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The aim of the present study is to analyze the saturation regime of the energetic-ion-driven resistive interchange mode (EIC) in the LHD plasma. A set of non linear simulations are performed by the FAR3d code that uses a reduced MHD model for the thermal plasma coupled with a gyrofluid model for the energetic particles (EP) species. The hellically trapped EP component is introduced through a modification of the averaged drift velocity operator to include their precessional drift. The non linear simulation results show similar 1/1 EIC saturation phases with respect to the experimental observations, reproducing the enhancement of the n/m = 1/1 resistive interchange modes (RIC) amplitude and width as the EP $\beta$ increases, the EP beta threshold for the 1/1 EIC excitation, the further destabilization of the 1/1 EIC as the population of the helically trapped EP increases and the triggering of burst events. The frequency of the 1/1 EIC calculated during the burst event is 9.4 kHz and the 2/2 and 3/3 overtones are destabilized, consistent with the frequency range and the complex mode structure measured in the experiment. In addition, the simulation shows the inward propagation of the 1/1 EIC due to the non linear destabilization of the 3/4 and 2/3 EPMs, leading to the partial overlapping between resonances during the burst event. Finally, the analysis of the 1/1 EIC stabilization phase shows the excitation of the 1/1 RIC as soon as the flattening induced by the 1/1 EIC in the pressure profile vanishes, leading to the retrieval of the pressure gradient at the plasma periphery and the overcoming of the RIC stability limit., Comment: arXiv admin note: text overlap with arXiv:2010.04598

The aim of this study is to analyze the stability of the Alfven eigenmodes (AE) in the Chinese First Quasi-axisymmetric Stellarator (CFQS). The AE stability is calculated using the code FAR3d that solves the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moment for the energetic particles (EP) species including the effect of the helical couplings and acoustic modes. The Landau damping and resonant destabilization effects are added in the model by a given closure relation. The simulation results indicate the destabilization of n = 1 to 4 AEs by EP during the slowing down process, particularly n = 1 and n = 2 toroidal AEs (TAE), n = 3 elliptical AE (EAE) and n = 4 non circular AE (NAE). If the resonance is caused by EPs with an energy above 17 keV (weakly thermalized EP), n = 2 EAEs and n = 3 NAEs are unstable. On the other hand, EPs with an energy below 17 keV (late thermalization stage) lead to the destabilization of n = 3 and n = 4 TAEs. The simulations for an off-axis NBI injection indicate the further destabilization of n = 2 to 4 AEs although the growth rate of the n = 1 AEs slightly decreases, so no clear optimization trend with respect to the NBI deposition region is identified. In addition, n = 2, 4 helical AE (HAE) are unstable above an EP β threshold. Also, if the thermal β of the simulation increases (higher thermal plasma density) the AE stability of the plasma improves. The simulations including the effect of the finite Larmor radius and electron-ion Landau damping show the stabilization of the n = 1 to 4 EAE/NAEs as well as a decrease of the growth rate and frequency of the n = 1 to 4 BAE/TAEs.

The optimized superconducting stellarator device Wendelstein 7-X (with major radius , minor radius , and plasma volume) restarted operation after the assembly of a graphite heat shield and 10 inertially cooled island divertor modules. This paper reports on the results from the first high-performance plasma operation. Glow discharge conditioning and ECRH conditioning discharges in helium turned out to be important for density and edge radiation control. Plasma densities of with central electron temperatures were routinely achieved with hydrogen gas fueling, frequently terminated by a radiative collapse. In a first stage, plasma densities up to were reached with hydrogen pellet injection and helium gas fueling. Here, the ions are indirectly heated, and at a central density of a temperature of with was transiently accomplished, which corresponds to with a peak diamagnetic energy of and volume-averaged normalized plasma pressure . The routine access to high plasma densities was opened with boronization of the first wall. After boronization, the oxygen impurity content was reduced by a factor of 10, the carbon impurity content by a factor of 5. The reduced (edge) plasma radiation level gives routinely access to higher densities without radiation collapse, e.g. well above line integrated density and central temperatures at moderate ECRH power. Both X2 and O2 mode ECRH schemes were successfully applied. Core turbulence was measured with a phase contrast imaging diagnostic and suppression of turbulence during pellet injection was observed.

In the framework of fusion energy research based on magnetic confinement, pulsed high-field tokamaks such as Alcator and FTU have made significant scientific contributions, while several others have been designed to reach ignition, but not built yet (IGNITOR, FIRE). Equivalent stellarator concepts, however, have barely been explored. The present study aims at filling this gap by: (1) performing an initial exploration of parameters relevant to ignition and of the difficulties for a high-field stellarator approach, and, (2) proposing a preliminary high-field stellarator concept for physics studies of burning plasmas and, possibly, ignition. To minimize costs, the device is pulsed, adopts resistive coils and has no blankets. Scaling laws are used to estimate the minimum field needed for ignition, fusion power and other plasma parameters. Analytical expressions and finite-element calculations are used to estimate approximate heat loads on the divertors, coil power consumption, and mechanical stresses as functions of the plasma volume, under wide-ranging parameters. Based on these studies, and on assumptions on the enhancement-factor of the energy confinement time and the achievable plasma beta, it is estimated that a stellarator of magnetic field B ~ 10 T and 30 m3 plasma volume could approach or reach ignition, without encountering unsurmountable thermal or mechanical difficulties. The preliminary conceptual device is characterised by massive copper coils of variable cross-section, detachable periods, and a lithium wall and divertor.

Energetic particle (EP) destabilized Alfvén eigenmode (AE) instabilities are simulated for a DIII-D experimental case with a pulsed neutral beam using a gyro-Landau moments model which introduces EP phase-mixing effects through closure relations. This provides a computationally efficient reduced model which is applied here in the nonlinear regime over timescales that would be difficult to address with more complete models. The long timescale nonlinear evolution and related collective transport losses are examined including the effects of zonal flow/current generation, nonlinear energy cascades, and EP profile flattening. The model predicts frequencies and mode structures that are consistent with experimental observations. These calculations address issues that have not been considered in previous modelling: The EP critical gradient profile evolution in the presence of zonal flows/currents, and the dynamical nature of the saturated state. A strong level of intermittency is present in the predicted instability-driven transport; this is connected to the zonal flow growth and decay cycles and nonlinear energy transfers. Simulation of intermittent AE-enhanced EP transport will be an important issue for the protection of plasma facing components in the next generation of fusion devices. This material is based upon work supported by the US Department of Energy, Office of Science using the DIII-D National Fusion Facility, a DOE Office of Science user facility, under Awards DE-AC05-00OR22725, DE-FC02-04ER54698, and the US DOE SciDAC ISEP Center. Support is also acknowledged from project 2019-T1/AMB-13648 founded by the Comunidad de Madrid and Comunidad de Madrid (Spain)—multiannual agreement with UC3M Excelencia para el Profesorado Universitario EPUC3M14 Fifth regional research plan 2016-2020. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a US Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02- 05CH11231. We would like to thank Matt Beidler of Oak Ridge National Laboratory for helpful suggestions on this manuscript.

