Search

Helicon waves have been recently proposed as an off-axis current drive actuator due to their expected high current drive efficiency in the mid-radius region in high beta tokamaks. This current drive efficiency has mostly been calculated ignoring the effects of the plasma in the scrape-off-layer (SOL) in the modeling. The net core current drive efficiency will decrease if helicon power is lost to the SOL. Previous efforts to estimate the loss of helicon power in the SOL have used the hot plasma code AORSA. The large computational cost of AORSA prevents large parametric scans, so to further the understanding of helicon power loss in the SOL, a reduced finite element, full wave plasma model with effective collision frequency for collisional and Landau damping has been developed to study the helicon wave power lost to the SOL. It will be shown that the reduced finite element model (FEM) can reproduce the magnitude and trends of helicon E field patterns and power loss in the SOL of the hot plasma AORSA model. The reduced FEM provides significant advantages over AORSA in reducing the computational time and memory requirements, and in simulating arbitrary tokamak vessel geometry. Parametric scans of antenna parallel refractive index, antenna location, minimum SOL density, SOL density gradient, and vacuum vessel geometry will be carried out to determine the dependencies of the helicon power lost to the SOL as a function of important parameters. The helicon cutoff density is shown to be an important quantity in determining helicon power lost to the SOL. Losses due to antenna loading and wave accessibility are also observed at different antenna and plasma parameters.

Energetic minority protons with ~100 keV effective temperature are routinely created in Alcator C-Mod plasmas with the application of ion-cyclotron-range-of-frequency (ICRF) heating. A multichannel compact neutral particle analyzer (CNPA) is used to make measurements of these distributions in Alcator C-Mod's unique and reactor-relevant operating space via active and passive charge-exchange techniques. A radially injected 50 keV diagnostic hydrogen neutral beam is used for active analysis. Using a detailed model that accounts for beam, halo and impurity electron donors, core proton temperatures of ~30–120 keV are directly measured for the first time in lower density (ne0 ~ (0.8–1.5) × 1020 m−3) Alcator C-Mod plasmas with up to only ~0.5 MW of ICRF power. The model found that the minority proton temperatures are peaked spatially away from r/a = 0, even for an on-axis resonance. Additionally, noticeable phase-space anisotropy is seen as expected for ICRF heating. The measured effective temperatures also scale approximately with the Stix parameter. The CNPA temperature measurements are compared with several leading simulation packages such as the TORIC/FPPRF and AORSA/CQL3D full-wave/Fokker–Planck (FW/FP) solvers. Preliminary comparisons with the AORSA/CQL3D code which include results from a new synthetic diagnostic show good agreement and demonstrate that accurate tracking of the minority distribution during iterations of the FW and FP solvers is required to simulate Alcator C-Mod's energetic minority populations with accuracy. Physically, poor wave focusing and preferential heating of trapped energetic protons are found to move the fast proton temperature profiles off-axis. These FW/FP analyses represent the first comparison between predictions of these detailed codes and core minority tail experimental measurements on Alcator C-Mod.

The AORSA global-wave solver is combined with the CQL3D bounce-averaged Fokker-Planck code to simulate the quasilinear evolution of non-thermal distributions in ion cyclotron resonance heating of tokamak plasmas. A novel re-formulation of the quasilinear operator enables calculation of the velocity space diffusion coefficients directly from the global wave fields. To obtain self-consistency between the wave fields and particle distribution function, AORSA and CQL3D have been iteratively coupled using Python. The combined selfconsistent model is applied to minority ion heating in the Alcator C-Mod tokamak. Results show the formation of a 70 keV ion tail near the minority ion cyclotron resonance layer in approximate agreement with measurements from charge exchange neutral particle analyzers.

Nonlinear interactions of ion cyclotron range of frequency (ICRF) waves with fusion plasmas are reviewed. Although the linear theory of ICRF waves, including fast waves (FWs), high-harmonic fast waves and ion Bernstein waves (IBWs), is widely applicable, nonlinear effects can still be important, especially in the edge plasma or for novel core applications. Here the topics of flow drive, ponderomotive forces, radiofrequency (rf) sheaths, parametric decay and related interactions with the edge plasma are considered. Primary emphasis is placed on the basic underlying physics and tokamak applications. For FW antennas, the parallel electric field near launching structures is known to drive rf sheaths which can give rise to convective cells, interaction with plasma 'blobs', impurity production and edge power dissipation. In addition to sheaths, IBW waves in the edge plasma are subject to strong ponderomotive effects and parametric decay. In the core plasma, slow waves can sometimes induce nonlinear effects. Mechanisms by which these waves can influence the radial electric field and its shear are summarized and related to the general (reactive-ponderomotive and dissipative) force on a plasma from rf waves. Standard ICRF codes have begun to incorporate the nonlinear topics described here. Further progress in integrated simulation should allow new predictive modelling capabilities.

