition to external magnetics and shaping field current data, and inclusion of vacuum vessel and passive plate currents following a ``partial kinetic'' approach used successfully in other devices. [2] In addition, up to 25 channels of Motional Stark Effect (MSE) data are used to constrain the local magnetic field pitch angle to produce reliable evaluation of the safety factor profile. The ramifications of the inclusion of the kinetic profiles and MSE data are examined in the context of plasma stability evaluation, and parameters and analysis used for disruption event characterization and forecasting (DECAF). [1] Y.S. Park, S.A. Sabbagh, J.W. Berkery, et al., Nucl. Fusion \textbf{51} (2011) 053001, [2] S.A. Sabbagh, A.C. Sontag, J.M . Bialek, et al., Nucl. Fusion 46 (2006) 635. $^{\mathrm{\ast }}$Supported by US DOE Grant DE-SC0016614.   

Evaluation of MSE Wavelength-Interpolation Background Subtraction on KSTAR

A ten-channel polychrometer that simultaneously measures the Motional Stark Effect polarized pi and sigma line emission and two neighboring wavelengths near the MSE spectrum, previously used on Alcator C-Mod, has been integrated into the KSTAR MSE diagnostic. This system provides accurate measurements of the partially-polarized MSE background emission even when the background varies rapidly in time and space. Data acquired during the 2017 KSTAR campaign and data-mining of older data will be used to assess four key issues: (1) what error in measured pitch angle is introduced by not compensating the MSE measurement for the presence of partially-polarized background light (the practice now); (2) how much larger will this error grow when KSTAR realizes higher-performance plasmas, particularly higher density; (3) how accurately can the background polychromator system estimate the polarized background light during beam injection; and (4) what is the relative statistical measurement error between the existing NFRI MSE diagnostic versus the background polychromator system? The answers to these questions will inform a decision in late FY17 about whether to proceed with construction of 15 additional background polychromator channels for installation on KSTAR before the start of its FY18 run campaign.   

First results from the US-PRC PMI collaboration on EAST

A US-PRC collaboration was formed to understand the plasma-material interface for improved long pulse discharge performance in EAST, with an emphasis on Li conditioning techniques. The US multi-institutional team consists of participants from PPPL, UI-UC, UT-K, ORNL, MIT, LANL, and JHU. In Dec. 2016, this team co-led experiments on the use of Li aerosol injection to mitigate ELMs, Li granule injection to pace ELMs, and a flowing liquid Li limiter to serve as a primary plasma-facing component. Li aerosol injection was shown to eliminate ELMs using the upper ITER-like W divertor, extending previous results of ELM suppression in the lower cabon divertor (J.S. Hu, PRL 2015). In addition Li granule injection was shown to trigger and even pace ELMs, although the paced ELM frequency was slower than the natural ELM frequency in this set of experiments; previously paced ELM frequency was comparable to natural ELMs frequency (D.K. Mansfield, NF 2013). Finally a second generation flowing liquid Li limiter was shown to be compatible with ELMy H-mode plasmas, pushed within 1 cm of the separatrix. The surface showed no damage to PMI and improved wetting as compared to the first generation limiter experiments (J.S. Hu, NF 2016 and G.Z. Zuo, NF 2017). *US scientists supported in part by US DoE contracts DE-AC02-09CH11466, DE-FG02-09ER55012, DE-AC05-00OR22725, and DE-FC02-04ER54698, and ASIPP scientists by Contract No. 11625524, No.11075185, No.11021565, and No.2013GB114004.   

Experimental investigation of LHCD's effect on plasma rotation on EAST

LHCD's effect on plasma rotation was reported. It was found that \textasciitilde 20km/s co-current rotation change was driven, which was linearly correlated with changes in \textit{li} and q$_{\mathrm{0}}$ and evolves over current diffusion time. Hysteresis between rotation and Te was observed, suggesting different transport between heat and momentum transport. Rotation profile shows that the change arises from the region where LHCD was deposited and then transported to the core, confirming the rotation drive was originated at the plasma edge. For NBI heated plasma, counter-rotation change was observed upon the injection of the LHCD and continued to co-rotation change shortly. Further experiments showed that the change of rotation induced by LHCD decreases with plasma current (Ip), plasma density and increase with LHCD power. A comparison between the rotation driven by 4.6G LHCD and 2.45G LHCD on EAST is also presented, in which higher frequency LHCD could induce more rotation change, due to the better heating and CD efficiency with 4.6GHz LHW.   

Electron heat transport in EAST steady-state H-mode discharges with a weak electron internal transport barrier

The global confinement (H$_{\mathrm{98}})$ increases with the internal inductance (1.0\textasciitilde 1.2) in the recent steady-state H-mode discharges, which exhibit a weak electron ITB started at \begin{figure}[htbp] \centerline{\includegraphics[width=0.44in,height=0.17in]{140720171.eps}} \label{fig1} \end{figure} $\rho =0.4$ in EAST. After turning off ECRH, the stored energy decreases by \textasciitilde 30{\%} in 2.5 s. Calculations suggest that both the lower hybrid electron heating and driven current move from the core to large radii after turning off ECRH. Power balance analysis show that the LH deposition profile shift from just inside the ITB to outside the ITB after ECRH termination appears to be responsible for the marked drop in stored energy. The slow stored energy decrease is believed to be connected to the long plasma current profile relaxation time. Linear gyrokinetic simulations indicate increasing low-k instability growth rate from small to large radii, which is consistent with the reduced diffusivity within the ITB. The calculations also show that the CTEM dominate within the ITB, ETG modes grow rapidly outside this region, and that ITG modes dominate near the pedestal top.   

Improved H mode with flat central q profile on EAST

High betaN (\textasciitilde 1.8) plasma with good confinement (H98y2\textasciitilde 1.1) on EAST tokamak has been reported recently. These ELMy H-mode plasmas with B$_{\mathrm{t}}=$1.6T, I$_{\mathrm{p}}=$400 kA and q$_{\mathrm{95}}\approx $4.5 were heated by lower hybrid wave and neutral beam injection. The internal transport barrier (ITB) and edge transport barrier (ETB) are both observed with m/n$=$1/1 fishbone, which were identified to clamp central~q~at values close to unity. Implying an improved H-mode with flat central q profile and absence of sawteeth, like other devices. Accurate q profile, key profile for developing scenarios aim at high performance H mode, were derived by Polarimeter-interferometer (POINT) measurement as constraint. Base on the optimized current profile, better confinement (H98y2\textasciitilde 1.4) with an electron ITB was obtained also with flat central q profile and absence of sawteeth at high betaP (\textasciitilde 2) regime with B$_{\mathrm{t}}=$2.5T, I$_{\mathrm{p}}=$400 kA. Both high betaN$_{\mathrm{\thinspace \thinspace }}$regime and high betaP$_{\mathrm{\thinspace }}$regime H mode, are characterized by a stationary flat central q profile q0$\ge $1, but typically close to 1, absence of sawteeth, H98(y,2) \textgreater 1 and simultaneously, with ITB.   

Measurements and simulations of quasi-coherent fluctuations during the inter-ELM phase in EAST

Quasi-coherent fluctuations have been commonly observed preceding type-I ELMs in EAST. They typically show up in two frequency domains. The lower frequency band (30-50 kHz) propagates in ion diamagnetic direction. It predominantly peaks on low field side, but not evidently contribute to local transport. The higher frequency band (180--220 kHz) is detected to propagate in the electron diamagnetic direction. Its amplitude exhibits an in-out symmetry. However, it drives strong particle transport into far SOL region on high field side. Study of these inter-ELM fluctuations are important for our understanding of pedestal physics,SOL width and ELM process itself. For this purpose, BOUT$++$ simulations for inter-ELM fluctuations are conducted based on EAST experiments. The preliminary simulation results suggest that peeling-ballooning and drift-alfven instabilities could be respectively responsible for the lower frequency band and higher frequency band fluctuations observed during the inter-ELM phase in experiments.Comparison of nonlinear simulations with experimental measurements will be presented.   

Current Density Profile Control via Model Predictive Control in EAST.

Extensive studies have shown that the current density profile, which is closely related to poloidal magnetic flux profile, is a key factor to achieving advanced tokamak operating scenarios that are characterized by improved confinement and possible steady-state operation. In this work, a first-principles-driven, control-oriented model of the poloidal magnetic flux profile evolution is used to design a feedback controller via model predictive control (MPC) for EAST. The goal of the feedback controller is to regulate the poloidal magnetic flux profile evolution around a desired trajectory by minimizing the difference between desired and actual profiles. Due to external disturbances, non-modeled dynamics, and perturbation in initial conditions, feedforward-only control solutions usually fail in achieving the desired trajectory. Simulation results illustrate the capability of the proposed model predictive controller in tracking the desired profile by optimizing in real time the actuator waveforms.   

Magnetic field amplitude and pitch angle measurements using Spectral MSE on EAST

We have developed the Spectral Motional Stark Effect technique for measuring magnetic field amplitude and pitch angle on EAST. The experiments were conducted using the tangential co-injection heating beam at A port and Beam Emission Spectroscopy array at D port. A spatial calibration of the observation channels was conducted before the campaign. As a first check, the measured magnetic field amplitude was compared to prediction. Since the toroidal field is dominant, we recovered the expected 1/R shape over the spatial range 1.75\textless R(m)\textless 2.32 with R$_{\mathrm{0}}=$1.89m. The objective is the spatially resolved pitch angle which follows from the ratio of the $\pi $ and $\sigma $ polarized Stark components. The excited state populations are far from local thermal equilibrium and a collisional-radiative model that takes into account the effect of the Lorentz field was used to predict the beam populations. The initial comparison is to an EFIT reconstruction. We are investigating sources of errors using a combination of simulations and calibrations arising from hardware non-idealities and approximations in the analysis. We are also investigating improvements in the EAST spectral MSE diagnostic.   

Stimulated L-H transition with SMBI in the HL-2A tokamak

In the HL-2A plasmas, the transition from low confinement mode (L-mode) to high confinement mode (H-mode) externally stimulated by supersonic molecular beam injection (SMBI) has been observed. SMBI, a fuelling tool with higher fuelling efficiency than that of gas puffing, can abruptly increases the electron density and its gradient. Then it helps to build the pedestal with steep gradient. It was found that more intense SMBI induces large turbulence intensity. Interesting, the intensity of geodesic acoustic mode (GAM) was enhanced by SMBI, then the turbulence intensity was clamped. When the plasma transited into the H-mode, the GAM disappeared. The enhanced GAM can also transits into another oscillating shear flow, limit cycle oscillation (LCO). The interplay between oscillating flows and turbulence was studied. The result suggests that the oscillating flows can be enhanced or triggered by SMBI and those flows initiate the L-H transition. Further, they play a important role in the continuous increase of the mean shear flow prior to the transition.   

