Session TP11: Poster Session VII: Diagnostics & Sources; Heating & Current Drive, Transport, & Diagnostics; Intense Beams, Ion Acceleration, and Laser-solid Interactions

Runaway Electrons Modeling and Nanoparticle Plasma Jet Penetration into Tokamak Plasma

A novel idea to probe runaway electrons (REs) [1] by superfast injection of high velocity nanoparticle plasma jet (NPPJ) from a plasma accelerator [2,3] needs to be sustained by both RE dynamics modeling and simulation of NPPJ penetration through increasing tokamak magnetic field. We present our recent progress in both areas. RE simulation is based on the model [4], including Dreicer and ``avalanche'' mechanisms of RE generation, with emphasis on high Zeff effects. The high-density hyper-velocity C60 and BN NPPJ penetration through transversal B-field is conducted with the Hybrid Electro-Magnetic code (HEM-2D) [5] in cylindrical coordinates, with 1/R B-field dependence for both DIII-D and ITER tokamaks. [1] I.N. Bogatu, J.R. Thompson, S.A. Galkin, J.S. Kim, ``Probing Runaway Electrons with Nanoparticle Plasma Jet'', Bull. APS DPP 59(15), NP8.00058 (2014); [2-3] I.N. Bogatu, S.A. Galkin, J.S. Kim: [2] J. Fusion Energy 27, 6, 2008, [3] J. Fusion Energy 28, 144, 2009; [4] H. Smith et al., Phys. Plasmas 13, 102502, 2006; [5] S.A. Galkin, Bull. APS DPP 2008, BO5.005, \underline {https://www.researchgate.net/publication/252593039}   

Nanoparticle Plasma Jet as Fast Probe for Runaway Electrons in Tokamak Disruptions

Successful probing of runaway electrons (REs) requires fast (1 - 2 ms) high-speed injection of enough mass able to penetrate through tokamak toroidal B-field (2 - 5 T) over $\sim$1 - 2 m distance with large assimilation fraction in core plasma. A nanoparticle plasma jet (NPPJ) from a plasma gun is a unique combination of millisecond trigger-to-delivery response and mass-velocity of $\sim$100 mg at several km/s for deep direct injection into current channel of rapidly ($\sim$1 ms) cooling post-TQ core plasma. After C$_{60}$ NPPJ test bed demonstration we started to work on ITER-compatible boron nitride (BN) NPPJ. Once injected into plasma, BN NP undergoes ablative sublimation, thermally decomposes into B and N, and releases abundant B and N high-charge ions along plasma-traversing path and into the core. We present basic characteristics of our BN NPPJ concept and first results from B and N ions on $Z_\mathrm{eff} > 1$ effect on REs dynamics by using a self-consistent model for RE current density. Simulation results of BN$^{Q+}$ NPPJ penetration through tokamak B-field to RE beam location performed with Hybrid Electro-Magnetic code (HEM-2D) are also presented.   

Synchrotron emission diagnostic of full-orbit kinetic simulations of runaway electrons in tokamaks plasmas

Developing avoidance or mitigation strategies of runaway electrons (RE) for the safe operation of ITER is imperative. Synchrotron radiation (SR) of RE is routinely used in current tokamak experiments to diagnose RE. We present the results of a newly developed camera diagnostic of SR for full-orbit kinetic simulations of RE in DIII-D-like plasmas that simultaneously includes: full-orbit effects, information of the spectral and angular distribution of SR of each electron, and basic geometric optics of a camera. We observe a strong dependence of the SR measured by the camera on the pitch angle distribution of RE, namely we find that crescent shapes of the SR on the camera pictures relate to RE distributions with small pitch angles, while ellipse shapes relate to distributions of RE with larger pitch angles. A weak dependence of the SR measured by the camera with the RE energy, value of the $q$-profile at the edge, and the chosen range of wavelengths is found. Furthermore, we observe that oversimplifying the angular distribution of the SR changes the synchrotron spectra and overestimates its amplitude.   

Reflectometry diagnostics on TCV

Both profile reflectometer and Doppler back-scattering (DBS) diagnostics are being developed for the TCV Tokamak using a steerable quasi-optical launcher and universal polarizers. First results will be presented. A pulse reflectometer is being developed to complement Thomson Scattering measurements of electron density, greatly increasing temporal resolution and also effectively enabling fluctuation measurements. Pulse reflectometry consists of sending short pulses of varying frequency and measuring the roundtrip group-delay with precise chronometers. A fast arbitrary waveform generator is used as a pulse source feeding frequency multipliers that bring the pulses to V-band. A DBS diagnostic is currently operational in TCV. DBS may be used to infer the perpendicular velocity and wave number spectrum of electron density fluctuations in the 3-15 cm-1 wave-number range. Off-the-shelf transceiver modules, originally used for VNA measurements, are being used in a Doppler radar configuration.   

Synthetic Microwave Imaging Reflectometry diagnostic using 3D FDTD Simulations

Microwave Imaging Reflectometry (MIR) has become a standard diagnostic [X Ren et al. Rev Sci Instrum 83 (10), 10E338 2012] for understanding tokamak edge perturbations, including the edge harmonic oscillations in QH mode operation [Garafalo et al., Phys. Plasmas 22, 056116 (2015)]. These long-wavelength perturbations are larger than the normal turbulent fluctuation levels and thus normal analysis of synthetic signals become more difficult. To investigate, we construct a synthetic MIR diagnostic for exploring density fluctuation amplitudes in the tokamak plasma edge by using the three-dimensional, full-wave FDTD code Vorpal. The source microwave beam for the diagnostic is generated and refelected at the cutoff surface that is distorted by 2D density fluctuations in the edge plasma. Synthetic imaging optics at the detector can be used to understand the fluctuation and background density profiles. We apply the diagnostic to understand the fluctuations in edge plasma density during QH-mode activity in the DIII-D tokamak, as modeled by the NIMROD code [King et.al, Phys. Plasmas and Nucl. Fus. 2017].   

Neural network based real-time reconstruction of KSTAR magnetic equilibria with Bayesian-based preprocessing

Obtaining plasma shapes during tokamak discharges requires real-time estimation of magnetic configuration using Grad-Shafranov solver such as EFIT. Since off-line EFIT is computationally intensive and the real-time reconstructions do not agree with the results of off-line EFIT within our desired accuracy, we use a neural network to generate an off-line-quality equilibrium in real time. To train the neural network (two hidden layers with 30 and 20 nodes for each layer), we create database consisting of the magnetic signals and off-line EFIT results from KSTAR as inputs and targets, respectively. To compensate drifts in the magnetic signals originated from electronic circuits, we develop a Bayesian-based two-step real-time correction method. Additionally, we infer missing inputs, i.e. when some of inputs to the network are not usable, using Gaussian process coupled with Bayesian model. The likelihood of this model is determined based on the Maxwell's equations. We find that our network can withstand at least up to 20{\%} of input errors. Note that this real-time reconstruction scheme is not yet implemented for KSTAR operation.   

Calibration of high-dynamic-range, finite-resolution x-ray pulse-height spectrometers for extracting electron energy distribution data from the PFRC-2 device

Knowledge of the full x-ray energy distribution function (XEDF) emitted from a plasma over a large dynamic range of energies can yield valuable insights about the electron energy distribution function (EEDF) of that plasma and the dynamic processes that create them. X-ray pulse height detectors such as Amptek's X-123 Fast SDD with Silicon Nitride window can detect x-rays in the range of 200eV to 100s of keV. However, extracting EEDF from this measurement requires precise knowledge of the detector's response function. This response function, including the energy scale calibration, the window transmission function, and the resolution function, can be measured directly. We describe measurements of this function from x-rays from a mono-energetic electron beam in a purpose-built gas-target x-ray tube. Large-Z effects such as line radiation, nuclear charge screening, and polarizational Bremsstrahlung are discussed [1]. [1] Avdonina, N. B., and R. H. Pratt. ``Bremsstrahlung Spectra from Atoms and Ions at Low Relativistic Energies.'' Journal of Physics B: Atomic, Molecular and Optical Physics 32, no. 17 (1999): 4261. doi:10.1088/0953-4075/32/17/310.   

Fractional pressure measurements inside of the divertor baffling at W7-X with a spectroscopically assisted Penning gauge

Studies of helium exhaust from stellarator divertors is important to qualify sufficient helium exhaust for future reactors. Penning gauges assisted by spectroscopy were used to measure total neutral pressure and to resolve the D and He partial pressures [T. Denner et al. RSI 67 (1996) 3515]. A generic feasibility test at W7-X gave successful measurements of the total as well as the fractional neutral pressures of He and H. A first prototype of a new Penning gauge probe head has been tested at UW Madison at 240 mT as well as at the PAX magnet at IPP Greifswald, Germany at 3 T and shows a near linear power law scaling between current and pressure: I = $C*P^n$ with n = 1.0 - 1.2 for the 240 mT case and 2.3 - 2.8 for the 3 T case. Pressure measurements were achieved starting at 10-2 mbar and down to 10-6 mbar. With the new probe head, it was possible to increase the time resolution of the spectroscopically assisted fractional neutral pressure measurements to up to 1MHz. This system is now implemented at three poloidal positions at one toroidal location in W7-X and is ready for measurements.   

Improved Fast, Deep Record Length, Time-Resolved Visible Spectroscopy of Plasmas Using Fiber Grids.

HyperV Technologies is developing a fiber-coupled, deep record-length, low-light camera head for performing high time resolution spectroscopy on visible emission from plasma events. By coupling the output of a spectrometer to an imaging fiber bundle connected to a bank of amplified silicon photomultipliers, time-resolved spectroscopic imagers of 100 to 1,000 pixels can be constructed. A second generation prototype 32-pixel spectroscopic imager employing this technique was constructed and successfully tested at the University of California at Davis Compact Toroid Injection Experiment (CTIX). Pixel performance of 10 Megaframes/sec with record lengths of up to 256,000 frames ($\sim$25.6 milliseconds) were achieved. Pixel resolution was 12 bits. Pixel pitch can be refined by using grids of 100~$\mu$m to 1000~$\mu$m diameter fibers. Experimental results will be discussed, along with future plans for this diagnostic.\\   

Development of the low-field side reflectometer for ITER

The Low-Field Side Reflectometer (LFSR) for ITER will provide real-time edge density profiles every 10 ms for feedback control and every 24 $\mu $s for physics evaluation. The spatial resolution will be better than 5 mm over 30 -- 165 GHz, probing the scrape-off layer to the top of the pedestal in H-mode plasmas. An antenna configuration has been selected for measurements covering anticipated plasma elevations. Laboratory validation of diagnostic performance is underway using a LFSR transmission line (TL) mockup. The 40-meter TL includes circular corrugated waveguide, length calibration feature, Gaussian telescope, vacuum windows, containment membranes, and expansion joint. Transceiver modules coupled to the input of the TL provide frequency-modulated (FM) data for evaluation of performance as a monostatic reflectometer. Results from the mockup tests are presented and show that, with some further optimization, the LFSR will meet or exceed the measurement requirements for ITER. An update of the LFSR instrumentation design status is also presented with preliminary test results.   

Progress in Development of the ITER Plasma Control System Simulation Platform.

We report on progress made and expected uses of the Plasma Control System Simulation Platform (PCSSP), the primary test environment for development of the ITER Plasma Control System (PCS). PCSSP will be used for verification and validation of the ITER PCS Final Design for First Plasma, to be completed in 2020. We discuss the objectives of PCSSP, its overall structure, selected features, application to existing devices, and expected evolution over the lifetime of the ITER PCS. We describe an archiving solution for simulation results, methods for incorporating physics models of the plasma and physical plant (tokamak, actuator, and diagnostic systems) into PCSSP, and defining characteristics of models suitable for a plasma control development environment such as PCSSP. Applications of PCSSP simulation models including resistive plasma equilibrium evolution are demonstrated..   

Detailed Performance Assessment for the ITER ECE Diagnostic

One of the primary diagnostics for electron temperature (T$_{\mathrm{e}})$ measurement on ITER is based on the detection of electron cyclotron emission (ECE) Here we describe the predicted performance of the newly completed ECE diagnostic design by quantitatively following the emission from the plasma to the instruments and including the calibration method to assess accuracy. Operation of the diagnostic at 5.3 T is the main interest here but critical features of the emission spectra for 2.65 T and 1.8 T will be described. ECE will be collected by two very similar optical systems: one a radial view, the other an oblique view. Both measurements are used for T$_{\mathrm{e}}$ while the oblique view also allows detection of non-thermal distortion in the electron distribution. An in-vacuum calibration source is included in the front end of each view to calibrate out the effect of any degradation of in-vessel optics. Following collection, the emission is split into orthogonal polarizations and transmitted to the detection instruments via waveguides filled with dry nitrogen, a choice that simplifies construction and analysis. Near the instruments, a switchyard is used to select which polarization and view is detected by each instrument. The design for the radiometer used for 5.3 T will be described in detail.   