Relativistic electron (RE) beams at high current density (low safety factor, q ( a )) yet very low free-electron density accessed with D-2 secondary injection in the DIII-D and JET tokamak are found to exhibit large-scale MHD instabilities that benignly terminate the RE beam. In JET, this technique has enabled termination of MA-level RE currents without measurable first-wall heating. This scenario thus offers an unexpected alternate pathway to achieve RE mitigation without collisional dissipation. Benign termination is explained by two synergistic effects. First, during the MHD-driven RE loss events both experiment and MHD orbit-loss modeling supports a significant increase in the wetted area of the RE loss. Second, as previously identified at JET and DIII-D, the fast kink loss timescale precludes RE beam regeneration and the resulting dangerous conversion of magnetic to RE kinetic energy. During the termination, the RE kinetic energy is lost to the wall, but the current fully transfers to the cold bulk thus enabling benign Ohmic dissipation of the magnetic energy on longer timescales via a conventional current quench. Hydrogenic (D-2) secondary injection is found to be the only injected species that enables access to the benign termination. D-2 injection: (1) facilitates access to low q ( a ) in existing devices (via reduced collisionality & resistivity), (2) minimizes the RE avalanche by 'purging' the high-Z atoms from the RE beam, (3) drives recombination of the background plasma, reducing the density and Alfven time, thus accelerating the MHD growth. This phenomenon is found to be accessible when crossing the low q ( a ) stability boundary with rising current, falling toroidal field, or contracting minor radius-the latter being the expected scenario for vertically unstable RE beams in ITER. While unexpected, this path scales favorably to fusion-grade tokamaks and offers a novel RE mitigation scenario in principle accessible with the day-one disruption mitigation system of ITER.

New simulations with the Kinetic Orbit Runaway electron (RE) Code KORC show RE deconfinement losses to the wall during plasma scrape off are the primary current dissipation mechanism in DIII-D experiments with high-Z impurity injection, and not collisional slowing down. The majority of simulations also exhibit an increase in the RE beam energy due to acceleration by the induced toroidal electric field, even while the RE beam current is decreasing. In this study, KORC integrates RE orbits using the relativistic guiding center equations of motion, and incorporates time-sequenced, experimental reconstructions of the magnetic and electric fields and line integrated electron density to construct spatiotemporal models of electron and partially-ionized impurity transport in the companion plasma. Comparisons of experimental current evolution and KORC results demonstrate the importance of including Coulomb collisions with partially-ionized impurity physics, initial RE energy, pitch angle, and spatial distributions, and spatiotemporal electron and partially-ionized impurity transport. This research provides an initial quantification of the efficacy of RE mitigation via injected impurities, and identification of the critical role played by loss of confinement due to plasma scrape off on the inner wall as compared to the relatively slow collisional damping., Forthcoming in Physics of Plasmas as of 2020/11/06

We analyze the effects of the passing energetic particles on the resistive ballooning modes (RBM) and the energetic particle driven modes in JT-60SA plasma, which leads to the prediction of the stability in N-NBI heated plasma. The analysis is performed using the code FAR3d that solves the reduced MHD equations describing the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particle (EP) species assuming an averaged Maxwellian EP distribution fitted to the slowing down distribution, including the effect of the acoustic modes. The simulations show the possible destabilization of a 3 / 2 − 4 / 2 TAE with a frequency (f) of 115 kHz, a 6 / 4 − 7 / 4 TAE with f = 98 kHz and a 6/4 or 7/4 BAE with f = 57 kHz in the ITER-like inductive scenario. If the energetic particle β increases, beta induced Alfven Eigenmodes (BAE), toroidal AEs (TAE) and elliptical AEs (EAE) are destabilized between the inner-middle plasma region, leading to the overlapping of AE of different toroidal families. If these instabilities coexist in the non-linear saturation phase the EP transport could be enhanced leading to a lower heating efficiency. For a hypothetical configuration based on the ITER-like inductive scenario but an center peaked EP profile, the EP β threshold increases and several BAEs are destabilized in the inner plasma region, indicating an improved AE stability with respect to the off-axis peaked EP profile. In addition, the analysis of a hypothetical JT-60SA scenario with a resonant q = 1 in the inner plasma region shows the destabilization of fishbones-like instabilities by the off-axis peaked EP profile. Also, the EPs have a stabilizing effect on the RBM, stronger as the population of EP with low energies (below 250 keV) increases at the plasma pedestal.

The aim of the present study is to analyze the stability of the pressure gradient driven modes (PM) and Alfvén eigenmodes (AE) in the large helical device (LHD) plasma if the rotational transform profile is modified by the current drive of the tangential neutral beam injectors (NBI). This study forms a basic search for optimized operation scenarios with reduced mode activity. The analysis is performed using the code FAR3d which solves the reduced MHD equations describing the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations for density and parallel velocity moments of the energetic particle (EP) species, including the effect of the acoustic modes. The Landau damping and resonant destabilization effects are added via the closure relation. On-axis and off-axis NBI current drive modifies the rotational transform which becomes strongly distorted as the intensity of the neutral beam current drive (NBCD) increases, leading to wider continuum gaps and modifying the magnetic shear. The simulations with on-axis NBI injection show that a counter (ctr-) NBCD in inward shifted and default configurations leads to a lower growth rate of the PM, although strong n = 1 and 2 AEs can be destabilized. For the outward shifted configurations, a co-NBCD improves the AEs stability but the PM are further destabilized if the co-NBCD intensity is 30 kA T−1. If the NBI injection is off-axis, the plasma stability is not significantly improved due to the further destabilization of the AE and energetic particle modes (EPM) in the middle and outer plasma region. This work is supported in part by NIFS under contract NIFS07KLPH004.