The radiation asymmetry in MGI rapid shutdown on J-TEXT tokamak

Disruptions, the sudden termination of tokamak fusion plasmas by instabilities, have the potential to cause severe material wall damage to large tokamaks like ITER. The mitigation of disruption damage is an essential part of any fusion reactor system. Massive gas injection (MGI) rapid shutdown is a technique in which large amounts of noble gas are injected into the plasma in order to safely radiate the plasma energy evenly over the entire plasma-facing first wall. However, the radiated energy during the thermal quench (TQ) in massive gas injection (MGI) induced disruptions is found toroidal asymmetric, and the degrees of asymmetry correlate with the gas penetration and MGI induced magnetohydrodynamics (MHD) activities. A toroidal and poloidal array of ultraviolet photodiodes (AXUV) has been developed to investigate the radiation asymmetry on J-TEXT tokamak. Together with the upgraded mirnov probe arrays, the relation between MGI triggered MHD activities with radiation asymmetry is studied.   

Formation and dissipation of runaway current by MGI on J-TEXT

Plasma disruptions are one of the major concern for ITER. A large fraction of runaway current may be formed due to the avalanche generation of runaway electrons (REs) during disruptions and ruin the device structure. Experiments of runaway current formation and dissipation have been done on J-TEXT. Two massive gas injection (MGI) valves are used to form and dissipate the runaway current. Hot tail RE generation caused by the fast thermal quench leads to an abnormal formation of runaway current when the pre-TQ electron density increases in a range of 0.5-2×10$^{\mathrm{19}}$m$^{\mathrm{-3}}$. 10$^{\mathrm{20-22}}$ quantities of He, Ne, Ar or Kr impurities are injected by MGI2 to dissipate the runaway current. He injection shows no obvious effect on runaway current dissipation in the experiments and Kr injection shows the best. The kinetic energy of REs and the magnetic energy of RE beam will affect the dissipation efficiency to a certain extent. Runaway current decay rate is found increasing quickly with the increase of the gas injection when the quantity is moderate, and then reaches to a saturation value with large quantity injection. A possible reason to explain the saturation of dissipation effect is the saturation of gas assimilation efficiency.   

Effect of pulse resonant magnetic perturbation on magnetic island rotation in the J-TEXT tokamak

The influence of the static resonant magnetic perturbation (RMP) on the magnetic island depends on the phase difference between the island and RMP. According to the numerical simulation, the pulse RMP, which is applied in certain island phase region, could accelerate and suppress island. Feedback control system has been developed on J-TEXT for passing pulse electricity through resonant magnetic perturbation (RMP) coil when the phase difference between the mode and RMP is in the unique range. It is confirmed by experiment that the effects on magnetic island by modulated RMP varies with the difference phase range, which agreement with theoretical expectation and simulation result. The pulse RMP could accelerate island until the electromagnetic torque generated by RMP is balanced by viscous torque.However,The mode frequency increases inconspicuousl for finite RMP strength and eddy currents   

Overview of the EUROfusion Medium Size Tokamak scientific program

Under the EUROfusion MST1 program, coordinated experiments are conducted at three European medium sized tokamaks (ASDEX Upgrade, TCV and MAST-U). It complements the JET program for preparing a safe and efficient operation for ITER and DEMO. Work under MST1 benefits from cross-machine comparisons but also makes use of the unique capabilities of each device. For the 2017/2018 campaign 25 topic areas were defined targeting three main objectives: 1) Development towards an edge and wall compatible H-mode scenario with small or no ELMs. 2) Investigation of disruptions in order to achieve better predictions and improve avoidance or mitigation schemes. 3) Exploring conventional and alternative divertor configurations for future high P/R scenarios. This contribution will give an overview of the work done under MST1 exemplified by the highlight results for each top objective from the last campaigns, such as evaluation of natural small ELM scenarios, runaway mitigation and control, assessment of detachment in alternative divertor configurations and highly radiative scenarios.   

Development of an I-mode scenario on the TCV tokamak

The I-mode is a promising regime of operation which offers high energy confinement, thanks to the formation of an edge temperature pedestal, low particle confinement and nearly stationary conditions, with the absence of ELMs. This regime is usually obtained by operating with unfavourable ion $\bm{B}\times\nabla\bm{B}$ drift, away from the active X-point, and keeping the heating power below the H-mode threshold. This has been achieved on several tokamaks such as Alcator C-Mod, ASDEX Upgrade and DIII-D. This paper reports on an ongoing effort to develop an I-mode scenario on the TCV tokamak as part of the TCV domestic campaign and the EUROfusion MST1 campaign. On other tokamaks the heating power window for accessing I-mode was found to be typically smaller at smaller magnetic field. With typical operation at $B_T=1.45\ \mathrm{T}$ and an absolute maximum of $B_T=1.54\ \mathrm{T}$, the TCV tokamak will help investigate whether the I-mode regime can be extended to low toroidal magnetic field. The results of this campaign will be discussed, in particular changes in energy confinement or in the pedestal temperature profiles will be closely investigated. The pedestal fluctuation characteristics will also be investigated using standard and Doppler reflectometer fluctuation measurements.   

Upgrade of JET AE Active Diagnostic for Low Frequency Eigenmodes Detection

The upgrade of the Toroidal Alfv\'{e}n Eigenmode Active Antenna diagnostic at JET was commissioned last year. The new amplifiers have an operational frequency range limited to bands within 10-1000 kHz by a choice of filters. In the last campaigns the AE excitation system was operated on the Alfv\'{e}nic range of frequencies (f $>$ 80 kHz). For the next campaigns we are proposing operation on the frequency range of 25-50 kHz to excite eigenmodes on the Alfv\'{e}n-acoustic range (GAMs, BAEs and Alfv\'{e}n Cascades). The next JET campaigns will involve use of deuterium, tritium and hydrogen, giving a wide range of parameters for the modes to be investigated. Details of the system modifications for operation in this new frequency range and experimental scenarios will be discussed.   

L-H transition studies in JET-ILW

Recent experiments at JET have produced new results about the L-H transition. We will present a selection here. We found the power threshold depends on H/(H+D) species concentration in a non-linear manner, with much of the variation taking place at the extremes of the mixture scan. It is unclear why this should be the case, but it may help explain the variability in results of earlier studies that don’t always report an isotope effect, and suggests that small levels of impurities could be important when interpreting isotope experiments. We found that the heating system has an impact on the power threshold in hydrogen and on the location of the density at which the threshold is lowest, ICRF heating being much more effective than NBI heating. This is the first time an effect of the heating system was found on JET. We also observe a stronger isotope effect in the low density branch than in the high density branch of the transition. On a related study, we have characterized axisymmetric magnetic oscillations present in the early H-mode phase, the M-mode, and show that their frequency scaling appears to be related to the poloidal Alfvén frequency in both H and D.   

Integrated modeling of temperature and rotation profiles in JET ITER-like wall discharges

Simulations of 78 JET ITER-like wall D-D discharges and 2 D-T reference discharges are carried out using the TRANSP predictive integrated modeling code. The time evolved temperature and rotation profiles are computed utilizing the Multi-Mode anomalous transport model [T. Rafiq, et \textit{al}., \textit{Phys. Plasmas} \textbf{20}, 032506 (2013)]. The discharges involve a broad range of conditions including scans over gyroradius, collisionality, and values of q$_{\mathrm{95.\thinspace \thinspace }}$ The D-T reference discharges are selected in anticipation of the D-T experimental campaign planned at JET in 2019. The simulated temperature and rotation profiles are compared with the corresponding experimental profiles in the radial range from the magnetic axis to the $\rho \quad =$ 0.9 flux surface. The comparison is quantified by calculating the RMS deviations and Offsets. Overall, good agreement is found between the profiles produced in the simulations and the experimental data. It is planned that the simulations obtained using the Multi-Mode model will be compared with the simulations using the TGLF model [G.M. Staebler, et \textit{al}., \textit{Phys. Plasmas} \textbf{14}, 055909 (2007)].   

Effects of external 3D fields on the core of high-beta hybrid tokamak plasmas

The core of high-beta hybrid tokamaks is sensitive to 3D fields, due to the response of a marginally-stable kink with large m=1/n=1 component as the minimum safety factor approaches unity. Helical core displacements of 1-2cm impact various quantities, as found in ASDEX Upgrade by probing the plasma with n=1 fields: central electron and ion temperature is reduced, causing confinement degradation; core rotation is braked, leading to performance-limiting 2/1 modes as rotation is roughly halved; outward W transport occurs, a potentially beneficial effect. Due to n=1 field amplification, these effects are largest near beta limits and error field correction is applied to minimize them. A modelling effort is ongoing to explain these results. Rotation braking is compared to neoclassical toroidal viscosity predicted by the MHD-kinetic hybrid code MARS-K. The drift-kinetic code NEO-2 is used to evaluate both NTV and the neoclassical W transport in the helical core, represented by a 3D equilibrium from V3FIT-VMEC.   

Rehabilitation of the Goal of Ignition, Sober Assessments of the Large Machine Approach to Fusion and the Ignitor Program

Although the value of investigating the physics of plasmas close to or at ignition condition has never been questioned. The ``relevance'' of efforts with this goal [1] has been too frequently passed under silence by supporters of large scale programs that cannot claim this objective. By now studies of the characteristics of ignited plasmas and of the requirements of power producing reactors have led to conclude that operating at ignition is necessary for a practically useful fusion reactor. The confinement scaling laws, that were identified originally when the line of high field compact experiments began to be proposed in order in order to investigate igniting plasmas [1], have been rediscovered and confirmed [2]. Both ``Damnatio Memoriae'' and ``Renovatio Memoriae'' [2] episodes have occurred in this context as well as in that of the first introduction of high field superconducting magnet technology [3] in fusion research. The record confinement parameters, beginning to approach the ideal ignition conditions, obtained recently by the Alcator C Mod machine have validated the perspectives of success of the Ignitor experiment [3]. [1] Coppi, B. AIP, 1721, 1, 020003-1 (2017). [2] Costley, A.E., et al., Nucl. Fus. 56, 066003 (2016). [3] Coppi, B. et al., Nucl. Fus. 55, 053011 (2015).   

HBT-EP Program: MHD Dynamics and Active Control through 3D Fields and Currents

The HBT-EP active mode control research program aims to: (i) advance understanding of the effects of 3D shaping on advanced tokamak fusion performance, (ii) resolve important MHD issues associated with disruptions, and (iii) measure and mitigate the effects of 3D scrape-off layer (SOL) currents through active and passive control of the plasma edge and conducting boundary structures.~Comparison of kink mode structure and RMP response in circular versus diverted plasmas shows good agreement with DCON modeling. SOL current measurements have been used to study SOL current dynamics and current-sharing with the vacuum vessel wall during kink-mode growth and disruptions. A multi-chord extreme UV/soft X-ray array is being installed to provide detailed internal mode structure information. Internal local electrodes were used to apply local bias voltage at two radial locations to study the effect of rotation profile on MHD mode rotation and stability and radial current flow through the SOL. A GPU-based low latency control system using 96 inputs and 64 outputs to apply magnetic perturbations for active control of kink modes is extended to directly control the SOL currents for kink-mode control. An extensive array of SOL current monitors and edge drive electrodes are being installed for pioneering studies of helical edge current control.   