3D-localized, high-resolution, non-perturbing, vectorizable magnetic field diagnostic using two-photon Doppler-free laser-induced fluorescence

A detailed description of a new plasma magnetic field diagnostic using Doppler-free two-photon laser-induced fluorescence is presented. The diagnostic is based on a method previously developed in the context of rubidium vapor experiments. Two counter-propagating diode laser beams at $\sim$394nm are directed into an argon plasma to excite Ar-II ions from the metastable level $3s^23p^44p\ {}^4D_{7/2} \longrightarrow 3s^23p^44p\ {}^4D^o_{5/2} \longrightarrow 3s^23p^45s\ {}^2P_{3/2}$. The levels involve two similar (394.43nm and 393.31nm) transition wavelengths, so the two counter-propagating beams effectively cancel out the Doppler effect. The excited ions then decay to the $3s^23p^44p\ {}^2D^o_{5/2}$ level, emitting a 410.38nm line which is to be detected by a photomultiplier tube. The Zeeman splitting -- normally unobservable because of the large Doppler broadening -- of the resultant fluorescence is then to be analyzed, yielding the magnetic field of the particular location. This method is expected to provide 3D localized, non-perturbing vector measurements of the magnetic field. The resolution of the diagnostic is only limited by the cross-section of the laser beam, which can easily be as small as hundreds of microns wide. An experimental implementation is currently in progress.   

OMEGA Supersonic Gas-Jet Target Characterization

A supersonic gas-jet target system has been characterized using a Mach--Zehnder interferometer, allowing for the study of the gas dynamics during the opening and closing of the valve. Gas-jet targets provide uniform plasmas with flexibility in size and density while also offering excellent diagnostic access to the plasma. The gas jet is the first component in the development of a new laser--plasma interaction platform to be implemented on the OMEGA Laser System. The platform will use a tunable UV laser from OMEGA EP, known as the tunable OMEGA port 9 beam, to facilitate the study of cross-beam energy transfer and the associated mitigation strategies. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.   

Recent progress of the Laser-driven Ion-beam Trace Probe

The Laser-driven Ion-beam Trace Probe (LITP) is a new method to diagnose the poloidal magnetic field and radial electric field in tokamaks [1, 2]. Recently significant progresses have been made as follows. 1) The experimental system has been set up on the PKU Plasma Test (PPT) linear device and begun to validate the principle of LITP, including the ion source, the ion detector and the poloidal magnetic field cable. Preliminary experimental results matched the theoretical prediction well. 2) The reconstruction principle has been improved including the nonlinear effect [3]. 3) Tomography methods have been applied in the reconstruction codes. Now the laser-driven ion-beam accelerator has been setup on the PPT device, and further test of LITP will start soon. After that a prototype of LITP system will be designed and setup on the HL-2A tokamak device. [1] Yang et al. Rev. Sci. Instrum. 85(11), 11E429 (2014). [2] Yang et al. Rev. Sci. Instrum. 87(11), 11D610 (2016). [3] Yang et al. JINST submitted.   

Development of a Wolter Optic X-ray Imager on Z

A Wolter optic x-ray imager is being developed for the Z Machine to study the dynamics of warm x-ray sources with energies above 10 keV. The optic is adapted from observational astronomy and uses multilayer-coated, hyperbolic and parabolic x-ray mirrors to form a 2D image with predicted 100-$\mu $m resolution over a 5x5-mm field of view. The imager is expected to have several advantages over a simple pinhole camera. In particular, it can form quasi mono-energetic images due to the inherent band-pass nature of the x-ray mirrors from Bragg diffraction. As well, its larger collection solid angle can lead to an overall increase in efficiency for the x-rays in the desirable energy band. We present the design of the imaging system, which is initially optimized to view Mo K-alpha x-rays (17.5 keV). In addition, we will present preliminary measurements of the point-spread function as well as the spectral sensitivity of the instrument.   

Determination of plasma sheath current distributions by comparison of Zeeman spectroscopy with B-dot measurements in laser ablation Z-pinch experiments

In plasma pinch experiments, measurements of current distributions and losses across the anode-cathode (A-K) gap are needed to ensure uniform and repeatable implosions. Traditional B-dots measure current a considerable distance away from the plasma source and provide little detailed information on the current distribution across the plasma sheath near the pinch. In the experiments presented here, visible spectroscopic techniques were used to measure magnetically induced Zeeman splitting. Ionic plasma species were chosen such that the Zeeman splitting of different fine structure doublets split non-uniformly with increasing magnetic field strength in the plasma. This differential splitting enables measurements of non-directional B-field strengths in the plasma across a wide range of conditions. More specifically, the optical emission of Al III, C IV, and O VI doublets, $^{\mathrm{2}}$P$_{\mathrm{3/2\thinspace }}$to $^{\mathrm{2}}$S$_{\mathrm{1/2}}$ and $^{\mathrm{2}}$P$_{\mathrm{1/2\thinspace }}$to $^{\mathrm{2}}$S$_{\mathrm{1/2\thinspace }}$transitions were measured and used to determine the Zeeman broadening. We have applied this technique to diagnose time- and space-resolved B-field strengths in laser ablation Z-pinch experiments (LAZE). Experiments were conducted at the Nevada Terawatt Facility (NTF) using the TW-class Leopard laser and the 1 MA Zebra Z-pinch. The currents inferred from Zeeman spectroscopy measurements were compared to those determined from the B-dot diagnostics.   

Progress Towards Spectroscopic Diagnostics of Plasma Parameters and Neutral Dynamics in Helicon Plasmas

The MARIA device at the UW-Madison is used primarily to investigate the dynamics and fueling of neutral particles in helicon discharges. A new systematic method is in development to measure key plasma and neutral particle parameters by spectroscopic methods. The setup relies on spectroscopic line ratios for investigating basic plasma parameters and extrapolation to other states using a collisional radiative model. Active pumping using a Nd:YAG pumped dye laser is used to benchmark and correct the underlying atomic data for the collisional radiative model. First results show a matching linear dependence between electron density and laser induced fluorescence on the magnetic field above 500G. This linear dependence agrees with the helicon dispersion relation and implies MARIA can reliably support the helicon mode and support future measurements.   

Vacuum Compatibility of Laser Sintered Metals with Post-processing

We present the results of the outgassing rate of selective laser sintered parts using the throughput method; this method gives the outgassing rate per unit area of the parts by taking the difference in pressure and multiplying it to the known conductance, and dividing it by the surface area of the sample. The samples undergo post-processing: the technique we are investigating is plasma vapor deposition, which turns the target material (silicon, copper, etc.) into a stream of charged particles creating a smooth and uniform layer onto the substrate. Plasma vapor deposition homogenizes the surface morphology of the sample, reducing the surface area and developing a surface layer which should decrease the outgassing rate and make it impermeable to gasses and unreactive to chemisorption. The outgassing data is compared for each sample before and after post-processing.   

Diagnostic for Measuring the Ion Density Ratio in a Plasma with Two Ion Species

Understanding of turbulence and transport in multi-ion species plasmas is important for establishing predictive capability for burning tokamak plasmas with comparable densities of D and T. In order to effectively analyze plasmas with multiple ion species, a new diagnostic is needed in order to measure the density profiles of the individual ion species. In plasmas with two ion species, an ion-ion hybrid resonance frequency exists, from which one can estimate the ratio of the two ion densities [1]. Previous work has been able to successfully measure this resonant frequency on a global scale via observing cutoff for shear Alfven waves [2]. However, in order to make spatially-resolved measurements a new diagnostic is needed. A new antenna diagnostic was developed to measure the ion-ion hybrid resonance frequency locally in the Large Plasma Device. Initial results using mixes of Helium and Neon will be presented. Additionally, theoretical work was done in order to expand the regime of plasma parameters in which this diagnostic may be applied. [1] Buchsbaum, S. J. (1960), Resonance in a plasma with two ion species, Phys. Fluids, 3, 418, doi:10.1063/1.1706052 [2] Vincena, S. T.,~W. A. Farmer,~J. E. Maggs, and~G. J. Morales~(2011),~Laboratory realization of an ion-ion hybrid Alfv\'{e}n wave resonator,~Geophys. Res. Lett.,~38, L11101, doi:10.1029/2011GL047399.   

Direct measurement of the concentration of metastable ions produced from neutral gas particles using laser-induced fluorescence

Extensive information can be obtained on wave-particle interactions and wave fields by direct measurement of perturbed ion distribution functions using laser-induced fluorescence (LIF). For practical purposes, LIF is frequently performed on metastables that are produced from neutral gas particles and existing ions in other electronic states. We numerically simulate the ion velocity distribution measurement and wave-detection process using a Lagrangian model for the LIF signal. The results show that under circumstances where the metastable ion population is coming directly from the ionization of neutrals (as opposed to the excitation of ground-state ions), the velocity distribution will only faithfully represent processes which act on the ion dynamics in a time shorter than the metastable lifetime. Therefore, it is important to know the ratio of metastable population coming from neutrals to that from existing ions to correct the LIF measurements of plasma ion temperature and electrostatic waves. In this paper, we experimentally investigate the ratio of these two populations by externally launching an ion acoustic wave and comparing the wave amplitudes that are measured with LIF and a Langmuir probe using a lock-in amplifier.   

Towards Direct DC Conductivity of Warm Dense Matter Measured by Single-Shot THz Spectroscopy

Single-shot terahertz time-domain spectroscopy (THz-TDS) is a promising tool for characterizing properties of materials undergoing irreversible changes (e.g. the complex refractive index or conductivity). The drawback to this is the low signal-to-noise ratio. Maximizing this is important for studies of irreversible processes with small signals or modulation. We present a method for balancing shot-to-shot fluctuations based on: (a) simultaneous detection of single-shot traces, and (b) the use of correlation functions. The method is compared against the state of the art polarization-gated balancing scheme. We use our technique to determine the conductivity of a gold thin film using a transmission configuration. Finally, we present preliminary results on laser heated gold films.   

Experimental Results from a Laser-Triggered, Gas-Insulated, Spark-Gap Switch.

We are performing experiments on a laser-triggered spark-gap switch with the goal of studying the transition from photoionization to current conduction. The discharge of current through the switch is triggered by a focused 532-nm wavelength beam from a Q-switched Nd:YAG laser with a pulse duration of about 10 ns. The trigger pulse is delivered along the longitudinal axis of the switch, and the focal spot can be placed anywhere along the axis of the 5-mm, gas-insulated gap between the switch electrodes. The switch test bed is designed to support a variety of working gases (e.g., Ar, N$_2$) over a range of pressures. Electrical and optical diagnostics are used to measure switch performance as a function of parameters such as charge voltage, trigger pulse energy, insulating gas pressure, and gas species. A Mach-Zehnder imaging interferometer system operating at 532 nm is being used to obtain interferograms of the discharge plasma in the switch. We are also developing a 1064-nm interferometry diagnostic in an attempt to measure plasma free electron and neutral gas density profiles simultaneously within the switch gap. Results from our most recent experiments will be presented.   

Maximum entropy reconstruction of poloidal magnetic field and radial electric field profiles in tokamaks

The Laser-driven Ion beam trace probe (LITP) [1, 2] is a new diagnostic method for measuring poloidal magnetic field (B$_{\mathrm{p}})$ and radial electric field (E$_{\mathrm{r}})$ in tokamaks. LITP injects a laser-driven ion beam into the tokamak, and B$_{\mathrm{p}}$ and E$_{\mathrm{r}}$ profiles can be reconstructed using tomography methods. A reconstruction code has been developed to validate the LITP theory, and both 2D reconstruction of B$_{\mathrm{p}}$ and simultaneous reconstruction of B$_{\mathrm{p}}$ and E$_{\mathrm{r}}$ have been attained [2]. To reconstruct from experimental data with noise, Maximum Entropy and Gaussian-Bayesian tomography methods were applied and improved according to the characteristics of the LITP problem. With these improved methods, a reconstruction error level below 15{\%} has been attained with a data noise level of 10{\%}. These methods will be further tested and applied in the following LITP experiments. [1] X. Y. Yang et al. Rev. Sci. Instrum. 85(11), 11E429 (2014). [2] X. Y. Yang et al. Rev. Sci. Instrum. 87(11), 11D610 (2016).   

Abstract Withdrawn

A heated emissive probe was developed for making direct plasma potential ($V_{p})$ measurements in rapidly fluctuating plasmas. Previous experiments on the Big Red Ball (BRB) were hindered by sudden potential drops, making Langmuir measurements of the plasma potential difficult. DC heating of a tungsten filament to emission allowed for fast ($ 4\ MHz$) floating potential measurements that closely matched $V_{p}$. Two BRB experiments currently use the emissive probe. The investigation of unmagnetized, collisionless shocks used plasma potential measurements to study the sub-structure of strong plasma shocks. A separate investigation of emulated magnetospheres in laboratory plasmas used the plasma potential to map the equilibria and instabilities in the electric field of such structures. Results showing electric field measurements and comparison with cold Langmuir measurements will be presented. Future plans for probe modifications and applications to other experiments on the BRB will also be shown.   

Progress in joining, reuse, and customization of WR284 waveguide in the laboratory.

A system of five 20 kW magnetrons is being installed for the Big Red Ball (BRB) to produce and heat the plasma with 2.45GHz RF energy. An existing system of two 6 kW magentrons of the same frequency is actively used for the same purpose on Plasma Couette Experiment Upgrade (PCX-U). In each experiment, the RF is transmitted to the vessel via WR284 waveguide. Waveguide occasionally needs to be disassembled, modified and rebuilt for different reasons such as physics interests, ongoing problems (arcing), or efficient utilization of laboratory space. Reuse of disassembled waveguide parts is desirable for cost savings. Methods of assembly, disassembly, and modification of waveguide will be discussed. Also, frequently used designs of chokes, windows, and limiters will be shown. Materials used include copper, brass, and even aluminum. The vacuum vessel of PCX-U is a 1 meter diameter, 1 meter tall cylinder comprised of \textonequarter '' thick stainless steel. PCX-U has one removable end. The vacuum vessel of the BRB is a 3 meter diameter, sphere comprised of two hemispheres of 1-\textonequarter '' thick cast A356 aluminum. Rings comprised of hundreds of SmCo magnets in each vessel create a cusp field to contain the plasma and provide a resonance surface for the RF.   

