Session CP1: Poster Session II: Reversed Field Pinch; Field Reversed Configuration and Spheromak; Waves and Instabilities; Beams and Coherent Radiation

Overview of MST Results and Plans

Ongoing optimization of MHD tearing control for improved confinement has focused on higher current and higher density operation. Both the electron and ion temperatures are now maintained above 1 keV in 0.5 MA plasmas. The duration of the MHD tearing control period has been modestly extended using new inductive control circuitry. Frozen D2 pellet injection increases the density without degrading tearing control. Simultaneous high beta and high current are thus achieved. The high ion temperature appears rapidly in fast reconnection events. Charge exchange spectroscopy measures global heating when both m=1 and 0 tearing modes are involved, whereas it appears more edge-localized for smaller, m=0 dominated events. Multipoint Thomson scattering permits improved measurements of the electron temperature profile evolution during these events. Oscillating Field Current Drive results for the dependence of current drive on the oscillator's relative phase compare reasonably well with nonlinear MHD computation. An increase in the OFCD power capability is underway. The launcher systems for lower hybrid and electron Bernstein waves have also been modified for higher power (300 kW). Other results and plans will be presented.   

MST Lower Hybrid Current Drive Program

Interdigital line antennas are being used to test the feasibility of lower hybrid current drive in the MST reversed field pinch. The goal for the LHCD program on MST is fluctuation suppression by edge current drive. To move the program forward with a modular design, an antenna capable of launching 300 kW has been constructed and installed in MST. The antenna, designed using CST Microwave Studio$^{TM}$, uses $\lambda $/4 resonators and launches slow waves at 800 MHz with n$_{\vert \vert } \quad \sim $ 7.5. Routine operation has been achieved and is only limited by the available transmitter power of 80 kW. A good impedance match between the antenna and the plasma is maintained over a wide range of plasma conditions. Rf instrumentation on all the antenna resonators allows for more detailed power deposition measurements. To complete the system, the pulse-forming network that drives the klystron is being upgraded to allow for a 50 kV / 16 A / 30 ms pulse. This power supply will allow the klystron to be pulsed to 300 kW. In addition to this work, filament and transmission line protection systems are being put in place.   

Lower Hybrid Experiments on MST

Current drive using rf waves has been proposed as a means to reduce the tearing fluctuations responsible for anomalous energy transport in the RFP. A traveling wave antenna that operates at 800 MHz and $n_{\|}\approx7.5$ is being used to launch lower hybrid waves into MST to assess the feasibility of this approach. A third generation antenna with a power handling capability of 300 kW has been installed. Studies at 80 kW are used to compare antenna/plasma coupling to that of the previous antenna. Routine operation at this lower input power exhibits good coupling in a variety of standard-confinement plasma conditions. Power-sensing diagnostics on the antenna will allow measurement of the power damping length, important for controlling the launched wave spectrum. Upgraded electronics allow phase information to be gathered providing a direct measurement of the wave spectrum. Langmuir probes have been installed on the antenna as previous studies have shown that edge density is a major factor in coupling. A two-tip rf probe is under development with the aim of verifying wave propagation and comparing with modeling results.   

Electron Bernstein Wave Experiments in the Madison Symmetric Torus

Electron Bernstein waves (EBW) are a possible method of non-inductively modifying the current profile to enhance confinement in the reversed field pinch. Efficient mode conversion to EBW for current drive first requires a suitable antenna and optimization of plasma and magnetic field conditions near the antenna. A system capable of transmitting a 10 ms, 275 kW pulse of 3.6 GHz RF power is installed and operational in the Madison Symmetric Torus (MST). Replacing a two-waveguide antenna limited by its maximum transmittable power, the new antenna is a four-waveguide half-width S-band phased array designed to improve coupling and power handling. A triple Langmuir probe is integrated into the antenna to measure local electron temperature and density for use in coupling predictions. Perturbations in the magnetic field due to the port in the conducting shell of MST are examined to accurately determine the position of resonance locations. Investigation of expected soft x-ray fluxes resulting from EBW heating is underway. Details and results of simulation and experiments on MST will be presented and discussed. This work is supported by the United States Department of Energy.   

Cause of m=0 mode reconnection in MST

We investigate the origin and coupling between different modes, focusing primarily on modes resonant near the edge of the plasma. We directly measure in the edge with probes the term in the MHD equations which represents the driving (or damping) of tearing modes due to the equilibrium magnetic field. We also examine the nonlinear coupling between modes with bi-spectral techniques. The cause for reconnection mode growth is determined experimentally for two cases: the standard RFP sawtooth crash, and m=0 bursts that occur during periods of enhanced confinement. The m=0 mode is damped by the equilibrium fields during the sawtooth crash and driven by the equilibrium fields during the EC burst. This suggests that the sudden reconnection in MST is driven by nonlinear coupling in the standard RFP sawtooth crash and by linear instability in m=0 bursts during enhanced confinement.   

Edge probe measurements of the dynamo in the MST RFP

Standard discharges in the MST RFP are characterized by cyclical rapid relaxation events (sawtooth oscillations), when the RFP dynamo is generated. Previous work [P. Fontana et al., PRL, ${\bf 85}$, 566 (2000)] indicated that the MHD dynamo $< {\bf \tilde v} \times {\bf \tilde b}>$ is operating at the plasma edge, but is substantially reduced at the reversal surface. Present dynamo measurements with a newly developed insertable optical probe (which has improved design and resolution) and magnetic probes are aimed to understand the cause of this reduction. It is observed that $\tilde b_t$ changes phase by $\pi$ near reversal surface, while phases of all the other fluctuating quantities remain unchanged. Thus, $< \tilde v_{r} \tilde b_{t} >$ component of MHD dynamo changes sign and cancels $< \tilde v_t \tilde b_r >$. The Hall dynamo $<{\bf \tilde j} \times {\bf \tilde b}>$ is believed to be important for balancing the parallel component of the generalized Ohm’s law near the reversal surface. A new probe, which combines 3 orthogonal Rogowski coils and 3 magnetic coils, is presently under construction and will be employed to study this effect. We are also developing a Mach probe with embedded magnetic coils, which will be used to measure other components of the MHD dynamo. This set of tools, combined with other MST diagnostics, will allow study of the relative importance of different terms in the generalized Ohm's law across the plasma minor radius. MST is jointly supported by US DOE and NSF.   

Measurements of global and localized ion heating during impulsive reconnection in MST

In the MST reversed field pinch, impulsive reconnection occurs at (a) sawtooth crashes in standard plasmas, in which many large tearing modes are present, and (b) bursts of edge-resonant tearing modes with poloidal mode number $m = 0$ in enhanced confinement plasmas. In both cases, magnetic energy decreases while ion thermal energy increases. Fast, localized measurements of the impurity ion temperature (T$_{i})$ are made using charge exchange recombination spectroscopy. Ion heating is observed to be limited to the outer half of the plasma for an $m=0$ burst, and is strongest near the $m=0$ resonant surface. Conversely, ion heating occurs at all radii during a sawtooth crash, as T$_{i}$ more than doubles over $\sim $ 100 $\mu $s. The results suggest that ions are heated primarily near the reconnection layer, and that global heating during a crash arises from activity at multiple reconnection sites throughout the plasma. Both the heating profile and degree of heating during a crash vary strongly with plasma current, density, the reversal parameter, and ion species. At high plasma current (0.5 MA), the large T$_{i}$ ($>$ 1 keV on-axis) generated during a crash can be sustained by reduction of magnetic fluctuations using auxiliary current drive. Work supported by U.S.D.O.E. and N.S.F.   

Fast Ion Generation and Confinement during Reconnection Events in the MST Reversed Field Pinch

Measurements of neutron flux from deuterium plasmas in the MST reversed field pinch used in conjunction with ion temperature measurements indicate the presence of a fast ion population generated at magnetic reconnection events. During a typical event, T$_{i}$ on-axis approximately doubles, from $\sim $ 0.5 keV to $\sim $ 1 keV, in less than 200 $\mu $s. These events often produce neutron fluxes up to ten times higher than from thermal fusion alone. This flux is consistent with, for example, a small (1{\%}), non-thermal population at $\sim $ 15 keV. After an event, the neutron flux decays with a time constant of 1 - 3 ms. However, if an event is followed by a period of reduced magnetic fluctuations (achieved either actively, by inductively driving a parallel current in the edge, or spontaneously), the neutron flux decays at a much slower rate, $\sim $ 20 ms, which indicates improved fast ion confinement.   

Evolution of Electron Thermal Transport Through a Magnetic Relaxation Event in MST

Magnetic relaxation events known as sawteeth are a consistent feature of the 400kA standard discharges in MST. At the sawtooth crash, global particle and energy confinement change substantially. Within 0.5 ms the global energy confinement time decreases by a factor of two or more (from 2 ms to less than 1 ms), and the pressure and current profiles flatten. The electron thermal diffusivity ($\chi_e$) profile evolves on the time scale of the sawtooth cycle (6 to 8 ms) peaking just before the crash, then flattening and reaching a minimum after the crash. The relatively low $\chi_e$ in the core after the crash allows the flattened pressure and current profiles to slowly peak once again. A quantitative analysis of these transport quantities is directly dependent on the input power ($P=\int \mathbf{E}\cdot \mathbf{J} \mathrm{dV}$). By applying Faraday's law, to get the internal loop voltage, and then Poynting’'s theorem, $\mathbf{E}\cdot \mathbf{J}$, and thus the input power, can be determined. The internal loop voltage can be found by either a finite difference of a time series of equilibrium reconstructions or by reconstructing the time derivative of the Grad-Shafranov equation directly. We compare both methods to the simple Ohm’'s law approximation, $\mathbf{E}=\eta \mathbf{J}$, using an assumed resistivity profile.   

Transport of parallel momentum during reconnection events in the MST Reversed Field Pinch

Transport of parallel momentum during reconnection events has been investigated in the MST. The events are characterized in part by a sudden increase of resistive tearing magnetic fluctuations and generation of magnetic flux, abrupt ion heating, and changes in the plasma rotation. The plasma parallel velocity abruptly decreases in the core and speeds up at the edge which results in the flattening of the parallel momentum profile. The parallel velocity is reconstructed from the poloidal velocity of bulk plasma measured with the Rutherford scattering diagnostic (core) and Mach probe (edge), and the toroidal phase velocity of resistive tearing modes measured with an edge array of magnetic pickup coils. This transport of parallel momentum can be understood within the framework of two-fluid turbulent relaxation theory and from detailed calculations of fluctuation induced Maxwell and Reynolds stresses resulting from multiple tearing modes. Edge measurements of fluctuation induced Maxwell stress will be presented.   

Hall Reconnection in MST

Previous measurements in MST have established that two-fluid Hall effects produce a dynamo effect (the radial transport of parallel current), and are thereby important in evaluating the macroscopic effects of reconnection. This was established by measuring the \textit{nonlinear} Hall term in Ohm’s law ($<\delta j \times \delta B>$, where $< >$ denotes a magnetic surface average). We report here measurements of the \textit{linear} Hall term ($\delta j \times B$) as a more direct indicator of the role of Hall effects in reconnection dynamics. The linear Hall term is compared with the other measured terms in Ohm’s law to assess its influence on the structure of the reconnected field and the reconnection current. Probes are inserted to the reversal surface to measure the radial structure of reconnection associated with modes with poloidal mode number $m = 0$.   

Oscillating Field Current Drive in MST

Oscillating field current drive (OFCD) is a proposed method of efficient, steady-state toroidal plasma current sustainment using AC poloidal and toroidal loop voltages. In MST, OFCD is applied to a baseline, standard RFP plasma, adding about 10{\%} to the current with Ohmic efficiency. The evolution of current and pressure profiles during OFCD, including a 50{\%} modulation in central pressure, is obtained using internal magnetic field and electron density and temperature data, from which resistivity and confinement characteristics are also inferred. The added current is maximal for positive, but not maximal, helicity injection, which is likely due in part to OFCD's modulating effect on magnetic fluctuations, which are smallest at maximal added current. OFCD also modulates the ion temperature and anomalous ion heating. The experimental results are generally consistent with detailed 3D resistive-MHD computation and 1D relaxed-state modeling. MST's OFCD system is being upgraded for a longer pulse at higher power.   

Improved confinement at high density in MST

MST plasmas with reduced fluctuations and improved confinement are routinely achieved using auxiliary inductive current drive, but only at relatively low density to avoid the onset of edge-resonant tearing instability. The confinement improvement in these plasmas is due almost entirely to an increase in the electron temperature (T$_{e})$, which can triple, while the ion temperature (T$_{i})$ changes very little. However, with D$_{2}$ pellet injection, the achievable density in these plasmas has been quadrupled without triggering edge instability. At high density, T$_{i}$ increases with T$_{e}$, arriving at about the same peak value (600 -- 700 eV) near the end of the current drive. The largest densities, approaching 4x10$^{13 }$cm$^{-3}$, are achieved at high toroidal plasma current (0.5 MA). This results in a total $\beta $ up to 15{\%}, compared to $<$4{\%} in standard plasmas at this current Pellet injection at low current (0.2 MA) drives beta to 26{\%}, the largest value yet attained in MST's improved confinement RFP plasmas. The central pressure gradient exceeds the Suydam interchange limit without any obvious adverse consequences. Work supported by USDOE.   

Single-shot measurements of $>1$ keV electron temperature and first Lundquist number profile scalings in the MST Reversed-Field-Pinch.

Electron temperatures greater than 1 keV are routinely observed during 550 kA improved confinement plasmas. Single-shot, time-evolved profile measurements using a new multipoint Thomson scattering diagnostic have confirmed previous profile data based on measurements at one spatial and temporal point per shot, averaging over many shots. However, the new measurements have revealed a substantial shot to shot profile variance. Typical best discharges have approximately a 25\% larger temperature than measured previously with shot averaging. For example, electron temperatures approaching 1 keV have been measured during 400 kA plasmas for the first time. These temperature variations are found over a range of plasma currents for both standard and improved-confinement plasmas. Other improved profile measurements, in particular Zeff, current density and the parallel electric field now allow for measurement of the radial dependence of the plasma conductivity. This allows the first measurements of the Lundquist number (S) profile in the MST. First results on the S-scaling of radial magnetic field and velocity fluctuations will be presented. *This work is supported by the USDOE.   

Spectral Motional Stark Effect Measurements in MST

Direct localized measurements of the magnetic field down to $\sim$ 0.2 Tesla in MST are made using a recently upgraded Motional Stark Effect diagnostic. Measurements of the magnetic field magnitude at the plasma axis and of the vector magnetic field at the mid radius provide strong constraints on the internal magnetic field profile and the current density profile. The full Stark spectrum for each location is recorded and fit with a model for the beam emission. Detailed modeling of the collisional excitation of the beam is performed to understand features of the spectrum not explained by simply assuming a statistical weights population for the atomic levels. Fast shutters allow exposures as short as 100 $\mu s$ and an EMCCD detector with 2.4 ms framing enables low noise single shot analysis of the evolution of the magnetic field throughout the 20 ms diagnostic neutral beam pulse. The magnetic field on axis drops during relaxation events in standard plasmas but is unaffected by smaller events in enhanced confinement plasmas. During inductive current drive experiments (Pulsed Poloidal Current Drive and Oscillating Field Current Drive), the magnetic field on axis closely follows the evolution of the toroidal plasma current. Work Supported by U.S.D.O.E. and N.S.F.   

Development of a Pulse-Burst Laser System for Fast Thomson Scattering on the MST RFP

A ``pulse-burst'' laser system is being developed for addition to the Thomson scattering diagnostic on the MST RFP. This laser will produce a burst of up to 200 approximately 1 J Q-switched pulses at repetition frequencies 5-250 kHz. The planned laser system will operate at 1064 nm and is based on existing Nd:YAG systems used to study fluid dynamics [Brian Thurow et al., Appl. Opt. 43, 5064 (2004)]. The burst train of laser pulses will enable the study of Te and ne dynamics in a single MST shot, and with ensembling, will enable correlation of Te and ne fluctuations with other fluctuating quantities.   

