Verification and validation of integrated simulation of energetic particles in fusion plasmas

Here, we report on verification and validation of linear simulations of Alf´ven eigenmodes in the current ramp phase of DIII-D L-mode discharge #159243 using gyrokinetic, gyrokinetic-MHD hybrid, and eigenvalue codes. Using a classical fast ion profile, all simulation codes find that reversed shear Alf´ven eigenmodes (RSAE) are the dominant instability. The real frequencies from all codes have a coefficient of variation of less than 5% for the most unstable modes with toroidal mode number n = 4 and 5. Due to uncertainty in the experimentally measured minimum safety factor (q_min) and the sensitivity of the RSAE’s frequency to q_min, the average difference in frequency between simulated and measured is df/f = 14.7%, 22.6%, for n = 4 and 5, respectively. If qmin is adjusted slightly, within experimental errors, an agreement of within 4.5% and 3.1%, for n = 4 and 5 respectively, is found for all codes. The simulated growth rates exhibit greater variation, and simulations find that pressure gradients of thermal plasmas make a significant contribution to the growth rates. Mode structures of the dominant modes agree well among all codes. Using a calculated fast ion profile that takes into account the action of the spectrum of multiple unstable modes, a toroidal Alf´ven eigenmode (TAE) with n = 6 is found to be unstable in the outer edge, consistent with the experimental data. Variations of the real frequencies and growth rates of the TAE are slightly larger than those of the RSAE. Lastly, electron temperature fluctuations and radial phase shifts from simulations show no significant differences with the experimental data for the strong n = 4 RSAE, but significant differences for the weak n = 6 TAE. The verification and validation for the linear simulations of Alf´ven eigenmodes is the first step to determine an integrated simulation of energetic particles confinement in burning plasmas incorporating multiple physical processes with kinetic effects of both energetic and thermal particles on an equal footing.