Plasma Wakefield Excitation in a Cold Magnetized Plasma for Particle Acceleration

A numerical study has been done to find a travelling wave solution for a highly relativistic electron beam driven cold magnetized plasma. The presence of magnetic field has an effect to reduce thetransformer ratio (the ratio of energy gain to the drive beam energy) from its unmagnetized value. The effects of beam shape and the non-relativistic ion motion on the nonlinear structures of different dynamical variables are also discussed. The results owe its significance in the laboratory context of particle acceleration or in the study of generation of ultrahigh accelerating charged particle by strong plasma wave in astrophysical situations.   

Fluid Simulation of relativistic electron beam driven wakefield in the blowout regime

Two-dimensional Fluid simulations are employed to study the Wakefield driven by an electron beam in a plasma medium. The 1-D results (Phys. of Plasmas, 22, 073109 (2015)) are recovered when the transverse extent of the beam is chosen to be much longer than its longitudinal extent. Furthermore, it is shown that the blowout structure matches closely with the PIC observations, before the phase mixing. A close comparison of the fluid observations with the analytical modeling made by Lu et al. (Phys. Rev. Lett., 96, 165002 (2006)) to PIC observations, have been provided. It is thus interesting to note that a simplified fluid simulation adequately represents the form of the wake potential obtained by sophisticated PIC studies. We also address issues related to particle acceleration in such a potential structure by studying the evolution of injected test particles. A maximum energy gain of $\sim 2.8 GeV$ by the electrons from the back of the driver beam of energy $\sim 28.5 GeV$ in a 10 cm long plasma is shown to be achieved. This is in conformity with the experimental result of ref. (Phys. Rev. Lett, 95, 054802 (2005)). We observe that maximum energy gain can get doubled to $\sim 5.7 GeV$ when the bunch of test particles was placed near the axial edge of the first blowout structure.   

Influence of proton bunch and plasma parameters on the AWAKE experiment

The Proton Driven Plasma Wakefield Acceleration Experiment (AWAKE) at CERN will test the concept underlying plasma wakefield acceleration using long proton beams that undergo the self-modulation instability. The effectiveness of the experiment hinges on the successful and predictable development of this instability, which fragments the initial proton bunch into smaller beamlets with lengths of the order of the plasma wavelength. Since the initial parameters of the experiment inevitably vary from event to event, this work will aim to understand the correlation between these variations and the resulting wakefield. Using both theoretical models and numerical particle-in-cell simulations, the influence of variations in initial bunch charge, bunch dimensions, bunch energy and plasma density profile on the excited accelerating gradients and on the final energies reached by the witness particles will be investigated. In addition, further options in the experiment setup will be explored with the aim of optimizing the results.   

Enhancement of the Transformer Ratio in a Plasma Wakefield Accelerator Using an Additional Long Laser Pulse

Direct laser acceleration (DLA) in both the plasma bubble accelerating regime and the plasma bubble decelerating regime has been recently proposed [1,2,3]. Here we introduce the DLA into the beam-driven plasma wakefield acceleration (PWFA), and report the increase of the transformer ratio through DLA. Instead of interacting with the witness beam directly, the long laser pulse interacts with the driving electron beam and accelerates it through the mechanism of DLA in the plasma bubble decelerating regime. The energy of the driving electron beam is maintained for much longer time compared with the standard PWFA. Therefore, the witness beam gains much more energy without losing its beam quality. Due to the long pump depletion length of the laser pulse, the above PWFA scheme is extended from the single stage to the multi-stage and verified through self-consistent 2D PIC simulations. [1] X. Zhang, V. N. Khudik and G. Shvets, Phys. Rev. Lett. , 184801 (2015). [2] X. Zhang, V. N. Khudik, A. Pukhov and G. Shvets, Plasma Phys. Control. Fusion 58 034011 (2016) [3] V. N. Khudik, X. Zhang and G. Shvets, arXiv: 1610.0945 (2015).   

Cherenkov wakefield excitation by relativistic electron beams in plasma channels

We report on our theoretical investigations of Cherenkov radiation excited by relativistic electron bunches propagating in plasma channels and in polaritonic channels [1]. Two surface plasmons (SPs) modes of the radiation are analyzed: the~longitudinal (accelerating) and the transverse (deflecting) ones. Both form Cherenkov cones that are different in the magnitude of the cone angle and the central frequency. We show that the Cherenkov field profile change dramatically depending on the driver velocity and the channel size, and the longitudinal mode forms a reversed~Cherenkov~radiation cone due~to the negative group~velocity for sufficiently small air gaps. In addition, we find that when the channel surface is corrugated, a strong deflecting wake is excited by a relativistic electron bunch. A trailing electron bunch experiencing this wake is forced to undergo betatron oscillations and thus to emit radiation. Numerical simulation showed that intense x-ray radiation can be generated. [1] B. Neuner, D. Korobkin, G. Ferro, and G. Shvets, Phys. Rev. ST Accel. Beams 15, 031302 (2012).~   

Cherenkov-cyclotron instability in a metamaterial loaded waveguide for high power generation

This work presents the analytical theory for an S-band high power microwave experiment at MIT utilizing a metamaterial (MTM) structure. A 490 kV, 84 A electron beam travels through a rectangular waveguide loaded with two MTM plates in a DC magnetic field $B_0$. The excited waveguide mode is deflecting with a transverse $E$ field on beam axis. Microsecond long megawatt level microwave pulses were generated under a low $B_0$ in the Cherenkov-cyclotron type of interaction. A linear theory has been developed to explain the high power generation due to the Cherenkov-cyclotron instability. The simplified model is a planar waveguide filled with a double negative dispersive medium, and in the mode being studied, the longitudinal $E$ field has an antisymmetric pattern in the direction perpendicular to the MTM plates. We have proved that the Cherenkov-cyclotron instability can happen with a zero initial transverse beam velocity when $B_0$ is below a threshold. Also this instability is a unique feature of the left-handed MTM, since it requires a propagating mode below the cut-off frequency. The minimum beam current to start the instability is calculated, and the scaling law different from that of the traditional backward wave oscillators operated by longitudinal bunching will be discussed.   

Experimental Testing of a Metamaterial Slow Wave Structure for High-Power Microwave Generation

A high-power L band source has been developed using a metamaterial (MTM) to produce a double negative slow wave structure (SWS) for interaction with an electron beam. The beam is generated by a 700 kV, 6 kA short pulse (10 ns) accelerator. The design of the SWS consists of a cylindrical waveguide, loaded with alternating split-rings that are arrayed axially down the waveguide. The beam is guided down the center of the rings, where electrons interact with the MTM-SWS producing radiation. Power is extracted axially via a circular waveguide, and radiated by a horn antenna. Microwaves are characterized by an external detector placed in a waveguide. Mode characterization is performed using a neon bulb array. The bulbs are lit by the electric field, resulting in an excitation pattern that resembles the field pattern. This is imaged using an SLR camera. The MTM structure has electrically small features so breakdown is a concern. In addition to high speed cameras, a fiber-optic-fed, sub-ns photomultiplier tube array diagnostic has been developed and used to characterize breakdown light.   

Absolute Instability near Band Edges in a Traveling Wave Tube

We re-examine the beam mode and its interaction with the circuit mode near the lower and upper band edges in a traveling wave tube. We find that an absolute instability may arise, according to the Briggs-Bers criterion, if the beam current is sufficiently high, even if the beam mode intersects with the circuit mode at a point in the (w, k)$=$(frequency, wavenumber) plane with a positive group velocity. This finding differs from the previous works [1, 2] for the lower band edge, and points to the vulnerability to absolute instabilities at both the upper and lower band edges of a TWT. When the threshold current is exceeded, the Green's function, at a fixed position, exponentiates in time as t**(1/3) initially, but as (wi*t) at later time, where wi is the imaginary part of w in the unstable pole-pinch root. [1] D. M. H. Hung, et al., \textit{Phys. Rev. Lett}. \textbf{115}, 124801 (2015). [2] A. P. Kuznetsov, et al., \textit{Sov. Radiophys. Electron.} \textbf{27}, 1575 (1984).   

An Exact Hot-Tube Solution For Thin Tape Helix Traveling-Wave Tube

The exact hot-tube dispersion relation for a thin tape helix traveling-wave tube (TWT) is derived for the first time, based on its exact cold-tube solution [1]. This is an attempt to provide a reliable determination of the Pierce parameters, in particular the "AC space-charge" parameter \textit{QC}, for a realistic TWT. The determination of \textit{QC} remains an outstanding issue [2]. The numerical results from the exact formulation will be compared with other approximate models of TWT that were commonly used in the literature for \textit{QC }[3]. [1] D. Chernin, et al., \textit{IEEE Trans. ED} \textbf{46}, 7 (1999). [2] D. H. Simon, et al., \textit{Phys. Plasmas} \textbf{24}, 033114 (2017). [3] G. M. Branch and T. G. Mihran, \textit{IRE Trans. ED} \textbf{2}, 3 (1955).   

Backward Wave Oscillation Thresholds in a Traveling-Wave Tube

The threshold for the onset of backward wave oscillation (BWO) in a traveling-wave tube (TWT) was formulated by Johnson [1]. In this paper, we extend Johnson's model to include random variations of circuit phase velocity along the tube axis. We find that Johnson's BWO threshold is minimally affected by these random variations. We next ignore these random variations, but include finite reflections at the two ends of a TWT and study their effects on Johnson's threshold. The latter theory is developed and being compared with results from an experimental helix test circuit. We will explore a 4-wave treatment [2] for BWO, and its connection with the Briggs-Bers criterion for the existence of absolute instability. [1] H. R. Johnson, \textit{Proc. IRE}. \textbf{43}, 684 (1955). [2] D. Chernin, \textit{et al}., \textit{IEEE Trans. Electron Devices} \textbf{59}, 1542 (2012).   

Modeling of Diamond Field-Emitter-Arrays for high brightness photocathode applications

We propose to employ Diamond Field-Emitter-Arrays (DFEAs) as high-current-density ultra-low-emittance photocathodes for compact laser-driven dielectric accelerators capable of generating ultra-high brightness electron beams for advanced applications. We develop a semi-classical Monte-Carlo photoemission model for DFEAs that includes carriers' transport to the emitter surface and tunneling through the surface under external fields. The model accounts for the electronic structure size quantization affecting the transport and tunneling process within the sharp diamond tips. We compare this first principle model with other field emission models, such as the Child-Langmuir and Murphy-Good models. By further including effects of carrier photoexcitation, we perform simulations of the DFEAs' photoemission quantum yield and the emitted electron beam. Details of the theoretical model and validation against preliminary experimental data will be presented.   

Research of the Electron Cyclotron Emission with Vortex Property excited by high power high frequency Gyrotron

Recently, it has been shown that the radiation from a single electron in cyclotron motion has vortex property. Although the cyclotron emission exists universally in nature, the vortex property has not been featured because this property is normally cancelled out due to the randomness in gyro-phase of electrons and the development of detection of the vortex property has not been well motivated. In this research, we are developing a method to generate the vortex radiation from electrons in cyclotron motion with controlled gyro-phase. Electron that rotates around the uniform static magnetic field is accelerated by right-hand circular polarized (RHCP) radiation resonantly when the cyclotron frequency coincides with the applied RHCP radiation frequency. A large number of electrons can be coherently accelerated in gyro-phase by a RHCP high power radiation so that these electrons can radiate coherent emission with vortex feature. We will show that vortex radiation created by purely rotating electrons for the first time.   

DD fusion neutron production at UW-Madison using IEC devices

An inertial electrostatic confinement (IEC) device using spherical, gridded electrodes at high voltage accelerates deuterium ions, allowing for neutrons to be produced within the device from DD fusion reactions. The effects of the device cathode voltage (30-170 kV), current (30-100 mA), and pressure (0.15-1.25 mTorr) on the neutron production rate have been measured. New high voltage capabilities have resulted in the achievement of a steady state neutron production rate of 3.3x10$^{\mathrm{8}}$ n/s at 175 kV, 100 mA, and 1.0 mTorr of deuterium. Applications of IEC devices include the production of DD neutrons to detect chemical explosives and special nuclear materials using active interrogation methods.   

Linear Inertial-Electrostatic Fusion Neutron Sources and Highly Enriched Uranium Detection

A newly initiated research project investigates methods for detecting shielded highly enriched uranium (HEU) and other special nuclear materials by combining multi-dimensional neutron sources, forward/adjoint calculations modeling neutron and gamma transport, and sparse data analysis of detector signals. An overview of the project will be presented, and progress will be described in: (1) developing optimized, adaptive-geometry, inertial-electrostatic confinement (IEC) neutron source configurations with neutron pulses distributed in space and/or phased in time, and (2) applying sparse data algorithms, such as principal component analysis (PCA) to enhance detection fidelity.   