Global wave solutions with self-consistent velocity distributions are calculated for ion cyclotron heating in non-Maxwellian plasmas. The all-orders spectral algorithm (AORSA) global wave solver is generalized to treat non-thermal velocity distributions arising from fusion reactions, neutral beam injection and wave driven diffusion in velocity space. Quasi-linear diffusion coefficients are derived directly from the wave electric field and used to calculate ion velocity distribution functions with the CQL3D Fokker–Planck code. Alternatively, the quasi-linear coefficients can be calculated numerically by integrating the Lorentz force equations along particle orbits. Self-consistency between the wave electric field and resonant ion distribution function is achieved by iterating between the global-wave and Fokker–Planck solutions.

Fast waves (FW) are a primary technique for heating and current drive (CD) on the proposed burning plasma device, International Tokamak Experimental Reactor (ITER) and lower hybrid (LH) waves are a candidate for edge current profile control. The models used to simulate these two waves rely on assumptions of Maxwellian populations that allow efficient analytic implementations of the plasma response, and in the case of the LH wave, the ray tracing models used are able to follow the very small wavelengths in a continuum manner without requiring a fine computational grid. Recent advances in algorithms and parallel computational methods have allowed these assumptions to be tested, permitting more accurate estimates of heating deposition and CD efficiencies in a burning plasma. Absorption by energetic particles for both waves can be significant, reducing electron heating and associated CD. Wave propagation and absorption are dependent on the velocity space distribution of particles in the plasma and geometric effects of focusing and diffraction. Fusion-born alpha particles and neutral beam ions may interact with these waves in a manner that cannot be accurately modelled by Maxwellian distributions. The AORSA2D code has been modified to use a generalized non-Maxwellian conductivity and applied to ITER reference scenarios. The effects of diffraction on LH waves in toroidal geometry are not well understood because computational limits have prohibited full-wave simulations at those small wavelengths. Simulations of LH waves have been restricted to WKB ray tracing techniques and one-dimensional full-wave in the past, but the availability of massively parallel architectures has made full-wave calculations using an electromagnetic field solver tractable. The TORIC code has been adapted to run on parallel architectures making it possible to resolve the slow electrostatic LH wave. We present full-wave simulations of LH slow and FW in toroidal geometry using a Maxwellian distribution with non-relativistic electron damping in Alcator C-Mod at values of (ωpe/ωce)2 comparable to those expected in the ITER device.

The major objective of the National Spherical Torus Experiment (NSTX) is to understand basic toroidal confinement physics at low aspect ratio and high βT in order to advance the spherical torus (ST) concept. In order to do this, NSTX utilizes up to 7.5 MW of neutral beam injection, up to 6 MW of high harmonic fast waves (HHFWs), and it operates with plasma currents up to 1.5 MA and elongations of up to 2.6 at a toroidal field up to 0.45 T. New facility, and diagnostic and modelling capabilities developed over the past two years have enabled the NSTX research team to make significant progress towards establishing this physics basis for future ST devices. Improvements in plasma control have led to more routine operation at high elongation and high βT (up to ~40%) lasting for many energy confinement times. βT can be limited by either internal or external modes. The installation of an active error field (EF) correction coil pair has expanded the operating regime at low density and has allowed for initial resonant EF amplification experiments. The determination of the confinement and transport properties of NSTX plasmas has benefitted greatly from the implementation of higher spatial resolution kinetic diagnostics. The parametric variation of confinement is similar to that at conventional aspect ratio but with values enhanced relative to those determined from conventional aspect ratio scalings and with a BT dependence. The transport is highly dependent on details of both the flow and magnetic shear. Core turbulence was measured for the first time in an ST through correlation reflectometry. Non-inductive start-up has been explored using PF-only and transient co-axial helicity injection techniques, resulting in up to 140 kA of toroidal current generated by the latter technique. Calculated bootstrap and beam-driven currents have sustained up to 60% of the flat-top plasma current in NBI discharges. Studies of HHFW absorption have indicated parametric decay of the wave and associated edge thermal ion heating. Energetic particle modes, most notably toroidal Alfven eigenmodes and fishbone-like modes result in fast particle losses, and these instabilities may affect fast ion confinement on devices such as ITER. Finally, a variety of techniques has been developed for fuelling and power and particle control.