Parameters of the post-disruption runaway electron (RE) beam in the low density background plasma achieved after secondary deuterium injection are investigated in DIII-D. The spatially resolved RE energy distribution function is measured for the first time during the RE plateau stage by inverting hard x-ray bremsstrahlung spectra. It has maximum energy up to 20 MeV and a non-monotonic feature at 5-6 MeV observed only in the core of the beam supporting the possibility of kinetic instabilities. Results of Fokker-Plank modelling qualitatively support the formation of the non-monotonic distribution function. The RE current profile is reconstructed for the first time using the spatially resolved RE energy distribution. It is found to be more peaked than the pre-disruption plasma current, with higher internal inductance, suggesting preferential formation of REs in the core plasma or potentially a radially inward motion of REs. The accessed relatively low current (180 kA) RE beam is found to be MHD stable, likely due to its elevated safety factor profile. From this base stable equilibrium, an internal beam instability is accessed by ramping up the current. The instability leads to a sawtooth-like relaxation of the RE current profile, but drives no RE loss. An internal kink mode proposed as a candidate instability is supported by results of MARS-F modelling. Electron cyclotron emission (ECE) spectrum measured during the low density RE plateau is found to be bifurcated, with a break point at & x224d; 100 GHz, suggesting resonant absorption of the ECE at low frequencies.

The utilization of composites layered on an additive manufactured substrate, for the production of coil supports for modular coils in small or middle size experimental stellarators is assessed. The focus of the study is a monolithic coil support comprising the coils of a half-period of a stellarator, somewhat similar to the ones in UST_2 and ARIES-CS stellarators. However, the concept may be applicable to quasi-monolithic coil supports (coil forms of NCSX type) or individual coil casings (W7-X type). Coil supports for stellarators require high precision, stiffness and strength for large contorted parts. Traditionally, monolithic coil supports are produced by steel casting/forging and final machining. This production method and material gives accurate, stiff and strong coil supports, but the method may be expensive for monolithic supports due to the geometrical complexity and required accuracy of the structure. In relation to those matters, this work investigates whether a monolithic coil support comprising an additive manufactured resin substrate, which is externally (outward from the coils) surrounded with a thick layer of fibre-reinforced resin, may achieve enough strength and stiffness under middle/high magnetic fields. Finite element calculations are produced to obtain the direction of the principal stresses and their values in compression and tension at different areas of the monolithic support, which is relevant for anisotropic materials. The feasibility of directional application of (carbon) fibres on the winding surface of the stellarator outward from the coils is experimentally tested on a scaled-down additively manufactured prototype of a monolithic support. The strength and stiffness of the composite structure appears sufficient for common magnetic fields in experimental stellarators, and the 3D-composite design and manufacturing was technically feasible.

We study Alfven eigenmodes (AEs) in the TJ-II heliac in hydrogen plasmas heated by hydrogen co-field neutral beam injector. Taking advantage of the unique TJ-II flexibility in a varying plasma current, we have observed strong variation of the AE frequency from fAE ∼ 30 to ∼220 kHz for selected modes. An advanced heavy-ion beam probe diagnostic determines the spatial location and internal amplitudes of the modes. The modes satisfy a local AE dispersion relation including the geodesic acoustic frequency that represents the lowest frequency of the mode. Linear MHD modeling with STELLGAP and FAR3D codes shows that the calculated temporal evolution of the mode frequency reproduces the observed maxima and minima at the same time intervals with a similar frequency range, and the radial profile peaks near the outer edge of the observed one.

In this paper, we analyze the impact of electron cyclotron resonance heating and electron cyclotron current drive on the Alfvénic instabilities driven by neutral beam injection observed in the TJ-II stellarator. An MHD stability analysis of driven Alfvén eigenmodes compatible with the experimental plasma parameters is carried out in order to compare with the data provided by magnetic coils, radiation monitors, and heavy ion beam probes. To this end, the vacuum magnetic configuration modified by the different levels of plasma current, the thermal plasma parameters and the fast ion pressure profiles generated by the co-injected neutral beam, are entered in the FAR3d gyro-fluid code in order to follow the linear evolution of the destabilized plasma equilibrium. Linear growth rates and radial location of the dominant predicted modes coincident in frequency with the observed fluctuations are presented. Despite the uncertainties related to the estimation of the rotational transform profile, the code predictions agree within reasonable accuracy with the experimental results.

Alfven Eigenmodes (AE) can be destabilized during ITER discharges driven by neutral beam injection (NBI) energetic particles (EP) and alpha particles. The aim of the present study is to analyze the AE stability of different ITER operation scenarios considering multiple energetic particle species. We use the reduced magneto-hydrodynamic (MHD) equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles species including the effect of the acoustic modes. The AEs driven by the NBI EP and alpha particles are stable in the configurations analyzed, only MHD-like modes with large toroidal couplings are unstable, although both can be destabilized if the EP beta increases above a threshold. The threshold is two times the model beta value for the NBI EP and alpha particles in the reverse shear case, leading to the destabilization of Beta induced AE (BAE) near the magnetic axis with a frequency of 25-35 kHz and Toroidal or Elliptical AE (TAE/EAE) in the reverse shear region with a frequency of 125-175 kHz, respectively. On the other hand, the hybrid and steady state configurations show a threshold 3 times larger with respect to the model beta for the alpha particle and 40 times for the NBI EP, also destabilizing BAE and TAE between the inner and middle plasma region. In addition, a extended analysis of the reverse shear scenario where the beta of both alpha particles and NBI EP are above the AE threshold, multiple EP damping effects are also identified as well as optimization trends regarding the resonance properties of the alpha particle and NBI EP with the bulk plasma., arXiv admin note: text overlap with arXiv:1807.04380, arXiv:1906.05701