A Compact Self-Driven Liquid Lithium Loop for Industrial Neutron Generation

A compact, closed liquid lithium loop has been developed at the University of Illinois to test and utilize the Li-7(d,n) reaction. The liquid metal loop is housed in a stainless steel trench module with embedded heating and cooling. The system was designed to handle large heat and particle fluxes for use in neutron generators as well as fusion devices, solely operating via thermo-electric MHD. The objectives of this project are two-fold, 1) produce a high energy, MeV-level, neutron source and 2) provide a self-healing, low Z, low recycling plasma facing component. The flowing volume will keep a fresh, clean, lithium surface allowing Li-7(d,n) reactions to occur as well as deuterium adsorption in the fluid, increasing the overall neutron output. Expected yields of this system are 10$^{\mathrm{7}}$ n/s for 13.5 MeV neutrons and 10$^{\mathrm{8}}$ n/s for 2.45 MeV neutrons. Previous work has shown that using a tapered trench design prevents dry out and allows for an increase in velocity of the fluid at the particle strike point. For heat fluxes on the order of 10's MW/m$^{\mathrm{2}}$, COMSOL models have shown that high enough velocities (\textasciitilde 70 cm/s) are attainable to prevent significant lithium evaporation. Future work will be aimed at addressing wettability issues of lithium in the trenches, experimentally determine the velocities required to prevent dry out, and determine the neutron output of the system. The preliminary results and discussion will be presented.   

Ion acceleration and neutron production from intense laser interactions with underdense plasmas using OMEGA EP.

The interaction of the OMEGA EP short pulse laser beam (up to 1.4 kJ at 10 psec) with underdense preformed plasmas was investigated. Using deuterated plastic targets significant neutron emission was measured using a Time-of-Flight neutron spectrometer. The spectrum of radially accelerated ions was also measured using a Thomson parabola ion spectrometer and was found to be complex, containing many narrow energy spread features. The experimental results are compared with numerical simulations.   

Ion acceleration driven by a relativistic electron beam under a strong magnetic field

We have been investigating about an electron beam propagation under a strong magnetic field and found a very interesting phenomena. It is a generation of a large amplitude whistler wave, which is amplified by a nonlinear coupling of obliquely propagating circularly polarized waves [1]. Since the previous work did not include ion motions, such a giant whistler wave mainly affects on beam electrons and they stagnate due to a large ponderomotive force of the electromagnetic wave. In order to investigate the influence of the strong wave on background ions, we have developed a new PIC code which has an open (upstream and downstream) boundaries. By using the new code, we have been studying the kinetic behavior of ions in a circumstance generating a large whistler wave. As a result, it is found that the electrostatic field induced by the stagnated beam electrons not only creates a density dip in the background electrons but also accelerates background ions. We will discuss the relation between the ion acceleration and a formation of a collisionless shock wave. [1] T. Taguchi et al., J. Plasma Phys. 83, 2, 905830204 (2017).   

Simulations of laser-driven ion acceleration from a thin CH target

2D and 3D computer simulations of laser driven ion acceleration from a thin CH foil using code WARP were performed. As the foil thickness varies from a few nm to $\mu$m, the simulations confirm that the acceleration mechanism transitions from the RPA (radiation pressure acceleration) to the TNSA (target normal sheath acceleration). In the TNSA regime, with the CH target thickness of $1\mu$m and a pre-plasma ahead of the target, the simulations show the production of the collimated proton beam with the maximum energy of about 10 MeV. This agrees with the experimental results obtained at the BELLA laser facility ($I\sim5\times18 W/cm^2$, $\lambda=800nm$). Furthermore, the maximum proton energy dependence on different setups of the initialization, i.e., different angles of the laser incidence from the target normal axis, different gradient scales and distributions of the pre-plasma, was explored.   

Laser- driven protons and electrons leave X-ray fluorescence signatures in Cu foam

Rapid energy delivery and local deposition make intense ion beams appealing for fundamental studies and their heating applications including creation of warm dense matter (WDM) samples in a controllable laboratory setting. The LFEX laser with \textasciitilde kilojoule energy and 1.5 ps pulse duration was used to direct an intense proton and electron beam into a copper foam sample. While they deposit energy, protons and electrons traveling in the Cu foam induce Cu K-alpha emissions, which are imaged to visualize the beam transport and spatial energy deposition throughout the foam. Simulations using a hybrid particle-in-cell (PIC) code clearly show that electrons stop rapidly while protons travel to a deeper depth in the foam. The modeled K-alpha generation spatial profile along the foam presents good agreement with experimental measurement. Detailed experimental results including proton spectrum for different target conditions and simulations explaining beam transport and energy deposition will be presented. This work was supported by the U.S. AFOSR under Contract FA9550-14-1-0346 and the Japanese NIFS project No. {\#}NIFS13KUGK069   

Investigation of self-induced transparency in laser-solid interaction

Interaction of an intense laser beam with a thin (\textless laser wavelength) target in the radiation pressure acceleration (RPA) regime can lead to efficient acceleration of ions. In this regime, the electrons are strongly heated when the target becomes transparent to the incident laser. Therefore, understanding the role of this self-induced transparency (SIT) is crucial for controlling the quality of the accelerated ion beam. In this work, we present detailed numerical investigation of SIT using the 1-D and 2-D Particle-In-Cell simulations. In particular, threshold target thickness below which SIT is effective will be reported for the wide range of laser parameters such as intensity (normalize vector potential \textasciitilde 10-30), pulse duration (10 -- 100 fs) and polarization (linear/circular). The mechanism of SIT in both 1-D and 2-D simulations will be presented.   

Using Microstructured Targets to Determine Energy Distribution and Number of Hot Electrons in Laser Ion Acceleration Experiments

Laser ion acceleration via microstructured targets is an emerging field of much interest. 2D pic simulations (EPOCH) using grating like microstructured targets show not only the enhancement of hot electron temperature and number but also that by adjusting target geometry we are able to selectively control hot electron temperature and number. This allows one to pre-select ion energies and number in laser ion acceleration experiments, which is a crucial next step in feasibility of laser ion acceleration applications (including hadron cancer therapy, neutron beam generation and warm dense matter studies). In addition to simulated results, preliminary experimental data from the University of Texas's Ghost laser (10\textasciicircum 19 W/cm2) will also be presented.   

Stochastic heating in laser interaction with ultra-thin foils

Stochastic heating of electrons in multiple counter-propagating electromagnetic waves has been investigated theoretically and numerically in numerous works since the 80s [e.g. Mendon\c{c}a {\&} Doveil, JPP 28, 485 (1982)]. \newline Stochastic heating has been invoked as a possible mechanism responsible for electron heating in scenarios such as laser interaction with thin foils for ion acceleration and electron heating in beat-wave injection. However, a clear experimental verification of this heating process has not been done, to our knowledge. \newline In this work, we examine electron heating during the interaction of multiple laser pulses with ultra-thin foils (a few atomic layers wide) through numerical particle-in-cell and particle-particle simulations. Such targets could prevent the development of instabilities/processes which could hinder the interpretation of observations. We include realistic temporally and spatially finite laser pulses and targets and explore in detail possible setups for an experimental observation of stochastic heating, analyzing signatures in the electron energy spectra, angular distribution, and radiation emission.   

Extreme laser-driven magnetic fields: from generation to possible detection

A remarkable feature of a solid density target irradiated by a high intensity laser pulse is its ability to sustain an extremely strong electron current that greatly exceeds the classical Alfv\'{e}n limit. As the target becomes relativistically transparent due to the electron acceleration by the laser pulse, the current becomes volumetrically distributed. This allows for a MT-level quasi-static magnetic field to be generated in an considerable volume inside the solid density material [D. Stark, T. Toncian, and A. Arefiev, PRL 116, 185003 (2016)]. The MT-level field can be extremely beneficial for particle acceleration and gamma-ray generation. What are the exact conditions for generating a strong magnetic field? How big is the resulting magnetic field filament and for how long does it exist? Finally, how can one detect such a field? In this work, we focus on answering these questions in the context of the experimental capabilities that should soon be available at the European XFEL and explore the feasibility of the magnetic field detection inside a solid-density material using XFEL photons.   

High frequency RF waves

ECH and LHCD- are scattered by the density and magnetic field turbulence from drift waves as measured in and Tore Supra-WEST, EAST and DIII-D. Ray equations give the spreading from plasma refraction from the antenna through the core plasma until and change the parallel phase velocity evolves to where RF waves are absorbed by the electrons. Extensive LH ray tracing and absorption has been reported using the coupled CP3O ray tracing and LUKE electron phase space density code with collisionless electron-wave resonant absorption. In theory and simulations are shown for the ray propagation with the resulting electron distributions along with the predicted X ray distribution that compared to the measured X-ray spectrum. Lower-hybrid is essential for steady-state operation in tokamaks with control of the high-energy electrons intrinsic to tokamaks confinement and heating. The record steady tokamak plasma is Tore Supra a steady 6 minute steady state plasma with1 Gigajoule energy passing through the plasma. WEST is repeating the experiments with ITER shaped separatrix and divertor chamber and EAST achieved comparable long-pulse plasmas. Results are presented from an IFS-3D spectral code with a pair of inside-outside LHCD antennas and a figure-8 magnetic separatrix are presented. Scattering of the slow wave into the fast wave wave is explored showing the RF scattering from drift wave $dn_e$ and dB increases the core penetration may account the measured broad X-ray spectrum.   

The scattering of electromagnetic waves from turbulent plasmas

In fusion devices, radio frequency (RF) electromagnetic waves encounter turbulent plasmas along their path from the excitation structures to the core of the plasma. In order to optimize heating and current drive by the RF waves, it is necessary to understand the effect of the density turbulence on the propagation characteristics of the waves. A common approach towards quantifying the effects of turbulence is the Kirchhoff technique. Here the wave fields and their normal derivatives are evaluated at a surface separating two different densities using physical optics. The fields at any point on this surface are approximated to be the same as the fields on a tangent plane at that point. Using the Kirchhoff technique, we show that turbulence can lead to changes in the propagation vector and polarization of the waves, side-scattering, and coupling between different plasma waves. This affects the spatial uniformity of power flow into the plasma. Full wave analytical calculations and numerical simulations confirm these physical results. The theory applies to all RF waves, irrespective of their frequency, and allows for arbitrary plasma density variations.   

Propagation of radio frequency waves through density fluctuations

On their way to the core of a tokamak plasma, radio frequency (RF) waves, excited in the vacuum region, have to propagate through a variety of density fluctuations in the edge region. These fluctuations include coherent structures, like blobs that can be field aligned or not, as well as turbulent and filamentary structures. We have been studying the effect of fluctuations on RF propagation using both theoretical (analytical) and computational models. The theoretical results are being compared with those obtained by two different numerical codes – a Finite Difference Frequency Domain code and the commercial COMSOL package. For plasmas with arbitrary distribution of coherent and turbulent fluctuations, we have formulated an effective dielectric permittivity of the edge plasma. This permittivity tensor is then used in numerical simulations to study the effect of multi-scale turbulence on RF waves. We not only consider plane waves but also Gaussian beams in the electron cyclotron and lower hybrid range of frequencies. The analytical theory and results from simulations on the propagation of RF waves will be presented.   

Quasilinear diffusion operator for wave-particle interactions in inhomogeneous magnetic fields

The Kennel-Engelmann quasilinear diffusion operator for wave-particle interactions is for plasmas in a uniform magnetic field. The operator is not suitable for fusion devices with inhomogeneous magnetic fields. Using drift kinetic and high frequency gyrokinetic equations for the particle distribution function, we have derived a quasilinear operator which includes magnetic drifts. The operator applies to RF waves in any frequency range and is particularly relevant for minority ion heating. In order to obtain a physically meaningful operator, the first order correction to the particle’s magnetic moment has to be retained. Consequently, the gyrokinetic change of variables has to be retained to a higher order than usual. We then determine the perturbed distribution function from the gyrokinetic equation using a novel technique that solves the kinetic equation explicitly for certain parts of the function. The final form of the diffusion operator is compact and completely expressed in terms of the drift kinetic variables. It is not transit averaged and retains the full poloidal angle variation without any Fourier decomposition. The quasilinear diffusion operator reduces to the Kennel-Engelmann operator for uniform magnetic fields.   

A similarity relation of the coupled equations for RF waves in a tokamak

The propagation and damping of RF waves in plasmas are modeled kinetically by solving the coupled equations between Maxwell's equation and Fokker-Planck equation. When the plasmas are magnetized, the wave dielectric tensor strongly depends on the background magnetic field, which can be calculated using Grad-Shafranov equation in a toroidally symmetric geometry. We found a similarity in the solutions of the coupled equations above, which keep the several dimensionless parameters constant. By changing plasma density and pressure, machine geometry (major radius), and RF wave frequency and power according to the similarity rule, there exists a set of solutions that show the consistent change in the background magnetic fields in the Grad-Shafranov equation, the electric and magnetic fields in the Maxwell's equation, and the distribution function of the Fokker-Planck equation. By investigating the numerical errors of the solutions from the expected results by the similarity rule, we verify the coupled numerical code for the RF waves in a tokamak (e.g. TORIC or AORSA/CQL3D/ECOM).   