In a magnetized plasma, such as in fusion devices or the Earth's magnetosphere, several different kinds of waves can simultaneously exist, having very different physical properties. Under the right conditions one wave can quite suddenly convert to another type. Depending on the case, this can be either a great benefit or a problem for the use of waves to heat and control fusion plasmas. Understanding and accurately modeling such behavior is a major computational challenge.

At the power levels required for significant heating and current drive in magnetically-confined toroidal plasma, modification of the particle distribution function from a Maxwellian shape is likely (Stix 1975 Nucl. Fusion 15 737), with consequent changes in wave propagation and in the location and amount of absorption. In order to study these effects computationally, both the finite-Larmor-radius and the high-harmonic fast wave (HHFW), versions of the full-wave, hot-plasma toroidal simulation code TORIC (Brambilla 1999 Plasma Phys. Control. Fusion 41 1 and Brambilla 2002 Plasma Phys. Control. Fusion 44 2423), have been extended to allow the prescription of arbitrary velocity distributions of the form . For hydrogen (H) minority heating of a deuterium (D) plasma with anisotropic Maxwellian H distributions, the fractional H absorption varies significantly with changes in parallel temperature but is essentially independent of perpendicular temperature. On the other hand, for HHFW regime with anisotropic Maxwellian fast ion distribution, the fractional beam ion absorption varies mainly with changes in the perpendicular temperature. The evaluation of the wave-field and power absorption, through the full wave solver, with the ion distribution function provided by either a Monte-Carlo particle and Fokker–Planck codes is also examined for Alcator C-Mod and NSTX plasmas. Non-Maxwellian effects generally tend to increase the absorption with respect to the equivalent Maxwellian distribution.

Different plasma responses to neutral beam injection in the directions co and counter to the plasma current have long been accepted as well understood in neutral beam heating of tokamak plasmas. Differences can also occur in fast wave heating and current drive in the ion cyclotron range of frequencies (ICRF) when antenna arrays are phased to drive current co and counter to the plasma current. The source of this asymmetry can be easily seen in the cold plasma wave equation with an applied magnetic field in the z direction and the parallel ICRF electric field set to zero (small electron mass limit). In the absence of absorption, the wave equation displays perfect up-down symmetry. However, when absorption is introduced, the up-down symmetry is destroyed by Hall terms, which depend on density and magnetic field gradients. This is confirmed by simple numerical solutions of the cold plasma wave equation with and without collisions. The same up-down asymmetry appears in three dimensional (3-D) antenna coupling calculations with outgoing boundary conditions. These show a natural poloidal shift in the antenna's radiated power spectrum even when no poloidal magnetic field is present. When a poloidal magnetic field is introduced, the up-down asymmetry acquires a toroidal component. This leads to differences in electron heating and current drive depending on the direction that fast waves are launched relative to the plasma current. Such differences are clearly seen in full wave modelling calculations of heating and current drive in NSTX, where poloidal and toroidal magnetic fields are comparable in magnitude near the antenna. When density gradients are forced to zero, both up-down and co-counter asymmetries disappear.

All major JET systems have been fully commissioned for D-T and the DTE1 series of experiments has started with the D-T fuel mixture and operating conditions foreseen for ITER. In the area of ITER physics, significant results have been produced in both D-D and D-T. In D-D, the LH threshold power database has been extended, the bounds on edge-electron temperature and density in ELMy H-modes have been defined and the advantages of Types I and III ELMy discharges have been compared. In D-T plasmas, the isotope effect on H-mode threshold power and transport has been determined so that a more accurate assessment can be made of the ignition margin and heating requirements for ITER. Trace tritium experiments have provided first particle transport measurements and an assessment of the ITER reference ion-cyclotron resonance-frequency heating scenarios has been started, In the area of fusion performance, record D-D neutron yields have been obtained by controlling the plasma and current profiles in hot ion ELM-free H-modes and optimized shear modes. In D-T, internal transport barriers have been readily established in optimized shear discharges and Alfven eigenmodes have been observed.