Alfvén Eigenmodes (AE) and magneto-hydrodynamic (MHD) modes are destabilized in DIII-D reverse magnetic shear configurations and may limit the performance of the device. We use the reduced MHD equations in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles (with gyro-fluid closures) as well as the geodesic acoustic wave dynamics, to study the properties of instabilities observed in DIII-D reverse magnetic shear discharges. The aim of the study consists in finding ways to avoid or minimize MHD and AE activity for different magnetic field configurations and neutral beam injection (NBI) operational regimes. The simulations show at the beginning of the discharge, before the reverse shear region is formed, a plasma that is AE unstable and marginally MHD stable. As soon as the reverse shear region appears, ideal MHD modes are destabilized with a larger growth rate than the AEs. Both MHD modes and AEs coexist during the discharge, although the MHD modes are more unstable as the reverse shear region deepens. The simulations indicate the destabilization of Beta induced AE (BAE), Toroidal AE (TAE), elliptical AE (EAE) and reverse shear AE (RSAE) at different phases of the discharges, showing a reasonable agreement between the frequency range of the dominant modes in the simulations and the diagnostic measurements (...) This material based on work is supported both by the U.S. Department of Energy, Office of Science, under Contract DE-AC05-00OR22725 with UT-Battelle, LLC and U.S. Department of Energy, Oce of Science, Oce of Fusion Energy Sciences, using the DIII-D National Fusion Facility, a DOE Oce of Science user facility, under Award No. DE-FC02-04ER54698. This research was sponsored in part by the Ministerio of Economía y Competitividad of Spain under project no.ENE2015-68265-P. DIII-D data shown in this paper can be obtained in digital format by following the links at https://fusion.gat.com/global/D3D DMP. Publicado

The radial structure of the continuum spectrum of shear Alfvén and Alfvén-acoustic waves in the beta-induced Alfvén eigenmode (BAE) frequency range is modeled for tokamak plasmas in the presence of 3D effects obtained from the bifurcated MHD equilibrium reconstruction. Plasma compressibility and geodesic curvature effects responsible for the low-frequency continuum spectrum calculations are invoked. In the equilibrium calculations we find that the helically distorted MHD equilibria may exist even for the axisymmetric devices if q = 1 rational surfaces are present. The continuum calculations with the bifurcated equilibria lead to a frequency splitting between the highest frequency branch and the lowest frequency branch continua at the frequency accumulation point. Radially localised shifting of modes happens via coupling of the adjacent n − 1 continuum around an accumulation point. Our modelling (including 3D effects) correctly reproduces the phenomenon of continuum frequency splitting and provides a possible solution for the differences of few kHz in frequency splitting, which remained unexplained with the 2D kinetic calculations (Curran et al 2012 Plasma Phys. Control. Fusion 54 055001). The pressure scaling confirms the increase of helical excursion of the magnetic axis in equilibrium reconstruction and hence the range of continuum frequency splitting. In our calculations, the existence of low-frequency continua is in agreement with the experimentally observed low-frequency modes. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily re ect those of the European Commission. Allah Rakha is grateful for an AGAUR FI predoctoral grant to support his PhD studies and a Severo Ochoa (SO) mobility grant to support his research stay at Max Planck Institute for Plasma Physics (IPP) Garching, Germany.

We report on the first comprehensive experimental and numerical study of fast ion transport in the helical reversed-field pinch (RFP). Classical orbit effects dominate the macroscopic confinement properties. The strongest effect arises from growth in the dominant fast ion guiding-center island, but substantial influence from remnant subdominant tearing modes also plays a critical role. At the formation of the helical RFP, neutron flux measurements indicate a drastic loss of fast ions at sufficient subdominant mode amplitudes. Simulations corroborate these measurements and suggest that subdominant tearing modes strongly limit fast ion behavior. Previous work details a sharp thermal transport barrier and suggests the helical RFP as an Ohmically heated fusion reactor candidate; the enhanced transport of fast ions reported here identifies a key challenge for this scheme, but a workable scenario is conceivable with low subdominant tearing mode amplitudes.

The multiphase simulations are conducted with the kinetic-magnetohydrodynamics hybrid code MEGA to investigate the spatial and the velocity distributions of lost fast ions due to the Alfvén eigenmode (AE) bursts in the Large Helical Device plasmas. It is found that fast ions are lost along the divertor region with helical symmetry both before and during the AE burst except for the promptly lost particles. On the other hand, several peaks are present in the spatial distribution of lost fast ions along the divertor region. These peaks along the divertor region can be attributed to the deviation of the fast-ion orbits from the magnetic surfaces due to the grad-B and the curvature drifts. For comparison with the velocity distribution of lost fast ions measured by the fast-ion loss detector (FILD), the ‘numerical FILD’ which solves the Newton–Lorentz equation is constructed in the MEGA code. The velocity distribution of lost fast ions detected by the numerical FILD during AE burst is in good qualitative agreement with the experimental FILD measurements. During the AE burst, fast ions with high energy (100–180 keV) are detected by the numerical FILD, while co-going fast ions lost to the divertor region are the particles with energy lower than 50 keV.

The advantages of using the catalyzed deuterium-deuterium (D-D) approach for a fusion reactor–lower and less energetic neutron flux and no need for a tritium breeding blanket–have been evaluated in previous papers, giving examples of both tokamak and stellarator reactors. This paper presents an update for the stellarator example, taking account of more recent empirical transport scaling results and design studies of lower-aspect-ratio stellarators. We use a modified version of the Generic Magnetic Fusion Reactor model to cost a stellarator-type reactor. Recently, this model has been updated to reflect the improved science and technology base and costs in the magnetic fusion program. It is shown that an interesting catalyzed D-D, stellarator power plant might be possible if the following parameters could be achieved: R/ ≈ 4, required improvement factor to ISS04 scaling, FR = 0.9 to 1.15

The aim of the study is to analyze the stability of the Energetic Particle Modes (EPM) and Alfven Eigenmodes (AE) in Helitron J and LHD plasma if the electron cyclotron current drive (ECCD) is applied. The analysis is performed using the code FAR3d that solves the reduced MHD equations describing the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particle (EP) species, including the effect of the acoustic modes. The Landau damping and resonant destabilization effects are added via the closure relation. The simulation results show that the n=1 EPM and n=2 Global AE (GAE) in Heliotron J plasma can be stabilized if the magnetic shear is enhanced at the plasma periphery by an increase (co-ECCD injection) or decrease (ctr-ECCD injection) of the rotational transform at the magnetic axis iota0. In the ctr-ECCD simulations, the EPM/AE growth rate decreases only below a given iota0, similar to the ECCD intensity threshold observed in the experiments. In addition, ctr-ECCD simulations show an enhancement of the continuum damping. The simulations of the LHD discharges with ctr-ECCD injection indicate the stabilization of the n=1 EPM, n=2 Toroidal AE (TAE) and n=3 TAE, caused by an enhancement of the continuum damping in the inner plasma leading to a higher EP beta threshold with respect to the co- and no-ECCD simulations.