Scrape-off-layer characterization and current-control of kink modes in HBT-EP

Scrape-off layer (SOL) currents and their paths through tokamaks are not well understood, but their control may prove crucial to the success of ITER and future fusion energy devices. We extend Columbia University's High Beta Tokamak-Extended Pulse (HBT-EP) experiment [1] and active GPU feedback system [2] to study the SOL and control MHD kink instabilities by actively controlling these currents. First, the radial plasma profiles and the edge structure of kink instabilities are measured with two triple probes. Second, we use active feedback control of a radially adjustable biased electrode to change the rotation and magnitude of slowly growing kink instabilities. By changing the phase between the probe's voltage and the edge instability with active feedback, we study its ability to influence and control plasma MHD structures. This work is in preparation for a planned 2018 multi-electrode SOL control upgrade. 1. J.P. Levesque, et al., Phys Plasmas 22, 056102 (2015). 2. N. Rath, et al., Rev Sci Instrum 85, 045114 (2014).   

Mode control using two electrodes on HBT-EP

Understanding the effects of plasma rotation on magnetohydrodynamic (MHD) modes and tokamak plasma stability is important for performance enhancement of current magnetic confinement experiments and to future fusion devices such as ITER. In order to control plasma rotation, two molybdenum electrodes have been installed on HBT-EP toroidally separated by 144 degrees. This allows independent biasing of the two probes both spatially and temporally. When the bias probes are inserted into the edge of the plasma and a voltage is applied, the probes drive radial currents and produce plasma flow from the torque induced by the currents. If the bias probe voltage is sufficiently positive, the MHD mode rotation transitions into a state with a rapid mode rotation frequency (in excess of 25 kHz) in the direction opposite to mode rotation without bias. The transition into this reversed rotation state occurs when the torque exceeds a threshold, which can depend upon the phase of an applied n = 1 error field [1]. We present recent studies of the two-electrode system on mode rotation, mode stability, and the toroidal symmetry of the radial current through the scrape-off-layer (SOL) during MHD activity and applied magnetic perturbations. [1] C.C. Stoafer, PhD, Columbia University (2015).   

Scrape-off-layer currents during MHD activity and disruptions in HBT-EP

We report scrape-off layer (SOL) current measurements during MHD mode activity and disruptions in the HBT-EP tokamak[1]. Currents are measured via Rogowski coils mounted on tiles in the low-field-side SOL, toroidal jumpers between otherwise-isolated vessel sections, and segmented plasma current Rogowski coils. These currents strongly depend on the plasma's major radius, mode amplitude, and mode phase. Plasma current asymmetries and SOL currents during disruptions reach 4\% of the plasma current. Asymmetric toroidal currents between vessel sections rotate at tens of kHz through most of the current quench, then symmetrize once $I_p$ reaches 30\% of its pre-disruptive value. Toroidal jumper currents oscillate between co- and counter-$I_p$, with co-$I_p$ being dominant on average during disruptions. Increases in local plasma current correlate with counter-$I_p$ current in the nearest toroidal jumper. Measurements are interpreted in the context of two models that produce contrary predictions for the toroidal vessel current polarity during disruptions. Plasma current asymmetries are consistent with both models, and scale with plasma displacement toward the wall. Progress of ongoing SOL current diagnostic upgrades is also presented. [1] J.P. Levesque et al 2017 Nucl. Fusion 57 086035   

Structure and Dynamics of Disruptive Kink Instabilities Measured by Fast Videography and Magnetics in HBT-EP

Measurements of kink instabilities, resonant magnetic perturbations (RMPs), and disruptions in the High Beta Tokamak-Extended Pulse (HBT-EP) are studied using toroidal and poloidal arrays of magnetic field sensors\footnote{Levesque, \textit{et al.}, \textit{Nuc Fus}, \textbf{57}, 086035 (2017).} and fast videography\footnote{Angelini, \textit{et al.}, \textit{Plasma Phys Contr Fus}, \textbf{57}, 045008 (2015).}. The fast camera (Phantom v7.3) is most sensitive to light from the plasma edge and detects the structure of the plasma boundary for all types of MHD activity. Large helical ``plumes'' and ``bubbles'' are detected during disruptions (when helical perturbations can exceed 20\%\ of the equilibrium poloidal field) and during kink mode precursors (when the mode amplitude can exceed 5\%\ of the equilibrium field.) We present videos of the distorted plasma boundary and compare high-speed videos with computations of the helical boundary based on magnetic measurements. A variety of disruptions show ``plume''/``bubble'' structures reach 5~cm (or 30\%\ of the plasma minor radius) from the plasma edge. The distortion and dynamics of the plasma boundary are discussed in relation to on-going investigations of scrape-off layer (SOL) currents during kink instabilities and disruptions.   

Observation and Modeling of External Kink Mode Structure in Shaped HBT-EP Plasmas

The first study of magnetohydrodynamic (MHD) equilibria and external kink modes in shaped plasmas on the High-Beta Tokamak - Extended Pulse (HBT-EP) is described. A poloidal field coil above the vertical midplane on the high-field side modifies the plasma cross section and allows diverted operation. High density magnetic probe arrays observe the structure of kink modes that arise naturally, and those that are excited by externally imposed 3D fields. These observations are compared to calculations of the DCON and VALEN codes, which calculate ideal kink stability and structure, and the influence of 3D eddy fields respectively. In both experiment and calculation, a short-wavelength feature, localized in a narrow poloidal arc near the X-point is discovered. This feature is predicted in external kinks of diverted tokamak plasmas, and is consistent with previous near-edge measurements$^{\dagger}$. The combination of DCON and VALEN provide calculations in good agreement with observations, suggesting generalization of this method to other experiments.\\ \newline $\dagger$ Huysmans, G.T.A., Hender, T.C., Alper B. Nuclear Fusion, 38(2) 901, 1998.   

Extreme ultraviolet and Soft X-ray diagnostic upgrade on the HBT-EP tokamak: Progress and Results

In order to understand internal MHD mode structure in a tokamak plasma, it is helpful to understand temperature and density fluctuations within that plasma. In the HBT-EP tokamak, the plasma emits bremsstrahlung radiation in the extreme ultraviolet (EUV) and soft x-ray (SXR) regimes, and the emitted power is primarily related to electron density and temperature. This radiation is detected by photodiode arrays located at several different angular positions near the plasma’s edge, each array making several views through a poloidal slice of plasma. From these measurements a 2-d emissivity profile of that slice can be reconstructed with tomographic algorithms. This profile cannot directly tell us whether the emissivity is due to electron density, temperature, line emission, or charge recombination; however, when combined with information from other diagnostics, it can provide strong evidence of the type of internal mode or modes depending on the temporal-spatial context. We present ongoing progress and results on the installation of a new system that will eventually consist of four arrays of 16 views each and a separate two-color, 16-chord tangential system, which will provide an improved understanding of the internal structure of HBT-EP plasmas.   

Non-Solenoidal Startup via Helicity Injection in the Pegasus ST

Research on the $A\sim 1.2$ Pegasus ST is developing the physics and technology basis for optimal non-solenoidal tokamak startup. Recent work explores startup via Local Helicity Injection (LHI) using compact, multi-MW current sources placed at the plasma edge in the lower divertor region. This minimizes inductive drive from poloidal fields and dynamic shaping. Plasmas with $I_{p} \le 200$ kA, $\Delta t_{pulse} \sim 20$ ms and $B_{T} \le 0.15$ T are produced to date, sustained by two injectors with $A_{inj} =4$ cm$^{\mathrm{2}}$, $V_{inj} \sim 1.5$ kV, and $I_{inj}  \sim 8$ kA, facilitated by improvements to the injectors, limiters, and divertor plates that mitigate deleterious PMI. These plasmas feature anomalous, reconnection-driven ion heating with $T_{i} \ge T_{e} \ge 50-100$ eV and large-amplitude MHD activity driven by the injectors. Under some conditions, MHD fluctuations abruptly decrease by over an order of magnitude without loss of LHI drive, improving realized $I_{p} $, and suggesting short-wavelength modes may relate to the current drive mechanism. The high $I_{N} \ge 10$, ion heating, and low $\ell_{i} $ driven by LHI, and the favorable stability of $A\sim 1$ STs allows access to record $\beta_{t}  \sim 100\% $ and high $\beta_{N} \sim 6.5$. Such high-$\beta_{t} $ plasmas have a minimum $\left| B \right|$ well spanning $\sim 50\% $ of the plasma volume. Enhancements to the Pegasus facility are considered to increase $B_{T} $ towards NSTX-U levels; establish coaxial helicity injection capabilities; and add auxiliary heating and current drive.   

Enhanced Control for Local Helicity Injection on the Pegasus ST

Local helicity injection (LHI) experiments on Pegasus rely upon programmable control of a $\sim 250$ MVA modular power supply system that drives the electromagnets and helicity injection systems. Precise control of the central solenoid is critical to experimental campaigns that test the LHI Taylor relaxation limit and the coupling efficiency of LHI-produced plasmas to Ohmic current drive. Enhancement and expansion of the present control system is underway using field programmable gate array (FPGA) technology for digital logic and control, coupled to new 10 MHz optical-to-digital transceivers for semiconductor level device communication. The system accepts optical command signals from existing analog feedback controllers, transmits them to multiple devices in parallel H-bridges, and aggregates their status signals for fault detection. Present device-level multiplexing/de-multiplexing and protection logic is extended to include bridge-level protections with the FPGA. An input command filter protects against erroneous and/or spurious noise generated commands that could otherwise cause device failures. Fault registration and response times with the FPGA system are 25 ns. Initial system testing indicates an increased immunity to power supply induced noise, enabling plasma operations at higher working capacitor bank voltage. This can increase the applied helicity injection drive voltage, enable longer pulse lengths and improve Ohmic loop voltage control.   

$V_{eff} $ Scaling of $T_{e} $ and $n_{e} $ Measurements During Local Helicity Injection on the Pegasus Toroidal Experiment

Understanding the electron confinement of local helicity injection (LHI) is critical in order to evaluate its scalability as a startup technique to MA-class devices. Electron confinement in the Pegasus Toroidal Experiment is investigated using multi-point Thomson scattering (TS). The Pegasus TS system utilizes a set of high-throughput transmission gratings and intensified CCDs to measure $T_{e} $ and $n_{e} $ profiles. Previous TS measurements indicated peaked $T_{e}_{\mathrm{\thinspace }}$profiles $\sim 120$ eV in outboard injector discharges characterized by strong inductive drive and low LHI drive. Injectors designed to have dominant non-inductive drive have recently been installed in the divertor region of Pegasus to understand the relationship between effective drive voltage, $V_{eff} $, and plasma performance. At low $V_{eff} $ and reduced plasma current, $I_{p} \sim 60$ kA, TS measurements reveal a flat $T_{e} $ profile $\sim 50$ eV, with a peaked $n_{e} $ profile $\sim 1\times 10^{19}$ m$^{\mathrm{-3}}$, resulting in a slightly peaked $p_{e} $ profile. As current drive is increased, the $T_{e} $ profiles become hollow with a core $T_{e} \sim 50$ eV and an edge $T_{e} \sim 120$--150 eV. These hollow profiles appear after the start of the $I_{p} $ flattop and are sustained until the discharge terminates. The $n_{e} $ profiles drop in magnitude to $<1\times 10^{19}$ m$^{\mathrm{-3}}$ but remain somewhat peaked. Initial results suggest a weak scaling between input power and core $T_{e} $. Additional studies are planned to identify the mechanisms behind the anomalous profile features.   