An ion cyclotron range of frequencies (ICRF) heating experiment was performed on the Compact Helical System (CHS) device in order to identify the problems in establishing this as a reliable heating method. Radiofrequency heating was applied to plasmas with two ion species produced by ECH. Stored energy increased upto 2.2 kJ with the application of a 590 kW ICRF heating pulse, giving a heating efficiency comparable to that of NBI heating. More importantly, the `flat-top' of the stored energy was maintained during the pulse. Good heating was realized with 30% proton and 70% deuteron plasmas at high density (4*1019 m-3). It was found that the best discharges are dominated by electron ICRF heating, which seems to be the reason for the successful results. On the contrary, a flat-top in stored energy has never been obtained in discharges where ion heating dominates. The loss of high energy ions with large pitch angles produced by ion heating appears to degrade the performance and limit the duration of the heating. A similar degradation was encountered in previous ICRF heating experiments in helical systems. A newly designed detector was used to study the loss of the helically trapped particles

A two-dimensional (r, z) fluid model is used to study plasma transport in inductively coupled plasmas (ICPS). Electron heating from external RF coil driven at 2 MHz is calculated self-consistently by solving for the time-averaged RF electric field. Radial plasma uniformity has been studied in both high (R/L=2.5) and low (R/L=1) aspect ratio ICP reactors driven with external planar or cylindrical coils. The effect of neutral gas pressure on plasma uniformity is presented for Ar discharges at 5 and 20 mTorr. The location of external coils and corresponding power deposition profile is predicted to have little effect on uniformity except at higher pressure (>or approximately= 20 mTorr) and for large aspect ratios. Planar coils appear superior to cylindrical coils for achieving relatively consistent uniformity over a wide range of pressures and reactor aspect ratios.

An account is given of the high performance plasmas established by development of the H-mode regime in JET in the experimental campaigns up to 1992. High performance in this case is measured in terms of the confinement enhancement achieved over the L-mode scaling as measured using the plasma diamagnetism. Three JET H-mode regimes have achieved enhancement factors (H G DIA ) over Goldston L-mode scaling of 2.5 < H G DIA < 4.0. These are the Pellet Enhanced Performance (PEP) H-MODE, the high bootstrap fraction (high β POL ) H-mode and the Hot Ion (HI) H-mode. The phenomenology of these three regimes is reviewed and contrasts and common threads are elucidated

Fast wave heating experiments in the ion cyclotron range of frequencies (ICRF) were performed on target plasmas produced by 350 kW of electron cyclotron heating at 53 GHz and also by neutral beam injection in the Advanced Toroidal Facility (ATF). Various heating regimes were investigated in the frequency range between 9.2 MHz and 28.8 MHz with magnetic fields of 0.95 T and 1.9 T on axis. The nominal pulse lengths of up to 200 kW RF power were in the range between 100 and 400 ms. Data from spectroscopy, loading measurements, and edge RF and Langmuir probes were used to characterize the RF induced effects on the ATF plasma. In the hydrogen minority regime at low plasma density, large suprathermal ion tails were observed with a neutral particle analyser. At high density (ne ≥ 5.0 × 1013 cm-3) substantial increases in antenna loading were observed, but ICRF power was insufficient to produce definitive heating results. A two-dimensional RF heating code, ORION, and a Fokker-Planck code, RFTRANS, were used to simulate these experiments. A simulation of future high power, higher density experiments in ATF indicates improved bulk heating results due to the improved loading and more efficient thermalization of the minority tail

Theoretical models are presented to explain the edge plasma-antenna interaction that occurs during ICRF heating. The periodic structure of the Faraday shield is found to result in strong ponderomotive force in the vicinity of the antenna. A fluid model, which incorporates the ponderomotive force, predicts an increase in particle transport to the Faraday shield. Kinetic modelling shows that the strong antenna near-fields act to increase the energy of deuterons that strike the shield, thereby increasing the sputtering of shield material. In addition, kinetic modelling shows that E1 induced between adjacent shield elements acts to heat edge electrons that transit close to the antenna. The predictions of the models are shown to be consistent with measurements of enhanced transport on PLT.