In this work, energetic-ion confinement and loss due to energetic-ion driven magnetohydrodynamic modes are studied using comprehensive neutron diagnostics and orbit-following numerical simulations for the Large Helical Device (LHD). The neutron flux monitor is employed in order to obtain global confinement of energetic ions and two installed vertical neutron cameras (VNCs) viewing different poloidal cross-sections are utilized in order to measure the radial profile of energetic ions. A strong helically-trapped energetic-ion-driven resistive interchange mode (EIC) excited in relatively low-density plasma terminated high-temperature state in LHD. Changes in the neutron emission profile due to the EIC excitation are clearly visualized by the VNCs. The reduction in the neutron signal for the helical ripple valley increases with EIC amplitude, which reaches approximately 50%. In addition to the EIC experiment, orbit-following simulations using the DELTA5D code with EIC fluctuations were performed to assess the energetic-ion transport and loss. Two-dimensional temporal evolution results show that the neutron emissivity at the helical ripple decreases significantly due to the EIC. The rapid reduction in neutron emissivity shows that the helically-trapped beam ions immediately escape from the plasma. The reduction in the VNC signals for the helical ripple valley and the total neutron emission rate increase with increasing EIC amplitude, as observed in the experiment. Calculated line-integrated neutron emission results show that the profile measured by VNC1 has one peak, whereas the profile measured by VNC2 has two peaks, as observed in the experiment. Although the neutron emission profile for VNC2 has a relatively wide peak compared with the experimental results, the significant decrease in neutron signal corresponding to the helical ripple valley was successfully reproduced.

Global gyrokinetic particle simulations of electrostatic ion temperature gradient (ITG) instability show that the most unstable eigenmode is localized to some magnetic fieldlines or discrete locations on the poloidal plane in the Wendelstein 7-X (W7-X) stellarator due to its mirror-like magnetic fields, which vary strongly in the toroidal direction and induce coupling of more toroidal harmonics (n) to form the linear eigenmode than in the Large Helical Device (LHD) stellarator. Nonlinear electrostatic simulation results show that self-generated zonal flows are the dominant saturation mechanism for the ITG instabilities in both the LHD and W7-X. Furthermore, radial widths of the fluctuation intensity in both the LHD and W7-X are significantly broadened from the linear phase to the nonlinear phase due to turbulence spreading. Finally, nonlinear spectra in the W7-X are dominated by low-n harmonics, which can be generated both by nonlinear toroidal coupling of high-n harmonics and by linear toroidal coupling with large amplitude zonal flows due to the 3D equilibrium magnetic fields.

The aim of the present study is to perform a theoretical analysis of different strategies to stabilize energetic-ion-driven resistive interchange mode (EIC) in LHD plasma. We use a reduced MHD for the thermal plasma coupled with a gyrofluid model for the energetic particles (EP) species. The hellically trapped EP component is introduced through a modification of the drift frequency to include their precessional drift. The stabilization trends of the 1/1 EIC observed experimentally with respect to the thermal plasma density and temperature are reproduced by the simulations, showing a reasonable agreement with the data. The LHD operation scenarios with stable 1/1 EIC are identified, leading to the stabilization of the 1/1 EIC if the thermal plasma density and temperature are above a given threshold. The 1/1 EIC are also stabilized if the rotational transform is modified in a way that the 1/1 rational surface is located further away than 0.9 times the normalized radius, or the magnetic shear in the plasma periphery is enhanced. Also, LHD discharges with large magnetic fields show a higher EIC destabilization threshold with respect to the thermal plasma density. If the perpendicular NBI deposition region is moved further inward than 0.875 times the normalized radius the 1/1 EIC are also stabilized. In addition, increasing the perpendicular NBI voltage such that the EP energy is higher than 30 keV stabilizes the 1/1 EIC. Moreover, Deuterium plasmas show a higher stability threshold for the 1/1 EIC than Hydrogen plasmas. The experimental data shows a larger time interval between EIC events as the power of the tangential NBI is increased providing that the perpendicular NBI power is at least 13 MW. This implies a stabilizing effect of the tangential NBI., Comment: arXiv admin note: text overlap with arXiv:1904.01964

This document is the product of a stellarator community workshop, organized by the National Stellarator Coordinating Committee and referred to as Stellcon, that was held in Cambridge, Massachusetts in February 2016, hosted by MIT. The workshop was widely advertised, and was attended by 40 scientists from 12 different institutions including national labs, universities and private industry, as well as a representative from the Department of Energy. The final section of this document describes areas of community wide consensus that were developed as a result of the discussions held at that workshop. Areas where further study would be helpful to generate a consensus path forward for the US stellarator program are also discussed. The program outlined in this document is directly responsive to many of the strategic priorities of FES as articulated in “Fusion Energy Sciences: A Ten-Year Perspective (2015–2025)” [1]. The natural disruption immunity of the stellarator directly addresses “Elimination of transient events that can be deleterious to toroidal fusion plasma confinement devices” an area of critical importance for the US fusion energy sciences enterprise over the next decade. Another critical area of research “Strengthening our partnerships with international research facilities,” is being significantly advanced on the W7-X stellarator in Germany and serves as a test-bed for development of successful international collaboration on ITER. This report also outlines how materials science as it relates to plasma and fusion sciences, another critical research area, can be carried out effectively in a stellarator. Additionally, significant advances along two of the Research Directions outlined in the report; “Burning Plasma Science: Foundations—Next-generation research capabilities”, and “Burning Plasma Science: Long pulse—Sustainment of Long-Pulse Plasma Equilibria” are proposed.

DIII-D experiments at low density (${n}_{e}\ensuremath{\sim}{10}^{19}\text{ }\text{ }{\mathrm{m}}^{\ensuremath{-}3}$) have directly measured whistler waves in the 100--200 MHz range excited by multi-MeV runaway electrons. Whistler activity is correlated with runaway intensity (hard x-ray emission level), occurs in novel discrete frequency bands, and exhibits nonlinear limit-cycle-like behavior. The measured frequencies scale with the magnetic field strength and electron density as expected from the whistler dispersion relation. The modes are stabilized with increasing magnetic field, which is consistent with wave-particle resonance mechanisms. The mode amplitudes show intermittent time variations correlated with changes in the electron cyclotron emission that follow predator-prey cycles. These can be interpreted as wave-induced pitch angle scattering of moderate energy runaways. The tokamak runaway-whistler mechanisms have parallels to whistler phenomena in ionospheric plasmas. The observations also open new directions for the modeling and active control of runaway electrons in tokamaks.