High frequency electron temperature fluctuation measurements with the multi-point, multi-pulse Thomson scattering diagnostic on MST

MST plasmas are rich in physics that can cause rapid changes in the electron temperature profile such as rotation of magnetic modes, reconnection events and electron turbulence. We present first results of electron temperature fluctuation measurements of about 5kHz and faster including temperature profile changes correlated with the quasi-single helicity state. The Thomson scattering diagnostic on MST consists of two independently triggerable Nd:YAG lasers and 15 four-channel and 6 eight-channel General Atomics polychromators equipped with avalanche photodiode modules. The two lasers can be fired arbitrarily close together in time and each can fire every 20 ms. Data acquisition becomes the limiting factor in time resolution. Overall the system is capable of measuring changes in the radial electron temperature profile on the order of 200 ns with a spatial resolution of 2 cm or less. It is also possible, on these fast timescales, to resolve non-Maxwellian electron distribution functions with the eight-channel polychromators.   

Measurements of Electron Diffusion via Hard X-ray Detection

An upgraded array of hard x-ray (HXR) detectors has been implemented on MST to measure electron particle diffusion in globally improved confinement pulsed parallel current drive (PPCD) plasmas and locally improved confinement quasi-single- helicity (QSH) plasmas. Each of these plasmas confines runaway electrons that emit HXRs. The diagnostic is a multichord array of CdZnTe detectors sensitive to 10-300 keV x-rays. Recently added lead shielding blocks x-rays from outside collimated lines of sight. The Fokker-Planck code CQL3D, now with HXR flux from the entire array as a constraint, is used to compute the diffusion coefficient as a function of radius during PPCD. In QSH plasmas, where one mode dominates the core tearing mode spectrum, HXRs are observed when a dominant island emerges, and the HXR flux oscillates in phase with the rotation of this island. Modeling with the ORBIT code shows that runaway electrons are better confined inside the island than in the exterior stochastic region.   

Hard x-ray tomography system on MST

A CdZnTe 16 channel hard x-ray camera, with excellent sensitivity to photons in the energy range 10-200 keV, has been tested on MST. These detectors are immune from vibration noise and are unaffected by electromagnetic noise from rf sources. Absolute calibration of these detectors is made using the 59 keV line from Am241 source. Hard x-ray generated during 60 kW of launched LH wave into MST plasma is measured and shows an increase in the hard x-ray intensity in the range of 10-50 kev. Three of these detectors will be configured to form a hard x-ray tomography system. Such a system will be capable of resolving x-ray intensity in space, time and energy. The measured hard x-ray energy spectrum is used as an input to the CQL3D code to calculate D(r), the energetic particle diffusion. This tomographic system will be placed near the LH and EBW antennas to look for signatures of energetic electrons generation and their radial diffusion. Hard x-ray contours at multiple energy ranges, and comparison with soft x-ray as well as magnetic surfaces will be presented.   

Measurements of Flow Fluctuations and the MHD Dynamo in MST

In many astrophysical and laboratory plasmas the magnitude and spatial distribution of the magnetic field is affected by fluctuations. In the Madison Symmetric Torus we investigate the redistribution of magnetic field by coupled velocity and magnetic field fluctuations (the MHD dynamo, $<$v $\times $ b$>)$. Carbon emission from neutral beam-induced charge exchange recombination is collected by a custom-built, high throughput spectrometer yielding measurements of carbon impurity ion velocity localized to +/- 1 cm with high bandwidth (100 kHz). We have measured the correlation of poloidal velocity fluctuations with magnetic fluctuations associated with tearing modes resonant across the plasma radius. Strong correlations are observed for a range of m=1 magnetic modes, and the relative phase implies a contribution to the MHD dynamo away from the magnetic axis. The correlations are narrow in space and greatest near the tearing mode resonant surfaces. The total measured MHD dynamo on axis is zero to within error bars. Initial Ohm's law modeling including all available measurements implies a need for a dynamo significantly larger than the measured upper bound on the MHD dynamo. Work supported by U.S.D.O.E. and N.S.F.   

Investigation of fast helium beam emission spectroscopy on MST.

A fast helium beam emission spectroscopy (BES) diagnostic is being investigated as a way to measure local plasma parameters on MST. A full collisional-radiative model was developed and compared with experimental measurements. The ratio of intensities of the lines at 667.8nm and 492.2nm (I$_{667}$/I$_{492})$ appears useful for local density measurements in that it has a strong density dependence while only weakly dependent on other parameters. The effect of $Z_{eff}$ profiles and ion impact affects triplet line intensities more strongly than singlet lines and modeling better reproduces experimental results with these effects properly considered. The comparison of theoretical and experimental line ratios shows good qualitative agreement. The quantitative agreement is within a factor of 2 for I$_{667}$/I$_{492}$. There is so far no good singlet line ratio identified for local $T_{e}$ measurement in the range of interest. An independent measurement of local metastable fraction would allow for the use of triplet lines for the line ratio technique.   

Reversed Field Pinch Equilibrium Reconstruction From Three-Wave Polarimeter-Interferometer Data

A high-speed three-wave far infrared (FIR) laser polarimeter- interferometer diagnostic is now available on the MST RFP to provide simultaneous measurement of electron density and toroidal current density profile evolution. These measurements along with the known average and edge toroidal magnetic field strengths can be fit with a two-parameter model to yield the toroidal magnetic field, q and pressure profiles. The derived on-axis toroidal magnetic field agrees quantitatively with independent MSE measurements under various plasma conditions. During the linear sawtooth ramp phase in standard discharges, q$_{0}$ decreases slowly towards 1/6 before, and increases to $>$0.2 after each sawtooth crash. In quasi-single-helicity discharges where the (1,5) mode dominates, q$_{0}$ hovers around 0.2, consistent with MHD simulation. In pulsed parallel current drive experiments, both current and toroidal magnetic field profiles peak on axis, while the $\lambda$-profile broadens. The stored thermal energy exceeds the sum of bulk electron and ion contributions by over 50\%, indicating a significant contribution from energetic particles, consistent with CQL-3D modeling.   

Combined Faraday Rotation and Cotton-Mouton Measurements on MST

A three-wave FIR laser Faraday rotation-interferometer system is now routinely available on MST for simultaneous measurement of electron density and poloidal magnetic field profiles. For more accurate equilibrium reconstruction, the perpendicular (toroidal) magnetic field can be obtained by measuring the Cotton-Mouton (CM) effect (difference between O- and X-mode refractive indices). To test the feasibility of this measurement, two collinear, orthogonal, linearly-polarized laser beams with a slight frequency offset will be passed through the plasma and the phase difference between them directly measured to give the CM effect. By adding a second detector to each channel of the Faraday rotation-interferometer system, so that both linear components of circularly-polarized probe beams are detected, the CM effect measurement can be combined with the Faraday rotation-interferometer system to provide simultaneous measurement of plasma electron density, poloidal magnetic field, and toroidal magnetic field profiles. The principle of this three-wave Faraday rotation and Cotton- Mouton interferometer system will be described along with its importance for accurate equilibrium reconstruction.   

Measurement of High-Frequency Core Magnetic and Density Turbulence in MST

Turbulence plays an important role in plasma physics and is thought to be responsible for both the dynamo and transport in the RFP. Magnetic and current density fluctuations produce a radial component to the mean fields. Particles stream along the field, producing a radial particle flux. Understanding the nature of these fluctuations can lead to methods of suppressing them, an important goal for fusion research. On MST, a high-speed laser-based Faraday rotation-interferometry system allows for non-perturbative measurement of core density and magnetic field, both equilibrium and fluctuating quantities. Recent upgrades permit simultaneous measurements of density and magnetic field fluctuations with broadband turbulence up to 500 kHz being observed. By correlating two displaced Faraday rotation or inteferometry chords, one can extract information on the fluctuation wavenumber spectrum. Preliminary results will be presented.   

Maxwell Stress Measurement by Laser Faraday Rotation in High Temperature Plasmas

The cross product of current density and magnetic field fluctuations, commonly referred to as the Maxwell stress, has been measured in the high-temperature core of Reversed Field Pinch (RFP) plasmas by using a fast laser Faraday rotation system. Both parallel and perpendicular components of the Maxwell stress show a significant increase during magnetic reconnection events such as the sawtooth crash. Spatially, the Maxwell stress peaks near tearing mode resonant surfaces due to the localized current density fluctuations and global magnetic field fluctuations. The surge of Maxwell stress at reconnection is associated with nonlinear tearing mode coupling. Measurement details and implications for current transport and zonal flow formation are presented. Work supported by US DOE and NSF.   

Plasma Rotation During Neutral Beam Injection In MST

The effect of fast ions from neutral beam injection (20 keV, 30 A, 1.5 ms) on plasma rotation and magnetic tearing modes is studied. We observe that during co-injected NBI (with the injection in the same direction as the plasma and mode rotation) the rotation of the core-resonant n = 5 magnetic mode decreases and in many instances lock to the vessel wall. There is an associated drop in the poloidal component of n = 5 magnetic mode amplitude. The drop in the mode velocity suggests a counter-directed torque, perhaps due to modification of the radial electric field. The rotation slows during the injection phase, then restores itself on the timescale of the fast ion slowing down time (5 ms @ T$_{e}$ = 100 eV). The fluctuation-induced j x b Maxwell stress is measured using MST's FIR diagnostic and presented for comparison. Equilibrium reconstruction suggests a small increase in on-axis J$_{\vert \vert }$, consistent with the presence of a localized fast ion population moving in the direction of the plasma current. Mode rotation during NBI counter-injection is also presented.   

Novel heavy ion beam computer-control to enable measurements in plasmas with significant temporal variations of equilibrium quantities

A novel heavy ion beam computer-control system applying pre-programmed time varying voltages to the electrostatic sweep-plates and the analyzer anode is under development. It is necessitated by plasmas in which equilibrium quantities vary significantly as a function of time and the heavy ion beam experiences substantial path changes. This is exhibited in discharges with time varying current drive or large magnetic reconnection events (sawteeth) when the magnetic field profiles undergo modification. Alteration of the beam path may prevent secondary ions from entering the analyzer (thus limiting the duration of signal detection) or it may alter the sample location. Similar limitations in signal acquisition also occur with large temporal variations in the electric field or plasma potential. Control of the sweep and analyzer voltages (and hence the beam trajectory) will permit measurements as a function of time at spatially stationary sample volumes. This technique will be used to probe the MST plasma core throughout enhanced confinement discharges where electrostatic transport may be the dominant loss mechanism. Status of the development and utilization of the computer-control system will be presented.   

Modeling of ion heating in RFPs at sawtooth crash.

Strong ion heating is observed in the reversed field pinch (RFP). During a sawtooth crash in the Madison Symmetric Torus RFP the ion temperature can spontaneously double in 100 microseconds. It is also observed that high Z impurities are heated stronger than bulk ions. The possibility of ion heating due to tearing instabilities is examined. Heating scenarios due to viscous damping of strongly localized perpendicular and parallel flows occurring in the vicinity of resonant surface in tearing mode are considered. Flow amplitudes are estimated from nonlinear resistive MHD modeling. The heating rate is found by solving the kinetic equation with Landau collision operator. The results of the study will be presented.   

Anomalous Impurity Ion Heating from Alfv\'{e}nic Cascade in the RFP

Recent impurity ion measurements in MST suggest that collisional energy transfer from anomalously heated impurities might be able to account for the anomalously high temperature of bulk ions relative to electrons. An anomalous heating mechanism for impurities must still be uncovered. However, mechanisms proposed for anomalous bulk ion heating that have met difficulty in explaining bulk ion temperature, may work better for impurities. Previous work$^{2}$ calculating the heating of bulk ions by gyro and Landau resonances with turbulent fluctuations cascading from unstable tearing modes is extended to impurity species measured in MST. The heavier mass of impurities allows gyro-resonant heating at lower frequencies where more energy is present in the fluctuations. Impurity heating rates are calculated for impurities found in MST and compared with observed rates inferred in the impurity temperature rise during sawtooth events. $^{2}$N. Mattor, et al., Comments Plasma Phys. Controlled Fusion \textbf{15}, 65 (1992).   

Numerical Studies of Tearing Mode Reduction and Suppression of the MHD Dynamo During Pulsed Poloidal Current Drive in the Reversed Field Pinch

We identify stabilizing properties of simulated PPCD transients amenable to the decline of interior resonant tearing modes using the 3D fully nonlinear MHD code NIMROD[1]. Our results show the applied transients have a direct stabilizing effect on the internal modes. We demonstrate that stabilization of fluctuations in the interior decreases the nonlinear power flow to other fluctuations. The subsequent evolution of the internal modes is influenced by the action of the penetrating transients and the significant decline in nonlinear coupling. Edge currents driven directly by the applied poloidal electric field initially stabilize core modes. However, the initial response of modes resonant near the exterior is observed to depend on the instantaneous nonlinear state of the standard RFP at application time. Simulations that maintain fixed toroidal electric field as poloidal electric field is applied show an early response in the interior that drains power transmitted out of the mean fields. Later in the evolution, flux surface compression by the poloidal transient may be destabilizing to several modes leading to increased fluctuation levels. When toroidal electric field is simultaneously reduced as the poloidal field is applied, the system is seen to maintain a more stable configuration. The dynamo activity is diminished to where parallel electric field is balanced by the resistive term with driven current density. [1] Sovinec, Gianakon, et al. POP 10, 1727 (2003). LA-UR-06-5139.   

MHD Simulations of single helicity and quasi-single helicity states in Reversed Field Pinches

We present a systematic MHD study of single helicity (SH) states and quasi-single helicity (QSH) states in RFPs. We begin with cylindrical paramagnetic pinch equilibria with uniform resistivity, characterized by a single dimensionless parameter proportional to the toroidal electric field, or the RFP toroidal current parameter $\Theta$. For sufficiently high $\Theta$, there are several unstable $m=1$ ideal MHD instabilities, typically one of which is nonresonant, with 1/n just above $q(r=0)$. We evolve these modes nonlinearly to saturation for low Hartmann number H. We then obtain the $m=k=0$ quasilinear profiles, which typically have toroidal field reversal, and study their stability. For typical cases, these profiles may remain unstable to tearing modes, but only for sufficiently high $H$. For lower $H$ these states are stable. We show results indicating the proximity of these thresholds to the thresholds between SH and QSH behavior.   

On the Role of the Electrostatic Fields in the Evolution of Tearing and Kink Modes

Recent work by the RFX group [1] has uncovered the crucial role played by the electrostatic field in sustaining the dynamo process in RFP devices. The study was conducted by simulation and was based on reaching a quasi-steady state starting from a paramagnetic pinch. The primary contribution of the electrostatic field to sustain the flows responsible for the dynamo processes was observed both in situations dominated by a main mode (quasi-single helicity) and in situation where a rich spectrum of modes is present (multi helicity). We revisit the problem here in a similar but different situation. We consider a single initially straight flux rope similar in configuration and property to the flux ropes created in the RSX device at LANL. We conduct a simulation study of the flux rope evolution and we confirm that the same processes observed in Ref. [1] hold also in the situation considered. Although a large fraction of the field is electromagnetic in nature, as expected for the kinking of a flux rope, the electrostatic field is almost single-handedly responsible for the flow involved in the magnetic reconnection and in the topological changes of the flux surfaces. Such processes are key to the non-linear evolution of the instability.   

MHD dynamo for the Reversed Field Pinch

MHD modelling is believed to provide a good description of large scale dynamics of the Reversed Field Pinch. In particular, 3-dimensional nonlinear simulations in a simple visco-resistive approximation [see Cappello PPCF 2004 and references therein] display many features in reasonable agreement with experiments. In recent times it has been shown that the general and basic tendency of the RFP to develop a more or less regular global kink type deformation of the plasma column forces a corresponding charge separation (consistent with quasi-neutrality) and a related electrostatic field. The ensuing electrostatic drift velocity (nearly) coincides with the dynamo velocity field traditionally considered to sustain the configuration [Bonfiglio,Cappello,Escande PRL 2005; Cappello,Bonfiglio,Escande PHP 2006]. In this presentation we review our present understanding in this subject. In particular we focus on the description of the formation of pure helical laminar RFP solutions, and study the relationship between the electrostatic structure and the topological properties of the magnetic field in the case of the less regular turbulent solutions, where the robustness of a chain of magnetic islands isolating the chaotic core from the edge has been recently highlighted [Spizzo,Cappello, Cravotta, Escande, Predebon, Marrelli, Martin, White, PRL 2006].   