Toroidal Ampere-Faraday Equations Solved Simultaneously with CQL3D Fokker-Planck Time-Evolution

A self-consistent, time-dependent toroidal electric field calculation is a key feature of a complete 3D Fokker-Planck kinetic distribution radial transport code for f(v,theta,rho,t). We discuss benchmarking and first applications of an implementation of the Ampere-Faraday equation for the self-consistent toroidal electric field, as applied to (1) resistive turn on of applied electron cyclotron current in the DIII-D tokamak giving initial back current adjacent to the direct CD region and having possible NTM stabilization implications, and (2) runaway electron production in tokamaks due to rapid reduction of the plasma temperature as occurs in pellet injection, massive gas injection, or a plasma disruption. Our previous results assuming a constant current density (Lenz' Law) model[1] showed that prompt ``hot-tail runaways'' dominated ``knock-on'' and Dreicer ``drizzle'' runaways; we perform full-radius modeling and examine modifications due to the more complete Ampere-Faraday solution. Presently, the implementation relies on a fixed shape eqdsk, and this limitation will be addressed in future work. [1] R.W. Harvey, V.S. Chan, et al., Physics of Plasmas 7, 4590 (2000).   

A Finite-Orbit-Width Fokker-Planck solver for modeling of RF Current Drive in ITER

The bounce-average (BA) finite-difference Fokker-Planck (FP) code CQL3D [1,2] now includes the essential physics to describe the RF heating of Finite-Orbit-Width (FOW) ions in tokamaks. The FP equation is reformulated in terms of constants-of-motion coordinates, which we select to be particle speed, pitch angle, and major radius on the equatorial plane thus obtaining the distribution function directly at this location. A recent development is the capability to obtain solution simultaneously for FOW ions and Zero-Orbit-Width (ZOW) electrons. As a practical application, the code is used for simulation of alpha-particle heating by high-harmonic waves in ITER scenarios. Coupling of high harmonic or helicon fast waves power to electrons is a promising current drive (CD) scenario for high beta plasmas. However, the efficiency of current drive can be diminished by parasitic channeling of RF power into fast ions such as alphas or NBI-produced deuterons, through finite Larmor-radius effects. Based on simulations, we formulate conditions where the fast ions absorb less than 10{\%} of RF power. [1] R.W. Harvey and M.G. McCoy, ``The CQL3D Fokker Planck Code'' (www.compxco.com/cql3d). [2] Yu.V. Petrov and R.W. Harvey, PPCF 58, 115001 (2016).   

Simulations of Low Power DIII-D Helicon Antenna Coupling

We present an overview and initial progress for a new project to model coupling of the DIII-D Helicon Antenna. We lay the necessary computational groundwork for the modeling of both low-power and high power helicon antenna operation, by constructing numerical representations for both the antenna hardware and the DIII-D plasma. CAD files containing the detailed geometry of the low power antenna hardware are imported into the VSim software's FDTD plasma model [1]. The plasma can be represented numerically by importing EQDSK or EFIT files. In addition, approximate analytic forms for the ensuing profiles and fields are constructed to facilitate parameter scans in the various regimes of anticipated antenna operation. To verify the accuracy of the numerical plasma and antenna representations, we will then run baseline simulations of low-power antenna operation, and verify that the predictions for loading, linear coupling, and mode partitioning (i.e. into helicon and slow modes) are consistent with the measurements from the low power helicon antenna experimental campaign [2], as well as with other independent models. Progress on these baseline simulations will be presented, and any inconsistencies and issues that arise during this process will be identified. Support provided by DOE Grant DE-SC0017843. [1] T. G. Jenkins and D. N. Smithe, Plasma Sources Sci. Technol. 24, 015020 (2015). [2] R. I. Pinkser, et. al., ``Measurements of helicon antenna coupling in DIII-D,'' APS-DPP (2016).   

Waveguide to Core: A New Approach to RF Modelling

A new technique for the calculation of RF waves in toroidal geometry enables the simultaneous incorporation of antenna geometry, plasma facing components (PFCs), the scrape off-layer (SOL) and core propagation [Shiraiwa, NF 2017]. Calculations with this technique naturally capture wave propagation in the SOL and its interactions with non-conforming PFCs permitting self-consistent calculation of core absorption and edge power loss. The main motivating insight is that the core plasma region having closed flux surfaces requires a hot plasma dielectric while the open field line region in the scrape-off layer needs only a cold plasma dielectric. Spectral approaches work well for the former and finite elements work well for the latter. The validity of this process follows directly from the superposition principle of Maxwell's equations making this technique exact. The method is independent of the codes or representations used and works for any frequency regime. Applications to minority heating in Alcator C-Mod and ITER and high harmonic heating in NSTX-U will be presented in single pass and multi-pass regimes.   

Progress on the development of \emph{FullWave}, a Hot and Cold Plasma Parallel Full Wave Code

\emph{FullWave} is being developed at FAR-TECH, Inc. to simulate RF waves in hot inhomogeneous magnetized plasmas without making small orbit approximations \footnote[2]{V. A. Svidzinski et al., Phys. Plasmas 23, 112101 (2016); L. Zhao et al. (this meeting)}. \emph{FullWave} is based on a meshless formulation in configuration space on non-uniform clouds of computational points (CCP) adapted to better resolve plasma resonances, antenna structures and complex boundaries. The linear frequency domain wave equation is formulated using two approaches: for cold plasmas the local cold plasma dielectric tensor is used (resolving resonances by particle collisions), while for hot plasmas the conductivity kernel is calculated. The details of \emph{FullWave} and some preliminary results will be presented, including: 1) a monitor function based on analytic solutions of the cold-plasma dispersion relation; 2) an adaptive CCP based on the monitor function; 3) construction of the finite differences for approximation of derivatives on adaptive CCP; 4) results of 2-D full wave simulations in the cold plasma model in tokamak geometry using the formulated approach for ECRH, ICRH and Lower Hybrid range of frequencies.   

Initial Simulations of RF Waves in Hot Plasmas Using the FullWave Code

FullWave is a simulation tool that models RF fields in hot inhomogeneous magnetized plasmas. The wave equations with linearized hot plasma dielectric response are solved in configuration space on adaptive cloud of computational points. The nonlocal hot plasma dielectric response is formulated by calculating the plasma conductivity kernel based on the solution of the linearized Vlasov equation in inhomogeneous magnetic field. In an rf field, the hot plasma dielectric response is limited to the distance of a few particles' Larmor radii, near the magnetic field line passing through the test point. The localization of the hot plasma dielectric response results in a sparse matrix of the problem thus significantly reduces the size of the problem and makes the simulations faster. We will present the initial results of modeling of rf waves using the Fullwave code, including calculation of nonlocal conductivity kernel in 2D Tokamak geometry; the interpolation of conductivity kernel from test points to adaptive cloud of computational points; and the results of self-consistent simulations of 2D rf fields using calculated hot plasma conductivity kernel in a tokamak plasma with reduced parameters.   

Development of {\textit FullWave} : Hot Plasma RF Simulation Tool

Full wave simulation tool, modeling RF fields in hot inhomogeneous magnetized plasma, is being developed. The wave equations with linearized hot plasma dielectric response are solved in configuration space on adaptive cloud of computational points. The nonlocal hot plasma dielectric response is formulated in configuration space without limiting approximations by calculating the plasma conductivity kernel based on the solution of the linearized Vlasov equation in inhomogeneous magnetic field. This approach allows for better resolution of plasma resonances, antenna structures and complex boundaries. The formulation of {\it FullWave} and preliminary results will be presented: construction of the finite differences for approximation of derivatives on adaptive cloud of computational points; model and results of nonlocal conductivity kernel calculation in tokamak geometry; results of 2-D full wave simulations in the cold plasma model in tokamak geometry using the formulated approach; results of self-consistent calculations of hot plasma dielectric response and RF fields in 1-D mirror magnetic field; preliminary results of self-consistent simulations of 2-D RF fields in tokamak using the calculated hot plasma conductivity kernel; development of iterative solver for wave equations.   

Overview of FAR-TECH's magnetic fusion energy research

FAR-TECH, Inc. has been working on magnetic fusion energy research over two-decades. During the years, we have developed unique approaches to help understanding the physics, and resolving issues in magnetic fusion energy. The specific areas of work have been in modeling RF waves in plasmas, MHD modeling and mode-identification, and nano-particle plasma jet and its application to disruption mitigation. ~Our research highlights in recent years will be presented with examples, specifically, developments of FullWave $^{\mathrm{1,2,3}}$(Full Wave RF code), PMARS$^{\mathrm{4}}$ (Parallelized MARS code), and HEM$^{\mathrm{5}}$ (Hybrid ElectroMagnetic code). In addition, nano-particle plasma-jet$^{\mathrm{6}}$ (NPPJ) and its application for disruption mitigation will be presented. [1]V. Svidzinski et al, Physics of Plasmas~23, no. 11 (2016),~ [2] J. A. Spencer et al (DPP17) [3] L. Zhao et al. (DPP17) [4] V. Svidzinski et al (DPP17) [5] S. A. Galkin et al (DPP17) [6] I. N. Bogatu et al (DPP17)   

ORNL diagnostic and modeling development for LAPD ICRF experiments

PPPL, UCLA, and ORNL scientists have recently collaborated on a three week ICRF campaign at the upgraded LAPD device to study near field-plasma interactions associated with a single strap antenna driven at 2.38 MHz with 100 kW of RF power. This poster highlights ORNL involvement through implementation of the following diagnostics: an optical emission probe to measure neutral density, a retarding field energy analyzer to measure fast ions, phase locked imaging to measure line integrated RF-driven optical emission fluctuations, and an RF compensated triple Langmuir probe to measure density and temperature. To interpret the results of the experimental campaign a 3D cold plasma finite element model with realistic antenna and vacuum vessel geometry was developed in COMSOL. A summary of these results will be discussed. Highlights include a proof of principle localized and spatially resolved measurement of the neutral density, a strong increase in RF-driven optical emission fluctuations directly in front of the RF antenna strap, a shift in fast ion energies near the plasma edge, and qualitative agreement between the COMSOL cold plasma model with the various diagnostics.   

RF Rectification on LAPD and NSTX: the relationship between rectified currents and potentials

RF rectification is a sheath phenomenon important in the fusion community for impurity injection, hot spot formation on plasma-facing components, modifications of the scrape-off layer, and as a far-field sink of wave power. The latter is of particular concern for the National Spherical Torus eXperiment (NSTX), where a substantial fraction of the fast-wave power is lost to the divertor along scrape-off layer field lines. To assess the relationship between rectified currents and rectified voltages, detailed experiments have been performed on the Large Plasma Device (LAPD). An electron current is measured flowing out of the antenna and into the limiters, consistent with RF rectification with a higher RF potential at the antenna. The scaling of this current with RF power will be presented. The limiters are also floated to inhibit this DC current; the impact of this change on plasma-potential and wave-field measurements will be shown. Comparison to data from divertor probes in NSTX will be made. These experiments on a flexible mid-sized experiment will provide insight and guidance into the effects of ICRF on the edge plasma in larger fusion experiments.   

Fast wave experiments in LAPD: RF sheaths, convective cells and density modifications

An overview is presented of recent work on ICRF physics at the Large Plasma Device (LAPD) at UCLA. The LAPD has typical plasma parameters $n_e \sim 10^{12}-10^{13}$cm$^{-3}$, $T_e \sim 1-10$eV and $B \sim 1000$G. A new high-power ($\sim$150 kW) RF system and fast wave antenna have been developed for LAPD. The source runs at a frequency of 2.4 MHz, corresponding to $1-7 f_{\rm ci}$, depending on plasma parameters. Evidence of rectified RF sheaths is seen in large increases ($\sim 10 T_e$) in the plasma potential on field lines connected to the antenna. The rectified potential scales linearly with antenna current. The rectified RF sheaths set up convective cells of local $E \times B$ flows, measured indirectly by potential measurements, and measured directly with Mach probes. At high antenna powers substantial modifications of the density profile were observed. The plasma density profile initially exhibits transient low frequency oscillations (~10 kHz). The amplitude of the fast wave fields in the core plasma is modulated at the same low frequency, suggesting fast wave coupling is affected by the density rearrangement.   

Excitation of slow waves in front of an ICRF antenna in a basic plasma experiment

Recent results of ICRF experiments at the Large Plasma Device (LAPD) indicate parasitic coupling to the slow wave by the fast wave antenna. Plasma parameters in LAPD are similar to the scrape-off layer of current fusion devices. The machine has a 17 m long, 60 cm diameter magnetized plasma column with typical plasma parameters $n_e \sim 10^{12} - 10^{13}$ cm$^{-3}$, $T_e \sim 1 - 10$ eV and $B_0 \sim 1000$ G. It was found that coupling to the slow mode occurs when the plasma density in front of the antenna is low enough such that the lower hybrid resonance is present in the plasma. The radial density profile is tailored to allow for fast mode propagation in the high density core and slow mode propagation in the low density edge region. Measurements of the wave fields clearly show two distinct modes, one long wavelength m=1 fast wave mode in the core and a short wavelength backward propagating mode in the edge. Perpendicular wave numbers compare favorably to the predicted values. The experiment was done for varying frequencies, $\omega/\Omega_i = 25, 6$ and 1.5. Future experiments will investigate the dependence on antenna tilt angle with respect to the magnetic field, with and without Faraday screen.   

