Pullback transformation in gyrokinetic electromagnetic simulations

Abstract

It is shown that a considerable improvement in the global gyrokinetic electromagnetic simulations can be achieved by a slight modification of the simulation scheme. The new scheme is verified, simulating a Toroidal Alfv\'en Eigenmode in tokamak geometry at low perpendicular mode numbers, the so-called "MHD limit". Also, an electromagnetic drift mode has been successfully simulated in a stellarator.Comment: Paper submitted for publicatio

Mitigation of the cancellation problem in the gyrokinetic particle-in-cell simulations of global electromagnetic modes

“…Due to the progress made in understanding the numerical issues inhibiting the electromagnetic gyrokinetic codes, it has become possible to simulate Alfvénic physics using the global gyrokinetic particle-in-cell code GYGLES: Toroidal Alfvén Eigenmodes (TAE) [16][17][18][19], Global Alfvén Eigenmodes [16], the internal m = 1, n = 1 kink mode and m = 1, n = 1 reconnecting modes [20]. Later on, another approach to the mitigation of the cancellation problem has been developed [21]. This approach is based on the so-called mixed-variable formulation [22] of the gyrokinetic theory.…”

An explicit large time step particle-in-cell scheme for nonlinear gyrokinetic simulations in the electromagnetic regime

“…The pullback transformation scheme proposed in [9] is a new scheme for the solution of the electromagnetic gyrokinetic equation by particle methods. While the scheme could already be used for linear simulations of fusion devices [10], we here aimed at investigating its numerical behaviour more fundamentally.…”

“…[9]. Contrary to the p -formulation, where p contains A , in the mixed formulation only the Hamiltonian part A h is absorbed into the new variable u .…”

“…In Ref. [9] the equations of motion have been linearised by neglecting quadratic field terms, thereby neglecting especially the "flutter" term 1/B * ∇ A s ·( b×∇ Φ ) in Eq. (14).…”

“…This approach was further extended in the "pullback transformation scheme" (PTscheme) to also apply to non-MHD modes [9] and showed good performance for different configurations and parameter regimes [10]. Nevertheless, some issues regarding this scheme remained and will be investigated here.…”