Feedback control of $m=0$ modes in the Reversed Field eXperiment

Recent theory and simulations have highlighted the role of tearing modes with poloidal mode number $m=0$ and $m=1$ in the edge of the reversed-field pinch (RFP)\footnote{G. Spizzo, S. Cappello, A. Cravotta, D.F.Escande \textit{et al.}, Phys. Rev. Lett. \textbf{96}, 025001 (2006).}. These results show that the nonlinear superposition of these modes allows for the formation of a chain of magnetic islands, responsible for a transport decrease in the region where the toroidal field $B_{\phi}$ vanishes and reverses direction. In particular, it has been demonstrated that the reduction of the total $m=0$ island dimension (due to $m=0$ modes and the beating of the $m=1$'s) is beneficial in terms of transport. As a first step to this end, in the RFX-mod reversed-field experiment, we exploited the feedback control of the 12 toroidal sectors used for producing the toroidal field, so as to actively cancel the $m=0$ mode amplitude. Indeed, experimental results show the reduction of $m=0$ fluctuation amplitude, associated to an overall temperature increase, and a reduction and redistribution of plasma-wall interaction due to the mode phase locking.   

Oscillating and pulsed poloidal current drive experiments in RFX-mod

The reversed field pinch (RFP) configuration is based on a delicate balance between the minimum amount of magnetic fluctuation required to sustain the configuration and its negative effect on transport. Pulsed and Oscillating Poloidal Current Drive (PPCD and OPCD) techniques aim at controlling the level of MHD fluctuations by providing externally the flux necessary to maintain the reversed configuration. PPCD experiments were successfully applied to all presently operating RFPs, though by its own nature it provides transient effects. On the other hand OPCD experiments done on RFX proved to be a good technique to extend the beneficial effect of the PPCD along the whole discharge. Both techniques were applied also in the new RFX-mod device (operated in the virtual shell scenario) with good results in terms of plasma performances and reduction of MHD fluctuation along with changes in its spectral composition. In particular, thanks to the flexible toroidal power supply of RFX-mod we could study OPCDs with oscillations charcterized by different frequencies, waveforms and amplitudes.   

Plasma Flows in the RFX-mod Reversed Field Pinch

Plasma rotation measurements are needed for the determination of radial electric field Er. This is a well known main character in tokamaks and reversed field pinches (RFPs) achieving improved confinement regimes. In this work passive spectroscopic measurements along multiple integrated poloidal and toroidal lines of sight in several experimental RFX-mod scenarios are presented. Due to the magnetic configuration of RFPs, toroidal and poloidal flow components have the same magnitude, and the latter cannot be neglected. The main objective of our analysis is studying the separate role of m=0 and m=1 magnetic perturbations in modifying the carbon flow pattern, and the radial electric field. We have already proved the presence of an edge flow opposite to the core co-current flow, that reverses its direction in presence of externally induced radial magnetic perturbations, and we have also related this behavior to a reversal of the radial electric field. The analysis is complemented by the comparison with the local evaluations of the flow as measured by the edge Gas Puffing Imaging (GPI) diagnostic.   

Soft x-ray emissivity characterization in RFX-mod

We present a characterization of the soft x-ray (SXR) plasma emissivity in the RFX-mod reversed field pinch (RFP) device. The measurements has been performed with the high spatial resolution SXR tomographic diagnostic installed in RFX-mod, consisting of 4 probes (for a total amount of 78 lines of observation) located in different poloidal portholes at the same toroidal section. The line integrated radial profiles have been analyzed in different scenarios, and operating conditions with and without the Virtual Shell (VS) have been considered. The regimes explored have been those of the Multiple Helicity (MH) and Quasi Single Helicity (QSH) states. In the latter case, asymmetric brightness profiles are indicators of the arising of a localized structure emerging from the plasma core, and corresponding to the presence of a dominant ($m$=1,$n)$ mode in the magnetic spectra. The profiles measured with the tomography have been also compared with those obtained with the new multifoil diagnostic for the estimation of electron temperature semi-profiles over the low field side of the RFX-mod chamber.   

Feedback Stabilization for the HIT-SI device

HIT-SI has successfully established spheromaks through the use of inductive helicity injection. During sustainment, the produced spheromaks experience plasma current decay despite continued driving. Soak-through in the copper flux-conserver and through the diagnostic gap is suspected as the cause, supported by data from the existing surface magnetic probe array, which suggests the occurrence of mode locking. To further study the possibility and effect of locked modes and to test the applicability of feedback control as a corrective measure, application of additional sensors to coincide with feedback sites is underway. Through feedback it may also be possible to suppress occasional current reversals. Application of fields outside of vacuum, through the stainless steel tank and through the Cu flux-conserver, is proposed. Results, and the design and modeling of the feedback system, will be presented for various HIT-SI spheromak conditions.   

Helicity Injected Torus Program Overview

The Helicity Injected Torus with Steady Inductive Helicity Injection (HIT--SI) spheromak experiment [Sieck, Nucl. Fusion v.46, p.254 (2006)] addresses critical issues for spheromaks, including current drive, high-beta operation, confinement quality and efficient steady-state operation. HIT--SI has a ``bow-tie'' shaped axisymmetric confinement region (major radius R=0.33 m, axial extent of 0.57 m) and two half-torus helicity injectors, one mounted on each end of the flux conserver. HIT--SI has produced spheromaks with up to 30 kA of toroidal current, using less than 4 MW of applied power, demonstrating that Steady Inductive Helicity Injection can generate and sustain discharges with modest power requirements. Fast camera images of HIT--SI discharges indicate a toroidally rotating n=1 structure, driven by the helicity injectors. The direction of the toroidal current is determined by the direction of rotation of the driven n=1. Measured surface and internal magnetic fields in HIT--SI discharges are consistent with that of the true 3D Taylor state, including the injectors. Recent HIT--SI physics studies, diagnostic improvements and machine upgrades will also be summarized.   

Spheromak Formation and Toroidal Mode Activity in HIT-SI

A spheromak is formed and sustained for the first time using Steady Inductive Helicity Injection (SIHI). A steady state spheromak with n=0 symmetry is formed and sustained through non-linear relaxation from the two inductive injectors, which provide a magnetic structure with n=1 symmetry. A spheromak with approximately 34 kA of toroidal current is achieved using injector current amplitudes of 20 kA. Internal magnetic probe data agree remarkably well with the plasma being in the 3D Taylor state. The Taylor state model predicts a separatrix between the injector fields and the spheromak core at a threshold that has been greatly exceeded in the experiment. The spheromak often undergoes a reversal of the n=0 toroidal current while the magnitude of an n=2 mode peaks. After the reversal, the toroidal current is equal or greater in magnitude than before and the magnetic helicity handedness is unchanged. Spheromak discharges often terminate with a growing n=1 locked mode. Comparisons will be presented between experimental data and predictions from the 3D Taylor state model for the n=0, n=1, and n=2 Taylor states.   

Internal Field Measurements of the Spheromak Equilibria in the HIT-SI Experiment

The formation of Spheromak equilibria with plasma currents as high as 30kA are now routinely achieved in the HIT-SI device with 4MW of input power. The axisymmetric equilibrium is formed using steady inductive helicity injection (SIHI). Helicity injection is maintained at a constant rate by means of two AC driven RFP sources phased in quadrature and connected to the main chamber so as to drive a rotating n=1 mode at 6kHz frequency. A magnetic probe consisting of three spatially separated radial arrays of 3d pickup coils has been designed to allow the direct measurement of the plasma current using finite differences of the magnetic field components. The probe is insertable at the mid-plane to a depth of 15cm. Measurements of the internal magnetic field structure, plasma current, poloidal and toroidal flux distributions are presented for operations varying the injector voltage, injector flux and fill density. Comparisons of the experimental data to numerical computations of the injector and Spheromak magnetic fields using the 3D Taylor state are also presented.   

HIT-SI Injector Voltage Measurements Using Injector Langmuir Probes

A pair of Langmuir probe arrays have been designed and built to measure floating potentials of the plasma at the injector mouth of the HIT-SI device. The Helicity Injected Torus using Steady Inductive Helicity Injection (HIT-SI) [1,2] is a ``bow tie'' spheromak using an electrodeless formation and sustainment concept. HIT-SI is powered by two inductive helicity injectors operated in quadrature to maintain a constant helicity injection rate. The electric probes consist of an array of four floating potential Langmuir probes measuring the voltage distribution in each injector from the shell to midpoint of the injector mouth. The probe measurements combine to determine the part of the injector loop voltage driving the n = 0 spheromak equilibrium region. Preliminary data suggest the spheromak voltage is the loop voltage minus the nearly constant injector voltage of 150-180 volts. These probe data will be used to calculate the helicity decay time of the spheromak. [1] T. R. Jarboe. Steady inductive helicity injection and its application to a high-beta spheromak. Fusion Technology, 36(1):85--91, July 1999. [2] P.E.Sieck et al., ``Demonstration of Steady Inductive Helicity Injection'', Nuc. Fusion, in press (2006).   

Ion Doppler Spectroscopy, Far Infrared Interferometry and Measuring the Lundquist Number on HIT-SI

Ion Doppler Spectroscopy (IDS) is used to measure ion velocity and temperature on HIT-SI. The spectrometer uses a 16 channel photo multiplier to track temperature and velocity continuously through the discharge. The spectrometer can view into the HIT-SI injector region as well as into the equilibrium region. Temperature and velocity data will be presented. A tangentially viewing far infrared (FIR) interferometer is now operating routinely to measure chord averaged electron density. The system uses two optically pumped diflouromethane gas lasers to produce a heterodyne signal. The system can achieve a heterodyne beat of up to 2 MHz compared to the older system frequency 250 kHz. The increased frequency is required to track density fluctuations on HIT-SI. Data from the new interferometer will be presented. A key scientific goal in the HIT-SI program is to measure the Lundquist Number,S, in the spheromak equilibrium. The measured value of S is needed to compare HIT-SI experimental results to computational results from the NIMROD code, in which S is a free parameter. This requires measurement of the Density, (which will be measured by FIR), the magnetic field on axis (by internal magnetic probing), and electron temperature (by a Langmuir Probe which is under development.) A discussion of experimental results and corresponding NIMROD calculations will be presented.   

Ongoing NIMROD Simulations of The Lundquist Number and Lambda Dependence of the HIT-SI Plasma

The Steady Inductive Helicity Injected Torus (HIT-SI) is a spheromak that uses dual semi-toroidal injectors to provide constant steady inductive helicity injection (SIHI), which maintains toroidal current by generating poloidal flux with relaxation current drive. Relaxation produces and sustains a spheromak in the confinement region A three-dimensional resistive MHD model was developed using the Non-Ideal Magnetohydrodynamics with Rotation Open Discussion (NIMROD) code to simulate HIT-SI operation. Both decaying and sustained spheromak runs were simulated. Previous decaying spheromak simulations show amplification of the poloidal flux with Lundquist number 1000 or greater. The NIMROD model was then employed to explore the effects of injector lambda and Lundquist number (S) on sustained plasma behavior in HIT-SI. In combination, the past and present results from these simulations form a data set with S ranging from 22 to 897 and injector lambdas ranging from 10 to 50. These data indicate that three distinct operating regimes exist with respect to Lundquist number and suggest that amplification of the axisymmetric mode increases with both S and injector lambda.   

Current drive experiments in the Helicity Injected Torus - II

The HIT-II spherical torus (ST) device has demonstrated four toroidal plasma current drive configurations to form and sustain a tokamak: 1) inductive (ohmic) current drive, 2) coaxial helicity injection (CHI) current drive, 3) CHI initiated plasmas with ohmic sustainment (CHI+OH), and 4) ohmically initiated plasmas with CHI edge current drive (OH+ECD). CHI discharges with a sufficiently high ratio of injector current to toroidal field current form a closed flux core, and amplify the injector poloidal flux through magnetic reconnection. CHI+OH plasmas are more robust than unassisted ohmic discharges, with a wider operating space and more efficient use of the transformer Volt-seconds. Finally, edge CHI can enhance the plasma current of an ohmic discharge without significantly degrading the quality of the discharge. Results will be presented for each HIT-II operating regime, including empirical performance scalings, applicable parametric operating spaces, and requirements to produce these discharges. Thomson scattering measurements and EFIT simulations are used to evaluate confinement in several representative plasmas. Finally, we outline extensions to the HIT-II CHI studies that could be performed with NSTX, SUNIST, or other ST devices.   

Overview of Recent Progress on the SSPX Spheromak

Recent results from SSPX show increased Te and better understanding of spheromak plasma confinement and magnetic field generation. Magnetic fluctuations are $<$ 1{\%} when the q-profile doesn't span low-order rational surfaces. The magnetic field can be built up and sustained with periodic current pulses or a steady-state discharge using a new modular capacitor bank. Magnetic reconnection is measured and modeled during plasma formation and compared with fast imaging diagnostics. New diagnostics include a neutral particle analyzer, soft x-ray detectors, and multi-pulse Thomson scattering. A neutral beam heating system is being procured to provide an independent heat source for confinement and pressure-limit studies. NIMROD 3-d MHD simulations examine long duration steady-state discharges and a next-generation spheromak experiment with reduced edge current losses and high flux amplification.   

Spheromak Buildup in SSPX using a Modular Capacitor Bank

The Sustained Spheromak Physics eXperiment uses DC coaxial helicity injection to produce plasmas with central Te $>$350eV and be $\sim$5\% with toroidal fields of 0.6T. We report here results from experiments using a new solid-state programmable modular capacitor bank that allows higher peak injection currents ($>$ 600kA), longer injection-current flattop ($>$8ms), and multiple current pulses (5) for step-wise buildup experiments. The increased flexibility allows study of the physics of magnetic field generation, which is key to development of the spheromak as a magnetic fusion concept. Experiments using the modular capacitor bank have produced discharges (long formation) with the highest edge poloidal fields measured on SSPX and multiple current pulse discharges that continue to build magnetic field in a stepwise manner. The design of the programmable bank and results from using the bank to increase the magnetic field in SSPX will be presented.   

Simulation of Planned Neutral Beam Heating Experiments in SSPX

Recent results from the SSPX spheromak (peak Te ~350eV) provide strong motivation for adding auxiliary heating to study energy transport and pressure limits. We are now procuring two 25keV 900kW neutral beam sources from Budker Institute in Russia. In parallel, we are using the CORSICA transport code to examine the effect of beam input geometry of the efficiency of neutral beam heating in a spheromak such as SSPX. A new fast-ion orbit-following algorithm was recently added to CORSICA to account for the low field, low aspect-ratio magnetic topology of the spheromak configuration [1]. We find a significant increase in fast ion confinement and subsequent plasma heating as the injection angle moves from strictly radial to more tangential injection. Variation of the heating rate with magnetic field, plasma density, and confinement time were also examined. The schedule for proposed beam installation and development of suitable target plasmas and diagnostics also will be presented. [1] L.D. Pearlstein, et al., Proceedings 33rd EPS Conf. on Plasma Physics, Rome (2006)   

Soft X-ray Measurements in SSPX

We seek to measure time-resolved electron temperatures in the SSPX plasma using soft X-rays. To increase sensitivity to changes in temperature over the range 100-300 eV, we use two photodiode detectors sensitive to different soft X-ray energies. The detectors, one with a Zr/C coating and the other with a Ti/Pd coating, view the plasma along a common line of sight tangential to the magnetic axis of the spheromak, where the electron temperature is a maximum. The comparison of the signals over a similar volume of plasma, should be a stronger function of temperature than a single detector in the range of Te< 300 eV. The success of using photodiodes to detect changing temperatures along a chord will make the case for designing an array of the detectors, which could provide a time changing temperature profile over a larger portion of the plasma. Photodiode characteristics, method of implementation and initial results will be presented.   

New Ion Temperature Measurements using the Compact Neutral Particle Analyzer on SSPX

We report here first measurements of the charge-exchange losses in SSPX using a newly installed neutral particle analyzer. Simultaneous measurements of the electron temperature (via Thomson scattering) and magnetic field fluctuations are obtained in SSPX discharges with Te $>$ 100eV. Standard turbulence parameters are derived from the magnetic field measurements. The ion temperatures are measured with 50$\mu $sec temporal resolution during the plasma pulse, allowing a correlation of these data with the evolution of turbulence in the local magnetic fields. The results are discussed in the context of the relationship between magnetic field fluctuations and high ion temperature spikes in spheromak plasmas and in the context of new approaches to a dynamical theory of turbulent plasmas.   

