Session YO4: Energetic Particles and Transport

Hybrid simulation of fishbone instabilities in the EAST tokamak

Hybrid simulations with the global kinetic- MHD code M3D-K[1,2] have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven fishbone in EAST experiment. Linear simulations show that a low frequency fishbone instability is excited at experimental value of beam ion pressure. The mode is mainly driven by low energy beam ions via precessional resonance. The results are consistent with the experimental measurement with respect to mode frequency and mode structure. When the beam ion pressure is increased to exceed a critical value, the low frequency mode transits to a BAE with much higher frequency. Nonlinear simulations show that the frequency of the low frequency fishbone chirps up and down with corresponding hole-clump structures in phase space, consistent with the Berk-Breizman theory. In addition to the low frequency mode, the high frequency BAE is excited during the nonlinear evolution. For the transient case of beam pressure fraction where the low and high frequency modes are simultaneously excited in the linear phase, only one dominant mode appears in the nonlinear phase with frequency jumps up and down during nonlinear evolution. [1] Park W. et al 1999 Phys. Plasmas 6 1796 [2] Fu G.Y. et al 2006 Phys. Plasmas 13 052517   

Low-Frequency Fishbone Driven by Passing Fast Ions in Tokamak Plasmas

After the first report in PDX [1], fishbone instabilities were commonly observed in tokamak plasmas with fast ions induced by NBI and/or RF heating. In PDX, with perpendicular NBI, it was understood that the fishbone instability was driven through the resonance with the trapped energetic ions' toroidal precessional drift frequency [2]. In PBX, fishbone instability driven by passing fast ions was first reported. In ITER-like plasmas, fast ions are mostly passing particles. Thus it is important to understand fishbone instability driven by passing fast ions. With finite FOW effects of passing fast ions, analytical results showed that there exist two branches of fishbone with low and high frequency [3-5]. For the low frequency fishbone, previously, the mode frequency of the low frequency fishbone was determined by the bulk ion-diamagnetic-drift frequency [3]. In this work, the fishbone dispersion relation is solved self-consistently and the obtained mode is of EPM type where the frequency is determined by fast ion dynamics. In addition to the analytical results, numerical study using HL-2A tokamak parameters is also presented. These results are helpful to understand the low frequency fishbone observed in HL-2A. [1] McGuire K. et al., 1983 Phys. Rev. Lett. 50, 891 [2] Chen L. et al., 1984 Phys. Rev. Lett. 52, 1122 [3] R. Betti et al., 1993 Rev. Lett. 70, 3428 [4] Wang S.J. 2001 Phys. Rev. Lett. 86, 8286 [5] Wang Feng et al., 2017 Nucl. Fusion 57, 056013   

A Two Species Bump-On-Tail Model With Relaxation for Energetic Particle Driven Modes

Energetic particle driven Alfv\'en Eigenmodes (AEs) observed in present day experiments exhibit various nonlinear behaviours varying from steady state amplitude at a fixed frequency to bursting amplitudes and sweeping frequency. Using the appropriate action-angle variables, the problem of resonant wave-particle interaction becomes effectively one-dimensional. Previously, a simple one-dimensional Bump-On-Tail (BOT) model has proven to be one of the most effective in describing characteristic nonlinear near-threshold wave evolution scenarios. In particular, dynamical friction causes bursting mode evolution, while diffusive relaxation may give steady-state, periodic or chaotic mode evolution. BOT has now been extended to include two populations of fast particles, with one dominated by dynamical friction at the resonance and the other by diffusion; the relative size of the populations determines the temporal evolution of the resulting wave. This suggests an explanation for recent observations on the TJ-II stellarator, where a transition between steady state and bursting occured as the magnetic configuration varied. The two species model is then applied to burning plasma with drag-dominated alpha particles and diffusion-dominated ICRH accelerated minority ions.   