Investigating High Frequency Magnetic Activity During Local Helicity Injection on the Pegasus Toroidal Experiment

Understanding the current drive mechanism(s) of Local Helicity Injection (LHI) is needed for confident scaling to next-step devices. 3D resistive MHD NIMROD simulations ascribe large-scale reconnection events of helical injector current streams as a current drive mechanism. The events generate $n=1 \quad \dot{{B}}$ fluctuations on outboard Mirnov coils, consistent with experiment. New results suggest additional mechanisms are also active during LHI. Reconnection-driven ion heating is better correlated with high frequency activity than the $n=1$ bursts. Experiments with inboard injectors can exhibit an abrupt ($\sim 250\;\mu s)$ transition to a reduced MHD state on outboard Mirnovs where the $n=1$ feature vanishes, while still maintaining current growth and/or sustainment. A new insertable magnetics probe was developed to investigate these phenomena. It measures $\dot{{B}}_{z} $ up to $3.5$ MHz at $15$ points over a $14$ cm radial extent ($\Delta R\sim 1$ cm). Measurements with this probe are consistent with the outboard Mirnovs when positioned far from the plasma boundary. However, measurements near the plasma edge lack the reduction in broadband power (up to 2 MHz) following the transition. The probe shows power is concentrated at higher frequencies during LHI, with mostly flat $\dot{{B}}$ spectra up to $\sim $600--800 kHz ($\sim f_{ci} )$ at which there is a resonance-like feature; at higher frequencies, the power decreases. These measurements suggest short-wavelength activity may play a significant role in LHI current drive.   

Studies of Impurities in the Pegasus Spherical Tokamak

Local Helicity Injection (LHI) is used to initiate ST plasmas without a solenoid. Testing predictive models for the evolution of $I_{p} (t)$ during LHI requires measurement of the plasma resistivity to quantify the dissipation of helicity. To that end, three diagnostic systems are coupled with an impurity transport model to quantify plasma contaminants. These are: visible bremsstrahlung (VB) spectroscopy; bolometry; and VUV spectroscopy. A spectral survey has been performed to identify line-free regions for VB measurements in the visible. Initial VB measurements are obtained with a single sightline through the plasma, and will be expanded to an imaging array to provide spatial resolution. A SPRED multichannel VUV spectrometer is being upgraded to provide high-speed ($\sim 0.2$ ms) spectral surveys for ion species identification, with a high-resolution grating installed for metallic line identification. A 16-channel thinistor bolometer array is planned. Absolutely calibrated VB, bolometer measurements, and qualitative ion species identification from SPRED are used as constraints in an impurity transport code to estimate absolute impurity content. Earlier work using this general approach indicated $Z_{eff} <3$, before the edge current sources were shielded to reduce plasma-injector interactions.   

Microstability Properties of the Local Minimum $|B|$ Regime in Pegasus

A local minimum $|B|$ region, or ``magnetic well,'' was recently observed in the low-aspect-ratio Pegasus device in high-$\beta$ scenarios with strong edge current peaking [1]. The $\nabla B$ reversal within the magnetic well alters particle drifts, orbits, fast ion losses, and instability drives. Here, we report on the microstability properties of the magnetic well region with calculations from the \texttt{GENE} gyrokinetic code [2]. In particular, we explore the dependence on magnetic well depth and the role of electromagnetic effects. Preliminary results from local electromagnetic calculations indicate unstable electron modes exist in the magnetic well region. Connections to NSTX-U and MAST-U operational scenarios are also discussed. Finally, probe measurements of electrostatic and magnetic fluctuations in the Pegasus magnetic well region are presented in Ref.\ 3.\\ \\ $[1]$ D.J. Schlossberg, Ph.D. thesis (2017), Phys.\ Rev.\ Lett.\ (in press)\\ $[2]$ F. Jenko and the \texttt{GENE} Development Team, URL http://genecode.org/\\ $[3]$ A.T. Rhodes et al, these proceedings   

Initial Measurements of Electrostatic Turbulence in Local Helicity Injection Plasmas

Investigation of the edge turbulence during local helicity injection (LHI) in the Pegasus Toroidal Experiment is being pursued using a pair of triple Langmuir probes. Temperature and density profiles in the plasma edge have been measured during LHI, showing 100 eV and $4\times 10^{19}$ m$^{\mathrm{-3}}$, and agree with Thomson scattering to within measurement uncertainty. Fluctuation spectra of the probe measurements show a shift in spectral power density from low (10--100 kHz) to high (300--400 kHz) frequency between the early and later times of the discharge. This change in the frequency spectra is aligned with a spontaneous reduction of the $n=1$ MHD signature observed by magnetics diagnostics. Correlation with magnetic fluctuations is observed in the higher frequency range of the probes. Experiments are being conducted to measure electric potential fluctuations in the edge for a larger frequency range (up to 2 MHz) to understand the effects of the MHD transition on the edge turbulence. Additionally, recent LHI plasmas with $\beta_{t} \sim 100\% $ have shown a minimum $\left| B \right|$ well spanning $\sim 50\% $ of the plasma volume. This $\left| B \right|$ well is theoretically predicted to be stabilizing of drift wave turbulence. Measurements to explore the turbulence behavior in high-$\beta $ LHI plasmas are in progress.   

High Field Side MHD Activity During Local Helicity Injection

MHD is an essential part of understanding the mechanism for local helicity injection (LHI) current drive. The new high field side (HFS) LHI system on the Pegasus ST permits new tests of recent NIMROD simulations. In that model, LHI current streams in the plasma edge undergo large-scale reconnection events, leading to current drive. This produces bursty $n=1$ activity around 30 kHz on low field side (LFS) Mirnov coils, consistent with experiment. The simulations also feature coherent injector streams winding down the center column. Improvements to the core high-resolution poloidal Mirnov array with Cat7A Ethernet cabling and differentially driven signal processing eliminated EMI-driven switching noise, enabling detailed spectral analysis. Preliminary results from the recovered HFS poloidal Mirnov coils suggest $n=1$ activity is present at the top of the vessel core, but does not persist down the centerstack. HFS LHI experiments can exhibit an operating regime where the high amplitude MHD is abruptly reduced by more than an order of magnitude on LFS Mirnov coils, leading to higher plasma current and improved particle confinement. This reduction is not observed on the HFS midplane magnetics. Instead, they show broadband turbulence-like magnetic features with near consistent amplitude in a frequency range of 90--200 kHz.   

Progress Towards a New Technique for Measuring Local Electric and Magnetic Field Fluctuations in High Temperature Plasmas

Local measurements of electrostatic and magnetic turbulence in fusion grade plasmas is a critical missing component in advancing our understanding of current experiments and validating nonlinear turbulence simulations. A novel diagnostic for measuring local electric and magnetic field fluctuations ($\tilde{{E}}$ and $\tilde{{B}})$ is being developed to address this need. It employs high-speed measurements of the spectral linewidth and/or line intensities of the Motional Stark Effect split neutral beam emission. This emission is split into several spectral components, with the amount of splitting being proportional to local magnetic and electric fields at the emission site. High spectral resolution ($\sim 0.025$ nm), high throughput ($\sim 0.01$ cm$^{\mathrm{2}}$str), and high speed ($f\sim 250$ kHz) are required for the measurement of fast changes in the MSE spectrum. Spatial heterodyne spectroscopy (SHS) techniques coupled to a CMOS detector can meet these demands. A prototype SHS has been deployed to DIII-D for initial testing in the tokamak environment, SNR evaluation, and neutral beam efficacy. In addition, design studies of the SHS interferogram are ongoing to further optimize the measurement technique. One major contributor to loss of fringe contrast is line broadening arising from employing a large collection lens. This broadening can be mitigated by making the lens at the tokamak wall optically conjugate with the interference fringes image field.   

Imaging of laboratory magnetospheric plasmas using coherence imaging technique

The ring trap 1 (RT-1) device creates a laboratory magnetosphere for the studies on plasma physics and advanced nuclear fusion. A levitated superconducting coil produces magnetic dipole fields that realize a high beta plasma confinement that is motivated by self-organized plasmas in planetary magnetospheres. The electron cyclotron resonance heating (ECRH) with 8.2 GHz and 50 kW produces the plasmas with hot electrons in a few ten keV range. The electrons contribute to the local electron beta that exceeded 1 in RT-1. For the ion heating, ion cyclotron range of frequencies (ICRF) heating with 2--4 MHz and 10 kW has been performed in RT-1. The radial profile of ion temperature by a spectroscopic measurement indicates the signature of ion heating. In the holistic point of view, a coherence imaging system has been implemented for imaging the entire ion dynamics in the laboratory magnetosphere. The diagnostic system and obtained results will be presented.   

Investigations of plasmoid reconnection in the presence of strong guide fields in CHI plasma start-up on HIST.

Plasmoid magnetic reconnections have been examined in the Coaxial Helicity Injection (CHI) experiments on HIST. Magnetic reconnections are required for the formation of closed flux surfaces in the transient-CHI start-up plasmas. So far, we have observed formation of plasmoids inside an elongated current layer to create the multiple X-points during the CHI process. According to the MHD simulation by F. Ebrahimi and R. Raman, the reconnection rate based on the plasmoid instability is faster than that by Sweet-Parker (S-P) model. To estimate the Lundquist number S number, we have measured spatial profiles of magnetic field strength, electron density and temperature in the current layer. In this meeting, we will present the effect of the guide (toroidal) magnetic field and mass (H, D and He) on the current layer thickness and reconnection rates of plasmoids. It is found that behavior of plasmoids is synchronized with Ion Doppler temperature, leading to ion heating.   

Improved computation of two-fluid flowing equilibrium of spherical torus

Two-fluid equilibrium system with small but non-zero two-fluid parameter is identified as a singular perturbation problem. This singularity is eliminated by nearby-fluids ordering that the ion and electron flow surfaces are assumed to be close to each other but do not coincide exactly [1]. This elimination of the singularity facilitates to obtain numerical equilibrium solution, but leads to a pseudo singularity when the Alfvén Mach number corrected by this ordering approaches unity. For solving this problem, a new equilibrium solver is developed to perform a high-speed, high-accuracy computation without using this ordering. This solver employs a high-speed iterative method, the multi-grid method to reduce an increase in CPU time due to an increase in the mesh numbers. The purpose of this study is to apply this solver to a two-fluid equilibrium for geometry and boundary conditions of the NSTX device and to investigate the convergence properties of the numerical solution and the CPU time. Numerical experiments show that the convergence rate of the residual for the numerical solution is kept at approximately constant with respect to the iteration number of the outer loop and that the average value of the toroidal current density at the symmetry plane converges at the inverse square with respect to the mesh numbers. The multi-grid method is effective for solving the two-fluid flowing equilibrium equations with numerical stability and high accuracy. $^{\mathrm{1}}$L.C. Steinhauer and A. Ishida, Phys. Plasmas \textbf{13}, 052513 2006.   