Electron cyclotron heating/current-drive system using high power tubes for QUEST spherical tokamak

Electron cyclotron heating (ECH) is the primary method to ramp up plasma current non-inductively in QUEST spherical tokamak. A 28 GHz gyrotron is employed for short pulses, where the radio frequency (RF) power is about 300 kW. Current ramp-up efficiency of 0.5 A/W has been obtained with focused beam of the second harmonic X-mode. A quasi-optical polarizer unit has been newly installed to avoid arcing events. For steady-state tokamak operation, 8.56 GHz klystron with power of 200 kW is used as the CW-RF source. The high voltage power supply (54 kV/13 A) for the klystron has been built recently, and initial bench test of the CW-ECH system is starting. The array of insulated-gate bipolar transistor works to quickly cut off the input power for protecting the klystron.   

Testing update on gyrotrons for electron cyclotron heating applications

Tests were recently performed on CPI gyrotrons at frequencies of 117.5 GHz and 140 GHz. At 117.5 GHz, output power levels of 1.67 MW were obtained under short-pulse conditions and long-pulse tests with pulse durations of 1-10 s have been performed with power levels up to 700 kW. The 117.5 GHz gyrotron was shipped to General Atomics where further long-pulse testing to higher power levels will be carried out with the goal of demonstrating power levels up to 1.5 MW for 5-second pulses. At 140 GHz, a CPI gyrotron was recently tested up to 810 kW output power for 30-minute pulses at W7-X in Greifswald, Germany. Design details and the latest test results for the two gyrotrons are presented.   

Repetitively Pulsed High Power RF Solid-State System

Eagle Harbor Technologies, Inc. (EHT) is developing a low-cost, fully solid-state architecture for the generation of the RF frequencies and power levels necessary for plasma heating and diagnostic systems at validation platform experiments within the fusion science community. In Year 1 of this program, EHT has developed a solid-state RF system that combines an inductive adder, nonlinear transmission line (NLTL), and antenna into a single system that can be deployed at fusion science experiments. EHT has designed and optimized a lumped-element NLTL that will be suitable RF generation near the lower-hybrid frequency at the High Beta Tokamak (HBT) located at Columbia University. In Year 2, EHT will test this system at the Helicity Injected Torus at the University of Washington and HBT at Columbia. EHT will present results from Year 1 testing and optimization of the NLTL-based RF system.   

High Voltage, Solid-State Switch for Fusion Science Applications

Eagle Harbor Technologies, Inc. is developing a series stack of solid-state switches to produce a single high voltage switch that can be operated at over 35 kV. During the Phase I program, EHT developed two high voltage switch modules: one with isolated power gate drive and a second with inductively coupled gate drive. These switches were tested at 15 kV and up to 300 A at switching frequencies up to 500 kHz for 10 ms bursts. Robust switching was demonstrated for both IGBTs and SiC MOSFETs. During the Phase II program, EHT will develop a higher voltage switch (\textgreater 35 kV) that will be suitable for high pulsed and average power applications. EHT will work with LTX to utilize these switches to design, build, and test a pulsed magnetron driver that will be delivered to LTX before the completion of the program. EHT will present data from the Phase I program as well as preliminary results from the start of the Phase II program.   

Phase I Development of Neutral Beam Injector Solid-State Power System

Neutral beam injection (NBI) is an important tool for plasma heating, current drive and a diagnostic at fusion science experiments around the United States, including tokamaks, validation platform experiments, and privately funded fusion concepts. Currently, there are no vendors in the United States for NBI power systems. Eagle Harbor Technologies (EHT), Inc. is developing a new power system for NBI that takes advantage of the latest developments in solid-state switching. EHT has developed a resonant converter that can be scaled to the power levels required for NBI at small-scale validation platform experiments like the Lithium Tokamak Experiment. This power system can be used to modulate the NBI voltages over the course of a plasma shot, which can lead to improved control over the plasma. EHT will present initial modeling used to design this system as well as experimental data showing operation at 15 kV and 40 A for 10 ms into a test load.   

JET DT Scenario Extrapolation and Optimization with METIS

Prospective JET (Joint European Torus) DT operation scenarios are modelled by the fast integrated code METIS. METIS combines scaling laws, e.g. for global and pedestal energy or density peaking, with simplified transport and source models, while retaining fundamental nonlinear couplings, in particular in the fusion power. We have tuned METIS parameters to match JET-ILW high performance experiments, including baseline and hybrid. Based on recent observations, we assume a weaker input power scaling than IPB98 and a $\sim$10\% confinement improvement due to the higher ion mass. The rapidity of METIS is utilized to scan the performance of JET DT scenarios with respect to fundamental parameters, such as plasma current, magnetic field, density or heating power. Simplified, easily parameterized waveforms are used to study the effect the ramp-up speed or heating timing. Finally, an efficient Bayesian optimizer is employed to seek the most performant scenarios in terms of the fusion power or gain.   

Toroidal Electromagnetic Particle-in-Cell Code with Gyro-kinetic Electron and Fully-kinetic ion

An electromagnetic kinetic simulation model has been developed using gyro-kinetic electron and fully-kinetic ion by removing fast gyro motion of electrons using the Lie-transform perturbation theory. An electromagnetic particle-in-cell kinetic code is developed based on this model in general magnetic flux coordinate systems, which is particularly suitable for simulations of toroidally confined plasma. Single particle motion and field solver are successfully verified respectively. Integrated electrostatic benchmark, for example the lower-hybrid wave (LHW) and ion Bernstein wave (IBW), shows a good agreement with theoretical results. Preliminary electromagnetic benchmark of electromagnetic lower hybrid wave is also presented. This code can be a first-principal tool to investigate high frequency nonlinear phenomenon, such as parametric decay instability, during lower-hybrid current drive (LHCD) and ion cyclotron radio frequency heating (ICRF) with complex geometry effect included.   

Gyrokinetic Simulations of JET Carbon and ITER-Like Wall Pedestals

Gyrokinetic simulations using the GENE code are presented, which target a fundamental understanding of JET pedestal transport and, in particular, its modification after installation of an ITER like wall (ILW). A representative pre-ILW (carbon wall) discharge is analyzed as a base case. In this discharge, magnetic diagnostics observe washboard modes, which preferentially affect the temperature pedestal and have frequencies (accounting for Doppler shift) consistent with microtearing modes and inconsistent with kinetic ballooning modes. A similar ILW discharge is examined, which recovers a similar value of H98, albeit at reduced pedestal temperature. This discharge is distinguished by a much higher value of eta, which produces strong ITG and ETG driven instabilities in gyrokinetic simulations. Experimental observations provide several targets for comparisons with simulation data, including the toroidal mode number and frequency of magnetic fluctuations, heat fluxes, and inter-ELM profile evolution. Strategies for optimizing pedestal performance will also be discussed.   

Gyrokinetic analysis of pedestal transport

Surprisingly, basic considerations can determine which modes are responsible for pedestal energy transport (e.g., KBM, ETG, ITG, MTM etc. ). Gyrokinetic simulations of experiments, and analysis of the Gyrokinetic-Maxwell equations, find that each mode type produces characteristic ratios of transport in the various channels: density, heat and impurities. This, together with the relative size of the driving sources of each channel, can strongly constrain or determine the dominant modes causing energy transport. MHD-like modes are not the dominant agent of energy transport - when the density source is weak as is often expected. Drift modes must fill this role. Detailed examination of experimental observations, including frequency and transport channel behavior, with simulations, demonstrates these points. Also see related posters by X. Liu, D.R. Hatch, and A. Blackmon.   

Pedestal turbulence simulations using GENE

We match frequencies, power balance, and other transport characteristics of several pedestals-two DIIID ELMy H-modes and a C-Mod I-mode, and attempt this for a C-Mod ELMy H-mode. Observed quasi-coherent fluctuations (QCFs) on the DIIID shots are identified as MTMs. The MTMs match frequency and power balance (with slight adjustment of temperature profile), and cause low transport in the density, ion heat and impurity channels- consistent with observed inter-ELM evolution of ion and electron temperature, electron and impurity density, or transport analysis of those channels. KBM can be ruled out as the dominant agent for heat transport. We find the Weakly Coherent Mode on C-Mod I-mode may be an electrostatic heavy particle/ITG mode. Analysis is ongoing for the C-Mod ELMy H-mode QCF. Pedestal density profiles in JET-ILW are consistent with ITG induced particle pinch.   

Streamer formation and transport for parameters characteristic of H-mode pedestals

We investigate, through gyrokinetic simulations, the formation of streamers as a consequence of electron temperature gradient driven, electron scale instabilities. We also study the interaction of velocity shear with streamers for parameters typical of H-mode pedestals, exploring both the higher as well as lower temperature gradient regions. Without ExB shear, the streamers form at the pedestal top causing large heat fluxes; the modes, however, did not saturate. When ExB shear was turned on, the streamers dissipated, and heat flux was lowered, though still of significant magnitude. In the middle of the pedestal, with high temperature gradient, heat flux was insignificant. There was no evidence of streamers in this region, leading to a conclusion that streamers have a strong influence on heat flux.   

Estimation of Kubo number and correlation length of fluctuating magnetic fields and pressure in BOUT$++$ edge pedestal collapse simulation

Stochastic magnetic fields are thought to be as one of the possible mechanisms for anomalous transport of density, momentum and heat across the magnetic field lines. Kubo number and Chirikov parameter are quantifications of the stochasticity, and previous studies show that perpendicular transport strongly depends on the magnetic Kubo number (MKN) [1]. If MKN is smaller than one, diffusion process will follow Rechester-Rosenbluth model [2]; whereas if it is larger than one, percolation theory [3] dominates the diffusion process. Thus, estimation of Kubo number plays an important role to understand diffusion process caused by stochastic magnetic fields. However, spatially localized experimental measurement of fluctuating magnetic fields in a tokamak is difficult, and we attempt to estimate MKNs using BOUT$++$ simulation data with pedestal collapse. In addition, we calculate correlation length of fluctuating pressures and Chirikov parameters to investigate variation correlation lengths in the simulation. We, then, discuss how one may experimentally estimate MKNs. [1] G. Zimbardo et al., Physical Review E, 61, 1940 (2000) [2] A. B. Rechester et al., Physical Review Letter, 40, 38 (1978). [3] M. B. Isichenko, Plasma Physics and Controlled Fusion, 33, 809 (1991).   

Particle and heat flux measurements from XGC1 simulations: Spatial patterns and SOL width implications.

Strong turbulence near the separatrix is believed to produce filamentary structures (blobs), whose detachment from the bulk can account for the intermittent nature of edge turbulence and impact the heat flux width. The SOL width is a parameter of paramount importance in modern tokamaks as it controls the amount of power deposited at the divertor plates, directly affecting thus the viability of fusion. Here, we analyze the results of simulations performed with the full-f, gyrokinetic code XGC1 which includes both turbulence and neoclassical effects in realistic divertor geometry. More specifically, we calculate the integrated particle and heat fluxes across the separatrix and present their spatial pattern. The flux is impacted by neoclassical effects and ExB turbulent-blobby motion. We isolate the ExB turbulent flux and estimate its contribution to the SOL width. Furthermore, we offer an interpretation of the observed patterns, tying them to the sheared perpendicular and parallel flows.   

Synthetic Gas Puff Imaging Diagnostic for the XGC1 Turbulence Code

The full-$f$ edge gyrokinetic code XGC1 has been used recently to study problems of significant interest, such as the divertor heat flux width\footnote{C.S. Chang et al., Nucl. Fusion 57 (in press; 2017).} and the L-H transition\footnote{C.S. Chang et al., Phys. Rev. Lett. 118, 175001 (2017).}. Moreover, XGC1 simulations of the heat flux width in ITER have different edge turbulence characteristics that lead to widths large relative to those based on empirical scalings. To be confident that this and other XGC1 predictions are accurate will require more detailed validation tests of the code against experimental data. One invaluable source of such data is the gas puff imaging (GPI) technique, which measures edge plasma turbulence. We have developed a synthetic GPI diagnostic for XGC1 based on the DEGAS 2 neutral transport code, allowing a direct comparison of simulated and observed turbulence characteristics, such as fluctuation amplitude, auto-correlation time, and correlation lengths. The DEGAS~2 simulations are 3-D and have sub-microsecond time resolution; both Alcator C-Mod fast camera and APD images are produced. We will describe the synthetic diagnostic and present an initial comparison of its results with the corresponding GPI data from two C-Mod discharges.   

Reduced model (SOLT) simulations of neutral-plasma interaction

The 2D scrape-off-layer turbulence (SOLT) code has been enhanced by the addition of kinetic-neutral physics. Plasma-neutral interactions include charge exchange (CX) and ionization (IZ). Under the assumption that the CX and IZ collision rates are independent of the ion-neutral relative velocity, a 1D (radial: x) Boltzmann equation has been derived [1] for the evolution of the (v$_{\mathrm{y}}$,v$_{\mathrm{z}})$-averaged neutral distribution function (G), and that evolution has been added to SOLT. The CX and IZ rates are determined by the poloidally (y) averaged plasma density and temperatures, and G $=$ G(x,v$_{\mathrm{x}}$,t). Results from 1D simulations that use diffusion as a proxy for turbulent transport are presented to illustrate the capability, including the approach to a steady state driven by sustained neutral injection in the far-SOL and source-driven heating in the core. Neutral density and energy profiles are obtained for the resulting \textit{self-consistent} \textit{equilibrium} plasma profiles. The effect of neutral drag on poloidal ExB mean flow and shearing rate is illustrated. Progress on 2D turbulence (blob) simulations is reported. [1] J. R. Myra and D. A. Russell, Transport Task Force Workshop, Williamsburg, Virginia, April 25-28, 2017, poster B23.   