Nonlinear Dynamics of Fast-electron Driven Beta-induced Alfven eigenmode

The fast-electron driven beta-induced Alfven eigenmode (e-BAE) has been routinely observed in HL-2A tokamak. We study e-BAE for the first time using global gyrokinetic GTC simulations, where the fast electrons are described by the drift kinetic model. Frequency chirping is observed in nonlinear simulations in the absence of sources and sinks, which provides a new nonlinear paradigm beyond the standard “bump-on-tail” model. Analysis of nonlinear wave-particle interactions shows that the frequency chirping is induced by the nonlinear evolution of the coherent structures in the fast electron phase space, where the dynamics of the coherent structure is controlled by the formation and destruction of phase space islands in the canonical variables. Furthermore, we put forward a new theory frame to demonstrate that the evolution of chirping phenomenon is essentially induced by balance and destruction of net shear flow in the toroidal direction combined by the background shear flow and perturbed shear flow, which provides a novel and clear physical image.   

Excitation of Low Frequency Alfven Eigenmodes in Toroidal Plasmas

Low frequency Alfven eigenmodes in toroidal geometry, such as beta-induced Alfven-acoustic eigenmode (BAAE) and beta-induced Alfven eigenmode (BAE), can cause significant loss of energetic particles in fusion plasmas. Our global gyrokinetic toroidal code (GTC) simulations find that unstable BAAE and BAE can be simultaneously excited with similar radial mode width and comparable linear growth rates even though the damping rate of BAAE is much larger than BAE in the absence of energetic particles. This surprising result is attributed to non-perturbative effects of the energetic particles that modify ideal MHD mode polarizations and nonlocal geometry effects that invalidate radially local acoustic dispersion relation. GTC simulations with various tokamak sizes show that dominant mode changes from the BAAE in a larger tokamak to the BAE in a smaller tokamak due to the dependence of wave-particle resonance condition on the tokamak size. In nonlinear GTC simulations, the lower frequency BAAE is nonlinearly driven after BAE saturates in the realistic simulation of a DIII-D experiment where low frequency Alfven eigenmodes are responsible for half of the fast ion loss. In collaborations with Yaqi Liu, Huasen Zhang, Wenlu Zhang.   

Stimulated Emission of Fast Alfv\'{e}n Waves within Toroidally Confined Low Beta Fusion Plasmas

A fast Alfv\'{e}n wave of initially low energy is shown to be greatly amplified by a new stimulated emission process [J. W. S. Cook, R. O. Dendy, and S. C. Chapman, Phys. Rev. Lett. 118, 185001 (2017)]. This extracts energy from a population inversion of fusion-born ions, which is observed to arise naturally in the outer mid-plane of large tokamak plasmas. The inward propagation of a fast Alfv\'{e}n wave through~the outboard edge of a tokamak plasma, in the presence of this fast ion population, is modeled using~full orbit kinetic~particle-in-cell simulations~using the nonlinear self-consistent Maxwell-Lorentz equations.~Within the constraints~of periodic boundary conditions, and initially uniform density and magnetic field, these simulations demonstrate this novel alpha-particle channelling scenario for the first time.   

Incorporating pedestals with feedback into sandpile models for fusion plasmas

The pedestal in a H-mode fusion plasma is thought to result from shear flow induced by a radial electric field. The size of the pedestal relates to the Larmor radius of the ions, and in turn to their temperature. This creates a feedback mechanism within the plasma as temperature changes cause changes in pedestal size. We present here modifications of a sandpile model (S C Chapman, Phys. Rev. E 62, 1905 (2000)) in which we incorporate feedback effects. A key parameter, $L_f$, defines the distance over which the sandpile can interact with itself, analogous to shear flow in the plasma. Decreasing the value of $L_f$ increases the energy in the sandpile. By changing $L_f$ at the edge of the sandpile over a distance related to the energy of the system, we produce a pedestal, and introduce an element of feedback analogous to changes in the shear flow in a fusion plasma. We also show other variants of the model which produce pedestals without introducing feedback. We observe that maximum waiting times between mass loss events (MLEs), and maximum MLE sizes, grow with pedestal size, consistent with the behaviour of ELMs in a fusion plasma, and that this occurs only in the presence of feedback in the model.   

