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The kinetic-MHD hybrid simulation approach for macroscopic instabilities in plasmas can be extended to include the kinetic effects of both thermal ions and energetic ions. The new coupling scheme includes synchronization of density and parallel velocity between thermal ions and MHD, in addition to pressure coupling, to ensure the quasineutrality condition and avoid numerical errors. The new approach has been implemented in the kinetic-MHD code M3D-C1-K, and was used to study the thermal ion kinetic effects and Landau damping in fishbone modes in both DIII-D and NSTX. It is found that the thermal ion kinetic effects can cause an increase of the frequencies of the non-resonant $n=1$ fishbone modes driven by energetic particles for $q_\mathrm{min}>1$, and Landau damping can provide additional stabilization effects. A nonlinear simulation for $n=1$ fishbone mode in NSTX is also performed, and the perturbation on magnetic flux surfaces and the transport of energetic particles are calculated., Comment: 18 pages, 16 figures

We report on a theoretical discovery of new regimes of Alfv\'en eigenmode (AE) induced fast ion transport in tokamak plasmas, where microturbulence plays the role of a mediator of fast ion relaxation. Coulomb collisional scattering alone leads to small AE amplitudes and does not reproduce the steady state regimes observed in experiments. We show that in nonlinear regimes the effective pitch angle scattering due to microturbulence can lead to steady state AE amplitude evolution. This indicates a new route for fast ion losses, which is beyond the scenarios described in "Energetic ion transport by microturbulence is insignificant in tokamaks" [D. C. Pace et al., Phys. Plasmas 20 (2013) 056108]. As a result, microturbulence can significantly increase the amplitude of AEs in predictive simulations of burning plasma experiments such as ITER.

A method is developed to analytically determine the resonance broadening function in quasilinear theory, due to either Krook or Fokker-Planck scattering collisions of marginally unstable plasma systems where discrete resonance instabilities are excited without any mode overlap. It is demonstrated that a quasilinear system that employs the calculated broadening functions reported here systematically recovers the nonlinear growth rate and mode saturation levels for near-threshold plasmas previously calculated from kinetic theory. The distribution function is also calculated, which enables precise determination of the characteristic collisional resonance width.

Abrupt large events in the Alfv\'{e}nic and sub-Alfv\'{e}nic frequency bands in tokamaks are typically correlated with increased fast ion loss. Here, machine learning is used to speed up the laborious process of characterizing the behaviour of magnetic perturbations from corresponding frequency spectrograms that are typically identified by humans. Analysis allows for comparison between different mode character (such as quiescent, fixed-frequency, chirping, avalanching) and plasma parameters obtained from the TRANSP code such as the ratio of the neutral beam injection (NBI) velocity and the Alfv\'{e}n velocity ($v_{\textrm{inj.}}/v_{\textrm{A}}$), the $q$-profile, and the ratio of the neutral beam beta and the total plasma beta ($\beta_{\textrm{beam},i}/\beta$). In agreement with previous work by Fredrickson et al. [Nucl. Fusion 2014, 54 093007], we find correlation between $\beta_{\textrm{beam},i}$ and mode character. In addition, previously unknown correlations are found between moments of the spectrograms and mode character. Character transition from quiescent to non-quiescent behaviour for magnetic fluctuations in the 50 - 200 kHz frequency band is observed along the boundary $v_{\varphi} \lessapprox \frac{1}{4}(v_{\textrm{inj.}} - 3v_{\textrm{A}})$ where $v_{\varphi}$ is the rotation velocity., Comment: 14 pages, 9 figures (accepted at IEEE TPS)

A closed-form analytical solution is found for the nonlinear dynamics of isolated, near-threshold waves in the presence of strong scattering. The proposed solution can be useful in verifying codes across several disciplines, including Alfv\'enic instabilities and thermal plasma turbulence in fusion plasmas and studies of viscous shear flows in fluid dynamics, as well as a rapid means for predicting and analyzing experimental outcome.