Measurements and models of spheromak formation at SSPX

Two hypotheses of spheromak formation with coaxial helicity injection are being investigated at SSPX. The first hypothesis comprises the formation of multiple magnetic reconnection sites prior to relaxation; in the second hypothesis an initial plasma column kinks at least twice and need only reconnect at a single site to form the spheromak. Two numerical tools are used to study formation, as well as steer the design of a new probe that will search for reconnection in the SSPX flux conserver. The first tool is NIMROD, a 3D resistive MHD code that simulates SSPX plasma evolution. The second is a program that solves for the magnetic field from current-carrying magnetic flux ropes with a wide range of conjectured shapes, from straight ropes, to complex knots. Virtual probes in these models are compared to experimental measurements from an insertable probe and probes at the flux conserver wall, and to flux rope shapes inferred from high-speed images.   

Study of temperature evolution in NIMROD simulations of SSPX

The sustainment of current in the core of a toroidal plasma by electrostatic edge-current drive requires the radial transport of current across imperfect magnetic surfaces. Tight coupling between surface-breaking MHD fluctuation activity and temperature evolution has been observed in NIMROD simulations of SSPX [1]. Its sensitivity with respect to physical (Zeff, density, viscosity, anisotropy of the thermal conductivity) and numerical parameters is examined here. One simulation, with high, fixed bank-current, run to nearly an L/R time, exhibits apparent steady-state cycles with time-averaged sustainment: intervals of closed surfaces and peaked temperature profiles, punctuated by short bursts with voltage spikes and open surfaces. The energy-confinement properties of this simulation will be presented. [1] B.I. Cohen, E.B. Hooper, et al., Phys. Plasmas 12, 056106 (2005).   

Options for a next-generation spheromak physics experiment

SSPX experiments and resistive MHD modeling suggest options for a next-generation experiment. Magnetic fluctuations are now $<$1{\%} when the q-profile does not cross low-order rational surfaces in the spheromak core, yielding good energy confinement.$^{1}$ Plasma current and magnetic field decay slowly; initial experiments suggest that the they can be rebuilt periodically by high current pulses.$^{2}$ Modeling predicts that flux amplification, typically 2-3 in SSPX, can be increased to $>$50 by actively reducing the bias (``ABR'') after spheromak formation, reducing edge ohmic losses proportionally. ABR is also predicted to improve stability and energy confinement. Neutral-beam experiments planned for SSPX$^{3}$ may provide a path to hotter plasmas. Next-generation spheromak geometries and scenarios building on these results are described to improve plasma parameters, explore additional stability control, and examine other physics issues. Work supported by U.S. DOE under Contract No. W-7405-ENG-48 at UC LLNL. $^{1}$H. S. McLean, et al., Phys. Plasmas \textbf{13}, 056105 (2006). $^{2}$S. Woodruff, et al., Phys. Rev. Letters \textbf{93}, 205002 (2004). $^{3}$D..N. Hill, et al., this meeting.   

Nonaxisymmetric relaxed state in an elongated cylinder

Co-helicity spheromak merging experiments within an elongated cylindrical flux conserver at the Swarthmore Spheromak Experiment (SSX) produce a final state magnetic configuration that is nonaxisymmetric, twisted along the geometric axis of the cylindrical flux conserving boundary, and quiescent. The lack of dynamics suggests a minimum energy state, and is tentatively identified as the Taylor state. The observed magnetic field structure is compared to the results of a finite element algorithm (Chu, Jensen, and Dy, Phys. Fluids {\bf 25}, 1611) which determines the nonaxisymmetric Taylor state within the cylindrical boundary. The algorithm iterates a two step procedure: the first step minimizes magnetic energy while obeying the ideal MHD constraints, and the second breaks the MHD constraints but enforces the Taylor state requirement of uniform J/B. Merging dynamics and final state structure computed using the 3D MHD code HYM are also compared.   

Experimental investigation of plasma jet detaching to form a spheromak

An axial plasma jet is formed from a planar electrode at the Caltech Spheromak Experiment. The jet ingests plasma from near the electrode and also becomes collimated. Finally, the jet detaches from the electrode to form a spheromak-like configuration. The dynamics of hydrogen plasma jets are investigated using a magnetic probe array, a high speed camera, and a newly built heterodyne HeNe density interferometer$^*$. Image intensity is found to directly correlate with the plasma density inferred by the interferometer. The observed density is also found to scale with the amount of gas available in the plenum leading to the vacuum chamber, thus confirming that wall recycling does not contribute substantially to the plasma density. Detailed investigation of the spheromak pre-formation stage is expected to give insights into the dependence of spheromak plasma density on bias flux, discharge voltage and amount of ionized gas available in the plenum. \newline $^*$D. Kumar, and P. M. Bellan, Rev. Sci. Instrum.(Accepted)   

Flow dynamics of spheromaks in SSX

We report several new experimental results related to flow dynamics from single dipole-trapped spheromaks and spheromak merging studies at SSX. Local spheromak flow is studied with two Mach probes ($r_1 \le \rho_i, r_2 \ge \rho_i$) calibrated by time-of-flight with a fast set of magnetic probes at the edge of the device. Both Mach probes feature six ion collectors housed in a boron nitride sheath. The larger Mach probe will ultimately be used in the MST reversed field pinch. Line averaged flow is measured by ion Doppler spectroscopy at the midplane. The SSX IDS instrument measures with $1~\mu s$ or better time resolution the width and Doppler shift of the $C_{III}$ impurity (H plasma) $229.7~nm$ line to determine the temperature and line- averaged flow velocity. We find axial flows up to $100~km/s$ during formation of the dipole trapped spheromak. Flow returns at the wall to form a large vortex. We also measure $T_i \ge 50~eV$ and $T_e \ge 20~eV$ during spheromak merging events after all plasma facing surfaces are cleaned with helium glow discharge conditioning. $T_e$ is measured with a 4-channel soft x-ray array. These studies are performed in the prolate $0.4~m$ diameter, $L=0.6~m$ length copper flux conserver in SSX. The spheromaks are also characterized by a suite of magnetic probe arrays for magnetic structure {\bf B}(r,t), and interferometry for $n_e$.   

Two-fluid simulations of counter-helicity spheromak merging and oblate FRC stability in MRX and SSX experiments

Results are presented of 2D and 3D simulations of counter-helicity spheromak merging in MRX and SSX experiments using Hall-MHD version of the HYM code. The observable changes in global profiles caused by the local Hall effects, are seen even in the collisional regime, when the reconnection rate is comparable to the MHD reconnection rate. Dependence of the reconnection rate on plasma resistivity is studied, and it is found to be similar to the scaling reported for the magnetic islands coalescence problem. These results are compared with MRX and SSX measurements. Three-dimensional MHD simulations have been performed in order to investigate stability properties of oblate FRCs. In was shown that strong equilibrium field shaping can stabilize the $n=1$ tilt mode in oblate FRCs, and improve stability of the $n>1$ MHD modes. The numerically-calculated structure of the perturbed magnetic field has been used to identify the most unstable modes in MRX experiments. It has been shown that the effects of external field shaping are much weaker for higher-n modes due to the more localized structure of these modes. Numerical simulations have also been performed to identify the effects of the central conductor and the residual small toroidal field on the stability properties of MRX-FRC plasmas.   

Studies of Equilibrium and Stability of Oblate FRCs in the Magnetic Reconnection Experiment

The equilibrium and stability of oblate FRCs have been studied in MRX using a comprehensive array of $>$200 magnetic pick-up coils. FRC plasmas are formed by the counter-helicity merging of two spheromaks; control of the plasma stability is provided by a flexible external field magnet set and (sometimes) passive conductors. The deadly external tilt can be mitigated by i) the introduction of a passive stabilizer (a conducting center column), or ii) the formation of extremely oblate FRCs. The radial shift mode is stabilized by the passive stabilizer, or saturates before the termination of the configuration without the center conductor. Even with passive stabilizers, ballooning-like co-interchange modes (with toroidal mode number n$>$=2) often terminate the plasma. Formation of extremely oblate plasmas leads to the minimum amplitude of co-interchange modes and the longest plasma lifetime. The improved linear and non-linear stability of highly oblate FRCs was verified with the HYM code. An ohmic solenoid system has been constructed for the study of FRC sustainment, aiming to provide up to 50mWb of magnetic flux at 50kA of solenoid current. A plasma biasing system has been constructed to drive controlled rotation, allowing an assessment of how rotation impacts the FRC stability.   

Improvements to Passively Switched CTIX Compact Toroid Accelerator

Recent changes in gas injection technique have enabled considerable improvements in plasma density, total mass, and energy conversion efficiency obtained in the CTIX compact-toroid (CT) experiment. A major remaining source of energy loss is magnetic energy stored in residual inductance of an external saturable inductor, used to delay application of CT acceleration voltage. Currently, over 50\% of accelerator capacitor energy is converted to inductive energy in this circuit, versus up to 25\% in plasma kinetic energy. Modifications to CTIX will reduce saturated circuit inductance to less than 40\% of its present value. Results of operation with reduced inductance will be presented, with a goal of increasing CT kinetic energy density, required for penetration of high-magnetic-field target plasmas.Accelerator-region gas puffing will be used to match plasma time of flight to relevant circuit time scales. Diagnostics will include interferometry, deflectometry, magnetic-field, and spectroscopic measurements. Plasma acceleration and mass accumulation will be compared with a one-dimensional plasma/gas/circuit model. Supported by U.S. DOE Grant DE-FG02-03ER54732.   

Preparing to compress a Field Reversed Configuration target for Magnetized Target Fusion

We summarize the our physics motivation for magnetized (MTF) target fusion and outline our engineering progress. A high pressure field reversed configuration (FRC) is shown that suits the MTF target and physics premises. Adiabatic MTF plasma compression should fall between magnetic and inertial fusion conditions. The small theta pinch FRC + Liner experiment (FRX-L) is designed to attain sufficient lifetime for MTF, at high pressure, with minimum pulsed power infrastructure. Small size begets large toroidal electric field for the formation FRC and initial shock heating followed by additional desirable ohmic heating prior to translation. Anomalously large resistivity is observed. FRX-L has demonstrated high target FRC plasma pressure (T$>$300 eV, n$_{e}>$ 5x10$^{22}$ m$^{-3})$ of 20-30 atmospheres. Design and implementation details are shown for a series of FRC translation and implosion on plasma experiments.   

Diagnosing the high density FRX-L Field Reversed Configuration plasma

The FRX-L plasma is a high pressure, high density, field reversed configuration (FRC), at n $\sim $1x10$^{16}$-1x10$^{17}$ cm$^{-3}$, and hundreds of eV electron temperature. In order to study formation, equilibrium, transport, flow, and confinement issues, we have a suite of diagnostics. Standard plasma diagnostics include B-dot probes, magnetic flux loops, single and multi-channel visible spectroscopy, optical light tomography arrays, up to 8 filtered visible fibers (546 nm or 486 nm) and an 8-chord side-on HeNe interferometer. Recent diagnostic additions include AXUV bolometers, VUV spectroscopy using a methly salicylate fluorescer converter and optical multichannel analyzer (OMA), eight simultaneous axial views of visible spectra with a 0.3 meter spectrometer and Princeton Instruments PI-Max camera, two-foil end-on surface barrier diode soft x-ray measurements, a hard x-ray/neutron plastic scintillator/ PMT, and indium activation foils to detect time-integrated absolute DD neutron emission. We also discuss plans for a soft x-ray framing camera, using end-on optical access and consisting of a pinhole/fluorescer geometry coupled to a high resolution DiCam camera.   

VUV Spectroscopy on the FRX-L Field Reversed Configuration Plasma

The FRX-L experiment at Los Alamos National Laboratory aims to demonstrate the formation and translation of a field-reversed configuration plasma (FRC) with parameters suitable for Magnetized Target Fusion: $n_e \approx 10^{17}$ $cm^{-3}$, $T_e+T_i \approx 300$ eV, and lifetimes $ \sim 10-20$ $\mu$s. Recently, a 0.3m axial viewing VUV spectrometer with an optical multichannel analyzer (OMA) and UV-visible fluorescer has been added to the FRX-L experiment. This system will be used for impurity content and ion (doppler) temperature measurements. Initial results from this system will be discussed.   

Modeling FRC Formation in Field Reversed Experiment -- Liner

The Field Reversed Experiment - Liner (FRX-L) is creating high pressure FRC-s as target plasmas for magnetized target fusion (MTF), in which magnetically confined plasma will be compressed by an imploding aluminum liner to achieve fusion conditions. Magnetic design is critical to ensure success for formation, translation, and implosion of the FRC. In this work, we used an eddy current code that computes the mutual inductances between all active magnetic coils with driven currents and passive magnetic shields (flux excluder plates) to calculate the self-consistent axi-symmetric magnetic fields in all three stages. The plasma in the formation stage was simulated with a conductive cylinder of the dimensions typical for FRX-L plasmas. The modeling resulted in the following conclusions: (1) resistive diffusion of the magnetic field into the plasma causes the reconnection of the field lines, ultimately leading to formation of a field reversed configuration; (2) the calculated profile of the axial (dominant) component of the magnetic field, $B_{z}(z)$, predicts gradients of the magnetic pressure, sufficient for translating the FRC-s out of the formation region, and (3) the magnetic shields successfully protect the slow guide coils from the fast varying magnetic fields created in the formation region, while maintaining a desired $B_{z}(z)$ profile. Supported by OFES and LANL/DOE contract DE-AC52-06NA25396.   

Irvine FRC Equilibria Measurements

We plan on launching lower hybrid waves into our axially-symmetric \textbf{F}ield \textbf{R}eversed \textbf{C}onfiguration. Lower hybrid wave propagation depends strongly on both the magnetic and density profiles. We therefore must have good maps of our magnetic field and densities as a function of radius and axial position. The field and density mapping is done using two 3-D magnetic probe arrays, two axial magnetic probe arrays, a 140 GHz interferometer, and a triple probe. Each 3-D array consists of 30 flux loops at 10 different radial positions. We have made magnetic field measurements at different axial positions, giving us all three field components as a function of radius and axial distance. Our two fixed axial arrays measure the axial field at two different radial positions. They provide a reference for comparisons between different shots when the radial array moves. Reversed fields of $\sim $100 Gauss have been observed. The 140 GHz interferometer and triple probe combination has given us line densities of high 10$^{14 }$cm$^{-2}$ with peak densities of 2x10$^{13}$ cm$^{-3}$.   

A Time-of-Flight Neutral Particle Detector for the Irvine FRC

A time-of-flight neutral particle detector\footnote{D. E. Voss and S. A. Cohen, Rev. Sci. Instrum. 53, 1696 (1982).} has been constructed to diagnose the ion contribution to the current in the Irvine FRC. Charge exchange neutrals are chopped by a slotted disk which then collide with a Channeltron electron multiplier. The 22cm diameter slotted disk has a rotation frequency of 30,000 RPM and a chopping frequency of 80kHz. This rotation frequency and a slot thickness of 152$\mu$m allow a snapshot of 0.8$\mu$s to be taken and spread out over a 1.5m streaming length. With these parameters, the time-dependent ion velocity distribution can be measured with 12.5$\mu$s time resolution.   

The Colorado FRC Experiment

A new experiment is under construction for the study of turbulence flow, stability and cross-field transport in a field-reversed configuration. The facility is a merged-spheromak device driven by magnetized coaxial plasma guns. Experimental emphasis is given to advanced diagnostic development, including high spatial resolution and high time resolution instruments for measurement of fluctuating quantities and bulk velocity in high $\beta$ plasmas. Details of the experimental facility status and planned studies will be presented.   

Diagnostic Systems for the Colorado FRC Experiment

A suite of diagnostics is under development for implementation on the Colorado FRC Experiment, a new field-reversed configuration presently under construction. Instruments at various stages of development include a multichord quadrature CO$_2$ interferometer, a multichannel Mach-probe array, a multifrequency reflectometry system, and a number of magnetic diagnostics. Each instrument in the diagnostic set is intended for measurement of fluctuating quanties, and all systems are frequency-limited only by the data acquisition rate ($\ge$10 MHz). Technical details and preliminary results will be presented.   