Advances in continuum kinetic and gyrokinetic simulations of turbulence on open-field line geometries

For weakly collisional (or collisionless) plasmas, kinetic effects are required to capture the physics of micro-turbulence. We have implemented solvers for kinetic and gyrokinetic equations in the computational plasma physics framework, Gkeyll. We use a version of discontinuous Galerkin scheme that conserves energy exactly. Plasma sheaths are modeled with novel boundary conditions. Positivity of distribution functions is maintained via a reconstruction method, allowing robust simulations that continue to conserve energy even with positivity limiters. We have performed a large number of benchmarks, verifying the accuracy and robustness of our code. We demonstrate the application of our algorithm to two classes of problems (a) Vlasov-Maxwell simulations of turbulence in a magnetized plasma, applicable to space plasmas; (b) Gyrokinetic simulations of turbulence in open-field-line geometries, applicable to laboratory plasmas.   

Continuum Gyrokinetic Simulations of Turbulence in a Helical Model SOL with NSTX-type parameters

We have developed the Gkeyll code to carry out 3D2V full-$F$ gyrokinetic simulations of electrostatic plasma turbulence in open-field-line geometries, using special versions of discontinuous-Galerkin algorithms to help with the computational challenges of the edge region. (Higher-order algorithms can also be helpful for exascale computing as they reduce the ratio of communications to computations.) Our first simulations with straight field lines were done for LAPD-type cases$^\dagger$. Here we extend this to a helical model of an SOL plasma and show results for NSTX-type parameters. These simulations include the basic elements of a scrape-off layer: bad-curvature/interchange drive of instabilities, narrow sources to model plasma leaking from the core, and parallel losses with model sheath boundary conditions (our model allows currents to flow in and out of the walls). The formation of blobs is observed. By reducing the strength of the poloidal magnetic field, the heat flux at the divertor plate is observed to broaden.\\{\footnotesize $^\dagger$ E.L. Shi et al., (2017) J. Plasma Physics 83, 905830304}   

Gyrokinetic continuum simulations of turbulence in the Texas Helimak

We have used the Gkeyll code to perform 3\emph{x}-2\emph{v} full-\emph{f} gyrokinetic continuum simulations of electrostatic plasma turbulence in the Texas Helimak. The Helimak is an open field-line experiment with magnetic curvature and shear. It is useful for validating numerical codes due to its extensive diagnostics and simple, helical geometry, which is similar to the scrape-off layer region of tokamaks. Interchange and drift-wave modes are the main turbulence mechanisms in the device, and potential biasing is applied to study the effect of velocity shear on turbulence reduction. With Gkeyll, we varied field-line pitch angle and simulated biased and unbiased cases to study different turbulent regimes and turbulence reduction. These are the first kinetic simulations of the Helimak and resulting plasma profiles agree fairly well with experimental data. This research demonstrates Gkeyll's progress towards 5D simulations of the SOL region of fusion devices.   

Diagnosing entropy production and dissipation in fully kinetic plasmas

Many plasma systems, from the core of a tokamak to the outer heliosphere, are weakly collisional and thus most accurately described by kinetic theory. The typical approach to solving the kinetic equation has been the particle-in-cell algorithm, which, while a powerful tool, introduces counting noise into the particle distribution function. The counting noise is particularly problematic when attempting to study grand challenge problems such as entropy production from phenomena like shocks and turbulence. In this poster, we present studies of entropy production and dissipation processes present in simple turbulence and shock calculations using the continuum Vlasov-Maxwell solver in the Gkeyll framework. Particular emphasis is placed on a novel diagnostic, the field-particle correlation, which is especially efficient at separating the secular energy transfer into its constituent components, for example, cyclotron damping, Landau damping, or transit-time damping, when applied to a noise-free distribution function.   

Thermal and Particle Transport in Strong Interchange-Type Turbulence .

The Helimak is an approximation to the infinite cylindrical slab with a size large compared with turbulence transverse scale lengths, but with open field lines of finite length. A pressure gradient in unfavorable magnetic curvature is unstable to interchange-type modes, leading to large amplitude nonlinear fluctuations similar to those in a tokamak SOL. A novel magnetically-baffled probe cluster permits full characterization of the turbulence, including particle and thermal radial transport rates across the plasma profile. Transport rates vary with plasma parameters, but they can be most strongly modified by the application of bias to alter the transverse (poloidal, orthogonal to B and R) flow patterns. The transport effects are mediated by two, often independent, mechanisms. First, the bias changes the amplitudes of the fluctuating fields responsible for the transport. Second, the bias changes the coherence between the fields (seen in either time or frequency domains), leading to changed net transport. Work supported by the Department of Energy OFES DE-FG02-04ER54766.   

Baffled-probe compact-cluster measurement of microturbulence and electron temperature fluctuation in the Texas Helimak

In magnetized-orbit plasma, a baffled-probe compact cluster [1] acquires simultaneous real-time separate measurements of pure space potential, electric field, density, and electron temperature. Time-series analysis yields cross-correlated frequency and phase of the plasma parameter fluctuations and inference of electrostatic particle flux [2]. Radial ac and dc profiles of space potential, electric field, density, and electron temperature were measured in the Texas Helimak [3] in an attempt to quantify field and flow structure associated with specific states of microturbulence. Each state, characterized by magnetic field line connection length and applied radial electric field, is identified by signatures in the plasma parameters measured by a baffled-probe compact cluster. [1] Koepke et al., Contrib. Plasma Phys. 46, 359 (2006); Demidov et al., Rev. Sci. Instrum. 81, 10E129 (2010). [2] Gentle et al., http://meetings.aps.org/Meeting/DPP16/Session/TP10.37 [3] Gentle and Huang, Plasma Sci. Technol. 10, 284 (2008).   

Global 3D Braginskii-based edge simulation of an L-H transition

We present a milli-seconds long pre L-H transiton simulation with the global edge turbulence code GDB. This study was carried out in a simple shifted circular flux surfaces magnetic configuration with IWL Alcator C-Mod parameters. The simulation domain is toroidally and poloidally global and spans $3~cm$ of the closed-flux region and $2~cm$ of the scrape-off layer ($-3~cm{<}r{-}a{<}2~cm$). The plasma is heated in the core region ($r{-}a{<}-3~cm$) and sourced near the separatrix ($r{\approx}a$). Several interesting features are exhibited in this simulation that concur with experiments, including enhanced $E{\times}B$ shear flow, suppressed turbulence, inward particle pinch and formation of pedestal via plasma heating. Detailed results and further analysis will be presented in the meeting.   

Investigation of energetic particle induced geodesic acoustic mode

Energetic particles are ubiquitous in present and future tokamaks due to heating systems and fusion reactions. Anisotropy in the distribution function of the energetic particle population is able to excite oscillations from the continuous spectrum of geodesic acoustic modes (GAMs), which cannot be driven by plasma pressure gradients due to their toroidally and nearly poloidally symmetric structures. These oscillations are known as energetic particle-induced geodesic acoustic modes (EGAMs) [G.Y.Fu’08] and have been observed in recent experiments [R.Nazikian’08]. EGAMs are particularly attractive in the framework of turbulence regulation, since they lead to an oscillatory radial electric shear which can potentially saturate the turbulence. For the presented work, the nonlinear gyrokinetic, electrostatic, particle-in-cell code GTS [W.X.Wang’06] has been extended to include an energetic particle population following either bump-on-tail Maxwellian or slowing-down [Stix’76] distribution function. With this new tool, we study growth rate, frequency and mode structure of the EGAM in an ASDEX Upgrade-like scenario. A detailed understanding of EGAM excitation reveals essential for future studies of EGAM interaction with micro-turbulence.   

Numerical simulation of 3D magnetic field and turbulence interaction in tokamak plasma using XGC1.

Understanding the physics of 3D magnetic field and turbulence interaction is critical for present and future tokamak experiments. In this work, we report our recent progress in numerical simulation of 3D magnetic field effects on plasma flow and turbulence using XGC1. Employing the full-f gyrokinetic simulation capabilities of XGC1 in realistic tokamak geometry, we perform extended neoclassical simulations including kinetic electrons for a tokamak plasma with assumed 3D magnetic field perturbations. From the simulations, non-axisymmetric kinetic equilibria with self-consistent 3D flows are obtained. Affected by the applied 3D fields, the plasma develops so called the vortex mode, which is mesoscopic convective flow driven by the 3D fields. Detailed analysis of the convective flow structure is presented. Then, using the numerically obtained non-axisymmetric kinetic equilibria, we study the impacts of the 3D fields on micro-instabilities. Both the neoclassical equilibrium flow and mesoscopic vortex mode are important in this study, and it is presented how these flows and combined ExB shearing affect the micro-instabilities, especially their spatial distributions. We also discuss the implication of the modified micro-instabilities on turbulence and transport near the resonant region with applied 3D magnetic fields.   

Reduced models for electron and ion heat diffusivities by gyro-kinetic simulation with kinetic electrons in helical plasmas

A reduced transport model of the turbulent ion heat diffusivity was proposed by the gyrokinetic simulation code (GKV-X) with the adiabatic electrons for the high-$T_{i}$ Large Helical Device discharge for the dynamical transport simualtion. The nonlinear gyro-kinetic simulation is performed with the kinetic electron. The plasma parameter region of the short poloidal wave-number is studied, where the ion temperature gradient mode becomes unstable. The models of the turbulent heat diffusivities are derived as the function of the squared electrostatic potential fluctuation and the squared zonal flow potential. Next, the squared electrostatic potential fluctuation is approximated with the mixing length estimate. The squared zonal flow potential fluctuation is shown as the linear zonal flow response function. The linear zonal flow response as the simulation result with the kinetic electron is found to be different from that with the adiabatic electron. The reduced models of the turbulent electron and ion heat diffusivities are derived as the function of the physical parameters by the linear simulation with the kinetic electron.   

Verification of fluid type electromagnetic modes with a gyrokinetic-fluid hybrid model in the XGC code

As an alternative option to kinetic electrons, the gyrokinetic total-f particle-in-cell (PIC) code XGC1 has been extended to the MHD/fluid type electromagnetic regime by combining gyrokinetic PIC ions with massless drift-fluid electrons analogous to Chen and Parker [Phys. Plasmas 8, 441(2001)]. This work complements - as a more economical alternative - the fully kinetic electromagnetic formulation that is also being developed for XGC1 [S. Ku, APS-DPP 2016; J. Chowdhury, APS-DPP 2017]. Two representative long wavelength modes, shear Alfvén waves and resistive tearing modes are verified in cylindrical and toroidal magnetic field geometries. In addition, results for intermediate wavelength drift-Alfvén waves such as ion temperature gradient driven modes, peeling modes, and kinetic ballooning modes are also presented. We plan to apply XGC1 to study the stability of resistive tearing modes in NSTX. These studies are the groundwork for the extension of the current delta-f hybrid model to the total-f method required to study fluid type electromagnetic modes in the tokamak edge plasma and develop a better understanding of the onset of edge localized modes.   

Electromagnetic gyrokinetic simulation in GTS

We report the recent development in the electromagnetic simulations for general toroidal geometry based on the particle-in-cell gyrokinetic code GTS. Because of the cancellation problem, the EM gyrokinetic simulation has numerical difficulties in the MHD limit where $k_\perp \rho_i \rightarrow0$ and/or $\beta>m_e/m_i$. Recently several approaches has been developed to circumvent this problem: (1) $p_\parallel$ formulation with analytical skin term iteratively approximated by simulation particles (Yang Chen) , (2) A modified $p_\parallel$ formulation with $\int dt E_\parallel$ used in place of $A_\parallel$ (Mishichenko); (3) A conservative theme where the electron density perturbation for the Poisson equation is calculated from an electron continuity equation (Bao) ; (4) double-split-weight scheme with two weights, one for Poisson equation and one for time derivative of Ampere’s law, each with different splits designed to remove large terms from Vlasov equation (Startsev). These algorithms are being implemented into GTS framework for general toroidal geometry. The performance of these different algorithms will be compared for various EM modes.   

Electromagnetic Stabilization of ITG Turbulence

Finite plasma $\beta$ strongly reduces transport due to ion-temperature-gradient-driven turbulence, far beyond the stabilization quasilinear mixing length models predict. Gyrokinetic simulations reveal that more efficient nonlinear mode coupling, as measured by triplet correlation lifetime, is the dominant mechanism behind nonlinearly-enhanced stabilization. Electromagnetic effects increase triplet correlation lifetime which causes the instability to saturate at lower amplitudes. We will discuss contribution factors to the triplet correlation lifetime. When modified to include the effects of triplet correlation lifetime, quasilinear predictions reproduce nonlinear heat fluxes through a range of temperature gradients and $\beta$ values. A second, weaker contributor is enhanced stable mode excitation which reduces energy production relative to the unstable eigenmode. This is only responsible for 10-20\% of the enhanced stabilization.   

