Effect of the electron redistribution on the nonlinear saturation of Alfvén eigenmodes and the excitation of zonal flows

Abstract

Numerical simulations of Alfvén modes driven by energetic particles are performed with the gyrokinetic (GK) global particle-in-cell code ORB5. A reversed shear equilibrium magnetic field is adopted. A simplified configuration with circular flux surfaces and large aspect ratio is considered. The nonlinear saturation of beta-induced Alfvén eigenmodes (BAE) is investigated. The roles of the wave–particle nonlinearity of the different species, i.e. thermal ions, electrons and energetic ions are described, in particular for their role in the saturation of the BAE and the generation of zonal flows. The nonlinear redistribution of the electron population is found to be important in increasing the BAE saturation level and the zonal flow amplitude.

Gyrokinetic investigation of Alfvén instabilities in the presence of turbulence

“…The saturation level of the BAE for this value of Krook is E r ≃ 1.0 × 10 5 V m −1 (lowering the value of the Krook corresponds to decreasing the artificial damping and reaching a higher saturation level). This value is found to be the same as in the absence of turbulence (see [36]). This means that the nonlinear effects of both the nonzonal field associated with the ITGs and the zonal field of the ITG-generated zonal flows, on the dynamics of the BAE, are negligible.…”

“…In order to understand this, we can calculate the value of the ion diamagnetic frequency, for a mode with n = 5 sitting at s = 0.4: ω * /Ω i = ρ * 2 nqκ ni = 8.8 × 10 −5 . The diamagnetic frequency is about two orders of magnitude lower than the mode frequency [36]. So, for our case, we have that an energetic species with the same concentration of the thermal species, is expected to carry a radial flux of about two orders of magnitude higher than the thermal species, due to the higher temperature (one order of magnitude) and higher density gradient (one order of magnitude).…”

“…For comparison, we also provide here the linear growth rate of two low-n modes which are important in the nonlinear simulations discussed in the next sections, namely the BAEs with n = 5 and n = 10 (whose dynamics in the presence of EPs has been described in [36]). In the absence of EPs, and in the absence of sources/sinks, the growth rates of these two modes are respectively γ = 0.5 × 10 −4 Ω i , and γ = 2.3 × 10 −4 Ω i .…”

“…a composition of several poloidal components and an amplitude of the scalar potential peaked at the low-field side. Note that in the presence of the nominal population of EPs (described in section 3), the BAE with n = 5 is the dominant instability, with γ = 6.9 × 10 −4 Ω i in the absence of sources/sinks (see the detailed description in [36]).…”

Nonlinear reversed shear Alfvén eigenmode saturation due to spontaneous zonal current generation

“…In this work, it is assumed that the RSAE is excited by a source outside this nonlinear system, such as EPs, and the nonlinear coupling is dominated by bulk plasma contribution. For the cases with EPs contributing significantly to nonlinear ZFZS generation (Todo, Berk & Breizman 2010;Biancalani et al 2020), interested readers may refer to Qiu et al (2016aQiu et al ( , 2017 for more systematic discussions. To start with, we consider the two-field coupled system which consists of a RSAE (subscript 'R') and ZFZS (subscript 'Z'), i.e.…”