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The confinement and slowing-down of energetic particles (EPs) generated by fusion reaction and/or neutral beam injection (NBI) are essential topics in achieving self-sustained burning plasma [1]. Alfvén instabilities, which can be driven unstable by EPs [2], can induce significant EPs transport [3], among which the toroidal Alfvén eigenmode (TAE) is an important component due to its minimal continuum damping in toroidicity-induced gaps [4, 5]. Thus, the nonlinear saturation mechanism of TAE is an essential topic. Previous studies focused on the nonlinear saturation of TAE due to EPs phase space nonlinearity, which predicted the quadratic dependence of saturation level of TAE on the linear growth rate. For future tokamaks with strong EPs activities due to fusion reaction and/or neutral beam injection, the saturation level of TAE due to EPs nonlinearity can be very high.
Thus, in this work, the effects of thermal plasma nonlinearities on the saturation of TAE are investigated using both gyrokinetic particle-in-cell (PIC) code ORB5 [6] and theory. More specifically, thermal plasma nonlinearity investigated here contributes to the excitation of zonal field fluctuations as well as phase space zonal structure (PSZS) of thermal ion and electrons [7], via beating of single-$n=6$ TAE and itself. The simulations are performed in both cases with/without $n=0$ zonal fields, while PSZS always exists in PIC simulation once the corresponding particle species evolves nonlinearly.
In the simulation without zonal fields, it is found that the saturation level of TAE is dominated by thermal plasma nonlinearity for $γ_L/ω>0.47%$, which is $eδϕ_n/T_e∼0.1$ and almost independent of linear drive; While the saturation level with only EPs nonlinearity is $eδϕ_n/T_e∼1$. Upon saturation, the decrease of mode frequency and separation of $m=10$ and 11 poloidal harmonics can be observed, resulting from PSZS of thermal plasmas. Meanwhile, the saturation level can be quantitatively obtained by the gyrokinetic theory.
In the simulation with zonal fields, it is found that their introduction can significantly counteract the effects of PSZS of thermal plasmas, leading to a factor 2 enhancement to the saturation level of TAE compared to the case without zonal fields, i.e., the case with only PSZS. Meanwhile, in both cases with/without zonal fields, the saturation level of TAE is found to be proportional to the square root of inverse aspect ratio, which is also predicted by the theory [8,9]. This fact implies a stronger TAE activity in devices with larger inverse aspect ratio.
Reference:
[1] L. Chen and F. Zonca, Review of Modern Physics 88, 015008 (2016).
[2] L. Chen, Physics of Plasmas 1, 1519 (1994).
[3] A. Fasoli, C. Gormenzano, H. Berk, et al., Nuclear Fusion 47, S264 (2007).
[4] C. Cheng, L. Chen, and M. Chance, Ann. Phys. 161, 21 (1985).
[5] G. Y. Fu and J. W. Van Dam, Physics of Fluids B 1, 1949 (1989).
[6] E. Lanti, N. Ohana, N. Tronko, et al., Computer Physics Communications 251, 107072 (2020).
[7] F. Zonca, L. Chen, S. Briguglio, et al., New Journal of Physics 17, 013052 (2015).
[8] F. Zonca, F. Romanelli, G. Vlad, and C. Kar, Phys. Rev. Lett. 74, 698 (1995).
[9] L. Chen, F. Zonca, R. Santoro, and G. Hu, Plasma Physics and Controlled Fusion 40, 1823 (1998).