Double Gap Alfvén Eigenmodes: Revisiting Eigenmodes Interaction with the Alfvén Continuum

A new type of global shear Alfvén Eigenmode is found in tokamak plasmas where the mode localization is in the region intersecting the Alfvén continuum. The eigenmode is formed by the coupling of two solutions from two adjacent gaps (akin to potential wells) in the shear Alfvén continuum. For tokamak plasmas with reversed magnetic shear it is shown that the toroidiciy-induced solution tunnels through the continuum to match the ellipticity-induced Alfvén eigenmode (TAE and EAE, respectively) so that the resulting solution is continuous at the point of resonance with the continuum. The existence of these Double Gap Alfvén Eigenmodes (DGAEs) allows for potentially new ways of coupling edge fields to the plasma core in conditions where the core region is conventionally considered inaccessible. Implications include new approaches to heating and current drive in fusion plasmas as well as its possible use as core diagnostic in burning plasmas

Shifting and splitting of resonance lines due to dynamical friction in plasmas

A quasilinear plasma transport theory that incorporates Fokker-Planck dynamical friction (drag) and scattering is self-consistently derived from first principles for an isolated, marginally-unstable mode resonating with an energetic minority species. It is found that drag fundamentally changes the structure of the wave-particle resonance, breaking its symmetry and leading to the shifting and splitting of resonance lines. In contrast, scattering broadens the resonance in a symmetric fashion. Comparison with fully nonlinear simulations shows that the proposed quasilinear system preserves the exact instability saturation amplitude and the corresponding particle redistribution of the fully nonlinear theory. Even though drag is shown to lead to a relatively small resonance shift, it underpins major changes in the redistribution of resonant particles. These findings suggest that drag can play a key role in modeling the energetic particle confinement in future burning fusion plasmas

HINST: A 2-D Code for High-n TAE Stability

A high-n stability code, HINST, has been developed to study the stability of TAE (Toroidicity-induced Alfvén Eigenmodes) in large tokamaks, such as ITER [International Thermonuclear Experimental Reactor], where the spectrum of unstable TAE modes is shifted toward medium- to high-n modes. The code solves the 2-D eigenmode problem by expanding the eigenfunction in terms of basis functions. Based on the Fourier-ballooning formalism the eigenmode problem is reduced to a system of coupled 1-D equations, which is solved numerically by using the finite element method and a SPARSE matrix solver. The numerical method allows including nonperturbatively non-ideal effects, such as: full ion FLR [Finite Larmor Radius], trapped-electron collisional damping, etc. The 2-D numerical results of TAE and Resonance TAE [RTAE] modes are compared with those from local ballooning calculations and global MHD NOVA code. The results show that for ITER-like plasma parameters, TAE and RTAE modes can be driven unstable by alpha particles for n = 10 - 20. The growth rate for the most unstable mode is within the range lambda divided by omega sub A approximately equal to 0.3 - 1.5%. The most unstable modes are localized near r = a approximately equal to 0.5 and have a broad radial mode envelope width

Kinetic theory of plasma adiabatic major radius compression in tokamaks

A kinetic approach is developed to understand the individual charged particle behavior as well as plasma macro parameters (temperature, density, etc.) during the adiabatic R-compression in a tokamak. The perpendicular electric field from Ohm`s law at zero resistivity E = {minus}v{sub E} x B/c is made use of to obtain the equation for particle velocity evolution in order to describe the particle motion during the R-compression. Expressions for both passing and trapped particle energy and pitch angle change are obtained for a plasma with high aspect ratio and circular magnetic surfaces. The particle behavior near the trapped passing boundary during the compression is also studied to understand the shift induced loss of alpha particles produced by D-T fusion reactions in Tokamak Fusion Test Reactor experiments. Qualitative agreement is obtained with the experiments. Solving the drift kinetic equation in the collisional case, i.e., when the collisional frequency {nu}{sub coll} of given species exceeds the inverse compression time {tau}{sub compr}{sup {minus}1}, the authors obtain that the temperature and the density evolution is reduced to the MHD results T {approximately} R{sup {minus}4/3} and n {approximately} R{sup {minus}2}, respectively. In the opposite case, {nu}{sub coll} {much_lt} {tau}{sub compr}{sup {minus}1}, the longitudinal component of the temperature evolve like R(superscript)-2(end superscript) and perpendicular components of the temperature evolve like T{sub {parallel}} {approximately} R{sup {minus}2} and T{sub {perpendicular}} {approximately} R{sup {minus}1}. The effect of toroidicity is negligible in both cases