Application of magnetized coaxial plasma gun for external control of field-reversed configuration

Magnetized coaxial plasma gun (MCPG) has been utilized to generate spheromak plasma. In this work, we propose to employ a MCPG as tools for pre-ionization, fueling and biasing of field- reversed configuration (FRC) plasma. Start-up experiments with a MCPG pre-ionization have been performed and a FRC has been formed successfully. In the case with a MCPG, the initial plasma density can be controlled with wider range comparing to conventional z-ionization method. As another application of a MCPG, biasing to control radial electric field through a ``plasma electrode'' has been proposed. The plasma electrode can be a method to control the electric filed with less perturbation on FRC plasma. Control of the radial electric field has a potential to improve confinement property, excite the toroidal flow and change the relaxation process of FRC plasma.   

Large Scale Spheromak for Magnetic Shielding of Spacecraft

Exposure to the energetic particles associated with solar energetic particle events and galactic cosmic rays are known radiation hazards for human exploration. Material shielding would add substantial mass to the spacecraft and provide shielding over very limited areas. The concept that will be explored here is the prospect of providing the shielding by making use of ambient low density plasma that supports the large scale currents needed to provide sufficient magnetic flux to deflect the energetic particles. Such a closed magnetic configuration can be produced by force-free currents (i.e. a spheromak). These plasmas have been created in several laboratories at high magnetic field, but small scale (meter scale vs the low field, 100 meter scale envisioned here). Unlike the fusion application all that is needed is a very low energy density structure that can be maintained with minimal power. The low power is possible if the expected confinement scaling with increasing radius observed in most experiments is obtained. The lack of a material vacuum boundary in space should considerably simplify the maintenance of the configuration. We aim to address several critical issues with the spheromak plasma shroud. Questions to be addressed are (1) How does cosmic ray deflection scale with plasma parameters, (2) Can the sustainment mechanisms presently known be scaled for the durations associated with space flight, and (3) What is the best path for development and validation of the concept. *This work was funded under a grant from the NASA Institute for Advanced Concepts.   

Adiabatic compression of a Field Reversed Configuration (FRC)

The adiabatic compression of magnetized plasmas has come to the fore in recent times as an interesting hybrid of both inertial and magnetic fusion energy schemes, opening up the high density route to fusion energy [1]. Magnetized target fusion, or MTF, is possible with a range of different magnetic configurations [2], although here we consider the compression of a FRC. The literature relating to the efficient adiabatic compression of FRCs is reviewed. The key issues with the MTF schemes lie with obtaining highly efficient compression (considering various drivers and liners), and maximizing the period that the plasma remains compressed (dwell time). We present analytic modeling, initial MHD simulations and an outline for an experiment (including diagnostic plan) to explore the physics of compression on a small-scale ($<$1MJ bank energy).\newline [1] Siemon, et al Com. Plas. Phys. Control. Fus., 18, p (1999). \newline [2] D.D. Ryutov, R.E. Siemon. Com. on Mod. Phys, 2, p185 (2001).   

Density and Temperature Diagnostics of the Pulsed High Density (PHD) FRC Experiment

The High Flux Source (HFS) of the Pulsed High Density Experiment (PHDX) has been constructed, and field-reversed configuration (FRC) plasmas are being produced. To obtain the electron density and temperature of the FRC plasma we set up a $\lambda $=632.8 nm He-Ne laser interferometer system near the midplane of the HFS, and to estimate the ion density and temperature a 16 channel spectrometer has been installed for end-on viewing. For more detailed density and temperature analyses a soft x-ray measurement system is being developed on the end flange of the HFS; this system consists of 5 AXUV100 photodiodes with directly deposited filters which have approximately 0.1-0.3 $\mu $m thick thin films (Al, Zr/C, Sn/Ge, Cr/Al, and Ti/Pd) on each diode. The electron density and temperature are approximately determined by comparing the response of the detectors to computed responses using the emissivity from an atomic model of the plasma. We will present both computational and experimental results from the soft x-ray measurement system and the comparison of all density and temperature diagnostics of FRC plasmas.   

Current Results and Direction of the Pulsed High Density (PHD) FRC Experiment

The goal of the Pulsed High Density experiment (PHD) experiment is to reach break-even conditions through the magneto-kinetic compression of the Field Reversed Configuration (FRC). Continuing experimental work on PHD is focused on generating a FRC that is stable, has a long lifetime, and has sufficient flux and particle inventories to be accelerated and compressed to fusion conditions. Initial experiments with a 20 cm radius vacuum vessel produced FRCs with the required flux and particle inventories, but insufficient ion temperature to provide strong stabilization and long lifetimes. The source section has now been replaced with a 40 cm radius fused silica tube and magnet power supply similar to the Large S experiment's (LSX) formation chamber. Initial experiments will be aimed at forming keV ion temperatures at densities of 1x10$^{21}$ m$^{-3}$. Numerical calculations indicate that a doubling of both density and temperature will be achieved in the first stage of acceleration/compression. A design of this next phase of the experiment will also be presented along with numerical modeling of the acceleration/compression process.   

Overview of the Inductive Plasma Accelerator (IPA) FRC Merging/Compression Experiment

The Inductive Plasma Accelerator (IPA) is a plasmoid accelerator/interaction experiment designed to explore the acceleration, reconnection and plasma liner compression of high beta compact toroids. The initial goal of the IPA experiment is to merge two accelerated FRCs having a mass of 0.1-0.2 mg at velocities ranging from 150-250 km/s. The interaction chamber is being designed to compress the merged CTs with a theta compression coil, but eventually with a Z-theta driven plasma liner. After compression ion temperatures are predicted to exceed several kV at densities greater than10\^{}22 m\^{}-3. The design of the experimental device now under construction will be detailed. Preliminary results from the acceleration and merging experiments will be presented, as well as results from 2D numerical calculations of the plasma liner compression.   

Initial Results from the TCS Upgrade

The TCS facility has demonstrated the robust ability to form and sustain FRCs in steady-state using Rotating Magnetic Fields (RMF). In past experiments, the plasma density was largely set by the RMF parameters, but the temperature was severely limited by impurity radiation. Since the FRC is a diamagnetic entity, its peak pressure $p_{m}=n_{m}$\textit{kT}$_{t}$ determines its external magnetic field, $B_{e}$ = (2$\mu _{o}p_{m})^{1/2}$. Higher FRC currents, magnetic fields, and poloidal fluxes can thus be obtained, with the same RMF parameters, simply by reducing impurity influxes and raising the plasma temperature. TCS/upgrade has been built with a clean, bakable vacuum system and active means for the control of impurities to produce high temperature steady state FRCs. This will allow for the study of RMF current drive physics in a more fusion relevant regime, and in particular, will allow the issue of the impact of the RMF on the FRC's energy confinement to be addressed, an issue previously masked by the high radiation levels. Detailed description of the extensive upgrade of the TCS vacuum system and initial results from TCS/upgrade will be presented.   

Magnetized Cascaded Arc Source for Ionization and Fuelling in TCSU

An easily translatable, ultra-high vacuum compatible, magnetized cascaded arc source has been designed and constructed to inject a directional plasma beam that will be used as source plasma for RMF driven FRCs in the TCSU experiment. In addition to providing initial background plasma, the arc source can also be run during FRC sustainment to provide steady state plasma fuelling. The deuterium plasma produced by the arc source is tied to the external axial magnetic field lines, providing an ideal pre-ionization source for FRC formation. A 3 kJ, IGBT controlled power supply has also been built and is used for initial breakdown and arc sustainment. Plasma densities of 10$^{20}$ m$^{-3}$ and electron temperatures of 15 eV are anticipated from the device that is currently being tested. Results from these tests and performance during preliminary operation of the TCSU experiment will be reported.   

Magnetic reconnection of two FRCs driven by rotating magnetic field

In order to study the magnetic reconnection of RMF-driven FRCs, a new device is built at Prairie View Plasma Physics Lab. The main feature of this device is one magnetic coil being added in the middle plane of a long cylindrical chamber. The magnetic field of the additional coil is applied to sever the FRC driven by rotating magnetic field into two FRCs. When that magnetic field is removed, magnetic reconnection occurs as the two FRCs merge into one. The advantage of this magnetic reconnection experiment is the enhanced stability of RMF driven FRCs in comparison with that created by pinch. The device uses our existing 2$\times $400kW rf power system, and the reconnection experiment is conducted in the condition without a toroidal magnetic field.   

Gas Puffing Experiments in Rotamak

To study the particle/power balance, a piezoelectric-valve puffing system has been installed in our Rotamak. By adjusting the duration and amplitude of valve opening we studied a response of plasma parameters for cases when puffing was adding from 10{\%} to 100{\%} to the neutrals' inventory. For 3 ms puffing duration, the electron temperature and density could be changed by 50{\%} during 40-ms shot. In several initial shots with puffing, the electron density increases from (1.0-1.3)$\times $10$^{12}$ up to 2$\times $10$^{12}$ cm$^{-3}$ but temperature drops from 40-60 to 15-20 eV. At the following stages, density gradually decreases to original level; temperature remains low. After the puffing is turned off, plasma discharges again undergo several stages until repeatable shots are obtained. It is shown that the behavior of T$_{e}$ and n$_{e}$ is consistent with a global particle/power balance, although it is not sufficient to explain all observed features. An unusual experimental result is the strong response of plasma current to puffing. At the initial stages, plasma current grows from 4 to 6 kA during a shot, but at later (repeatable) stages, it experiences a sudden drop from 4 to 0.8 kA level during each shot.   

Heating and Current drive of FRC plasma formed by Rotating Magnetic Field

Additional heating and current drive of FRC plasma formed by rotating magnetic field (RMF) is studied in FIX (FRC Injection Experiment) device. The RMF is a novel formation and sustainment method of FRC plasma and quasi-steady FRC discharge in a quartz vacuum vessel was reported [1]. In FIX device, we have demonstrated that the RMF method is available for a metal chamber [2]. Since the RMF antennas are located inside the vessel, large power loss arises from induced current on the vessel wall, which prevents the plasma density and temperature to increase. Nevertheless, FRC formation process by the RMF method is quite stable and reproducible, and the combination of the RMF and other current drive/heating method will provide efficient formation method to achieve FRC plasma with high temperature and density. In addition to the existing NBI system, we are constructing a center solenoidal coil for Ohmic heating and current drive of FRC plasma formed by RMF. Experimental results of FRC discharge with RMF and Ohmic /NBI heating will be presented. [1] A.L. Hoffman, et al., Nucl. Fus. 45, 176 (2005); Phys, Plasmas 13, 012507 (2006). [2] K. Kitano, et al., Bulletin of the Am. Phys. Soc. 49, 189 (2004).   

New approach for the study of linear Vlasov stability of inhomogeneous systems

We have devised a new approach for the study of the linear Vlasov stability of inhomogeneous systems, alternative to the well-known integration over the unperturbed orbits. The perturbed distribution function is described as an infinite series of Hermite polynomials in velocity space, and the problem is reduced to an eigenvalue problem. A major advantage of the approach is that the direct physical meaning of the low-order coefficients is clear, and although the solutions are approximate (because of the truncation of the series) the accuracy of the solution appears to be merely a problem of computational power. Furthermore the method includes some free parameters, that can be properly set to reduce the computational effort (that is to reduce the number of polynoms needed in the series to reach good accuracy). This approach can be used for studying both growing or damping waves, as well as marginal stability. The method has been tested for an Harris sheet equilibrium and several instabilities (lower-hybrid drift, drift kink, tearing), showing good agreement with classical method [1]. Future work will involve the study of more realistic current equilibria proposed theoretically [2]. [1] E. Camporeale, G.L. Delzanno, G. Lapenta, W. Daughton, submitted. [2] E. Camporeale, G. Lapenta, J. Geophys. Res., Vol. 110, No. A7,A07206, 10.1029/2004JA0110779, 2005.   

Resonant transparency of materials with negative permittivity

It is shown that the transparency of opaque material with negative permittivity exhibits resonant behavior. The resonance occurs as a result of the excitation of the surface waves at slab boundaries. Dramatic field amplification of the incident evanescent fields at the resonance improves the resolution of the the sub-wavelength imaging system (superlens). A finite thickness plasma slab can be totally transparent to a p-polarized obliquely incident electromagnetic wave for certain values of the incidence angle and wave frequency corresponding to the excitation of the surface modes. At the resonance, two evanescent waves have a finite phase shift providing non-zero energy flux through the non-transparent region. In a warm plasma case, the excitation of the propagating longitudinal (electrostatic) modes becomes possible. The longitudinal excitations facilitate the total transparency of an opaque plasma slab creating additional resonances in the transmission function of the system.   

Modified Budden problem associated with energetic particles in fusion plasmas

The classic Budden problem is a double-conversion process, whereby a primary incoming wave is converted to a localized secondary wave which then converts to an outgoing (reflected) primary wave. Using ray phase-space methods [1], we investigate the modification of the Budden problem associated with the presence of a localized tertiary wave supported by an energetic-particle population in an inhomogeneous magnetized plasma.~The calculation of the reflection coefficient for this modified Budden problem is based on a simple one-dimensional model where the tertiary wave is parameterized by the energetic-particle density and its separation from the localized secondary wave. Note that, since an energetic-particle population can support waves of either positive or negative energy, interference effects are taken into account for each case by using~a modular-eikonal approach [2]. \newline ~ \newline [1] E.R. Tracy, A.N. Kaufman, and A.J. Brizard, Phys. Plasmas\underline { 10}, 2147 (2003). \newline ~ \newline [2] A.J. Brizard, J.J. Morehead, A.N. Kaufman, and E.R. Tracy, Phys. Plasmas\underline { 5}, 45 (1998).   

Review of Mode Conversion in Phase Space, and Applications to Ray Tracing Codes

We review the problem of two coupled harmonic oscillators with slowly varying frequencies as a simple model for mode conversion. For an interval of time when the two frequencies are nearly equal, energy can be transfered from one to the other in a process called ``resonance crossing''. This is a simple example of a very general phenomenon in physics: the breakdown of adiabaticity by resonant interactions, and it is called different names in different contexts: ``Landau-Zener crossings'', ``avoided crossings'', ``mode conversion'', etc. In this poster, we provide a brief pedagogic review of how to solve this simple time dependent problem using matched asymptotic expansions. We then describe in some detail how the same problem can be solved using phase space techniques, for example by computing the Wigner matrix of the two interacting oscillators. The advantage of phase space methods is that they can be extended to problems in higher dimensions and more complex geometries [1]. We then show some numerical results for mode conversion in a cold plasma model. \\ 1] See related poster by A. Jaun, E. R. Tracy, and A. N. Kaufman, this meeting.   

Propagating Whistler Spheromaks

Whistler modes with wave magnetic field exceeding the ambient field are excited in a large laboratory plasma [PRL 96, 095004 (2006)]. A loop antenna with axis along the dc field produces a field-reversed configuration (FRC). Upon reversal of the ac antenna current, the FRC splits into two oppositely propagating wave packets with field topologies resembling spheromaks. Since no helicity is injected, the two spheromaks have opposite helicities. Their propagation speed is lower than that of linear whistlers and decreases with amplitude. With increasing excitation, the axial size $w$ contracts while the amplitude $B$ grows, making it a form of a whistler soliton ($B w^2 \sim$ const). The duration of the wave burst can become much shorter than half a wave period. The collisions of two whistler solitons is inelastic: Two counter-propagating spheromaks of opposite helicity merge into a stationary FRC. When the antenna current reverses sign, the wave field adds to the ambient field and produces a single mirror-type field. It also excites two propagating waves (``whistler mirror'') with different nonlinear properties from whistler spheromaks. Interactions between these waves will be shown.   

Electron Heating and Light Emission from Whistler Spheromaks

Large amplitude whistler modes with wave magnetic field exceeding the ambient field have been produced in a laboratory plasma. In one configuration, the topology resembles that of spheromaks. In this case, strong electron acceleration and heating are observed. Energetic electrons ($>$10 eV) produce light emission in the ambient dark afterglow plasma ($T_{e0}\sim$ 2 eV). The light source travels along with the slow whistler spheromak ($v_\parallel \sim$ 20~cm/${\mu}$s $< v_{e, th}$). Space and time resolved probe and light emission measurements indicate that the heating mechanism is due to the acceleration of electrons in a magnetic null layer by an inductive electric field associated with the decay of the free magnetic energy. The electron distribution has both energetic tails and exhibits bulk heating. Due to heat conduction and radiation, little heat and light remains after the passage of the spheromak. In a whistler mirror, supported by electron Hall currents, there is negligible electron heating. Near the antenna exists an \textit{X}-type null line where also energetic electrons are produced.   