The global wave propagation code ORION is extended to include a non-zero component of the wave electric field parallel to . With the inclusion of E||, it is possible to calculate the detailed structure of wave fields in the low density plasma immediately surrounding the antenna and Faraday shield structure. Artificial absorbers on the plasma side of the antenna simulate a boundary condition for outgoing waves. Surface charge induced on the Faraday shield elements causes enhanced parallel electric fields in the gaps between the shield elements. Numerical surveys show the parametric dependence of E|| on the average rotational transform, edge density and wave number.

Several experiments on different machines and in different fast wave (FW) heating regimes, such as hydrogen minority heating and high harmonic fast waves (HHFW), have found strong interaction between radio-frequency (RF) waves and the scrape-off layer (SOL) region. This paper examines the propagation and the power loss in the SOL by using the full wave code AORSA, in which the edge plasma beyond the last closed flux surface (LCFS) is included in the solution domain and a collisional damping parameter is used as a proxy to represent the real, and most likely nonlinear, damping processes. 2D and 3D AORSA results for the National Spherical Torus eXperiment (NSTX) have shown a strong transition to higher SOL power losses (driven by the RF field) when the FW cut-off is removed from in front of the antenna by increasing the edge density. Here, full wave simulations have been extended for ‘conventional’ tokamaks with higher aspect ratios, such as the DIII-D, Alcator C-Mod, and EAST devices. DIII-D results in HHFW regime show similar behavior found in NSTX and NSTX-U, consistent with previous DIII-D experimental observations. In contrast, a different behavior has been found for C-Mod and EAST, which operate in the minority heating regime.

Full wave simulations of fusion plasmas show a direct correlation between the location of the fast-wave cut-off, radiofrequency (RF) field amplitude in the scrape-off layer (SOL) and the RF power losses in the SOL observed in the National Spherical Torus eXperiment (NSTX). In particular, the RF power losses in the SOL increase significantly when the launched waves transition from evanescent to propagating in that region. Subsequently, a large amplitude electric field occurs in the SOL, driving RF power losses when a proxy collisional loss term is added. A 3D reconstruction of absorbed power in the SOL is presented showing agreement with the RF experiments in NSTX. Loss predictions for the future experiment NSTX-Upgrade (NSTX-U) are also obtained and discussed.

We describe fully self-consistent time-dependent simulations of radio frequency (RF) generated ion distributions in the ion cyclotron range of frequencies and RF-generated electron distributions in the lower hybrid range of frequencies using combined Fokker–Planck and full wave electromagnetic field solvers. In each regime, the non-thermal particle distributions have been used in synthetic diagnostic codes to compare with diagnostic measurements from experiment, thus providing validation of the simulation capability. The computational intensive simulations require multiple full wave code runs that iterate with a Fokker–Planck code. We will discuss advanced algorithms that have been implemented to accelerate both the massively parallel full wave simulations as well as the iteration with the distribution code. A vector extrapolation method (Sidi A 2008 Comput. Math. Appl. 56) that permits Jacobian-free acceleration of the traditional fixed point iteration technique is used to reduce the number of iterations needed between the distribution and wave codes to converge to self-consistency. The computational burden of the parallel full wave codes has been reduced by using a more efficient two level parallel decomposition that improves the strong scaling of the codes and reduces the communication overhead.

Fast-wave heating and current drive efficiencies can be reduced by a number of processes in the vicinity of the antenna and in the scrape off layer (SOL). On NSTX from around 25% to more than 60% of the high-harmonic fast-wave power can be lost to the SOL regions, and a large part of this lost power flows along SOL magnetic field lines and is deposited in bright spirals on the divertor floor and ceiling. We show that field-line mapping matches the location of heat deposition on the lower divertor, albeit with a portion of the heat outside of the predictions. The field-line mapping can then be used to partially reconstruct the profile of lost fast-wave power at the midplane in front of the antenna, and the losses peak close to the last closed flux surface (LCFS) as well as the antenna. This profile suggests a radial standing-wave pattern formed by fast-wave propagation in the SOL, and this hypothesis will be tested on NSTX-U. Advanced RF codes must reproduce these results so that such codes can be used to understand this edge loss and to minimize RF heat deposition and erosion in the divertor region on ITER.

