Particle-in-cell investigation of the nonlinear saturation of Shear Alfvén Modes in hollow-q-profile tokamaks

The stability and dynamics of Shear Alfvén modes in Tokamak equilibria characterized by non-monotonic q profiles is a relevant issue in the investigation of auxiliary-heated as well as ignited-plasma properties because of the role that such q profiles could play in obtaining improved confinement regimes. Two main elements could play a specific role in determining the Alfvén mode behaviour in these equilibria: first, the existence of an improved confinement region in an ignited plasma implies the formation of a steep thermal-plasma temperature profile, and, possibly, a much steeper alpha-particle radial distribution, with very high values of the energetic (“hot”) ion pressure gradient, β′ H . Second, the particular shape of the q profile affects both the gap and the resonant-excitation frequencies, the radial extension and the toroidal coupling of the different poloidal harmonics as well as the energetic-ion drive intensity (estimated by α ≡ −R0qβ H). In this paper we want to address the latter point by analysing the results obtained by means of the Hybrid MHD-Gyrokinetic Code (HMGC) [1]. This code solves the set of reduced, O( 3) ( ≡ a/R), MHD equations for a low-β core plasma and the Vlasov equation for the energeticion population, using particle-in-cell techniques. Energetic particles contribute to the dynamic evolution of the electromagnetic fields through an energetic-ion pressure term in the MHD equations. The code, then, allows us to describe, in a self-consistent way, the resonant interaction between the Alfvénic modes and the energetic ions. Several approximations are however intrinsic to HMGC, such as large-aspect-ratio expansion, shifted circular magnetic surface equilibria and the assumption of an isotropic Maxwellian distribution function for the energetic ions. Much cautiousness has then to be used when comparing the simulation results with JET or other device’s experimental ones. Moreover, in the specific numerical simulations presented here, we only retain full nonlinear wave-particle interactions, while neglecting nonlinear mode-mode couplings among different toroidal mode numbers n.