Multi-phase simulation of fast ion profile flattening due to Alfvén eigenmodes in a DIII-D experiment

Abstract

We have developed a multi-phase simulation that is a combination of classical and hybrid simulations for energetic particles interacting with an MHD fluid to simulate the nonlinear dynamics on slowing down time scales of the energetic particles [1]. The hybrid simulation code MEGA is extended with realistic beam deposition profiles, collisions, and losses, and is used for both the classical and hybrid phases. The code is run without MHD perturbations in the classical phase, while the interaction between the energetic particles and the MHD fluid is simulated in the hybrid phase. In a multi-phase simulation of DIII-D discharge #142111 [2], the stored fast ion energy is saturated due to Alfvén eigenmodes (AE) at a level lower than in the classical simulation. Figure 1 shows the time evolutions of stored fast ion energy and MHD kinetic energy. After the stored fast ion energy is saturated, the hybrid simulation is run continuously. We see in Fig The dominant modes found are toroidal Alfvén eigenmodes (TAE), which is consistent with the experimental observation at the simulated time. The n=1 and 2 modes have also a property like energetic particle mode such that their peak is located on the continuum. The amplitude of the temperature fluctuations brought about by the TAEs is of the order of 1% of the equilibrium temperature which is comparable to electron cyclotron emission measurements in the experiment. In the standard run, the amplitude of the TAE modes is v/v A~δ B/B~3-6 10 -4 for n=1-4, and the fast ion pressure profile is more flattened than that in the experiment. We expect that the half and third energy beam components, which are not included in the present simulations with the beam deposition power 4.95 MW, would increase the beam deposition power to 6.25 MW and make the fast ion pressure closer to the experiment.We carried out two more multi-phase simulations with different dissipation coefficients. Significant flattening of fast ion spatial profile takes place over a range of one order of magnitude for the dissipation coefficients. The kinetic energy of the MHD fluctuations is roughly in proportion to the inverse of the dissipation coefficients. This is consistent with the result that the significant flattening of fast ion spatial profile takes place for all the dissipation coefficients. The physics model in this study does not include kinetic damping of AE modes such as radiative damping and thermal ion Landau damping. The dissipation coefficients enable us to control the damping rate, and we can adjust dissipation coefficients to match the experimental fast ion profile.

Observation of Critical-Gradient Behavior in Alfvén-Eigenmode-Induced Fast-Ion Transport

“…Although recent progress has been impressive [22,23], this approach is very expensive computationally. As an alternative, reduced models aim to make computation efficient by avoiding detailed nonlinear calculations of wave-particle resonances and saturated mode amplitudes, but accuracy must be evaluated through experimental validation.…”

Electron cyclotron heating can drastically alter reversed shear Alfvén eigenmode activity in DIII-D through finite pressure effects

“…In this figure, as well several others throughout this paper, a composite spectrogram is constructed by averaging the cross power spectrum of several adjacent ECE channels. Discharge 157737 in figure 4(a) is a reproduction of a very well documented beam driven AE discharge in DIII-D (142111) that has been studied and modeled extensively with great success [35][36][37][38][39][40][41]. It was the intent of this experiment to begin with this well understood discharge and then move away from it using ECH.…”

Fast-ion transport by Alfvén eigenmodes above a critical gradient threshold

“…Excellent agreement with observed AE amplitudes and mode structures is obtained, and the calculated fast-ion profile is close to the measured profile. 18 Surfaces of section plots demonstrate that the resonance overlap of multiple eigenmodes is responsible for the sudden increase in fast-ion transport above threshold. 19 Intermittent avalanches take place with contributions from the multiple eigenmodes.…”

“…16 The new method successfully reproduced the old results for discharge #122 117. 17 Todo et al 18,19 have analyzed a different DIII-D discharge that is above the stochastic threshold, discharge #142 111. The simulations employ a kinetic treatment for the fast ions and a resistive magnetohydrodynamic (MHD) model with artificially enhanced dissipation 20 for the background plasma.…”