Numerical modelling of the effects of ion cyclotron resonance heating (ICRH) on the stability of the internal kink mode suggests that ICRH should be considered as an essential sawtooth control tool in ITER. Sawtooth control using ICRH is achieved by directly affecting the energy of the internal kink mode rather than through modification of the magnetic shear by driving localized currents. Consequently, ICRH can be seen as complementary to the planned electron cyclotron current drive actuator, and indeed will improve the efficacy of current drive schemes. Simulations of the ICRH distribution using independent RF codes give confidence in numerical predictions that the stabilizing influence of the fusion-born alphas can be negated by appropriately tailored minority 3 He ICRH heating in ITER. Finally, the effectiveness of all sawtooth actuators is shown to increase as the q = 1 surface moves towards the manetic axis, whilst the passive stabilization arising from the alpha and NBI particles decreases. (Some figures in this article are in colour only in the electronic version)

Recent progress on ITER steady-state (SS) scenario modelling by the ITPA-IOS group is reviewed. Code-to-code benchmarks as the IOS group's common activities for the two SS scenarios (weak shear scenario and internal transport barrier scenario) are discussed in terms of transport, kinetic profiles, and heating and current drive (CD) sources using various transport codes. Weak magnetic shear scenarios integrate the plasma core and edge by combining a theory-based transport model (GLF23) with scaled experimental boundary profiles. The edge profiles (at normalized radius ρ = 0.8–1.0) are adopted from an edge-localized mode-averaged analysis of a DIII-D ITER demonstration discharge. A fully noninductive SS scenario is achieved with fusion gain Q = 4.3, noninductive fraction f NI = 100%, bootstrap current fraction f BS = 63% and normalized beta βN = 2.7 at plasma current I p = 8 MA and toroidal field B T = 5.3 T using ITER day-1 heating and CD capability. Substantial uncertainties come from outside the radius of setting the boundary conditions (ρ = 0.8). The present simulation assumed that βN (ρ) at the top of the pedestal (ρ = 0.91) is about 25% above the peeling–ballooning threshold. ITER will have a challenge to achieve the boundary, considering different operating conditions (T e/T i ≈ 1 and density peaking). Overall, the experimentally scaled edge is an optimistic side of the prediction. A number of SS scenarios with different heating and CD mixes in a wide range of conditions were explored by exploiting the weak-shear steady-state solution procedure with the GLF23 transport model and the scaled experimental edge. The results are also presented in the operation space for DT neutron power versus stationary burn pulse duration with assumed poloidal flux availability at the beginning of stationary burn, indicating that the long pulse operation goal (3000 s) at I p = 9 MA is possible. Source calculations in these simulations have been revised for electron cyclotron current drive including parallel momentum conservation effects and for neutral beam current drive with finite orbit and magnetic pitch effects.

The Integrated Plasma Simulator (IPS) provides a framework within which some of the most advanced, massively-parallel fusion modeling codes can be interoperated to provide a detailed picture of the multi-physics processes involved in fusion experiments. The presentation will cover four topics: 1) recent improvements to the IPS, 2) application of the IPS for very high resolution simulations of ITER scenarios, 3) studies of resistive and ideal MHD stability in tokamk discharges using IPS facilities, and 4) the application of RF power in the electron cyclotron range of frequencies to control slowly growing MHD modes in tokamaks and initial evaluations of optimized location for RF power deposition.

The rf-SciDAC collaboration is developing computer simulations to predict the damping of radio frequency (rf) waves in fusion plasmas. Here we extend self-consistent quasi-linear calculations of ion cyclotron resonant heating to include the finite drift of ions from magnetic flux surfaces and rf induced spatial transport. The all-orders spectral wave solver AORSA is iteratively coupled with a particle based update of the plasma distribution function.

Recent results obtained with high harmonic fast wave (HHFW) heating and current drive (CD) on NSTX strongly support the hypothesis that the onset of perpendicular fast wave propagation right at or very near the launcher is a primary cause for a reduction in core heating efficiency at long wavelengths that is also observed in ICRF heating experiments in numerous tokamaks. A dramatic increase in core heating efficiency was first achieved in NSTX L-mode helium majority plasmas when the onset for perpendicular wave propagation was moved away from the antenna and nearby vessel structures. Efficient core heating in deuterium majority L-mode and H-mode discharges, in which the edge density is typically higher than in comparable helium majority plasmas, was then accomplished by reducing the edge density in front of the launcher with lithium conditioning and avoiding operational points prone to instabilities. These results indicate that careful tailoring of the edge density profiles in ITER should be considered to limit radio frequency (rf) power losses to the antenna and plasma facing materials. Finally, in plasmas with reduced rf power losses in the edge regions, the first direct measurements of HHFW CD were obtained with the motional Stark effect (MSE) diagnostic. The location and radial dependence of HHFW CD measured by MSE are in reasonable agreement with predictions from both full wave and ray tracing simulations.