Plasma shape reconstruction of merging spherical tokamak based on modified CCS method

The merging start-up method is the one of the CS-free start-up schemes that has the advantage of high plasma temperature and density because it involves reconnection heating and compression processes. In order to achieve optimal merging operations, the initial two STs should have identical plasma currents and shapes, and then move symmetrically toward the center of the device with appropriate velocity. Furthermore, from the viewpoint of the compression effect, controlling the plasma major radius is also important. To realize the active feedback control of the plasma currents, the positions, and the shapes of the two initial STs and to optimize the plasma parameters described above, accurate estimation of the plasma boundary shape is highly important. In the present work, the Modified-CCS method is demonstrated to reconstruct the plasma boundary shapes as well as the eddy current profiles in the UTST (The University of Tokyo) and ST40 device (Tokamak Energy Ltd). The present research results demonstrate the effectiveness of the M-CCS method in the reconstruction analyses of ST merging   

Power Balance Modeling of Local Helicity Injection for Non-Solenoidal ST Startup

A zero-dimensional power balance model for predicting $I_{p} (t)$ for Local Helicity Injection (LHI) discharges has been used to interpret experimental results from recent experimental campaigns using high-field-side (HFS) helicity injection. This model quantifies LHI's effective drive ($V_{eff} )$ through helicity balance while enforcing the Taylor relaxation current limit and tracking inductive effects to determine $I_{p} (t)$. Recent analysis of HFS LHI discharges indicate LHI is the dominant source of drive and provides $V_{eff} $ up to 1.3 V while geometric effects and inductive drive provide $<0.1$ V throughout much of the discharge. In contrast to previous analysis of low-field-side (LFS) LHI discharges, which were driven by $V_{eff} =0.3$ V and 2.0 V from geometric effects and inductive drive. A significant remaining uncertainty in the model is the resistive dissipation of LHI discharges. This requires greater understanding of LHI confinement scaling and impurity content, which are currently under investigation. However, the model and experimental $I_{p} (t)$ exhibit good agreement for parameters consistent with previous experimental findings. Extrapolation of plasma parameters and shaping from recent experiments allow for the model to project the performance of LHI systems. These projections indicate $I_{p} \sim 0.3$ MA can be accessed on Pegasus via HFS LHI through changes to injector geometry to provide more $V_{eff} $. This regime can be accessed via a LFS system by increasing the Taylor relaxation current limit early in the discharge.   

The High Field Ultra Low Aspect Ratio Tokamak (HF-ULART)

Recently, a medium-size HF-ULART has been proposed[1]. The major objective is to explore the high beta and pressure under the high toroidal field, using present day technology. This might be one of pathway scenarios for a potential ultra-compact pulsed neutron source (UCP-NS) based on the spherical tokamak (ST) concept, which may lead to more steady-state NS or even to a fusion reactor, via realistic design scaling. The HF-ULART pulsed mode operation is created by quasi-simultaneous adiabatic compression (AC) in both minor and major radius of a very high beta plasma, possibly with further help of passive-wall stabilization, as envisaged in the RULART concept[2]. This may help the revival of the studies of the AC technique in tokamaks, alongside the less compact and more complex ST-40 device, currently under construction[3]. In addition, by similarities, studies in HF-ULART as a UCP-NS may also help to test the feasibility of the compact NS via the spheromak concept, which also uses the AC technique[4]. Simulations of AC in HF-ULART plasmas will be presented. [1] C Ribeiro IAEA-RUSFD 2017 [2] C Ribeiro Proc. 26th SOFE 2015 [3] M Gryaznevich et al 18th Inter. Spherical Torus Workshop (ISTW) 2015 [4] P Sieck et al US-Japan Workshop on Compact-Torus 2016   

The LTX-$\beta $ Research Program

LTX-$\beta $, the upgrade to the Lithium Tokamak Experiment, approximately doubles the toroidal field (to 3.4 kG) and plasma current (to 150 -- 175 kA) of LTX. Neutral beam injection at 20 kV, 30 A will be added in February 2018, with systems provided by Tri-Alpha Energy. A 9.3 GHz, 100 kW, short-pulse (5-10 msec) source will be available in summer 2018 for electron Bernstein wave heating. New lithium evaporation sources will allow between-shots recoating of the walls. Upgrades to the diagnostic set are intended to strengthen the research program in the critical areas of equilibrium, core transport, scrape-off layer physics, and plasma-material interactions. The LTX-$\beta $ research program will combine the capability for gradient-free temperature profiles, to stabilize ion and electron temperature gradient-driven modes, with approaches to stabilization of $\nabla $n-driven modes, such as the trapped electron mode (TEM). Candidate stabilization mechanisms for the TEM include sheared flow stabilization, which can be tested on LTX-$\beta $. The goal will be to minimize anomalous transport in a low aspect ratio tokamak, which would lead to a very compact, tokamak-based fusion core.   

Active spectroscopy upgrades and neutral beam injection on LTX-$\beta $

The LTX-$\beta $ upgrade includes the addition of neutral beam injection (NBI) and increased active spectroscopy. Typical plasmas have been and are expected to remain inboard limited, at 14 cm with minor radii of 18-23 cm. The NBI, 35 Amps of 20 keV particles, will enable active diagnosis of ion velocity distribution profiles through charge exchange (CHERS). 18 CHERS views will cover more than a full minor radius, each sampling 2 cm of major radius. The system has both a set of beam directed ``active'' views and a symmetric set of views pointing away from the beam for stray light subtraction. Along with measuring ion temperatures and impurity transport, the CHERS diagnostic will measure the plasma rotation profiles. The recently described low recycling regime is predicted to allow for high rotational velocities due to the low neutral drag. The planned NBI has been predicted to give on axis velocities near 100 km/s. Flow shear is expected to increase confinement in this regime by suppressing trapped electron mode and other microturbulence enhanced transport. Upgrades to the Thomson scattering system, including an array of polychromators and a new camera, will assist in diagnosing the low density hot edge in this low recycling regime.   

Overview of Upgrades to the Lithium Tokamak Experiment, LTX-$\beta $

Exploration of the low-recycling regime at higher plasma performance and with key parameters closer to equilibrium motivated extensive upgrades to the Lithium Tokamak Experiment, now LTX-$\beta $. The toroidal field, plasma current, and discharge length will approximately double. The addition of a neutral beam will increase plasma heating by a factor of \textasciitilde 5 and also provide core fueling, enabling constant density in low-recycling conditions without edge fueling. Between-shot lithium evaporation, Li granule injection during discharges, and improved vacuum systems will allow expanded studies into the effects of surface conditions on recycling and performance. The Thomson scattering system will have increased spatial coverage and resolution. New baffles, polychromators, and an intensified camera will also reduce background and increase sensitivity at low density. Planned diagnostic upgrades also include tangential AXUV diode arrays for recycling and radiated power measurements, an additional resistive bolometer array, high- and low-field side Langmuir probes, and enhancements to VUV spectroscopy and fast camera diagnostics. A description and status of these upgrades and diagnostics, with first plasma planned for October 2017 and neutral beam operations in February 2018, will be presented.   

Magnetic Diagnostics Suite Upgrade on LTX-$\beta$

LTX-$\beta$ will be exploring a new regime of flat temperature-profile tokamak plasmas first demonstrated in LTX [D.P. Boyle \emph{et al. PRL} July 2017]. The incorporation of neutral beam core-fueling and heating in LTX-$\beta$ is expected to increase plasma beta and drive increased MHD activity. An upgrade of the magnetic diagnostics is underway, including an expansion of the reentrant 3-axis poloidal Mirnov array, as well as the addition of a toroidal array of poloidal Mirnov sensors and a set of 2-axis Mirnov sensors measuring fields from shell eddy currents. The poloidal and toroidal arrays will facilitate the study of MHD mode activity and other non-axisymmetric perturbations, while the new shell eddy sensors and improvements to existing axisymmetric measurements will support enhanced equilibrium reconstructions using the PSI-Tri equilibrium code [C. Hansen \emph{et al. PoP} Apr. 2017] to better characterize these novel hot-edge discharges.   

Characterization of the Scrape-off Layer of Lithium Tokamak eXperiment-$\beta$ (LTX-$\beta$) using a Retarding Field Energy Analyzer

The Lithium Tokamak eXperiment (LTX) is a spherical tokamak device designed to study lithium plasma facing components (PFCs). The lithium coated wall of LTX has been demonstrated to produce a low density, high temperature, and hence low collisionality plasma edge. The recent upgrade to LTX-$\beta$ includes installation of a neutral beam, which will provide further heating and fueling of the plasma. Core and edge diagnostics will also be expanded. As part of this expansion, a Retarding Field Analyzer (RFEA) has been developed for the scrape-off layer (SOL) of LTX-$\beta$. Measurements of the ion temperature, ion energy distribution, and the local space potential will be performed in the SOL plasma using this RFEA. Since a high temperature, low collisional edge is expected for LTX-$\beta$, the plasma in the SOL will be mirror-trapped, and could produce an ambipolar potential via differential loss of the electrons and ions, known as the Pastukhov potential in the literature [1]. A simple numerical prediction of the ambipolar potential profile will be presented, along with the design of the RFEA system. $^1$ Pastukhov, V. P.,  Nucl. Fusion  \textbf{14}.1 (1974).   

Simulation of the Microwave/Millimer-Wave Diagnostics on LTX-$\beta$ for Density Fluctuation Measurements

Fluctuation measurements and their relation to transport will be of key interest in the LTX-$\beta$ device, which will have higher $B_T$ and $I_P$, and neutral beam heating. UCLA plans to provide a suite of microwave/millimeter-wave diagnostics to measure internal electron density fluctuations: a 296 GHz single-chord interferometer, an FM-CW (frequency-modulated continuous-wave) reflectometer (13.5$-$33 GHz), and two tunable fixed-frequency quadrature reflectometer channels (13.5$-$20.5 and 27$-$40) GHz. Key to the interpretation of the experimental data will be extensive modeling of the target fluctuations and simulations of the reflectometry/scattering response. To this end a set of simulation tools has been developed to calculate the effects of density fluctuations on the measured signals: 3-D geometrical and physical optics, as well as 1-D and 2-D full-wave codes. The sensitivity of these diagnostics to various density profile shapes and turbulence models will be presented. Possible configurations for future microwave diagnostics on LTX-$\beta$, such as a Doppler backscattering, will also be explored.   

Investigation of lithium PFC surface characteristics and low recycling at LTX/LTX-Beta

Lithium coatings on high-Z PFCs at LTX have led to improved plasma performance. The initial hypothesis was that lithium retains hydrogen by forming lithium hydride and thereby enabling low recycling in LTX. However, recent in-vacuo measurements indicate the presence of lithium oxide in deposited lithium coatings. Improved plasma performance continued to be observed in the presence of lithium oxide. These observations raise questions like what is the nature of the lithium oxide surface, whether the PFC is an amorphous mixture of lithium and lithium oxide or something more ordered like a lithium oxide layer growing on top of lithium, and whether lithium oxide is responsible for any retention of hydrogen from the plasma. To investigate the mechanism by which the LTX PFC might be responsible for low recycling, we discuss the results of deuterium retention measurements using NRA/RBS and sample characterization using high resolution XPS (HR-XPS) in bulk lithium samples. Baseline HR-XPS scans indicate the presence of Lithium Oxide on sputtered lithium samples. Status of related planned experiments at LTX-$\beta$ will also be discussed.   