The burning plasma performance is limited by the confinement of the superalfvenic fusion products such as alpha particles and the auxiliary heating ions capable of exciting the Alfv\'enic eigenmodes (AEs). In this work the effect of AEs on fast ions is formulated within the quasi-linear (QL) theory generalized for this problem recently. The generalization involves the resonance line broadened interaction of energetic particles (EP) with AEs supplemented by the diffusion coefficients depending on EP position in the velocity space. A new resonance broadened QL code (or RBQ1D) based on this formulation allowing for EP diffusion in radial direction is built and presented in details. We reduce the wave particle interaction (WPI) dynamics to 1D case when the particle kinetic energy is nearly constant. The diffusion equation for EP distribution evolution is then one dimensional and is solved simultaneously for all particles with the equation for the evolution of the wave angular momentum. The evolution of fast ion constants of motion is governed by the QL diffusion equations which are adapted to find the fast ion distribution function. We make initial applications of the RBQ1D to DIII-D plasma with elevated q-profile where the beam ions show stiff transport properties. AE driven fast ion profile relaxation is studied for validations of the QL approach in realistic conditions of beam ion driven instabilities in DIII-D.

Rare Alfv\'enic wave transitions between fixed-frequency and chirping phases are identified in NSTX, where Alfv\'enic waves are normally observed to exhibit either chirping or avalanching responses. For those transitions, we apply a criterion [Duarte et al, Nucl. Fusion 57, 054001 (2017)] to predict the nature of fast ion redistribution in tokamaks to be in the convective or diffusive nonlinear regimes. For NSTX discharges in which the transition is not accompanied by changes in the beam deposited power or modifications in the injected radiofrequency power, it has been found that the anomalous fast ion transport is a likely mediator of the bifurcation between the fixed-frequency mode behavior and rapid chirping. For a quantitative assessment, global gyrokinetic simulations of the effects of electrostatic ion temperature gradient turbulence and trapped electron mode turbulence on chirping were pursued using the GTS code. The investigation is extended by means of predictive studies of the probable spectral behavior of Alfv\'enic eigenmodes for baseline ITER cases consisting of elmy, advanced and hybrid scenarios. It has been observed that most modes are found to be borderline between the steady and the chirping phases.

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., Comment: 13 pages, 21 figures

A general methodology is proposed to differentiate the likelihood of energetic-particle-driven instabilities to produce frequency chirping or fixed-frequency oscillations. The method employs numerically calculated eigenstructures and multiple resonance surfaces of a given mode in the presence of energetic ion drag and stochasticity (due to collisions and micro-turbulence). Toroidicity-induced, reversed-shear and beta-induced Alfven-acoustic eigenmodes are used as examples. Waves measured in experiments are characterized and compatibility is found between the proposed criterion predictions and the experimental observation or lack of observation of chirping behavior of Alfvenic modes in different tokamaks. It is found that the stochastic diffusion due to micro-turbulence can be the dominant energetic particle detuning mechanism near the resonances in many plasma experiments, and its strength is the key as to whether chirping solutions are likely to arise. The proposed criterion constitutes a useful predictive tool in assessing whether the nature of the transport for fast ion losses in fusion devices will be dominated by convective or diffusive processes., Comment: 15 pages, 13 figures

A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfv\'enic eigenmodes in tokamak plasma experiments. The model includes realistic eigenfunction structure, detailed phase-space dependences of the instability drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. The latter mechanism is essential to accurately identify the transition between the fixed-frequency mode behavior and rapid chirping in tokamaks and to resolve the disparity with respect to chirping observation in spherical and conventional tokamaks.

Continuum resonance damping is an important factor in determining the stability of certain global modes in fusion plasmas. A number of analytic and numerical approaches have been developed to compute this damping, particularly in the case of the toroidicity-induced shear Alfv\'en eigenmode. This paper compares results obtained using an analytical perturbative approach with those found using resistive and complex contour numerical approaches. It is found that the perturbative method does not provide accurate agreement with reliable numerical methods for the range of parameters examined. This discrepancy exists even in the limit where damping approaches zero. When the perturbative technique is implemented using a standard finite element method, the damping estimate fails to converge with radial grid resolution. The finite elements used cannot accurately represent the eigenmode in the region of the continuum resonance, regardless of the number of radial grid points used., Comment: 19 pages, 9 figures