The broad scientific objectives of the SWIM (Simulation of Wave Interaction with MHD) project are: (A) To improve our understanding of interactions that both RF wave and particle sources have on extended-MHD phenomena, and to substantially improve our capability for predicting and optimizing the performance of burning plasmas in devices such as ITER: and (B) To develop an integrated computational system for treating multi-physics phenomena with the required flexibility and extensibility to serve as a prototype for the Fusion Simulation Project (FSP).

A simple neoclassical point model is presented for the ELMO Bumpy Torus experiment. Solutions for steady state are derived. Comparison with experimental observations is made and reasonable agreement is obtained.

One important area of disagreement between radial transport theory and the ELMO Bumpy Torus (EBT) experiment has been the degree of collisionality of the toroidal plasma electrons. Experiment shows relatively warm electrons (kTe ≈ 300–600 eV) and collisionless scaling, i.e. energy confinement increasing with temperature. But results of early one-dimensional (1-D), neoclassical transport models with radially inward pointing electric fields are limited to relatively cool electrons (kTe ~ 100–200 eV) and collisional scaling. In this paper these early results are extended to include lowest-order effects of ion diffusion in regions where poloidal drift frequencies are small. The effects of direct, or non-diffusive, losses in such regions are neglected along with the effects of finite radial electric fields on electron transport coefficients and of self-consistent poloidal electric fields on ion transport coefficients. Results show that solutions in the collisionless electron regime do exist. Furthermore, when the effects of finite electron ring beta on magnetic fields near the plasma edge are included, these solutions occur at power levels consistent with experiment.

The best currently available transport coefficients for neoclassical transport of ions in EBT i n the plateau regime are based on the assumption of a lowest-order ion velocity distribution function that is Maxwellian. Experimental evidence, however, suggests the presence of an enhanced high-energy tail on the ion distribution function, and a simple theoretical analysis indicates that an enhanced tail may be a major contributor to neoclassical losses. For a study of these effects, a kinetic model for neoclassical transport is developed assuming isotropic velocity distributions. Three coupled non-linear integrodifferential equations i n one velocity dimension are solved numerically; this includes, for the first time, a self-consistent solution for the lowest-order ion distribution function which proves to be non-Maxwellian and has an enhanced high-energy tail due to electron-ion collisions. It is shown that this non-Maxwellian lowest-order solution leads to higher core ion temperatures and to much larger ion diffusion rates than those obtained when a Maxwellian distribution is assumed.

A steady state, three-dimensional, Fokker-Planck code, RFTRANS, has been developed that includes real-space radial diffusion at the kinetic level as well as models of auxiliary heating. The RFTRANS code has been coupled with the one-dimensional full-wave code ORION-S which calculates the electric fields and power absorption profiles for waves in hot plasmas in the ion cyclotron range of frequencies (ICRF). The differences between fast wave (FW) absorption and ion Bernstein wave (IBW) absorption by a minority plasma species have been studied, using simple models to map the ORION-S power profiles into cylindrical geometry. The effects of the absorbed ICRF power are calculated by the RFTRANS code, and the resulting minority distribution function is decomposed into two Maxwellian distribution functions at each radial location for input into the dispersion relation used by the ORION-S code. The process is iterated until convergence is reached. There is a significant difference between the effects of FW absorption and the effects of IBW absorption in velocity space which is due to the differences in perpendicular wavelength. When a simple kinetic real-space diffusion coefficient is used, the strong gradients in the heated minority distribution function are relaxed and the absorption profiles are affected. The results indicate that the application of high power fast waves launched from the low field side into a hydrogen minority/deuterium majority plasma can cause a strong shift of the radial absorption peak towards the antenna structure. Thus, at high power levels, the absorption becomes peaked near the magnetic axis when the ion cyclotron resonance is on the high field side of the magnetic axis; this is due to the combined effects of the radial diffusion of the hot tail components of the distribution function and the Doppler shift of the resonance.

