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Energetic particles (EPs) include fusion alpha particles and the fast ions from auxiliary heating. These particles can drive instabilities in a toroidal plasma. The instabilities then push the EPs outward. This lowers the heating efficiency and raises the heat load on the first wall.
These instabilities are studied with the MEGA code. MEGA is a hybrid code: the bulk plasma is a nonlinear MHD fluid, the EPs are treated kinetically, and the two are coupled through the EP contribution to the MHD momentum equation. The equilibrium and the plasma profiles come from ASDEX Upgrade (AUG) discharge #36267 at t = 4.09 s. The EP distribution is an anisotropic slowing-down distribution, Gaussian in pitch angle. The NBI energy is 93 keV, and the EPs are born at about half the Alfven speed.
One dominant instability is found in the plasma core. Its mode numbers are m/n = 3/1 and its frequency is 0.11 times the Alfven frequency, about 60 kHz. The mode appears only above a threshold in the EP beta, between 0.2% and 0.4%. Between 0.4% and 1.2% the growth rate rises steadily, while the mode structure and the frequency hardly change. Above 1.5% the growth rate becomes larger than the frequency, and the frequency itself falls by 17%. The mode is then no longer a weakly driven eigenmode. The numerical convergence was also checked. With eight times more markers, the growth rate changes by 0.4% and the frequency by 1.1%.
None of these scans reproduced the frequency measured in the experiment. The reason lies in the equilibrium. The safety factor q in the plasma core is the least reliable part of the reconstruction. The same equilibrium gives a core q of 2.05 or 2.40, depending on how it is computed. The reconstructed profile has a small maximum of q close to the magnetic axis. This maximum was removed, and the simulations were repeated. The mode is still there, and its growth rate is almost the same. Its frequency, however, moves up by 52%. The core q profile therefore controls the frequency of the mode, but not its existence. This correction is what brought the simulations close to the experiment.
Two of the simulated frequencies then agree with the measurement. The radial position of the EP pressure peak was scanned on both equilibria. The two scans give almost the same results, except at one position. When the EP pressure peaks near mid-radius, only the modified equilibrium gives a mode at 0.0817 times the Alfven frequency, which is 44.89 kHz. The original equilibrium gives a different mode there. This match therefore appears only after the core q maximum is removed. When the EP pressure peaks further out, both equilibria give the same mode at 0.1896 times the Alfven frequency, which is 104.14 kHz. This mode is carried mainly by the m = 4 harmonic. It lies in the m = 3/4 continuum gap, but it also crosses the continuum, so it is not a gap mode in the strict sense. These two frequencies, 44.89 and 104.14 kHz, are the strongest link between the simulations and the experiment so far.
Next, the nonlinear behaviour and the redistribution of resonant particles will be examined, and a detailed comparison with the experiment will be made.