High frequency whistler excitations in spheromaks

Using a loop antenna with axial magnetic field opposing the ambient field ($B_{0}\sim$ 7~G) nonlinear whistler modes are generated which create magnetic null points in the total field. The time scale of such spheromak-like fields is imposed by the oscillating antenna current ($< 0.1$ MHz $\ll \omega_{ce}$). However, within the propagating whistler spheromaks, high frequency ($\sim 10$ MHz), small-amplitude magnetic oscillations are excited spontaneously above a certain threshold. Their space-time dependence and parameter scaling is measured in order to determine the mechanism for this magnetic instability.   

Autoresonant BGK Modes

Coherent electron phase-space structures are formed and controlled in plasmas by adiabatic nonlinear phase locking (autoresonance) with a chirped frequency driving wave. The process involves dragging a low density region in phase space into the bulk of the distribution via persistent Cherenkov-type resonance. This perturbation in electron density leads to creation of electrostatic self-field (BGK mode) in the plasma. A simplified kinetic theory of this excitation process is developed in cases of flattop [1] and Gaussian velocity distributions. The self-field dependence on the driving frequency and plasma parameters is discussed and theoretical predictions are compared with computer simulations. [1] L. Friedland, P. Khain, and A.G. Shagalov, Phys. Rev. Lett. \textbf {96}, 225001 (2006).   

The role of emitter-base capacitances in the behavior of nonlinear oscillations in a unijunction transistor (UJT) oscillator.

The plasma double-layers in a triple-plasma device provide the necessary nonlinearities that allow nonlinear oscillations to occur (1). In comparison, the nonlinear oscillations in a UJT circuit are due to the nonlinear behavior of the emitter-base pn junction (2). Besides the well known UJT conductivity modulation that produces nonlinear damping, there are additional nonlinear effects due to charge storage at the emitter base junction: the depletion or junction capacitance, and the diffusion capacitance (3). Recent analytic and numerical studies that include the effects of these two capacitances will be provided along with a comparison of processes that occur in plasma double layers and the UJT emitter base junction. 1) M. Wendt, I Axnas, S. Torven, Amplitude collapse of nonlinear double-layer oscillations, Phys. Rev. E, 57, 4638, 1998. 2) M. Koepke, D. Hartley, Experimental verification of periodic pulling in a nonlinear electronic oscillator, Phys. Rev. A, 44, 6877, 1991 3) J. Carroll, Physical models for semiconductor devices, Crane, Russak and Co., 1974   

Theory of nonperturbative frequency-sweeping modes

Recent numerical studies have investigated the response of 1-D plasma with source and sink which, without a perturbation, would in steady state produce a highly unstable two stream configuration despite an additionally imposed linear damping term. Starting from this state, the system undergoes strong relaxation. Ultimately the system reaches a state far from the initial two stream configuration that exhibits bursting events which frequency up-shift only, initially linearly in time. This is in contrast to the well-understood up-down frequency-sweeping events of perturbative modes. We interpret these results as a system near marginal stability as given by the Penrose criterion. The maximum frequency reached appears close to the maximum that is allowed from free energy considerations: this large sweeping allows for the maintenance of a nearly steady state near the marginally stable configuration. It is expected that there is a universality to this nonperturbative response. For example there is a striking similarity between the frequency-sweeping pattern observed here and frequency-sweeping patterns observed on MAST.   

Self-consistent model of nonlinear mirror mode structures

Mirror mode structures have been observed for decades in both laboratory and space plasmas. They are characterized by predominately magnetic compressional perturbations, {\it i.e.} $\delta B_{\|}$, a plasma pressure response 180$^{\circ}$ out of phase with the magnetic perturbation, high plasma pressure $(\beta=8\pi n T_{\perp}/B^2\sim 1-100)$, and a perpendicular temperature $T_{\perp}$ sufficiently higher than the parallel temperature $T_{\|}$ such that the linear instability criterion is satisfied. We consider a bi-Maxwellian homogeneous plasma with uniform external magnetic field and a population of electrons whose energy is well below that of the ions but which can reduce any parallel electric fields to negligible levels. We construct a self-consistent model of mirror mode structures by separating the plasma response into two components: i) a bulk population, which responds linearly and 180$^{\circ}$ out of phase with the compressional magnetic perturbation, and ii) a beam population, whose individual nonlinear particle dynamics are dictated by the adiabatic invariance of the magnetic moment and the mirror force. The system is closed by considering total pressure balance. Numerical simulations of the resulting model are presented and the saturation mechanism is examined in detail.   

Nonlinear Dynamics of Charged Particles Motion in Shear Alfv\'en Waves

The nonlinear dynamics of ions in the presence of shear Alfv\'en waves is a fundamental issue in a wide range of plasma enviroments. In this work, we present analytical as well as numerical studies of the simplest model; a single linearly polarized shear Alfv\'en wave in a uniform background magnetic field. Analytically, we have carried out, in the wave frame, Lie perturbation analysis to the second order in the wave amplitude parameter, $\epsilon \equiv B_W / B_0$. At the lowest order, the familiar cyclotron resoance, $\omega - k_z v_z + n \Omega = 0$, is recoverd; where n is a non-zero integer. In the second order, however, we not only recover the expected Landau resonance, $\omega = k_z v_z$, due to the finite mirror force; but, more interestingly, the nonlinear subharmonic cyclotron resonance at $\omega = k_z v_z + n \Omega / 2$. The predicted phase space structures agree well with those of numerically computed Poincare plots. Detailed dependances of nonlinear dynamics on the wave properties will be presented.   

Electron Velocity and Temperature Gradients Driven Electrostatic Flucuations in Nonuniform Magnetized Plasmas

We consider the excitation of electrostatic fluctuations in the presence of electron parallel velocity and electron temperature gradients in nonuniform magnetized plasmas. For this purpose, we use the guiding center electron drift approximation, mass conservation and electron momentum conservation equations to derive a linear dispersion relation. The latter is numerically analyzed to study the interplay between the parallel electron velocity and the temperature gradients. The transport resulting from the excitation of these modes is discussed.   

Short wavelength turbulence and coherent modes associated with electron temperature gradients

The effects of a background of short wavelength modes that are associated with the combined effects of a sheared magnetic field and an electron temperature gradient are shown to be relevant to the resolution of two theoretical issues: i) the excitation of drift-tearing modes and ii) the particle inflow process in high temperature regimes [1]. First, electrostatic modes whose potentials are even relative to a ${\mathbf k\cdot B}=0$ surface can form quasi-modes which have a parallel electron thermal gradient suggesting a state of enhanced ``thermal resistivity'' favoring the onset of drift-tearing modes. Electromagnetic modes, whose electrostatic potential has the opposite parity, involve fine-scale magnetic reconnection leading to microscopic magnetic islands. A superposition of individual modes at different ``radial'' positions form strings of propagating island chains that can occupy the reconnection layer of the drift-tearing mode and can provide a stochastic component to the electron orbits which also favors the onset of drift-tearing modes. Second, in the central region of the plasma column the short wavelength modes can produce a particle inflow, which in the outer region of the plasma column is associated [1] with the effects of finite electron collisional thermal conductivity. [1] B. Coppi and C. Spight, \textit{Phys. Rev. Lett.} \textbf{41}, 551 (1978).   

Experimental investigation of spatiotemporal phase coupling in drift wave turbulence.

Intermittent coherent structures are a common feature of edge magnetized plasmas. Such structures, large compared to typical turbulent scales, can significantly contribute to the high cross-field particles and energy transport in fusion experiments. Since a net energy transfer must be accompanied by a finite phase coherence between the involved structures, it can be investigated using a bicoherence analysis, which provides a direct measurement of nonlinear phase coupling. Although the physical process happens in $k$ and not in \textit{$\omega $} space, experimental diagnostics usually suffer from a very limited spatial resolution. Thus, frequency-based bicoherence techniques are generally performed along with attempts to connect $k$ with \textit{$\omega $} representations. In this contribution, we will present results of a direct $k$-bicoherence analysis, performed with measurements from a poloidal array of 64 probes, in the linear magnetized helicon device VINETA. A wavelet bicoherence is used in order to refine the description of spatiotemporal intermittent regimes. The $k$-bicoherence is shown to be much more accurate than the \textit{$\omega $}-bicoherence, revealing a bursty behaviour with a characteristic burst duration shorter than the characteristic period of the signals. It is shown that during these events small structures can be produced by phase coupling processes between large structures, and vice-versa.   

Investigating plasma-rotation methods for the Space-Plasma Physics Campaign at UCLA's BAPSF.

In D'Angelo \textit{et al}., JGR \textbf{79}, 4747 (1974), rigid-body ExB plasma flow was inferred from parabolic floating-potential profiles produced by a spiral ionizing surface. Here, taking a different approach, we report effects on barium-ion azimuthal-flow profiles using either a non-emissive or emissive spiral end-electrode in the WVU Q-machine. Neither electrode produced a radially-parabolic space-potential profile. The emissive spiral, however, generated controllable, radially-parabolic structure in the floating potential, consistent with a second population of electrons having a radially-parabolic parallel-energy profile. Laser-induced-fluorescence measurements of spatially resolved, azimuthal-velocity distribution functions show that, for a given flow profile, the diamagnetic drift of hot ($>>$0.2eV) ions overwhelms the ExB-drift contribution. Our experiments constitute a first attempt at producing controllable, rigid-body, ExB plasma flow for future experiments on the LArge-Plasma-Device (LAPD), as part of the Space-Plasma Physics Campaign (at UCLA's BAPSF).   

Laboratory measurements of the electron distribution function via whistler wave absorption

Measurements of the electron distribution function parallel to a background magnetic field have been made on the Large Plasma Device (LAPD) at UCLA using wave absorption near the electron cyclotron frequency. Whistler waves are launched and received by a pair of dipole antennas immersed in the plasma at two positions along the background magnetic field. The wave frequency is swept from somewhat below up to $f_{ce}$ (the whistler wave resonance frequency). As the frequency is swept, the wave will be resonantly absorbed by those parts of electron phase space density which are Doppler shifted into resonance according to $\omega-k_{\parallel}v_{\parallel}=n\Omega_{ce}$ . Since the antenna-plasma coupling efficiency can be calculated, a measurement of the wave absorption versus wave frequency can be used to determine the parallel electron distribution function. A thorough discussion of background theory will be given, followed by a presentation of results from experiments performed with B=2300g, n$\sim$6-10x10$^{11}$ cm$^{-3}$, and T$_e$$\sim$1-10 eV. Future use of this technique to measure ``sloshing" in the electron distribution function due to electron interactions with inertial Alfv\`{e}n waves will also be discussed.   

Studies of large amplitude Alfv\'{e}n waves and wave-wave interactions in LAPD

Electromagnetic turbulence is thought to play an important role in plasmas in astrophysical settings (e.g. the interstellar medium, accretion disks) and in the laboratory (e.g. transport in magnetic fusion devices). From a weak turbulence point of view, nonlinear interactions between shear Alfv\'{e}n waves are fundamental to the turbulent energy cascade in magnetic turbulence. An overview of experiments on large amplitude shear Alfv\'{e}n waves in the Large Plasma Device (LAPD) will be presented. Large amplitude Alfv\'{e}n waves ($\delta B/B \sim 1$\%) are generated either using a resonant cavity or loop antennas. Properties of Alfv'{e}n waves generated by these sources will be discussed, along with evidence of heating, background density modification and electron acceleration by the waves. An overview of experiments on wave-wave interactions will be given along with a discussion of future directions.   

Nonlinear Alfv\'{e}n wave interactions in the Large Plasma Device

The nonlinear dynamics of large amplitude Alfv\'{e}n waves are believed to play a major role in the evolution of the macroscopic properties of numerous laboratory plasmas and astrophysical systems. However, despite their importance the nonlinear dynamics of these fluctuations remains a point of great controversy with few prior experimental measurements. Nonlinear interactions between Alfv\'{e}n waves are being studied \footnote[2]{T.A. Carter, B. Brugman, P. Pribyl and W. Lybarger, Phys. Rev. Lett. 96, 155001 (2006)} in the Large Plasma Device Upgrade (LAPD) at UCLA, using large amplitude, $\delta B / B_{0} \sim 1 \%$, waves generated by LAPD's Alfv\'{e}n wave MASER or by antennas. In these experiments the interaction of two co-propagating large amplitude shear Alfv\'{e}n waves is extensively studied. The nonlinear generation of density fluctuations at the beat frequency along with the formation of numerous discrete Alfv\'{e}nic sidebands has been observed using both wave launching mechanisms over a broad range of plasma parameters and launch wave frequencies. Detailed measurements of these interactions and comparisons with a nonlinear Braginskii fluid calculation will be presented. Preliminary results from counter-propagating Alfv\'{e}n wave interaction experiments will also be discussed.   

Electron Heating and Acceleration from High Amplitude Driven Alfv\'en Waves in the LAPD

High amplitude ($\delta B/B \sim 1 \%$) shear Alfv\'en waves are generated in the Large Plasma Device Upgrade (LAPD) at UCLA, and elevated electron temperatures and high energy electrons are observed using triple probes and Langmuir current traces. The Poynting flux of the observed waves is calculated, and wave power is compared to estimates of power input required to cause the observed heating. Theoretical calculations of power transfer from wave to plasma due to Landau damping and collisional heating are also presented and compared to experimental measurements. Heating by antenna near field effects is also being explored. The density and potential structures of these waves are explored using interferometer and triple probe measurements. Applications to Auroral generation and plasma heating are discussed.   

Drift-Alfv\'{e}n Waves Excited by Internal Density Gradients in the Large Plasma Device

The auroral ionosphere is filled with field-aligned density enhancements and depletions. In this experiment a density enhancement is produced with a small BaO-coated cathode ($d \sim 10$ cm). It generates an electron current in the core of the Large Plasma Device (LAPD) at UCLA ($n \sim 2 \times 10^{12}$ cm${}^{-3}$, $0.5$ kG${} \le B \le 2.0$ kG, $d \sim 60$ cm, and $L \sim 18$ m). The background plasma is formed by a pulsed DC discharge from a large ($d \sim 70$ cm) emissive cathode. The small cathode is located 10 m downstream from and faces the background plasma source. It is biased relative to a local molybdenum mesh anode and can be pulsed with a capacitor bank or modulated with an AC signal. The density gradients excite coherent drift waves that couple to Alfv\'{e}n waves. Plasma flows are measured with Mach probes and radial electron temperature profiles are determined with swept Langmuir probes. Correlation measurements from magnetic and Langmuir probes are used extensively to characterize these drift-Alfv\'{e}n waves.   

Ion distribution function perturbations due to propagating Alfven waves.

A number of mechanisms for ion heating in the fast solar wind have been proposed. For example, the ions could be directly heated by ion-cyclotron damping of Alfven waves or counter-propagating, low-frequency, Alfven waves could generate a turbulent cascade that heats ions by exciting higher frequency waves that then damp on the ions. In this preliminary study, we report measurements of shear Alfven wave propagation and damping at wave frequencies near the ion cyclotron frequency. The low amplitude waves are excited by a steady state loop antenna immersed in high-density, argon and helium, helicon source plasmas. The propagating waves were detected with an absolutely calibrated magnetic pick up coil located 30 cm downstream from the launching antenna. The experiments were conducted in the West Virginia University HELIX (Hot hELIcon eXperiment) device. In argon plasma, perturbations of the ion velocity space distribution due to the Alfven wave are measured with laser induced fluorescence and compared to theoretical predictions.   

Alfv\'{e}n wave measurements in HelCat

Alfv\'{e}n waves, though ubiquitous in space plasmas, are difficult to study in the lab because of their typically long wavelengths. In order to make detailed measurements of their propagation characteristics and mode structure, the HelCat (\underline {Hel}icon-\underline {Cat}hode) device uses a high-density helicon source to generate the background plasma. This reduces the Alfv\'{e}n wavelength to tractable values in the four meter device. In contrast to previous work on ALESPI with steady-state discharges, we are using pulsed discharges to allow the use of smaller, less robust magnetic probes. Nonetheless, the typically one second quiescent discharge insures that we can follow the evolution of the Alfv\'{e}n waves in the bounded plasma column, from initial transients through the boundary condition dependent steady state mode structure.   