Effect of 3-D magnetic fields on neutral particle fueling and exhaust in MAST

The application of resonant magnetic perturbations (RMPs) is used to suppress edge localized modes but causes in many cases a density pump-out. At MAST, this particle pump out was found to be connected to an amplifying MHD plasma response. An analysis is presented on past MAST discharges to understand the effect of these RMPs on the neutral household and on changes in neutral fueling and exhaust during the pump out. A global, 0-D particle balance model [G. Maddison et al. PP{\&}CF 48 (2006) 71] was used to study the neutral dynamics and plasma confinement during shots with and without RMP application. Using the D$\alpha $ emission measured by filterscopes and a calibrated 1-D CCD camera, as well as S/XB coefficients determined by the edge plasma parameters, globally averaged ion confinement times were calculated. In L-mode, discharges with RMPs that caused an MHD response had a 15-20{\%} decrease in confinement time but an increase in total recycling flux. The application of RMPs in H-mode caused either a decrease or no change in confinement, like those in L-mode, depending on the configuration of the RMPs and plasma response. A spectroscopically assisted Penning gauge is being prepared for the next campaign at MAST-U to extend this particle balance to study impurity exhaust with RMPs.   

2D Kinetic Particle in Cell Simulations of a Flow-Shear Stabilized Z-Pinch

The lifetime of Z-pinch plasmas is typically limited by MHD instabilities, e.g. the m = 0 “sausage” and m = 1 “kink” modes. An attractive strategy to suppress these and related instabilities and extend the lifetime of a Z-pinch is to drive sheared axial flows in the plasma, $dv_{z}/dr \neq 0$. This stabilization was demonstrated in a series of experiments at the UW and these long-lived Z-pinches may offer viable sources of ion beams, neutrons and radiation, or potentially, a fusion reactor. LLNL is running 2D simulations using the particle-in-cell(PIC) code, LSP, to study flow-shear Z-pinch stability and performance. The suppression of the sausage mode by axial flow-shear is seen under the present experimental conditions as well as at reactor scales, with multiple shear-flow profiles. The longevity of these sheared-flows depends on the plasma viscosity, and a preliminary viscosity and shear-flow longevity analysis is also presented. This work represents the first fully-kinetic modeling results for the flow-shear stabilized Z-pinch.   

Overview of the FuZE Fusion Z-Pinch Experiment

Successful results of the sheared flow stabilized (SFS) Z-pinch from ZaP and ZaP-HD have motivated the new FuZE project to scale the plasma performance to fusion conditions. The SFS Z-pinch is immune to the instabilities that plague the conventional Z-pinch yet maintains the same favorable radial scaling. The plasma density and temperature increase rapidly with decreasing plasma radius, which naturally leads to a compact configuration at fusion conditions. The SFS Z-pinch is being investigated as a novel approach to a compact fusion device in a collaborative ARPA-E ALPHA project with the University of Washington and Lawrence Livermore National Laboratory. The project includes an experimental effort coupled with high-fidelity physics modeling using kinetic and fluid simulations. Along with scaling law analysis, computational and experimental results from the FuZE device are presented.   

Producing High-Performance, Stable, Sheared-Flow Z-Pinches in the FuZE project.

The Fusion Z-Pinch Experiment (FuZE) has made significant strides towards generating high-performance, stable Z-pinch plasmas with goals of n$_{\mathrm{e}}=$10$^{\mathrm{18}}$ cm$^{\mathrm{-3}}$ and T$=$1 keV. The Z-pinch plasmas are stabilized with a sheared axial flow that is driven by a coaxial accelerator. The new FuZE device has been constructed and reproduces the major scientific achievements the ZaP project at the University of Washington; n$_{\mathrm{e}}=$10$^{\mathrm{16}}$ cm$^{\mathrm{-3}}$,T$=$ 100 eV, r\textless 1 cm, and t$_{\mathrm{stable}}$ \textgreater 20 $\mu $s. These parameters are measured with an array of magnetic field probes, spectroscopy, and fast framing cameras. The plasma parameters are achieved using a small fraction of the maximum energy storage and gas injection capability of the FuZE device. Higher density, n$_{\mathrm{e}}=$5x10$^{\mathrm{17}}$ cm$^{\mathrm{-3}}$, and temperature, T$=$ 500 eV, Z-pinch plasmas are formed by increasing the pinch current. At the higher voltages and currents, the ionization rates in the accelerator increase. By modifying the neutral gas profile in the accelerator, the plasma flow from the accelerator is maintained, driving the flow shear. Formation and sustainment of the sheared-flow Z-pinch plasma will be discussed. ~Experimental data demonstrating high performance plasmas in a stable Z-pinches will be shown.   

Control of Z-pinch plasma properties through the initial neutral gas distribution in the FuZE Fusion Z-pinch Experiment

The FuZE project investigates scaling the sheared flow stabilized (SFS) Z-pinch to fusion conditions. FuZE will generate a 1 mm radius Z-pinch with a 300 kA plasma current. Sheared flow Z-pinches are formed by a coaxial accelerator operating in a deflagration mode. The ionization front can be controlled by the neutral gas injection. Fast-acting valves located inside the inner electrode and at 8 locations on the outer electrode provide spatial and temporal control of the gas distribution. Line-integrated plasma density inside the coaxial accelerator are obtained by an interferometry system. Magnetic field topology is measured by an array of 94 surface-mounted magnetic field probes embedded in the outer copper electrode. Coaxial accelerator current measurements obtained through the magnetic field probes and density are compared with the downstream Z-pinch properties, such as stability, temperature, and density with the goal of understanding the relation between neutral gas injection and Z-pinch plasma parameters and behavior.   

Measurements of the Time Evolution of Ion Temperature Profiles on the FuZE Fusion Z-Pinch Experiment

FuZE investigates the scaling of sheared-flow stabilized Z-pinches to fusion-relevant densities and temperatures. Long-lived (\textgreater 20 $\mu $s) pinches with an embedded axial flow and stabilizing velocity shear are formed by radial compression of a flowing plasma produced in a coaxial plasma accelerator. In the near term, we plan to operate with trace amounts of deuterium to produce a small but detectable flux of D-D neutrons. This flux can be estimated if the ion temperature and density profiles are known. Density profiles are obtained from interferometry. Ion Doppler spectroscopy measures the line-integrated ion temperature along 20 chords spaced 1.2 mm apart in the plasma based on Doppler broadening of impurity lines. The time evolution of T$_{\mathrm{i}}$ profiles is measured by varying the time at which the spectrum is acquired over a series of repeatable plasma pulses. Based on experimental ion temperature and density profiles, we calculate the expected neutron flux. This estimate can be compared to the measured neutron flux to ascertain whether the neutrons are of thermonuclear origin.   

High Energy Density Plasma Jet Studies in the ZaP-HD Experiment

The ZaP-HD Flow Z-Pinch device produces high energy density plasma jets that are magnetically confined in a Z-pinch configuration with a 50 cm length and 0.5 cm diameter. Conditions in the pinch exceed temperatures of 800 eV and densities of 2e17 cm$^{\mathrm{-3}}$. Plasma properties are characterized with a suite of diagnostics including magnetic field probes, digital holographic interferometry, Doppler spectroscopy, and fast-framing photography. Magnetic field probes indicate an extended quiescent period. Recent investigations include impingement of the high-speed, high-energy-density plasma jet onto a solid body. A 0.3 cm diameter boron nitride rod is inserted into the Z-pinch plasma to study plasma-material interactions. Digital holographic interferometry produces a two-dimensional map of the plasma density around the tripping probe. Fast framing photography images laminar and turbulent boundary layer behavior. Spectroscopic data indicate subsonic flow speeds throughout the pulse. A time-resolved ion Doppler spectrometer is developed to produce velocity contours for the entire plasma pulse.   

High resolution digital holographic interferometry on the FuZE Fusion Z-Pinch Experiment

The recently constructed sheared flow stabilized (SFS) Z-pinch experiment, the Fusion Z-Pinch Experiment (FuZE), is operational. The experiment is investigating scaling of SFS Z-pinch plasmas towards fusion conditions. Cylindrical plasmas are compressed to small radii ($< 1$ cm), and high densities ($> 10^{18}/$cm$^3$) as plasma current is increased. Diagnosing the size, density and internal structure of these small radii cylindrical plasmas require a high spatial resolution plasma density diagnostic. Motivated by this, a holographic interferometer with 10 micron spatial resolution has recently been installed on FuZE [1]. A Nd:YAG laser is used with a digital camera to produce holograms from the plasma assembly region. Digital holograms are numerically reconstructed to obtain chord-integrated electron density of compressed plasma, with fine spatial resolution. Assuming cylindrical symmetry in the assembly region, plasma radial density profiles are reconstructed from these chord-integrated electron density data. Both chord-integrated and radial plasma density data from FuZE are presented. [1] M.P. Ross & U. Shumlak, RSI 87, 103502 (2016)   

Laser Beat-Wave Magnetization of a Dense Plasma

We present results from the first of a series of experiments to demonstrate and characterize laser beat-wave magnetization of a dense plasma, motivated by the desire to create high-beta targets with standoff for magneto-inertial fusion. The experiments are being conducted at the Jupiter Laser Facility (JLF) at LLNL. The experiment uses the JLF Janus 1$\omega $ (1053 nm) beam and a standalone Nd:YAG (1064 nm) to drive the beat wave, and the Janus 2$\omega $ (526.5 nm) beam to ionize/heat a gas-jet target as well as to provide Thomson-scattering (TS) measurements of the target density/temperature and scattered light from the beat wave. Streaked TS data captured electron-plasma-wave and ion-acoustic-wave features utilizing either nitrogen or helium gas jets. Effects of initial gas density as well as laser intensity on target have been measured, with electron densities ranging from 1E18 to 1E19 cm-3 with temperatures of tens to hundreds of eV, near the desired range for optimal field generation. LSP simulations were run to aid experimental design and data interpretation.   

Experimental characterization of plasma-liner formation via merging supersonic plasma jets

The Plasma Liner Experiment-ALPHA (PLX-$\alpha$) is investigating the merging of supersonic plasma jets into a spherically imploding plasma liner as a compression driver for magneto-inertial fusion (MIF). Concurrently, we are also studying the fundamental physics of plasma shocks, from collisional to collisionless regimes, using the same platform. The present work is focused on characterizing the merging of six and/or seven plasma jets, converging in a cone of solid angle 0.4$\pi$ over a distance of 1.3 meters, as well as studies with fewer jets to isolate and vary shock properties. Data will be presented on plasma jet/liner velocities, electron/ion densities and temperatures, and mean ionization state. Diagnostics include a multi-chord interferometer, visible survey and high-resolution spectrometers, fast-framing camera, and photodiode arrays. Spectroscopy and interferometry data are compared with synthetic data from 3D front-tracking and smooth-particle-hydrodynamic simulations. Results will provide new understanding of plasma shock structure/dynamics and assessment of plasma liners as an MIF driver.   