Gyrokinetic simulations of DIII-D near-edge L-mode plasmas

In order to understand the L-H transition, a good understanding of the L-mode edge region is necessary. We perform nonlinear gyrokinetic simulations of a DIII-D L-mode discharge with the GENE code in the near-edge, which we define as $\rho_{tor}\ge 0.8$. At $\rho =0.9$, ion-scale simulations reproduce experimental heat fluxes within the uncertainty of the experiment. At$\thinspace \rho =0.8$, electron-scale simulations reproduce the experimental electron heat flux while ion-scale simulations do not reproduce the respective ion heat flux due to a strong poloidal zonal flow. However, we reproduce both electron and ion heat fluxes by increasing the local ion temperature gradient by $80\% $. Local fitting to the CER data in the domain $0.7\le \thinspace \rho \le 0.9$ is compatible with such an increase in ion temperature gradient within the error bars. Ongoing multi-scale simulations are investigating whether radial electron streamers could dampen the poloidal zonal flows at $\rho =0.8\thinspace $and increase the radial ion-scale flux.   

Can the Time-Spectral Method GWRM Advance Fusion Transport Modelling?

Transport phenomena in fusion plasma pose a daunting task for both real-time experiments and numerical modelling. The transport is driven by micro-instabilities caused by a host of unstable modes, for example ion temperature gradient and trapped electron modes. These modes can be modelled using fluid or gyrokinetic equations. However, the equations are characterised by high degrees of freedom and high temporal and spatial numerical requirements. Thus, a \textit{time-spectral} method GWRM has been developed in order to efficiently solve these multiple time scale equations. The GWRM assumes a multivariate Chebyshev expansion ansatz in time, space, and parameter domain. Advantages are that time constraining CFL criteria no longer apply and that the solution accurately averages over small time-scale dynamics. For benchmarking, a two-fluid 2D drift wave turbulence model has been solved in order to study toroidal ion temperature gradient growth rates and nonlinear behaviour.   

ExB shear damping of geodesic acoustic mode in tokamak

ExB shearing effect on geodesic acoustic mode (GAM) is investigated both as an initial value problem in the shearing frame and as an eigenvalue value problem in the lab frame. The novel effects are that ExB shearing couples the standard GAM perturbations to their complimentary poloidal parities. The resulting GAM accuires an effective inertia increasing in time leading to GAM damping. Eigenmode analysis shows that GAMs are radially localized by ExB shearing with the mode width being inversely proportional and radial wave number directly proportional to the shearing rate for weak shear. The physics of GAM disappearance during LH transition will be discussed.   

Isotope and mixture effects on neoclassical transport in the pedestal

The isotope mass scaling of the energy confinement time in tokamak plasmas differs from gyro-Bohm estimates, with implications for the extrapolation from current experiments to D-T reactors. Differences in mass scaling in L-mode and various H-mode regimes suggest that the isotope effect may originate from the pedestal. In the pedestal, sharp gradients render local diffusive estimates invalid, and global effects due to orbit-width scale profile variations have to be taken into account. We calculate neoclassical cross-field fluxes from a radially global drift-kinetic equation using the PERFECT code [Landreman et al. (2014) PPCF {\bf 56} 045005], to study isotope composition effects in density pedestals. The relative reduction to the peak heat flux due to global effects as a function of the density scale length is found to saturate at an isotope-dependent value that is larger for heavier ions. We also consider D-T and H-D mixtures with a focus on isotope separation. The ability to reproduce the mixture results via single-species simulations with artificial ``DT'' and ``HD'' species has been considered. These computationally convenient single ion simulations give a good estimate of the total ion heat flux in corresponding mixtures.   

Understanding helium transport: experimental and theoretical investigations of low-Z impurity transport at ASDEX Upgrade

The presence of helium is fundamentally connected to the performance of a fusion reactor. To predict the helium density profile in future fusion devices, understanding of helium transport is indispensable, as are experimentally validated theoretical models of the low-Z impurity turbulent transport. At ASDEX Upgrade, detailed, multi-species investigations of low-Z impurity transport have been undertaken in dedicated experiments, resulting in an extensive database of helium and boron density profiles over a wide range of parameters relevant for turbulent transport (normalised gradients of the electron density, the ion temperature and the toroidal rotation). Detailed comparisons of the experimental density gradients of both impurities with gyrokinetic simulations of the turbulent transport have shown that a qualitative agreement between experiment and theory cannot always be obtained, with strong discrepancies observed in some cases. The role of rotodiffusion and fast ions will be discussed as possible explanations for these discrepancies, which indicate a missing element in our understanding of low-Z impurity transport.