Mirror-induced Alfv\'{e}n Eigenmodes (MAE) in Periodic Magnetic Mirror Geometry

Waves in a periodic medium (optical Floquet-Bloch waves in dielectric gratings, electron wavefunctions in a 1D solid-state lattice, etc.) have propagation gaps in frequency. The famous Toroidicity-induced Alfv\'{e}n Eigenmodes (TAE) are also caused by toroidal and poloidal periodicities. As part of the fast-ion campaign in the LArge Plasma Device (LAPD), the magnetic field profile was modulated spatially into a mirror array (4 to 5 mirror throats separated by $\sim$ 4 m) to study Mirror-induced Alfv\'{e}n Eigenmodes (MAE) and the associated frequency gap. In a typical Helium plasma in LAPD, modulated sine waves and impulsive bursts drive Shear Alfv\'{e}n Waves (SAW) ($\lambda$ $_{//}$ $\sim$ 1 m, f $\sim$ 300 kHz, $\delta$ B/B $\sim$ 0.1\%) through antennae including a field-aligned copper cylinder (disk) and a picture-frame loop. The observed frequency spectra for a variety of mirror configurations and boundary conditions are compared with the predictions of the MHD model.   

Kelvin-Hemholtz/Drift Wave Coupling to Kinetic Shear Alfven Waves

Two-component fluid models are proposed to study the coupling of $\mathbf E\times\mathbf B$ shear flow driven turbulence with the Alfv\'en waves in the Large Plasma Device (LaPD). Shear Alfv\'en waves can be easily excited and measured in the LaPD as reported by Vincena {\it et.~al.} \newblock{\em Phys. Plasmas}, \textbf{8}(9), 3884, 2000. Here we present new $\delta\mathbf B$ measurement that show low frequency Alfv\'enic-like magnetic fluctuation driven by a strong localized shear flow layer created by a localized radial electric field. The electrostatic Kelvin-Helmholtz features have been extensively analyzed with computer simulations and the vorticity probe in Perez {\it et.~al.} \newblock {\em Phys. Plasmas}, \textbf{13}(055701), 2006, and Horton {\it et.~al.} \newblock {\em Phys. Plasmas}, \textbf{12}(022303), 2005. The simulations are extended to include the kinetic Alfv\'en wave (KAW) and intertial Aflv\'en wave physics. Comparisons between the electromagnetic $\mathbf E_\perp$ and the simulations are presented in some detail.   

Simulations of a Relativistic Electron Beam Penetrating an Overdense Plasma

Previous\footnote{A. G. Sgro and T. J. T. Kwan, Phys. Plasmas 10, 849 (2003)} work by means of 2D simulations has shown that over long time scales an electron beam encountering an overdense background plasma ejects the background electrons from the region where the beam is propagating, leaving the background ions to neutralize the beam charge, thus stabilizing the beam. Subsequently, long timescale simulations with coarse spatial resolution were presented\footnote{A. G. Sgro, Bull. Am. Phys. Soc. 49 (11), 96 (2004).} which seemed to show that the 2D behavior carried over to 3D, although a firm conclusion was not possible because of the coarse resolution. The purpose present paper is to present simulations of the interaction between the beam and the overdense plasma in 3D with a finer spatial resolution than has been presented previously. These simulations reinforce the conclusion that the beam can propagate stabily for long times. Three dimensional perturbations do not destabilize the beam. The beam essentially digs a hole in the background plasma through which it can propagate.   

Computationally efficient description of relativistic electron beam transport in dense plasma

A reduced model of the Weibel instability and electron beam transport in dense plasma is developed. Beam electrons are modeled by macro-particles and the background plasma is represented by electron fluid. Conservation of generalized vorticity and quasineutrality of the plasma-beam system are used to simplify the governing equations. Our approach is motivated by the conditions of the FI scenario, where the beam density is likely to be much smaller than the plasma density and the beam energy is likely to be very high. For this case the growth rate of the Weibel instability is small, making the modeling of it by conventional PICs exceedingly time consuming. The present approach does not require resolving the plasma period and only resolves a plasma collisionless skin depth and is suitable for modeling a long-time behavior of beam-plasma interaction. An efficient code based on this reduced description is developed and benchmarked against the LSP PIC code. The dynamics of low and high current electron beams in dense plasma is simulated. Special emphasis is on peculiarities of its non-linear stages, such as filament formation and merger, saturation and post-saturation field and energy oscillations. *Supported by DOE Fusion Science through grant DE-FG02-05ER54840.   

High-density relativistic electron beam propagation in gas

The ionization front induced by a relativistic high-density electron beam in gas was studied in 1D approximation. We extended the approach of [1] to the relativistic beam energies and calculated the ionization front velocity for a wide range of beam energies and gas densities. The asymptotic expressions for the ionization front velocity were found in the limits of small and large gas density. The estimated amplitude of the front velocity is in a good agreement with the experimental data [2] where it was shown that the ionization front velocity is much smaller than the beam electron velocity. We also present the results from the ionization front computer simulation using a 1D PIC code with field ionization. [1] S. I. Krasheninnikov, B. K. Frolov, Phys. Plasmas \textbf{13} 033101 (2006) [2] D. Batani, S. D. Baton, M. Manclossi, \textit{et al}, Phys. Rev. Lett. \textbf{94, }055004 (2005) This work was supported by DOE/NNSA-UNR under grant DE-FC52-01NV14050.   

High efficiency electron injection for plasma accelerators using higher-order laser modes

Using higher-order transverse laser modes for plasma wakefield excitation, and, in particular, using a ring profile with maximum intensity off-axis, results in shifting the focusing and defocusing phase regions of the plasma wave in a wakefield accelerator.\footnote{P. Michel et al., submitted (2006)} This results in improved performance of electron injection schemes. It is shown that using higher-order modes for wakefield excitation results in a significant decrease in the trapping threshold required for optical injection of electrons and an increase in the maximum energy gain of the trapped electrons. This scheme could also be of interest for the generation of ring electron beams or for beam conditioning purposes.   

Colliding pulse injection experiments in non-collinear geometry for controlled laser plasma wakefield acceleration of electrons

A method for controlled injection of electrons into a plasma wakefield relying on colliding laser pulses [1] has been proposed a decade ago to produce high quality relativistic electron beams with energy spread below 1{\%} and normalized emittances $<$ 1 micron from a laser wakefield accelerator (LWFA). The original idea uses three pulses in which one pulse excites the plasma wake and a trailing laser pulse collides with a counterpropagating one to form a beat pattern that boosts background electrons to catch the plasma wave. Another, two-beam off-axis injection method [2] with crossing angles varying from 180 to 90 degrees avoids having optical elements on the path of the electron beam and has been studied at the LOASIS facility of LBNL as a viable method for laser triggered injection. It allows low dark current operation with controllable final beam energy and low energy spread. Here, we report on progress of electron optical injection via the two-beam non-collinear colliding pulse scheme using multi-terawatt Ti:Sapphire laser beams (45 fs, 100s of mJ) focused onto a Hydrogen gas plume. Experimental results indicate that electron beam properties are affected by the second beam. *This work is supported by DoE under contract DE-AC02-05CH11231. \newline [1] E. Esarey, et al, Phys. Rev. Lett 79, 2682 (1997) [2] G. Fubiani, Phys. Rev. E 70, 016402 (2004)   

Cyclotron radiation emission from electron beams having a horseshoe velocity distribution

When an electron beam is subject to significant magnetic compression, conservation of the magnetic moment results in the formation of a horseshoe shaped velocity distribution. Such a distribution in the terrestrial auroral zone may responsible for generating the Auroral Kilometric Radiation (AKR) -- an intense RF emission sourced at high altitudes in the Earth's magnetosphere. We present results from an experimental and numerical investigation of radiation emission from an electron beam subject to significant magnetic compression. Results from both simulations and a laboratory experiment show radiation emission close to the electron cyclotron frequency. Electron transport measurements also indicate the formation of a horseshoe distribution and integration of the experimentally measured antenna patterns provide an estimate of 2{\%} for the RF conversion efficiency. This is comparable with estimates of the AKR generation efficiency.   

Electron Beam Optimization for a High-Brightness Gamma-Ray Source

Compton-Scattering based systems offer a path to high-brightness high-energy ($>$ 1 MeV) x-ray \& gamma-ray sources due to their favorable scaling with electron energy. LLNL is currently engaged in an effort to build such a device, dubbed the ``Thomson-Radiated Extreme X-Ray'' (T-REX) source. Presented here is an overview of the system design, which includes both a UV-laser-driven electron photoinjector and an intense scattering laser. Also shown are the results of detailed electron beam and gamma-ray generation modeling designed to optimize the brightness and flux of the gamma-ray beam, including UV drive laser profile effects, charge v. emittance tradeoffs, thermal emittance effects, and contributions of focusing geometry.   

Rotational Mismatches and Emittance Growth in Intense Beams.

Particle Accelerators with intense beams have many applications for probing the structure of matter at a multitude of scales. Using a scaled low-energy electron beam, UMER (The University of Maryland Electron Ring) cleverly accesses the intense, high brightness, regime of beam operation in accelerators, at a much lower cost than larger and more energetic machines. This is a numerical study of the effects of a rotation of the UMER beam at injection. A closely related mismatch is the presence of a skew quadrupole in the transport channel. In both cases, the mismatch is a source of free energy and thus can lead to beam instabilities. The evolution and dissipation of such instabilities causes emittance growth that degrades the beam quality. In our simulations, we used the WARP computer code to simulate the UMER beam and we have indeed seen a substantial emittance growth for both cases of mismatch.   

Electron-beam dynamics in a cold plasma

There is unexplained plasma behavior, such as particle acceleration and heating, in space plasmas enclosing the earth, whereas linear and nonlinear phenomena have been observed. Thus it is necessary to simulate such plasmas in laboratory experiments. Electron two-stream instabilities, which are easily observed in laboratory and space plasmas, cause nonlinear phenomena because excited waves grow up to large amplitudes. It is very important to investigate nonlinear interaction between waves and particles, which may be related to particle acceleration. In our study, phase-space holes surrounded by electrons self-trapped by electron-beam waves were experimentally observed in a cold plasma. The holes evolved to large scale in electron response time, meanwhile their lifetimes were extremely short. In the case of a denser electron beam, the beam branches expanding to higher velocity were also observed next to the holes, which meant that detrapped electrons were accelerated. We discussed the magnitude of the wave potential and the local source of the acceleration energy. \newline \newline [1] T. Takeda and K. Yamagiwa, Phys. lett. A, \textbf{339}, 118-122 (2005).   

Characterization of the ``Dose Effect'' in secondary electron emission

Secondary electron emission(SEE) results from bombarding materials with electrons, atoms, or ions. When studying SEE, one is interested in determining the \textbf{\textit{true}} secondary electron yield (as opposed to scattered secondary electrons), defined as the number of secondary electrons produced per incident primary electron. It is well known that the amount of secondary emission depends on factors such as bulk and surface properties of materials, energy of incident particles, and their angle of incidence. However, it has been observed in experiments presented here that secondary electron yield also \textbf{\textit{largely}} varies with the amount (dosage) of incident primary electrons. There has been little effort in the literature to quantify this effect. Experimental results presented here aim to fill this gap. It is also proposed that discrepancies observed in literature -- such as large variations in secondary electron yield and temporal dependence -- could arise due to usage of different primary doses. Experiments are conducted in the low-energy range (5eV to 2000eV) and in the DC regime. Cu, TiN, and plasma sprayed boron carbide samples were used. Characterization of surface modifications arising from different primary doses and pulsed measurements are planned for the future.   

Modeling and Experiments on Injection into University of Maryland Electron Ring (UMER)*

The University of Maryland Electron Ring (UMER) is built as a low-cost testbed for intense beam physics for benefit of larger ion accelerators. The beam intensity is designed to be variable, spanning the entire range from low current operation to highly space-charge-dominated transport. The ring has been closed and multi-turn commissioning has begun. One of the biggest challenges of multi-turn operation of UMER is correctly operating the Y-shaped injection/recirculation section. It is a challenge because the system requires several quadrupoles and dipoles in a very stringent space, resulting in mechanical, electrical, and beam control complexities. Also, the earth's magnetic field and the image charge effects have to be investigated because they are strong enough to impact the beam centroid motion. This paper presents both simulation and experimental study of the beam centroid motion in the injection region to address above issues.   

Electron Beam Transport in Gas and Plasma-filled Cells for Radiography

In flash x-ray radiography, the paraxial diode utilizes a gas-filled transport cell to focus an electron beam into a small spot. In simulations, it has been shown that the primary limitation to achieving a small spot is due to time-dependent net currents in the transport cell which cause the beam's focal position to shift axially. This leads to a larger time-integrated spot than is desired. Further simulations suggest that replacing the gas with a preionized plasma significantly slows down the net current growth in the transport cell, thereby achieving a smaller spot. Recent experiments have been performed on the RITS-3 accelerator (4.5 MV, 70 ns). The basic physics principle of stabilizing the beam spot by incorporating a preionized plasma in the transport cell was demonstrated.   

Experimental observations of Longitudinal Space-Charge Waves in a Long Solenoid Experiment System

In the space-charge dominated beams, the nonlinear space-charge forces will introduce many collective effects, which may limit the maximum current or beam quality. Some of these collective behaviors are not well understood. One of the effects is the physics of longitudinal space-charge waves, which can be generated by density perturbations or energy perturbations caused by many factors, such as the discontinuity of the beam transport modules, fluctuations in the bunch, or the mismatch of the focusing channels. Studies of the dynamics of longitudinal space-charge waves in space-charge dominated beams propagating through a transport channel with a long solenoid are performed at the University of Maryland. In this paper, we report some experimental results on the energy modulations converted from density modulations. By changing the working conditions of the electron gun, pure initial density modulations are generated. Energy perturbation waveforms are measured with a high-resolution energy analyzer. The experimental results are compared with both the linear theory and the simulation results. Good agreements are achieved for the relationship between the energy and current perturbation strengths.   

Energy control of monoenergetic electron beams in laser-driven plasma acceleration

Monoenergetic electron beams with the energy of up to 25 MeV have been obtained in laser-driven plasma acceleration. A monoenergetic electron beam of 7 MeV was generated from a plasma with the electron density of $1.5 \times 10^{20}~{\rm cm}^{-3}$ produced by a 2 TW, 50 fs laser pulse.[1] On the other hand, a monoenergetic electron beam of 25 MeV was generated from a plasma with the electron density of $4 \times 10^{19}~{\rm cm}^ {-3}$ produced by a 3-5 TW, 50 fs laser pulse using the focusing optics with the longer focal length.[2] The monoenergetic beams were obtained only in the narrow electron density range according to the irradiation conditions. The energy of the monoenergetic beams can be controlled by the plasma density, the laser power, and the laser focusing condition.[2] Our Ti:sapphire laser system is upgraded to obtain more than 10 TW. Experiments to obtain a monoenergetic electron beam with higher energy ($> 50~{\rm MeV}$) are carried out. A part of this work is supported by the Budget for Nuclear Research of the MEXT. \newline \newline [1] E. Miura et al., Appl. Phys. Lett. \underline{86} 251501(2005). \newline [2] S. Masuda et al., submitted to Phys. Plasma.   

A Study of Laser and Electron Beam Interactions for Plasma Wave Diagnostic Experiments

A low energy electron beam (5 to 50 keV), a CO2 laser and a YAG laser are focused through a common interaction point, and the scattering of the electrons and photons is studied using various diagnostic devices. Experiments have been performed to study the effects of varying the temporal sequencing, intensity, spatial alignment and angular separation of the three pulsed beams. Information on the electron beam is gained by studying the scattering of the laser and vice versa. A numerical model was developed in order to help design and interpret the experiment. Experiments to follow will involve adding a plasma at the common interaction point and exciting plasma waves, and using the lasers and electron beam as plasma wave diagnostics.   