Characterization and optimization of the HyperV PLX-$\alpha$ coaxial-gun plasma jet

We present results from characterizing and optimizing performance of the contoured gap coaxial plasma guns under development for the ARPA-E Accelerating Low-Cost Plasma Heating And Assembly (ALPHA) program. Plasma jet diagnostics include fast photodiodes for velocimetry and interferometry for line integrated density. Additionally we present results from spectroscopy, both time resolved high resolution spectroscopy using a novel detector and time integrated survey spectroscopy, for measurements of velocity and temperature as well as impurities. Fast imaging gives plume geometry and time integrated imaging gives overall light emission. Results from a novel long record length camera developed by HyperV will also be presented. Experimental results are compared to the desired target parameters for the plasma jets. The target values for the plasmoid are velocity of 50 km/s, mass of 3.5 mg, and length of 10 cm. The best results so far from the exploration of parameter space for gun operation are: $\sim$4 mg at $>$50 km/s, with a length of 10 cm. Peak axial density 34 cm downstream from the muzzle is $\sim 2 \times 10^{16}$ cm$^{-3}$.   

Engineering design of the PLX-$\alpha$ coaxial gun

We describe the engineering and technical improvements, as well as provide a detailed overview of the design choices, of the latest PLX-$\alpha$ coaxial gun designed for the 60-gun scaling study of spherically imploding plasma liners as a standoff driver for plasma-jet-driven magneto-inertial fusion [1]. Each coaxial gun incorporates a fast, dense gas injection and triggering system, a compact low-weight pfn with integral sparkgap switching, and a contoured gap designed to suppress the blow-by instability [2]. The evolution of the latest Alpha gun is presented with emphasis on its upgraded performance. Changes include a faster more robust gas valve, better-quality ceramic insulator material and enhancements to overall design layout. These changes result in a gun with increased repeatability, reduced potential failure modes, improved fault tolerance and better than expected efficiency. A custom 600-$\mu$F, 5-kV pfn and a set of six inline sparkgap switches operated in parallel are mounted directly to the back of the gun, and are designed to reduce inductance, cost, and complexity, maximize efficiency and system reliability, and ensure symmetric current flow. [1] Hsu et al., IEEE Trans. Plasma Sci. 40, 1287 (2012). [2] Witherspoon et al., Rev. Sci. Instr. 80, 083506 (2009).   

Simulation Study of Structure and Properties of Plasma Liners for the PLX-$\alpha $ Project

Detailed numerical studies of the propagation and merger of high-Mach-number plasma jets and the formation and implosion of plasma liners have been performed using the FronTier code in support of the Plasma Liner Experiment-ALPHA (PLX-$\alpha )$ project. Physics models include radiation, physical diffusion, plasma-EOS models, and an anisotropic diffusion model that mimics deviations from fully collisional hydrodynamics in outer layers of plasma jets. Detailed structure and non-uniformity of plasma liners of due to primary and secondary shock waves have been studies as well as averaged quantities of ram pressure and Mach number. Synthetic data from simulations have been compared with available experimental data from a multi-chord interferometer and survey and high-resolution spectrometers. Numerical studies of the sensitivity of liner properties to experimental errors in the initial masses of jets and the synchronization of plasma gun valves have also been performed.   

Effects of equation of state, transport, and initial conditions on plasma liner formation and implosion from hypervelocity jets

The PLX-{\$}$\backslash $alpha{\$} project is studying plasma liner formation and implosion by merging a spherical array of plasma jets as a standoff driver for magneto-inertial fusion (MIF). A three-dimensional smoothed particle hydrodynamics (SPFMax) code is used to conduct simulations of merging of discrete plasma jets to form a plasma liner and the subsequent implosion of that liner. Peak ram pressure, Mach number, and uniformity of the liner are presented as a function of initial jet properties and assumptions about transport physics. The initial conditions include the number of jets, density, temperature, and implosion velocity. Solid-angle-averaged and standard deviation of liner ram pressure and Mach number reveal variations during liner formation and implosion. Spherical-harmonic mode-number analysis of spherical slices of ram pressure at various radii and times provide a quantitative means to assess the evolution of liner non-uniformity. Comparisons are made with select and equivalent cases of a uniform, imploding liner. Simulations of 6 and 7 jets are provided for select cases to support near-term experiments on PLX-{\$}$\backslash $alpha{\$} and will include synthetic spectra and line-integrated densities.   

Estimates of Fusion Gain of Plasma Jet Driven Magneto-Inertial Fusion

A main goal of the PLX-\alpha project is to identify parameters \(for example, jet velocities and densities\) that could result in gain>1 in plasma-jet-driven magneto-inertial fusion [S. C. Hsu et al., IEEE Trans. Plasma Sci. 40, 1287, 2012]. We are employing 2D MHD simulations of a spherically imploding plasma liner compressing a magnetized target using the USim code [K. Beckwith, et al., IEEE Trans. Plasma Sci. 43, 4, 2015] to identify those parameters. The simulations include realistic EOS and alpha-deposition models. We look at how different levels of density and velocity perturbations change the gain results, specifically using perturbation levels informed by 3D hydrodynamic simulations. Some of these simulation results come from many-core runs on the Los Alamos high-performance computing resources, and we discuss the performance and scaling of our simulations.   

Nuclear Fusion Blast and Electrode Lifetimes in a PJMIF Reactor

We present an analysis and numerical simulation of the nuclear blast from the micro-explosion following the completion of the fusion burn for a baseline design of a PJMIF fusion reactor with a fusion gain of 20. The stagnation pressure from the blast against the chamber wall defines the engineering requirement for the structural design of the first wall and the plasma guns. We also present an analysis of the lifetimes of the electrodes of the plasma guns which are exposed to (1) the high current, and (2) the neutron produced by the fusion reactions. We anticipate that the gun electrodes are made of tungsten alloys as plasma facing components reinforced structurally by appropriate steel alloys. Making reasonable assumptions about the electrode erosion rate (100 ng/C transfer), the electrode lifetime limited by the erosion rate is estimated to be between 19 and 24 million pulses before replacement. Based on known neutron radiation effects on structural materials such as steel alloys and plasma facing component materials such as tungsten alloys, the plasma guns are expected to survive some 22 million shots. At 1 Hz, this equal to about 6 months of continuous operation before they need to be replaced.   

Staged Z-pinch Experiments on the NTF Zebra Facility

We report results from the latest Staged Z-pinch\footnote{H. U. Rahman, F. J. Wessel, and N. Rostoker, “Staged Z Pinch”, Phys. Rev. Lett. 74, 714 (1995)} experiments conducted on the 1 MA, 100 ns Zebra facility at the University of Nevada, Reno. In these experiments, a high-Z annular gas liner (Ar, Kr) with initial radius of 1.2 cm implodes onto a deuterium target on axis. Measurements are presented, including data from pinch current, X-ray photodiodes and PCDs signals, visible streak imaging, XUV gated imaging, laser shadowgraphy, neutron time-of-flight and neutron yield detectors, and preliminary data analysis is discussed. The implosion velocity exceeding 300 km/s, and pinch time are consistent with MHD simulations performed with the MACH2 code. The imaging diagnostics indicates that the target column is more stable than the surrounding liner during the implosion. Primary (DD) neutrons of thermonuclear nature were produced with yields higher than 1x10$^9$ per shot, reproducibly. In addition, preliminary neutron time-of-flight results indicate that secondary (DT) neutrons can be produced above the detection threshold.   

Staged Z-pinch Experiments at the 1MA Zebra pulsed-power generator: Neutron measurements

We report on neutron measurements from the latest Staged Z-pinch experiments at the 1MA Zebra pulsed-power generator. In these experiments a hollow shell of argon or krypton gas liner, injected between the 1 cm anode-cathode gap, compresses a deuterium plasma target of varying density. Axial magnetic field $B_z \le 2 kGs$, applied throughout the pinch region, stabilizes the Rayleigh-Taylor instability. The standard silver activation diagnostics and 4 plastic scintillator neutron Time of Flight (nTOF) detectors are augmented with a large area ($\sim 1400cm^2$) liquid scintillator detector to which fast \it gated \rm Photek photomultipliers are attached. Sample data from these neutron diagnostics systems is presented. Consistently high neutron yields $Y_{DD} > 10^9$ are measured, with highest yield of $2.6 \times 10^9$. A pair of horizontally and vertically placed plastic scintillator nTOFs suggest isotropic i.e. thermonuclear origin of the neutrons produced. nTOF data from the liquid scintillator detector was cross-calibrated with the silver activation detector, and can be used for accurate calculation of the neutron yield.   

Analysis of staged Z-pinch implosion trajectories from experiments on Zebra

The Staged Z-pinch plasma confinement concept relies on compressing an annular liner of high-Z plasma onto a target plasma column of deuterium fuel. The interface between the liner and target is stable against the Magneto-Rayleigh-Taylor Instability, which leads to effective fuel compression and makes the concept interesting as a potential fusion reactor. The liner initiates as a neutral gas puff, while the target plasma is a partially ionized (Z$_{eff} <$ 10 percent column ejected from a coaxial plasma gun. The Zebra pulsed power generator (1 MA peak current, 100 ns rise time) provides the discharge that ionizes the liner and drives the Z-pinch implosion. Diverse diagnostics observe the 100-300 km/s implosions including silicon diodes, photo-conducting detectors (PCDs), laser shadowgraphy, an XUV framing camera, and a visible streak camera. The imaging diagnostics track instabilities smaller than 0.1 mm, and Z-pinch diameters below 2.5 mm are seen at peak compression. This poster correlates the data from these diagnostics to elucidate implosion behavior dependencies on liner gas, liner pressure, target pressure, and applied, axial-magnetic field.   

Staged Z-pinch experiments on the Mega-Ampere current driver COBRA

Experiments were conducted on the Cornell's 1 MA, 100 ns current driver COBRA with the goal of better understanding the Staged Z-pinch physics and validating MHD codes. We used a gas injector composed of an annular (1.2 cm radius) high atomic number (e.g., Ar or Kr) gas-puff and an on-axis plasma gun that delivers the ionized hydrogen target. Liner implosion velocity and stability were studied using laser shadowgraphy and interferometry as well as XUV imaging. From the data, the signature of the MRT instability and zippering effect can be seen, but time integrated X-ray imaging show a stable target plasma. A key component of the experiment was the use of optical Thomson scattering (TS) diagnostics to characterize the liner and target plasmas. By fitting the experimental scattered spectra with synthetic data, electron and ion temperature as well as density can be obtained. Preliminary analysis shows significant scattered line broadening from the plasma on-axis (\textasciitilde 0.5 mm diameter) which can be explained by either a low temperature H plasma with Te$=$Ti$=$75eV, or by a hot plasma with Ti$=$3keV, Te$=$350eV if an Ar-H mixture is present with an Ar fraction higher than 10{\%}.   