A recent DIII-D experiment investigating the impact of electron cyclotron heating (ECH) on neutral beam driven reversed shear Alfvén eigenmode (RSAE) activity is presented. The experiment includes variations of ECH injection location and timing, current ramp rate, beam injection geometry (on/off-axis), and neutral beam power. Essentially all variations carried out in this experiment were observed to change the impact of ECH on AE activity significantly. In some cases, RSAEs were observed to be enhanced with ECH near the off-axis minimum in magnetic safety factor ( q min ), in contrast to the original DIII-D experiments where the modes were absent when ECH was deposited near q min . It is found that during intervals when the geodesic acoustic mode (GAM) frequency at q min is elevated and the calculated RSAE minimum frequency, including contributions from thermal plasma gradients, is very near or above the nominal TAE frequency (f TAE), RSAE activity is not observed or RSAEs with a much reduced frequency sweep range are found. This condition is primarily brought about by ECH modification of the local electron temperature (T e) which can raise both the local T e at q min as well as its gradient. A q-evolution model that incorporates this reduction in RSAE frequency sweep range is in agreement with the observed spectra and appears to capture the relative balance of TAE or RSAE-like modes throughout the current ramp phase of over 38 DIII-D discharges. Detailed ideal MHD calculations using the NOVA code show both modification of plasma pressure and pressure gradient at q min play an important role in modifying the RSAE activity. Analysis of the ECH injection near the q min case where no frequency sweeping RSAEs are observed shows the typical RSAE is no longer an eigenmode of the system. What remains is an eigenmode with poloidal harmonic content reminiscent of the standard RSAE, but absent of the typical frequency sweeping behavior. The remaining eigenmode is also often strongly coupled to gap TAEs. Analysis with the non-perturbative gyro fluid code TAEFL confirms this change in RSAE activity and also shows a large drop in the resultant mode growth rates.

We report the first observation of chirping instabilities driven by runaway electrons (REs) in a tokamak. The instabilities are accessed during the post-disruption RE beam stage in a low density background plasma ( m-3) on DIII-D. The chirping instabilities are observed when a decelerating loop voltage is applied to the RE beam. The frequency chirping is detected in two distinct frequency bands: 0.1-10 MHz and 30-80 MHz. The mode frequency increases linearly when the toroidal magnetic field sensed by the RE beam increases. The frequency chirps by 0.3-2.4 MHz on a timescale of 1 ms. Modification of the RE distribution function is directly measured during the chirping in the low-frequency band consistent with the hole-clump model for frequency chirping. The low-frequency instabilities also correlate with an increase of intermittent RE loss from the plasma. These observations provide a novel experimental platform for fundamental studies of nonlinear chirping. They also support continued investigation of opportunities to utilize kinetic instabilities for RE mitigation in a tokamak reactor.

Comprehensive magnetohydrodynamic (MHD) hybrid simulations with neutral beam injection and collisions were conducted to investigate the Alfven eigenmode (AE) bursts and the fast-ion losses in the large helical device (LHD) for the realistic conditions close to the experiments. It is found in the simulation of the slowing-down time scale that the AE bursts take place repetitively accompanied by fast-ion redistribution and losses leading to lower saturation levels of stored fast-ion energy than those in a classical calculation where the MHD perturbations are neglected. The fast-ion loss rate caused by the AE burst has the quadratic dependence on AE amplitude, which was observed in the LHD experiment. The majority of the lost fast ions are counter-passing particles whose velocity and pitch-angle are close to those of the beam injection. The second component of the lost fast ions is transit particles whose velocity is close to thermal velocity. The loss of the counter-passing particles occurs mainly during the AE bursts, while the transit particles are lost both during the AE bursts and the quiescent periods with larger loss rate than that in the classical calculation. The initial location of the lost counter-injected particles spreads from the plasma edge to the plasma center, while only the particles initially located in the peripheral region are lost for the co-injected beam.

The aim of this study is to analyze the destabilization of Alfven Eigenmodes (AE) by multiple energetic particles (EP) species in DIII-D and LHD discharges. We use the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles species, including the effect of the acoustic modes, diamagnetic currents and helical couplings. We add the Landau damping and resonant destabilization effects using a closure relation. The simulations with multiple NBI lines show three different regimes: the non damped regime where the multi beam AEs growth rate is larger compared to the growth rate of the AEs destabilized by the individual NBI lines, the interaction regime where the multi beam AEs growth rate is smaller than the single NBI AEs and the damped regime where the AEs are suppressed. Operations in the damped regime requires EP species with different density profile flatness or gradient locations. In addition, the AEs growth rate in the interaction regime is further reduced if the combined NBI lines have similar beam temperatures and the beta of the NBI line with flatter EP density profile increases. Then, optimization trends are identified in DIII-D high poloidal beta and LHD low density / magnetic field discharges with multiple NBI lines as well as the configuration requirements to operate in the damped and interaction regimes. DIII-D simulations show a decrease of the n=2 to 6 AEs growth rate and n=1 AE are stabilized in the LHD case. The helical coupling effects in LHD simulations lead to a transition from the interaction to the damped regime of the n=2,-8,12 helical family., arXiv admin note: text overlap with arXiv:1807.04380, arXiv:1906.05700

© 2019 IAEA, Vienna. Novel measurements and modeling of runaway electron (RE) dynamics in DIII-D have resolved experimental discrepancies and validated predictions for ITER, improving confidence that RE avoidance and mitigation can be predictably achieved. Considering RE formation, first experimental assessments of the RE seed current demonstrates that present hot-tail theories are not yet accurate and require improved treatment of the pellet dynamics. Novel measurements of kinetic instabilities in the MHz-range have been made in the RE formation phase, with the intensity of these modes correlated with previously unexplained empirical thresholds for RE generation. Controlled RE dissipation experiments in quiescent regimes have validated RE distribution function dependencies on collisional and synchrotron damping, both in terms of distribution function shape and dissipation rates. Measurements of RE bremsstrahlung and synchrotron emission are now used in tandem to resolve energy and pitch-angle effects. A resolution to long-standing dissipation anomalies in the quiescent regime is offered by taking into account kinetic instability effects on RE phase-space dynamics. Kinetic instabilities in the 100-200 MHz range are directly observed, though modeling finds the largest dissipation arises from GHz range instabilities that are beyond the reach of existing diagnostics. Kinetic instabilities are also observed in the mature post-disruption RE plateau phase, so long as the collisional damping rate is reduced with low-Z injection. Experiments with high-Z injection find that the dissipation rate saturates with injection quantity, likely due to neutral diffusion rates being slower than vertical instability rates in DIII-D. Considering the final loss, a 0D model for first-wall Joule heating is found to be in agreement with experiment, and controlled access to RE equilibria with edge safety factor of two identifies novel dynamics brought about by large-scale kink instabilities. These dynamics are typified by fast (tens of microseconds) RE loss rates without RE beam regeneration. The above measurements and comparison with theory represent significant advances in the understanding of RE dynamics and indicate possible new opportunities for RE avoidance or mitigation via kinetic instabilities.