Laser guiding in a 33mm, 1GeV capillary discharge laser plasma accelerator

Recently, 1 GeV monoenergetic electron beams were generated in a capillary discharge laser plasma wakefield accelerator (LWFA), by using a capillary with a 312 micron diameter and 33 mm length. We will present analysis of the guiding properties of the capillary discharge waveguide, both at low and high ($3\ 10^{18} W/cm^2$) intensities. Measurements to diagnose the guiding structure will be discussed, including energy transmission, mode profile and transmitted laser spectrum.   

Plasma channels for electron accelerators

The pre-formation of full ionized plasma waveguides in low Z gases may increase the energy gain and improve the electron bunch properties of plasma accelerators by extending the length of the high intensity interaction. High-voltage capacitive discharges can be used to produce and heat a plasma line. The discharges can be made through a dielectric capillary tube in order produce a straight plasma waveguide. On the other hand, the initial plasma line produced by the discharge can be on an open geometry (free space between electrodes) if we use a fast rise-time high-voltage pulse and use a laser pulse with enough intensity to trigger the discharge by optical-field-ionization. In this work we present the first results of a new scheme to produce plasma wave-guides for electron accelerators. It uses high-voltage discharge through a sequence of thin plates allowing the radial expansion of the plasma. This scheme can be used in a broad range of pressures and introduces a reduced amount of gas in the laser focusing region.   

Monoenergetic electron acceleration in plasmas by an ultrashort petawatt laser pulse

Focusing an ultra-short (tens of fs) petawatt laser pulse in a wide focal spot ($\sim100$~$\mu$m) in rarefied plasma ($\sim10^ {17}$~cm$^{-3}$) enables accelerating electrons up to 1 GeV by a laser wake-field without a channel. An ultrashort laser pulse with an overcritical power for relativistic self- focusing propagates in plasmas as in vacuum. The nonlinear quasi-plane plasma wake effectively traps and accelerates injected electrons with a wide range of initial energies. The accelerating and focusing phases of the nonlinear three- dimensional axi-symmetric laser wake can almost entirely overlap starting from a certain distance behind the laser pulse in homogeneous plasma. Such a field structure results from the curvature of phase fronts due to the transversely inhomogeneous relativistic plasma frequency shift. Consequently, the number of trapped low-energy electrons can be much greater than that predicted by the linear wake theory. This effect is favorable for quasi-monoenergetic acceleration of several hundreds of pC to about 1 GeV per electron. External electron injection into the plasma wake (RF-based, colliding laser pulses etc.) is discussed.   

Electron acceleration in long scale laser - plasma interactions

Broad energy electron bunches are produced through the Self-Modulated Laser Wakefield Acceleration scheme at the 30J, 300 fsec laser, LULI, France, with long scale underdense plasmas, created in a He filled gas cell and in He gas jet nozzles of various lengths. With c$\cdot \tau _{laser}>>\lambda _{plasma}$, electrons reached E$_{max }\sim $ 200MeV. By carefully controlling the dynamics of the interaction and by simultaneous observations of the electron energy spectra and the forward emitted optical spectrum, we found that a plasma density threshold ($\sim $5$\cdot $10$^{18 }$cm$^{-3})$ exists for quasi-monoenergetic ($\sim $30MeV) features to appear. The overall plasma channel size was inferred from the collected Thomson scattered light. 2D PIC simulations indicate that the main long laser pulse breaks up into small pulselets that eventually get compressed and tightly focused inside the first few plasma periods, leading to a bubble like acceleration of electron bunches.   

Electron trapping in a plasma wake field accelerator by an ultra relativistic electron beam in the presence of ionization

An ultra relativistic (28.5 GeV) ultra short ($\sim $30 fs) electron beam produced at the Stanford linear accelerator center creates a plasma wave with very large accelerating gradients ($>$30 GeV/m). Although~ 1D theories of wave breaking for highly relativistic waves predict that the wave breaking and trapping would require fields on the order of TV/m, we observed self trapped plasma electrons. We also observed a clear onset for~ the particle trapping~ which was done by controlling the plasma wave amplitude by controlling the drive bunch length. We attribute this lower trapping threshold to effect of self ionizing plasma which causes electrons to be born in a more favorable place inside the wake for trapping. The trapping occurs in the boundary regions of a lithium column confined by a helium gas. the Lithium electrons support the wake however, the higher ionization potential Helium electrons are born inside the wake in the transition region the measured trapping threshold of 32 GV/m is in excellent agreement with predictions of an analytical model and detailed PIC code simulations of the experiment. Other optical diagnostics supported by PIC simulations showed that the trapped electrons reach multi GeV energies, are produced in multiple buckets and has ultra short features ($\sim $2fs) emitting visible coherent light.   

Terahertz Radiation As A Bunch Diagnostic For Laser-Wakefield-Accelerated Electron Bunches

Experimental results are reported on the single shot temporal and spectral characterization of coherent terahertz (THz) radiation. The radiation is emitted by relativistic electron bunches, which in turn are produced by a laser-driven plasma- based accelerator. As the femtosecond electron bunches exit the plasma-vacuum interface, coherent transition radiation (at THz frequencies) is emitted. Measuring the properties of this radiation allows characterization of the electron bunches. Theoretical work on the emission mechanism is also presented, including a model that calculates the THz waveform from a given bunch profile. It is found that the spectrum of the THz pulse is coherent up to the 200 $\mu$m thick ZnTe detection limit of 4 THz, which corresponds to the production of sub-50 fs (root-mean-square) electron bunch structure. The measurements demonstrate both the shot-to-shot stability of bunch parameters that are critical to THz emission (such as total charge and bunch length), as well as femtosecond synchronization between bunch, THz pulse, and laser beam.   

Plasma afterburners and related issues

In plasma wakefield acceleration experiments, the drive beam moves at the speed of light in the plasma and excites an accelerating plasma wakefield behind the driver. Therefore it is possible to use a trailing electron beam to extract energy from the plasma wave wake. Such a design, called the plasma afterburner, has been proposed to double the energy of the incoming beam train for a future linear collider. We investigate the nonlinear beam-plasma interaction in such scenario using a 3D computer modeling code, QuickPIC. We will report on the simulation results of a 1 TeV plasma afterburner design. Several issues such as efficient beam-loading and the stability of the beam in the plasma are also analyzed. The electron hosing instability in the blow-out regime of plasma wakefield acceleration is also investigated using linear perturbation theory upon the electron blow-out trajectory. The growth of the hosing instability is found to be affected by the plasma self-fields, the relativistic mass, the axial motion of plasma electrons and the position-dependent ion channel radius respectively. Therefore the hosing growth has dependence on the beam current, which is not found in the fluid theory. PIC simulations agree very well with this new theory.   

Effects of Light Ion Contaminants on the Laser Break-Out Afterburner

A novel laser ion acceleration mechanism was reported by Yin et al. [Laser and Particle Beams \textbf{24}, 291; see also invited talk by L. Yin this meeting] that allows, through careful target and laser conditioning, greatly enhanced peak beam ion energy ($>2$~GeV energy carbon ions with an $I=10^{21}$~W/cm$^2$ laser) and conversion efficiency from laser to fast ions. After a brief phase of target normal sheath acceleration (TNSA), the break-out afterburner (BOA) undergoes a period of enhanced TNSA followed by intense ion acceleration associated with penetration of the laser through the thin target. One of the outstanding questions regarding realization of the BOA experimentally is whether cleaning of ultra-thin targets is required to remove protons that collect on the target. Particle-in-cell simulations of BOA with and without contaminants will be shown. These simulations, using the LANL VPIC code, can be used to assess the effects on ion acceleration and beam quality resulting from the presence of contaminants.   

Initial 3D VORPAL Simulations of Channeled LWFA

A series of two- and three-dimensional simulations of laser wake field accelerators have been carried out. The 2D simulations have been reasonably converged in spatial resolution. They show (as noted before) that the 2D dynamics can be very different from 3D, and that the 2D trapping process is very different for in-plane and out-of-plane electric field polarization with the ratio of produced charge varying by factors of several. In addition, the laser pulse itself undergoes complex dynamics from the time of trapping through the period of acceleration. Results of the convergence studies and the morphology will be presented.   

Numerical algorithms for cold-relativistic plasma models in the presence of discontinuties

A numerical algorithm is presented to solve cold-relativistic electron fluid equations in the presence of sharp gradients and discontinuities. The intended application is to laser wake-field accelerator simulations in which the laser induces accelerating fields thousands of times those achievable in conventional RF accelerators. The relativistic cold-fluid equations are formulated as non-classical system of hyperbolic balance laws. It is shown that the flux Jacobian for this system can not be diagonalized which causes numerical difficulties when developing shock-capturing algorithms. Further, the system is shown to admit generalized delta-shock solutions, first discovered in the context of sticky-particle dynamics (Bouchut, \emph{Ser. Adv. Math App. Sci.}, {\bf 22} (1994) pp. 171--190). A new approach, based on relaxation schemes proposed by Jin and Xin (\emph{Comm. Pure Appl. Math.} {\bf 48} (1995) pp. 235--276) and LeVeque and Pelanti (\emph{J. Comput. Phys.} {\bf 172} (2001) pp. 572--591) is developed to solve this system of equations. The method consists of finding an exact solution to a Riemann problem at each cell interface and coupling these to advance the solution in time. Applications to an intense laser propagating in an under-dense plasma are presented.   

Simulating Anisotropic Dielectrics for Photonic Crystal Accelerator Structures

The selective reflection of photonic crystals offers many potential benefits for accelerator structures, including the elimination of high order modes and wake fields. In addition, photonic crystals can be made out of dielectrics that can outperform metals at high frequencies. Compared to traditional metal accelerator cavities, dielectric photonic crystal structures have many more parameters to optimize---while the large number of possible configurations may allow greater optimization, those configurations will need to be explored via computer simulation. Although isotropic dielectrics are fairly easy to simulate, anisotropic dielectrics present more difficulty---and the ``best'' dielectrics tend to be pure crystals (like sapphire) with anisotropic dielectric tensors. Simulating anisotropic dielectrics may also be important for improving accuracy when simulating oblique interfaces between isotropic dielectrics. We present an algorithm to evolve Maxwell’s equations in the presence of three-dimensional anisotropic dielectrics; the algorithm reduces to the standard Yee algorithm in an isotropic dielectric; moreover, we show that this algorithm supports only eigenmodes with real frequencies, unlike some other seemingly reasonable choices, which lead to instabilities in non-uniform anisotropic dielectrics. This work was supported by the U.S. DOE grant DE-FG02-04ER41317 and Air Force Office of Scientific Research grant FA9550-04-C-0041.   

Modeling Electron Sources with Time-Dependent Green's Functions

Modern electron sources which are utilized in accelerators and microwave sources can be difficult to model due to a combination of complicated effects. In general, these sources may produce tight electron bunches which have small length and time scales associated with them. In addition, the conducting boundary conditions of the source itself may give rise to non-trivial electromagnetic effects on the beam. We demonstrate how both of these effects can be successfully modeled using a time-dependent Green's function method, and show preliminary examples of simulations based on this technique of electron sources found in experiments.   

Reflection of single cycle THz pulses by ionization fronts

The propagation of short intense laser pulses in gas targets can generate relativistic ionization fronts via tunneling ionization of the background gas. The interface gas/plasma can act as a relativistic mirror, reflecting, up-shifting and compressing incident electromagnetic waves. The cut-off condition for reflection, in a gas target, limits the frequencies of the incoming radiation to the THz range. Recent developments in THz sources have opened the way to observe the relativistic mirror effect with single cycle pulses colliding with ionization fronts. We have performed detailed fully relativistic one-dimensional particle-in-cell simulations with Osiris 2.0. Our study relies on the systematic use of the Wigner transform for the electromagnetic field, thus allowing for a complete diagnostic of the frequency modulation in the probe pulse. We demonstrate controlled tunability and strong pulse compression. Relativistic ionization fronts imprint a chirp on the reflected pulse due to the finite rise time of the front, while maintaining the bandwidth required for single cycle generation in UV range. Control of this chirp is possible by a careful choice of the gas.   

Quasi-static Modeling of Plasma Wake Field Acceleration of Electron/Positron Beams

A quasi-static particle in cell code QuickPIC is used to model Plasma Wake Field Acceleration (PWFA) by a relativistic electron or positron beam. Field-ionization, synchrotron radiation effects are included in the model. For an electron beam driver, the parameters in recent afterburner relevant experiments (E167) are used. Head erosion turns out to be a key factor limiting further energy gain for these parameters. The erosion speed in the simulation are compared with a simple theoretical calculation. The final energy spectrum measured in the experiment agreed very well with simulation predictions. For a positron beam driver, beam parameters relevant to the future SABER facilities are considered. Simulations show a pattern of positron beam evolution, i.e. a rapid modulation followed by an envelope stabilization. Up to 5.7 GeV energy gain were observed within 39 centimeters of plasma. At the end, a method of including the trapped particles into the quasi-static model will be described. Preliminary results will be shown.   

Calculation of beam loading and particle trapping using a quasistatic simulation code

Plasma based particle acceleration requires the generation of plasma wave wakes which maintain their coherence over long distances. For example in Laser Wake Field Acceleration (LWFA) schemes the laser pulse must propagate tens of centimeters, which corresponds to many Rayleigh lengths, and in Plasma Wake Field Acceleration (PWFA) the particle beam must be propagated many meters. These wakes, and their effect on the driver (Laser or particle beam) can be simulated efficiently in the quasistatic approximation [1,2]. In this approximation the driver does not evolve during the time a plasma electron spends in the driver. Particles that are trapped in the wake must be treated by an alternate algorithm. Here we modify the 2D code WAKE [1] to treat such particles. We also implement an algorithm that allows for plasma particle to become trapped particles if they gain sufficient energy. Similar implementations have been made in the 3D code QUICKPIC [2]. These changes in WAKE will give users a tool that can be used on a desk-top machine to simulated GeV acceleration. \newline [1] P. Mora and T. M. Antonsen Jr., Phys Plasma 4, 217 (1997) \newline [2] C. Huang et al., J. Comp Phys., to be published.   

PIC simulations of CTR from electron bunches exiting a plasma

Laser wakefield accelerator (LWFA) concepts are characterized by ultra-high gradients and ultra-short bunch lengths. Non-invasive bunch-length diagnostics, at or very near the plasma exit, are key to continuing the rapid advances in LWFA technology. These short bunches can radiate strongly at THz frequencies via coherent transition radiation (CTR) as they exit the plasma [1,2]. Careful measurements of the THz spectrum will provide the necessary bunch-length diagnostic [3], once the effects of various secondary complications have been quantified. We present particle-in-cell (PIC) simulations of characteristic electron bunches exiting a plasma, and discuss numerical issues such as transforming near-field radiation on the grid to the far-field radiation that would be observed by a detector. [1] W.P. Leemans et al., Phys. Rev. Lett. 91, 074802 (2003) [2] C.B. Schroeder et al., Phys. Rev. E 69, 016501 (2004) [3] J. van Tilborg et al., Phys. Rev. Lett. 96, 014801 (2006)   

Modeling laser wake field acceleration with QUICKPIC

We model laser wake field acceleration with the Quasi Static PIC code QUICKPIC, in both uniform and parabolic plasma channels. Since in LWFA the laser evolution is much slower than the plasma response, QUICKPIC employs the Quasi Static Approximation, where the plasma response is calculated through a quasi-static field solver for each 2d slice. The laser is evolved according to the ponderomotive guiding center approximation, with time steps that correctly resolve distances on the order of the rayleigh length. We focus our research in the current state of the art experimental laser and plasma parameters. Our simulations show computational speed up of 2 to 3 orders of magnitude in comparison to full 3D PIC simulations in OSIRIS. We find very good agreement between the codes.   

Simulation and diagnostics of high density plasmas for multiple electron bunch wakefield generation

The wakefield generated in a plasma from an electron beam can be enhanced if instead of a single bunch the beam is modulated into multiple bunches. Then the wakefields generated from the microbunches can add up in phase if the plasma density is tuned precisely at the separation between them. In the experimental setup at Brookhaven's Accelerator Test Facility the 45MeV electron beam is IFEL modulated into 150 microbunches 10.6$\mu $m apart. Here we present plasma simulations that confirm the wakefield enhancement and diagnostics we performed to tune the plasma density (Stark broadening, HeNe laser interferometry).