Nonlinear velocity redistribution caused by energetic-particle-driven geodesic acoustic modes, mapped with the beam-plasma system

Abstract

The nonlinear dynamics of energetic particle (EP) driven geodesic acoustic modes (EGAM) in tokamaks is investigated, and compared with the beam-plasma system (BPS). The EGAM is studied with the global gyrokinetic (GK) particle-in-cell code ORB5, treating the thermal ions and EP (in this case, fast ions) as GK and neglecting the kinetic effects of the electrons. The wave-particle nonlinearity only is considered in the EGAM nonlinear dynamics. The BPS is studied with a 1D code where the thermal plasma is treated as a linear dielectric, and the EP (in this case, fast electrons) with an n-body hamiltonian formulation. A one-to-one mapping between the EGAM and the BPS is described. The focus is on understanding and predicting the EP redistribution in phase space. We identify here two distint regimes for the mapping: in the low-drive regime, the BPS mapping with the EGAM is found to be complete, and in the high-drive regime, the EGAM dynamics and the BPS dynamics are found to differ. The transition is described with the presence of a non-negligible frequency chirping, which affects the EGAM but not the BPS, above the identified drive threshold. The difference can be resolved by adding an ad-hoc frequency modification to the BPS model. As a main result, the formula for the prediction of the nonlinear width of the velocity redistribution around the resonance velocity is provided.

Contributions to the linear and nonlinear theory of the beam–plasma interaction

“…In the following, with the aim of illustrating the direct implementation of the BPS as a paradigm for describing the burning plasma scenario, we introduce a mapping technique between the reduced radial profile of real systems and the velocity coordinate of the BPS. A validation of this approach can be found in Carlevaro et al (2019) (see also Carlevaro et al 2016b), where the ITER 15 MA baseline scenario is addressed in the presence of the least damped 27 toroidal AEs, and also in Biancalani et al (2018) for an application to the case of EP-driven geodesic acoustic modes.…”

“…Without entering the details of this step, η can be evaluated by assuming a direct proportionality between the linear growth rates (normalized to the mode frequency) of the BPS and the AE/EP scenario. The proportionality constant can be fixed requiring that the nonlinear transport is preserved (Biancalani et al 2018;Carlevaro et al 2019). Then, the integration of the linear dispersion relation for the BPS, which is analysed in the next section, directly provides the value of the density parameter.…”

“…2016 b ), where the ITER 15 MA baseline scenario is addressed in the presence of the least damped 27 toroidal AEs, and also in Biancalani et al. (2018) for an application to the case of EP-driven geodesic acoustic modes.…”

“…The proportionality constant can be fixed requiring that the nonlinear transport is preserved (Biancalani et al. 2018; Carlevaro et al. 2019).…”

Gyrokinetic modelling of anisotropic energetic particle driven instabilities in tokamak plasmas

“…Whereas, positive gradients of the distribution functions in velocity space are needed to drive EGAMs, and as a consequence of which a certain portion of EPs will be redistributed to lower energies. [26]. In previous work, analytical anisotropic distribution functions are bump-on-tail [9,26,8] and slowing down with pitch dependency [6,11,20,8], as well as single pitch Maxwellian [8].…”