This paper reports verification and validation of linear simulations of Alfvén eigenmodes in the current ramp phase of DIII-D L-mode discharge #159243 using gyrokinetic, gyrokinetic-MHD hybrid, and eigenvalue codes. Using a classical fast ion profile, all simulation codes find that reversed shear Alfvén eigenmodes (RSAE) are the dominant instability. The real frequencies from all codes have a coefficient of variation of less than 5% for the most unstable modes with toroidal mode number n = 4 and 5. The simulated RSAE frequencies agree with experimental measurements if the minimum safety factor is adjusted, within experimental errors. The simulated growth rates exhibit greater variation, and simulations find that pressure gradients of thermal plasmas make a significant contribution to the growth rates. Mode structures of the dominant modes agree well among all codes. Moreover, using a calculated fast ion profile that takes into account the diffusion by multiple unstable modes, a toroidal Alfvén eigenmode (TAE) with n = 6 is found to be unstable in the outer edge, consistent with the experimental observations. Variations of the real frequencies and growth rates of the TAE are slightly larger than those of the RSAE. Finally, electron temperature fluctuations and radial phase shifts from simulations show no significant differences with the experimental data for the strong n = 4 RSAE, but significant differences for the weak n = 6 TAE. The verification and validation for the linear Alfvén eigenmodes is the first step to develop an integrated simulation of energetic particles confinement in burning plasmas incorporating multiple physical processes.

Gyrokinetic simulations of DIII-D tokamak with axisymmetric equilibrium show that the reduction in the radial electric field shear at the top of the pedestal during edge localized mode (ELM) suppression with the n = 2 resonant magnetic perturbations (RMPs) leads to enhanced drift-wave turbulence and extended turbulence spreading to the top of the pedestal relative to ELMing plasmas with similar RMP and pedestal parameters. The simulated turbulent transport at the top of the pedestal in ELM suppressed conditions is consistent with experimental observations of enhanced turbulence at the top of the pedestal during ELM suppression by the RMPs. These results imply that enhanced drift-wave turbulence due to reduced shear at the pedestal top can contribute to the additional transport required to prevent the pedestal growing to a width that is unstable to ELMs.

The reversed-field pinch (RFP) can spontaneously transition from an axisymmetric magnetic topology to a 3D-helical geometry. Investigations on fast ion transport associated with energetic particle driven Alfven instabilities, tearing mode induced stochasticity, and neoclassical effects have been performed on the Madison Symmetric Torus. STELLGAP produced shear-Alfven continua seeded with V3FIT 3D-equilibrium reconstructions describe the response of Alfvenic bursting activity as a direct consequence of the equilibrium change on the fast ion resonance. Far infrared interferometry resolved electron density perturbations associated with the bursts provide a spatial measurement of the mode structure and support the reconstructions. The bursts produce no global resonant fast ion transport; however, their disappearance at a high core-resonant amplitude implies other transport mechanisms at play. Neutral particle analysis and neutron signals suggest fast ion losses at sufficient core tearing mode strength, supporting the lack of Alfvenic activity. The guiding-center code ORBIT corroborates rapid fast ion loss times in the helical state largely as a consequence of remnant tearing modes. Additionally, ORBIT simulations demonstrate little neoclassical enhancement of particle transport. While superbanana orbits may exist, the growth in the core-resonant fast ion island and the associated secondary mode overlap govern the largest transport process, leading to robust fast ion losses in the 3D-RFP.The reversed-field pinch (RFP) can spontaneously transition from an axisymmetric magnetic topology to a 3D-helical geometry. Investigations on fast ion transport associated with energetic particle driven Alfven instabilities, tearing mode induced stochasticity, and neoclassical effects have been performed on the Madison Symmetric Torus. STELLGAP produced shear-Alfven continua seeded with V3FIT 3D-equilibrium reconstructions describe the response of Alfvenic bursting activity as a direct consequence of the equilibrium change on the fast ion resonance. Far infrared interferometry resolved electron density perturbations associated with the bursts provide a spatial measurement of the mode structure and support the reconstructions. The bursts produce no global resonant fast ion transport; however, their disappearance at a high core-resonant amplitude implies other transport mechanisms at play. Neutral particle analysis and neutron signals suggest fast ion losses at sufficient core tearing mode strength, suppor...

Fast particles in fusion plasmas may drive Alfvén modes unstable leading to fluctuations of the internal electromagnetic fields and potential loss of particles. Such instabilities can have an impact on the performance and the wall-load of machines with burning plasmas such as ITER. A linear benchmark for a toroidal Alfvén eigenmode (TAE) is done with 11 participating codes with a broad variation in the physical as well as the numerical models. A reasonable agreement of around 20% has been found for the growth rates. Also, the agreement of the eigenfunctions and mode frequencies is satisfying. However, they are found to depend strongly on the complexity of the used model. © EURATOM 2018.

The confinement of energetic ions generated by neutral beam injection (NBI) and ion cyclotron resonance frequency heating is studied using GNET simulation code, in which the drift kinetic equation ...

Energetic ion-driven magnetohydrodynamic instabilities such as Alfven eigenmodes (AEs), energetic particle modes (EPMs), and their impacts on energetic ion confinement are being studied on the Larg...

Toroidal Alfven eigenmodes (TAE) and ellipticity induced Alfven eigenmodes (EAE) driven by fast electrons are observed for the first time in steady-state EAST plasmas heated by lower hybrid wave (LHW). For the analyzed discharge four modes appear after the injection of LHW. Comparing experimental observations with simulation, high frequency modes are located near and low frequency mode is near . The two positions are very close to where most of the heating power is deposited and population inversion occurs. Analysis of resonance condition between particles and waves indicates that barely-passing, deeply trapped and barely-trapped electrons can drive the mode.