We examine the possibility that diamagnetic currents in the hot electron rings in the ELMO Bumpy Torus (EBT) plasma are strong enough to reverse gradients in line integral dl/B, thereby providing gross magnetohydrodynamic stability. Using a two-dimensional solution to the Grad-Shafranov equation with tensor pressure, we compute the electromotive force induced in a diamagnetic loop surrounding the EBT plasma. This allows direct comparison between calculated and measured diamagnetic loop signals for different values of perpendicular energy stored in the electron rings. Signals required for a local minimum in B and maximum in line integral dl/B are found to be sensitive functions of ring width for which there is presently no direct measurement. However, theoretical arguments provide estimates for the hot electron gyrodiameter (approx. 1.0 cm for 400 keV) and for the dispersion in guiding center drift orbits (1 cm for the measured ring length of 10 cm). Thus, a ring with a width of 2 cm or 2 gyrodiameters (full-width at half-maximum) and length of 10 cm requires a diamagnetic loop signal of 443 mV (W/sub perpendicular/ approx. 49 J and ..beta../sub perpendicular,max/ approx. 0.45) for a local maximum in line integral dl/B.

An essential feature of the ELMO Bumpy Torus (EBT) concept is the presence of a relativistic electron annulus in each of the toroidal mirror sectors. These high-beta annuli are formed and sustained by microwave heating and are of sufficient density and temperature that diamagnetic currents produce the necessary minimum in the magnetic field required for MHD stability of the toroidal core plasma. Since electron rings play an important role in confinement characteristics and performance of EBT, the trade off between the quality of the confinement afforded by the rings and the power required to sustain them represents an important consideration in a fusion reactor. A power balance for the rings that includes energy transfer between the hot annulus electrons and the core electrons via Coulomb collisions (drag cooling), in addition to radiation (synchrotron and bremsstrahlung) and pitch-angle scattering of the ring electrons, indicates that drag dominates the annulus energy balance in EBT-I. Drag cooling of the relativistic annulus electrons on the toroidal core plasma appears to provide a reasonable explanation for the decrease in the annulus electron temperature in going from ELMO to EBT-I. Theoretical estimates of the microwave power required to sustain the annulus are found to be within a factor of two of the experimentally determined value. Scaling projections for both EBT-I and EBT-S are shown, enabling one to examine the sensitivity of the annulus electron temperature as a function of core plasma density for various microwave power levels. The results indicate that a range of annular beta values between 15–30% are achievable for projected EBT-S toroidal plasma parameters if the microwave power levels are in the range of ~ 10–15 kW. Further extrapolations to future planned experiments are also included. The sensitivity of these results to the details of the hot-electron distribution function and geometric and scaling parameters are also discussed.

The theory of single particle electron cyclotron resonance heating in a magnetic mirror is treated analytically and numerically, using the techniques of (a) integration of the Lorentz force equation and (b) transformation to a Hamiltonian approximation, to study both short time scale and adiabatic effects. The force equation is analytically integrated in the vicinity of the resonance plane to obtain the energy dependence of the effective time spent in resonance per bounce te. For electrons passing through the resonant zone at constant parallel velocity vzR, te varies as vzR-12/. For electrons which turn in or near the resonant zone, te varies as vperpendicular to R, P=2/3, where vperpendicular to R is the transverse velocity at resonance. These results agree with the exact numerical integration of the force equation, for which P approximately=0.5-0.7.

The sixth order wave equation which results from a finite temperature expansion of the Vlasov equation is solved globally in the ion cyclotron range of frequencies. A perpendicularly stratified, onedimensional slab plasma is assumed. The diamagnetic drift and the associated anisotropy are included in the unperturbed distribution function to ensure a self-adjoint system. All x-dependence in the plasma pressure and magnetic field is retained along with the electric field parallel to B⃗. Thus, Landau damping of the ion Bernstein wave is included self-consistently. Because of the global nature of the solution, the evanescent short wavelength Bernstein waves do not grow exponentially as in shooting methods. Strong variations occur in the absorption and in the structure of the wave fields as resonance topology is varied. Solutions to the complete sixth order differential equation are compared to those from an approximate second order equation based on local dispersion theory.