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

Abstract

A new algorithm for electromagnetic gyrokinetic simulations, the so called "pullback transformation scheme" proposed by Mishchenko et al. [Physics of Plasmas, 21, 092110 (2014)] is motivated as an elaborated explicit time integrator and investigated in detail. Using a numerical dispersion relation valid in slab geometry, it is shown that the linear properties of the scheme are comparable to those of an implicit v -scheme. A nonlinear extension of the mixed variable formulation, derived consistently from a field Lagrangian, is proposed. The scheme shows excellent numerical properties with a low statistical noise level and a large time step especially for MHD modes. The example of a nonlinear slab tearing mode simulation is used to illustrate the properties of different formulations of the physical model equations.

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

“…This expression is completely general and can also be used in the nonlinear simulations [23], implying in practice that the marker weight is kept fixed during the transformation, but its position "jumps" according to the coordinate transformation…”

“…[23]. These new terms reflect the fact that although the original p -Lagrangian and the mixed-variable Lagrangian describe the same physics, this symmetry is broken by the truncation involved into the perturbative Lie transform.…”

“…Clearly, this freedom can be used to taylor the numerical properties of the equations to be solved by a code as desired. For electromagnetic particlein-cell gyrokinetic codes, the mixed-variable formulation [21][22][23] is such a good choice reducing the numerical burden by proper coordinates. In this formulation, the v -and the p -gyrokinetics are "mixed" in such a way that the resulting equations have superior numerical properties compared to both original formulations without any significant computational penalty.…”

“…Further understanding of the mixed-variable mitigation has been achieved in Ref. [23]. The global particle-in-cell code EUTERPE [24] has been used in the papers [21][22][23].…”

“…[23]. The global particle-in-cell code EUTERPE [24] has been used in the papers [21][22][23]. Recently, a number of simulations have been performed addressing the Alfvénic physics, both in the linear and nonlinear regimes, using the gyrokinetic EUTERPE [25][26][27] and ORB5 [28,29] codes.…”