Energetic-particle driven instabilities have been extensively observed in both tokamaks and stellarators. In order for such devices to ultimately succeed as D-T fusion reactors, the super-Alfvenic 3.5 Mev fusion-produced alpha particles must be sufficiently well confined. This requires the evaluation of losses from classical collisional transport processes as well as from energetic particle-driven instabilities. An important group of instabilities in this context are the discrete shear Alfven modes, which can readily be destabilized by energetic particles (with velocities of the order of vAlfven) through wave-particle resonances. While these modes in three-dimensional systems have many similarities to those in tokamaks, the detailed implementation of modeling tools has required development of new methods. Recent efforts in this direction will be described here, with an emphasis on reduced models (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Alfven Eigenmodes are destabilized at the DIII-D pedestal during transient beta drops in high poloidal beta discharges with internal transport barriers (ITBs), driven by n=1 external kink modes, leading to energetic particle losses. There are two different scenarios in the thermal beta recovery phase: with bifurcation (two instability branches with different frequencies) or without bifurcation (single instability branch). We use the reduced MHD equations in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particles as well as the geodesic acoustic wave dynamics, to study the properties of the instabilities observed in the DIII-D high poloidal beta discharges and identify the conditions to trigger the bifurcation. The simulations suggest that instabilities with lower frequency in the bifurcation case are ballooning modes driven at the plasma pedestal, while the instability branch with higher frequencies are low n (n

An engineering upgrade to the neutral beam system at the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] enables time-dependent programming of the beam voltage and current. Initial application of this capability involves pre-programmed beam voltage and current injected into plasmas that are known to be susceptible to instabilities that are driven by energetic ( E ≥ 40 keV) beam ions. These instabilities, here all Alfven eigenmodes (AEs), increase the transport of the beam ions beyond a classical expectation based on particle drifts and collisions. Injecting neutral beam power, P beam ≥ 2 MW, at reduced voltage with increased current reduces the drive for Alfvenic instabilities and results in improved ion confinement. In lower-confinement plasmas, this technique is applied to eliminate the presence of AEs across the mid-radius of the plasmas. Simulations of those plasmas indicate that the mode drive is decreased and the radial extent of the remaining modes is reduced compared to a higher beam voltage case. In higher-confinement plasmas, this technique reduces AE activity in the far edge and results in an interesting scenario of beam current drive improving as the beam voltage reduces from 80 kV to 65 kV.An engineering upgrade to the neutral beam system at the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] enables time-dependent programming of the beam voltage and current. Initial application of this capability involves pre-programmed beam voltage and current injected into plasmas that are known to be susceptible to instabilities that are driven by energetic ( E ≥ 40 keV) beam ions. These instabilities, here all Alfven eigenmodes (AEs), increase the transport of the beam ions beyond a classical expectation based on particle drifts and collisions. Injecting neutral beam power, P beam ≥ 2 MW, at reduced voltage with increased current reduces the drive for Alfvenic instabilities and results in improved ion confinement. In lower-confinement plasmas, this technique is applied to eliminate the presence of AEs across the mid-radius of the plasmas. Simulations of those plasmas indicate that the mode drive is decreased and the radial extent of the remaining modes is reduced compared to a higher b...

Numerical simulations of runaway electrons (REs) with a particular emphasis on orbit dependent effects in 3-D magnetic fields are presented. The simulations were performed using the recently developed Kinetic Orbit Runaway electron Code (KORC) that computes the full-orbit relativistic dynamics in prescribed electric and magnetic fields including radiation damping and collisions. The two main problems of interest are synchrotron radiation and impurity-based RE dissipation. Synchrotron radiation is studied in axisymmetric fields and in 3-D magnetic configurations exhibiting magnetic islands and stochasticity. For passing particles in axisymmetric fields, neglecting orbit effects might underestimate or overestimate the total radiation power depending on the direction of the radial shift of the drift orbits. For trapped particles, the spatial distribution of synchrotron radiation exhibits localized “hot” spots at the tips of the banana orbits. In general, the radiation power per particle for trapped particles is higher than the power emitted by passing particles. The spatial distribution of synchrotron radiation in stochastic magnetic fields, obtained using the MHD code NIMROD, is strongly influenced by the presence of magnetic islands. 3-D magnetic fields also introduce a toroidal dependence on the synchrotron spectra, and neglecting orbit effects underestimates the total radiation power. In the presence of magnetic islands, the radiation damping of trapped particles is larger than the radiation damping of passing particles. Results modeling synchrotron emission by RE in DIII-D quiescent plasmas are also presented. The computation uses EFIT reconstructed magnetic fields and RE energy distributions fitted to the experimental measurements. Qualitative agreement is observed between the numerical simulations and the experiments for simplified RE pitch angle distributions. However, it is noted that to achieve quantitative agreement, it is necessary to use pitch angle distributions that depart from simplified 2-D Fokker-Planck equilibria. Finally, using the guiding center orbit model (KORC-GC), a preliminary study of pellet mitigated discharges in DIII-D is presented. The dependence of RE energy decay and current dissipation on initial energy and ionization levels of neon impurities is studied. The computed decay rates are within the range of experimental observations.

A nonlinear bump-on-tail model for the growth and saturation of energetic particle driven plasma waves has been extended to include two populations of fast particles—one dominated by dynamical friction at the resonance and the other by velocity space diffusion. The resulting temporal evolution of the wave amplitude and frequency depends on the relative weight of the two populations. The two species model is applied to burning plasma with drag-dominated alpha particles and diffusion-dominated ICRH accelerated minority ions, showing the stabilization of bursting modes. The model also suggests an explanation for the recent observations on the TJ-II stellarator, where Alfven Eigenmodes transition between steady state and bursting as the magnetic configuration varied.

Engineering innovation is required to reduce cost and risk in fabrication for the Quasi-Poloidal Stellarator being developed to test key physics issues at very low plasma aspect ratio. Complex, highly accurate, stainless steel modular coil winding forms are cast and machined; conductor is wound directly onto the winding forms; a vacuum-tight cover is welded over each coil pack; the coils are vacuum pressure impregnated; the completed coils are installed in an external vacuum vessel. An internally cooled, compacted cable conductor that can be wound into complex 3-D shapes was developed. The largest and most complex of the winding forms has been cast using a patternless process (machined sand molds) and a high-temperature pour. The resulting casting required