Particle Distribution Modification by Low Amplitude Modes

Modification of a high energy particle distribution by a spectrum of low amplitude modes is investigated using a guiding center code. Only through resonance are modes effective in modifying the distribution. Diagnostics are used to illustrate the mode-particle interaction and to find which effects are relevant in producing significant resonance, including kinetic Poincare plots and plots showing those orbits with time averaged mode-particle energy transfer. Effects of pitch angle scattering and drag are studied, as well as plasma rotation and time dependence of the equilibrium and mode frequencies. A specific example of changes observed in a DIII-D deuterium beam distribution in the presence of low amplitude experimentally validated Toroidal Alfven (TAE) eigenmodes and Reversed Shear Alfven (RSAE) eigenmodes is examined in detail. Comparison with experimental data shows that multiple low amplitude modes can account for significant modification of high energy beam particle distributions. It is found that there is a stochastic threshold for beam profile modification, and that the experimental amplitudes are only slightly above this threshold

Global Confinement, Sawtooth Mixing, and Stochastic Diffusion Ripple Loss of Fast ICRF-driven H+ Minority Ions in TFTR

This paper presents studies of ICRF-driven H+ minority ions in TFTR (Tokamak Fusion Test Reator) deuterium plasmas using primarily passive Ho flux detection in the energy range of 0.2-1.0 MeV with some corroborating active (lithium pellet charge exchange) measurements. It is shown that in the passive mode the main donors for the neutralization of H+ ions in this energy range are C5+ ions. The measured effective H+ tail temperatures range from 0.15 MeV at an ICRF power of 2 MW to 0.35 MeV at 6 MW. Analysis of the ICRF-driven H+ ion energy balance has been performed on the basis of the dependence of effective H+ temperatures on the plasma parameters. The analysis showed that H+ confinement times are comparable with their slowing-down times and tended to decrease with increasing ICRF power. Radial redistribution of ICRF-driven H+ ions was detected when giant sawtooth crashes occurred during the ICRF heating. The redistribution affected ions with energy below 0.7-0.8 MeV. The sawtooth crashes displace H+ ions outward along the plasma major radius into the stochastic ripple diffusion domain were those ions are lost in about 10 milliseconds. These observations are consistent with the model of the redistribution of energetic particles developed previously to explain the results of deuterium-tritium alpha-particle redistribution due to sawteeth observed in TFTR. The experimental data are also consistent with ORBIT code simulations of H+ stochastic ripple diffusion losses

Stochastic effects on phase-space holes and clumps in kinetic systems near marginal stability

The creation and subsequent evolution of marginally-unstable modes have been observed in a wide range of fusion devices. This behaviour has been successfully explained, for a single frequency shifting mode, in terms of phase-space structures known as a `hole' and `clump'. Here, we introduce stochasticity into a 1D kinetic model, affecting the formation and evolution of resonant modes in the system. We find that noise in the fast particle distribution or electric field leads to a shift in the asymptotic behaviour of a chirping resonant mode; this noise heuristically maps onto microturbulence via canonical toroidal momentum scattering, affecting hole and clump formation. The profile of a single bursting event in mode amplitude is shown to be stochastic, with small changes in initial conditions affecting the lifetime of a hole and clump. As an extension to the work of Lang and Fu, we find that an intermediate regime exists where noise serves to decrease the effective collisionality, where microturbulence works against pitch-angle scattering