Shock formation and Magneto-Rayleigh-Taylor instability mitigation in double-shell Staged Z-pinch implosions

Target preheating in a magneto-inertial fusion scheme like the Staged Z-pinch is required to reduce the required convergence ratio for reaching fusion conditions. The current iteration of the Staged Z-pinch uses a single, high-Z gas-puff liner to compress a deuterium (D) target. Prior MHD simulations1 of similar implosions on a 1 MA driver predicted peak and average implosion velocities of 20 and 10 cm/us, respectively, which resulted in shock temperatures far below the ~100 eV required for target preheating\footnote{J. Narkis et al., Phys. Plasmas 23, 122706 (2016)}. Reduction of liner mass is an effective approach to increasing implosion velocity – experimental implosion velocities exceeding 30 cm/$\mu$s have been reported – and therefore shock strength, however this also results in increased magneto-Rayleigh-Taylor (MRT) instability growth. Both using a double liner and an axial magnetic field are effective mitigation mechanisms for MRTI growth. However, a double liner provides better MRTI mitigation and a fortuitous increase in shock strength and implosion velocity over a single liner, as demonstrated in simulated Kr / D and Ne / Kr / D implosions.   

One-dimensional MHD simulations of MTF systems with compact toroid targets and spherical liners

One-dimensional (1D) MHD code is developed in General Fusion (GF) for coupled plasma-liner simulations in magnetized target fusion (MTF) systems. The main goal of these simulations is to search for optimal parameters of MTF reactor, in which spherical liquid metal liner compresses compact toroid plasma. The code uses Lagrangian description for both liner and plasma. The liner is represented as a set of spherical shells with fixed masses while plasma is discretized as a set of nested tori with circular cross sections and fixed number of particles between them. All physical fields are 1D functions of either spherical (liner) or small toroidal (plasma) radius. Motion of liner and plasma shells is calculated self-consistently based on applied forces and equations of state. Magnetic field is determined by 1D profiles of poloidal and toroidal fluxes -- they are advected with shells and diffuse according to local resistivity, this also accounts for flux leakage into the liner. Different plasma transport models are implemented, this allows for comparison with ongoing GF experiments. Fusion power calculation is included into the code. We performed a series of parameter scans in order to establish the underlying dependencies of the MTF system and find the optimal reactor design point.   

Temperature Measurements in Compressed and Uncompressed SPECTOR Plasmas at General Fusion

Accurate temperature measurements are critical to establishing the behavior of General Fusion’s SPECTOR plasma injector, both before and during compression. As compression tests impose additional constraints on diagnostic access to the plasma, a two-color, filter-based soft x-ray electron temperature diagnostic has been implemented. Ion Doppler spectroscopy measurements also provide impurity ion temperatures on compression tests. The soft x-ray and ion Doppler spectroscopy measurements are being validated against a Thomson scattering system on an uncompressed version of SPECTOR with more diagnostic access. The multipoint Thomson scattering diagnostic also provides up to a six point temperature and density profile, with the density measurements validated against a far infrared interferometer. Temperatures above 300 eV have been demonstrated to be sustained for over 500 microseconds in uncompressed plasmas. Optimization of soft x-ray filters is ongoing, in order to balance blocking of impurity line radiation with signal strength.   

MHD simulation of plasma compression experiments

General Fusion (GF) is working to build a magnetized target fusion (MTF) power plant based on compression of magnetically-confined plasma by liquid metal. GF is testing this compression concept by collapsing solid aluminum liners onto plasmas formed by coaxial helicity injection in a series of experiments called PCS (Plasma Compression, Small). We simulate the PCS experiments using the finite-volume MHD code VAC. The single-fluid plasma model includes temperature-dependent resistivity and anisotropic heat transport. The time-dependent curvilinear mesh for MHD simulation is derived from LS-DYNA simulations of actual field tests of liner implosion. We will discuss how 3D simulations reproduced instability observed in the PCS13 experiment and correctly predicted stabilization of PCS14 by ramping the shaft current during compression. We will also present a comparison of simulated Mirnov and x-ray diagnostics with experimental measurements indicating that PCS14 compressed well to a linear compression ratio of 2.5:1.   

Physics objectives of PI3 spherical tokamak program

Achieving net energy gain with a Magnetized Target Fusion (MTF) system requires the initial plasma state to satisfy a set of performance goals, such as particle inventory $(~10^{21}$ ions), sufficient magnetic flux $(~0.3 Wb)$ to confine the plasma without MHD instability, and initial energy confinement time several times longer than the compression time. General Fusion (GF) is now constructing Plasma Injector 3 (PI3) to explore the physics of reactor-scale plasmas. Energy considerations lead us to design around an initial state of Rvessel = 1 m. PI3 will use fast coaxial helicity injection via a Marshall gun to create a spherical tokamak plasma, with no additional heating. MTF requires solenoid-free startup with no vertical field coils, and will rely on flux conservation by a metal wall. PI3 is 5x larger than SPECTOR so is expected to yield magnetic lifetime increase of 25x, while peak temperature of PI3 is expected to be similar (400-500 eV) Physics investigations will study MHD activity and the resistive and convective evolution of current, temperature and density profiles. We seek to understand the confinement physics, radiative loss, thermal and particle transport, recycling and edge physics of PI3.   

Passive MHD Spectroscopy for Enabling Magnetic Reconstructions on Spherical Tokamak Plasmas at General Fusion Inc.

Magnetic reconstructions on lab based plasma injectors at General Fusion relies heavily on edge magnetic (“Bdot”) probes. On plasma experiments built for field compression (PCS) tests, the number and locations of Bdot probes is limited by mechanical constraints. Additional information about the q profiles near the core in our Spector plasmas is obtained using passive MHD spectroscopy. The coaxial helicity injection (CHI) formation process naturally generates hollow current profiles and reversed shear early in each discharge. Central Ohmic heating naturally peaks the current profiles as our plasmas evolve in time, simultaneously reducing the core safety factor, q(0), and reverse shear. As the central, non-monotonic q-profile crosses rational flux surfaces, we observe transient magnetic reconnection events (MRE’s) due to the double tearing mode. Modal analysis allows us to infer the q surfaces involved in each burst. The parametric dependence of the timing of MRE’s allows us to estimate the continuous time evolution of the core q profile. Combining core MHD spectroscopy with edge magnetic probe measurements greatly enhances our certainty of the overall q profile.   

Magnetized Target Fusion At General Fusion: An Overview

Magnetized Target Fusion (MTF) involves compressing an initial magnetically confined plasma on a timescale faster than the thermal confinement time of the plasma. If near adiabatic compression is achieved, volumetric compression of 350X or more of a 500 eV target plasma would achieve a final plasma temperature exceeding 10 keV. Interesting fusion gains could be achieved provided the compressed plasma has sufficient density and dwell time. General Fusion (GF) is developing a compression system using pneumatic pistons to collapse a cavity formed in liquid metal containing a magnetized plasma target. Low cost driver, straightforward heat extraction, good tritium breeding ratio and excellent neutron protection could lead to a practical power plant. GF (65 employees) has an active plasma R&D program including both full scale and reduced scale plasma experiments and simulation of both. Although pneumatic driven compression of full scale plasmas is the end goal, present compression studies use reduced scale plasmas and chemically accelerated aluminum liners. We will review results from our plasma target development, motivate and review the results of dynamic compression field tests and briefly describe the work to date on the pneumatic driver front.   

Magnetic Compression Experiment at General Fusion with Simulation Results

The magnetic compression experiment at GF was a repetitive non-destructive test to study plasma physics applicable to Magnetic Target Fusion compression. A spheromak compact torus (CT) is formed with a co-axial gun into a containment region with an hour-glass shaped inner flux conserver, and an insulating outer wall. External coil currents keep the CT off the outer wall (levitation) and then rapidly compress it inwards. The optimal external coil configuration greatly improved both the levitated CT lifetime and the rate of shots with good compressional flux conservation. As confirmed by spectrometer data, the improved levitation field profile reduced plasma impurity levels by suppressing the interaction between plasma and the insulating outer wall during the formation process. We developed an energy and toroidal flux conserving finite element axisymmetric MHD code to study CT formation and compression. The Braginskii MHD equations with anisotropic heat conduction were implemented. To simulate plasma / insulating wall interaction, we couple the vacuum field solution in the insulating region to the full MHD solution in the remainder of the domain. We see good agreement between simulation and experiment results.   

Reconstruction of Axial Energy Deposition in Magnetic Liner Inertial Fusion Based on PECOS Shadowgraph Unfolds Using the AMR Code FLASH

Magnetic Liner Inertial Fusion (MagLIF) experiments incorporate a laser to preheat a deuterium filled capsule before compression via a magnetically imploding liner. In this work, we focus on the blast wave formed in the fuel during the laser preheat component of MagLIF, where approximately 1kJ of energy is deposited in 3ns into the capsule axially before implosion. To model blast waves directly relevant to experiments such as MagLIF, we inferred deposited energy from shadowgraphy of laser-only experiments preformed at the PECOS target chamber using the Z-Beamlet laser. These energy profiles were used to initialize 2-dimensional simulations using by the adaptive mesh refinement code FLASH. Gradients or asymmetries in the energy deposition may seed instabilities that alter the fuel's distribution, or promote mix, as the blast wave interacts with the liner wall. The AMR capabilities of FLASH allow us to study the development and dynamics of these instabilities within the fuel and their effect on the liner before implosion. FLASH was developed in part by the DOE NNSA ASC and DOE Office of Science ASCR-supported Flash Center at the University of Chicago.   

Three Dimensional Magneto-Hydrodynamics Simulations of Auto-Magnetizing Imploding Liners for ICF.

AutoMag [Slutz et al., Phys. Plasmas 24, 012704 (2017)] is a potential next step in the magnetized liner inertial fusion (MagLIF) program. In standard MagLIF, external coils are used to magnetize deuterium gas inside a metal cylindrical liner, which is imploded by the Z-machine at Sandia National Laboratories. In AutoMag, helical slots are cut into the liner and filled with dielectric insulator to form a solenoid, producing an axial magnetic field from the drive current and removing the need for external field coils. Alternatively with external field coils, AutoMag could produce a field-reversed configuration inside the liner. Recent work at Sandia has found that the breakdown of the dielectric material corresponds to the geometry of the liner/dielectric. We explore this finding in 3D resistive-MHD simulations, modeling geometries relevant to both the 20-MA Z facility, and to the 1-MA MAIZE facility at the University of Michigan.   

Pulsed Laser Gate Experiment for Magnetized Liner Inertial Fusion (MagLIF)

Fuel preheating in full scale magnetized liner inertial fusion (MagLIF) currently has low efficiency. This loss is thought to occur from laser-plasma interactions (LPI) at the laser entrance window (LEW). The gaseous fuel is held in a pressurized vessel by the thin mylar LEW that must be removed right before heating. To ensure more laser energy heats the fuel, the LEW could be weakened at an early time [1]. One proposed solution [1] is to use the current from a small pulse generator to break the LEW allowing it to open outward from the fuel. With the LEW removed away from the laser path, LPI losses would be reduced. Wire attached to a 13 kV mini-pulser will be used to remove the LEW from the laser path. We will report on LEW fabrication and the current state of the laser gate project. [1] S. A. Slutz, C. A. Jennings, T. J. Awe, G. A. Shipley, B. T. Hutsel, and D. C. Lamppa, ``Auto-magnetizing liners for magnetized inertial fusion'', Phys. Plasmas \textbf{24}, 012704 (2017); S. A. Slutz, personal communication (2017).