A gyro-kinetic model for trapped electron and ion modes

Abstract

In tokamak plasmas, it is recognized that ITG (ion temperature gradient instability) and trapped electron modes (TEM) are held responsible for turbulence giving rise to anomalous transport. The present work focuses on the building of a model including trapped kinetic ions and trapped kinetic electrons. For this purpose, the dimensionality is reduced by averaging the motion over the cyclotron motion and the "banana" orbits, according to the fact that the instabilities are characterized by frequencies of the order of the low trapped particle precession frequency. Moreover, a set of action-angle variables is used. The final model is 4D (two-dimensional phase space parametrized by the two first adiabatic invariants namely the particle energy and the trapping parameter). In this paper, the trapped ion and electron modes (TIM and TEM) are studied by using a linear analysis of the model. This work is currently performed in order to include trapped electrons in an existing semi lagrangian code for which TIM modes are already taken into account. This study can be considered as a first step in order to include kinetic trapped electrons in the 5D gyrokinetic code GYSELA [J. Abiteboul et al., ESAIM Proc. 32, 103 (2011)].

Transport Barrier Triggered by Resonant Three-Wave Processes Between Trapped-Particle-Modes and Zonal Flow

“…In particular, we present numerical results obtained from the numerical integration of a reduced hamiltonian (Vlasov) gyrokinetic model for the trapped particle modes, and based on the action-angle model discussed in [12,13,26] and in Refs. [27][28][29] for two species. We address here the physical mechanisms responsible to strong amplification of ZF and the resulting TB's formation.…”

Stimulated zonal flow generation in the case of TEM and TIM microturbulence

“…Our reduced model with trapped kinetic ions and electrons covers both TIM/TEM regimes simultaneously [16,17]. The turbulence driven by trapped particles is characterized by frequencies of the order of a slow trapped particle precession frequency.…”

“…The gyro-bounce average filters the fast frequencies ω c (cyclotron frequency) and ω b (bounce frequency) and the small space scales ρ c (Larmor radius) and δ b (banana width). It reduces the dimensionality of the model from 6D to 4D [11,16,17].…”

“…More information on the model can be found in [11,12,16,17,19]. The same assumptions are used hereafter and the model can be summarized as follows.…”

“…Recently, a semi-Lagrangian nonlinear simulation code, TERESA-4D (Trapped Element REduction in Semi lagrangian Approach), has been developed based on this model for trapped ions, making efficient use of parallel computing [14,15]. We recently expanded TERESA to simultaneously describe both trapped-ion (TIM) and trapped-electron (TEM) driven modes [16,17,18]. The code's most interesting property is that it enables the processing of the full f problem for trapped ions and trapped electrons at very low numerical cost [17].…”