A Derivation of Critical Balance from Two-Point Evolution in Gyrokinetic Turbulence

The critical balance of parallel and perpendicular correlation times has been postulated for anisotropic turbulence ranging from weak-guide-field MHD to strong-guide-field gyrokinetics. While observed in simulations, an analytical derivation establishing the mechanisms responsible for critical balance has not been given. From a calculation of the temporal evolution of two-point phase-space correlation for turbulence in a reduced gyrokinetic model with a Lenard-Bernstein collision operator critical balance is demonstrated. Using a phase-space conserving closure, differential equations for the temporal evolution of relative separation are derived and solved. When the collision rate is smaller than the turbulent decorrelation rate, critical balance holds as observed in simulation$^2$. When the collision rate becomes comparable to the turbulent decorrelation rate, the perpendicular decorrelation rate lags for large eddies. Critical balance is maintained in a collisional regime where collisions set the decorrelation rate, but the relationship between perpendicular and parallel scales is modified by the collision rate through the eddy-damping propagator of the turbulent diffusivity. \noindent{$^2$}D.R. Hatch et al., Phys. Rev. Lett. {\bf 111}, 175001 (2013).   

Non-inductive current generation in fusion plasmas with turbulence.

It is found that plasma turbulence may strongly influence non-inductive current generation. This may have radical impact on various aspects of tokamak physics. Our simulation study employs a global gyrokinetic model coupling self-consistent neoclassical and turbulent dynamics with focus on electron current. Distinct phases in electron current generation are illustrated in the initial value simulation. In the early phase before turbulence develops, the electron bootstrap current is established in a time scale of a few electron collision times, which closely agrees with the neoclassical prediction. The second phase follows when turbulence begins to saturate, during which turbulent fluctuations are found to strongly affect electron current. The profile structure, amplitude and phase space structure of electron current density are all significantly modified relative to the neoclassical bootstrap current by the presence of turbulence. Both electron parallel acceleration and parallel residual stress drive are shown to play important roles in turbulence-induced current generation. The current density profile is modified in a way that correlates with the fluctuation intensity gradient through its effect on k//-symmetry breaking in fluctuation spectrum. Turbulence is shown to deduct (enhance) plasma self-generated current in low (high) collisionality regime, and the reduction of total electron current relative to the neoclassical bootstrap current increases as collisionality decreases. The implication of this result to the fully non-inductive current operation in steady state burning plasma regime should be investigated. Finally, significant non-inductive current is observed in flat pressure region, which is a nonlocal effect and results from turbulence spreading induced current diffusion.   

Hermite-Laguerre Spectral Velocity Formulation of Gyrokinetics

First-principles simulations of tokamak turbulence have proven to be of great value in recent decades. We develop a spectral velocity formulation of the turbulence equations that smoothly interpolates between the highly efficient but lower resolution 3D gyrofluid representation and the conventional but more expensive 5D gyrokinetic representation. Our formulation is a straightforward projection of the nonlinear gyrokinetic equation onto a Hermite basis in parallel velocity and a Laguerre basis in perpendicular velocity. This results in a system that describes the evolution of an arbitrary number of gyrofluid-like velocity moments of the kinetic distribution. We address issues related to collisions, closures, and free energy. The final model is appropriate for the study of instabilities, turbulence, and transport in a wide range of geometries, including tokamaks and stellarators. We provide numerical results from a new code that solves the 5D gyrokinetic equation in our Hermite-Laguerre spectral velocity basis.   

Gyrokinetic Dynamic Fidelity Refinement

Gyrokinetic Dynamic Fidelity Refinement is described and demonstrated. The basic problems are familiar from AMR techniques, but there are differences. Our proposed method is pseudo-spectral in all five dimensions $(x, y, z, v_\parallel, \mu B)$. Mesh refinement occurs by changing the number of Fourier, Hermite, or Laguerre basis functions, according to a dynamic target refinement metric. Low amplitude turbulence (near marginal stability) requires relatively high resolution in Hermite-Laguerre space, but modest resolution in $k$-space. High amplitude turbulence (away from marginal stability) requires relatively low resolution in Hermite-Laguerre space, but higher resolution in $k$. Stochastic echoes limit the $v$-space resolution requirements at high amplitude. Nonlinear phase-mixing ultimately limits the required $k_\perp$ resolution, as it provides a physical hyperviscosity mechanism. Depending on the quality of the closures available at low $v$-space resolution, GKDFR should be the optimal algorithm for evaluating small $\rho_*$, electromagnetic, gyrokinetic turbulence within the TRINITY multiscale transport framework.   

Particle transport in a wave spectrum with a thermal distribution of Larmor radii

Test particle $\bf E\times B$ transport is studied due to an infinite spectrum of drift waves in two dimensions using a Hamiltonian approach, which can be reduced to a 2D mapping. Finite Larmor radius (FLR) effects are included taking a gyroaverage. When the wave amplitude is increased there is a gradual transition to chaos but the chaos level is reduced when FLR grows, implying that fast particles are better confined. The fraction of confined particles is found to be reduced as the wave amplitude rises. The statistical properties of transport are studied finding that, in the absence of a background flow, it is diffusive with a Gaussian PDF, when all particles have the same FLR. In contrast, for a thermal FLR distribution, the PDF is non-Gaussian but the transport remains diffusive. A theoretical explanation of this is given showing that a superposition of Gaussians produces a PDF with long tails. When a background flow is introduced that varies monotonically with radius, the transport becomes strongly super-diffusive due to the appearance of long Levy flights which dominate the particles. The PDF develops long tails as the flow strength is increased. The particle variance scales as $\sigma\sim t^3$ for chaotic regime but reduces to ballistic ($\sim t^2$) for low chaos.   

Control of ITBs in Magnetically Confined Burning Plasmas

In the magnetically confined burning plasma devices (in this case Tokamaks), internal transport barriers (ITBs) are those regimes in which the turbulence is suppressed by the E X B velocity shear, reducing the turbulent transport. This often occurs at a critical gradient in the profiles. The change in the transport then modifies the density and temperature profiles feeding back on the system. These transport barriers have to be controlled both to form them for improved confinement and remove them to both prevent global instabilities and to remove the ash and unnecessary impurities in the device. In this work we focus on pellet injection and modulated RF heating as a way to trigger and control the ITBs. These have an immediate consequence on density and temperature and hence pressure profiles acting as a control knob. For example, depending upon pellet size and its radial position of injection, it either helps to form or strengthen the barrier or to get rid of ITBs in the different transport channels of the burning plasmas. This transport model is then used to investigate the control and dynamics of the transport barriers in burning plasmas using pellets and RF addition to the NBI power and alpha power.   

Controlling the Cross-phase: A mechanism for the I-mode and other enhanced confinement regimes?.

The I-mode and similar new transport regimes offer good confinement properties with reduced density limit issues and better control. While a number of different mechanisms have been identified for the formation and maintenance of enhanced confinement regimes few if any allow enhanced confinement in one channel but not another which is seen in the I-mode. We propose differential cross-phase modification as a possible mechanism for different transport in different channels. Simple dynamical models have been able to capture a remarkable amount of the dynamics of the core and edge transport barriers found in many devices. By including in this rich though simple dynamic transport model a simple model for cross phase effects, due to multiple instabilities, between the transported fields such as density and temperature, we can investigate whether the dynamics of more continuous transitions such as the I-mode can be captured and understood. This is backed up by multi-scale simulations on full gyro-kinetic codes. If correct this could have broad implications for transport in many systems. If this mechanism is valid, what can the model tell us about control knobs for these promising regimes?.   

Towards a better understanding of critical gradients and near-marginal turbulence in burning plasma conditions

Developing accurate predictive transport models of burning plasma conditions is essential for confident prediction and optimization of next step experiments such as ITER and DEMO. Core transport in these plasmas is expected to be very small in gyroBohm-normalized units, such that the plasma should lie close to the critical gradients for onset of microturbulence instabilities. We present recent results investigating the scaling of linear critical gradients of ITG, TEM, and ETG modes as a function of parameters such as safety factor, magnetic shear, and collisionality for nominal conditions and geometry expected in ITER H-mode plasmas. A subset of these results is then compared against predictions from nonlinear gyrokinetic simulations, to quantify differences between linear and nonlinear thresholds. As part of this study, linear and nonlinear results from both GYRO [1] and CGYRO [2] codes will be compared against each other, as well as to predictions from the quasilinear TGLF [3] model. Challenges arising from near-marginal turbulence dynamics are addressed.\\ \\$[1]$ J. Candy and R. E. Waltz, J. Comput. Phys \textbf{186} 545 (2003) \newline [2] J. Candy, E. A. Belli, and R. V. Bravenec, J. Comput. Phys. \textbf{324} 73 (2016)\newline [3] G. M. Staebler, J. E. Kinsey, and R. E. Waltz, Phys. Plasmas \textbf{14} 055909 (2007)   

Abstract Withdrawn

In this study of flow curvature effects, a two-dimensional hybrid model is used to simulate the Kelvin-Helmholtz instability (KHI). The hybrid model treats the ions as particles, and electrons as massless fluid. Pressure and resistivity are assumed as isotropic. A classical configuration for the study of KHI is investigated, i.e. transverse shear flow to uniform background magnetic field. This is thought as the most unstable situation in magnetohydrodynamic (MHD) theory. There are 50 super particles per cell in the current simulations, which number could be increased to as much as 200 in the future. The boundary is periodic along the flow direction and reflective in the perpendicular direction. The code was originally developed by the Los Alamos National Laboratory and has been successfully applied to the study of Kelvin-Helmholtz instability on the Earth's magnetopause. In this study, the code has been running on the Advanced Research Computing (ARC) platforms of Virginia Tech. Four distinct shear profiles are simulated to investigate the effects of flow curvature on the growth of the KH instability: uniform flow, linear shear without curvature, quadratic profile with positive curvature, and quadratic profile with negative curvature.   

Cross-verification of the GENE and XGC codes in preparation for their coupling

A high-fidelity Whole Device Model (WDM) of a magnetically confined plasma is a crucial tool for planning and optimizing the design of future fusion reactors, including ITER. Aiming at building such a tool, in the framework of the Exascale Computing Project (ECP) the two existing gyrokinetic codes GENE (Eulerian delta-f) and XGC (PIC full-f) will be coupled, thus enabling to carry out first principle kinetic WDM simulations. In preparation for this ultimate goal, a benchmark between the two codes is carried out looking at ITG modes in the adiabatic electron limit. This verification exercise is also joined by the global Lagrangian PIC code ORB5. Linear and nonlinear comparisons have been carried out, neglecting for simplicity collisions and sources. A very good agreement is recovered on frequency, growth rate and mode structure of linear modes. A similarly excellent agreement is also observed comparing the evolution of the heat flux and of the background temperature profile during nonlinear simulations.   

XGC developments for a more efficient XGC-GENE code coupling

In the Exascale Computing Program, the High-Fidelity Whole Device Modeling project initially aims at delivering a tightly-coupled simulation of plasma neoclassical and turbulence dynamics from the core to the edge of the tokamak. To permit such simulations, the gyrokinetic codes GENE [1] and XGC [2] will be coupled together. Numerical efforts are made to improve the numerical schemes agreement in the coupling region. One of the difficulties of coupling those codes together is the incompatibility of their grids. GENE is a continuum grid-based code and XGC is a Particle-In-Cell code using unstructured triangular mesh. A field-aligned filter is thus implemented in XGC. Even if XGC originally had an approximately field-following mesh, this field-aligned filter permits to have a perturbation discretization closer to the one solved in the field-aligned code GENE. Additionally, new XGC gyro-averaging matrices are implemented on a velocity grid adapted to the plasma properties, thus ensuring same accuracy from the core to the edge regions.$\backslash $[1] F. Jenko, W. Dorland, M. Kotschenreuther, and B. Rogers 2000 Phys. Plasmas 7 1904 $\backslash $cf2 [2] Ku S, Chang C and Diamond P 2009 Nucl. Fusion 49 115021   

Development of Extended Ray-tracing method including diffraction, polarization and wave decay effects

Geometrical Optics Ray-tracing is a reasonable numerical analytic approach for describing the Electron Cyclotron resonance Wave (ECW) in slowly varying spatially inhomogeneous plasma. It is well known that the result with this conventional method is adequate in most cases. However, in the case of Helical fusion plasma which has complicated magnetic structure, strong magnetic shear with a large scale length of density can cause a mode coupling of waves outside the last closed flux surface, and complicated absorption structure requires a strong focused wave for ECH. Since conventional Ray Equations to describe ECW do not have any terms to describe the diffraction, polarization and wave decay effects, we can not describe accurately a mode coupling of waves, strong focus waves, behavior of waves in inhomogeneous absorption region and so on. For fundamental solution of these problems, we consider the extension of the Ray-tracing method. Specific process is planned as follows. First, calculate the reference ray by conventional method, and define the local ray-base coordinate system along the reference ray. Then, calculate the evolution of the distributions of amplitude and phase on ray-base coordinate step by step. The progress of our extended method will be presented.   

Self-consistent gyrokinetic Vlasov-Maxwell system for nonlinear processes in plasmas

A self-consistent gyrokinetic Vlasov-Maxwell system which is capable of studying phenomenons related to ponderomotive force is developed with long wavelength approximation and background Maxwellian distribution in the present of electromagnetic fluctuations. According to the ordering analysis, the introduction of quadratic Hamiltonian would raise the order of the Vlasov-Maxwell system. Therefore, guiding-center transformation is proceeded up to the order of $\epsilon^2_B$, and gyrocenter transformation is proceeded up to the order of $\epsilon^2_\delta$. And higher order terms of the first order gyrocenter Hamiltonian $\bar{H}_1$ and gauge field $S_1$ are brought back. In this way, effects are also presented which are resulted from the inhomogeneities of equilibrium profile but the curvature of equilibrium magnetic field on the moments of distribution.