Electromagnetic gyrokinetic PIC simulation with an adjustable control variates method

Nonlinear interplay of Alfvén instabilities and energetic particles in tokamaks

“…Dirichlet boundary conditions are imposed to the potentials. In PIC codes written in p formulation, a numerical problem called "cancellation problem" [27,28] arises in particular in the numerical resolution of the Ampère's equation. This is due to fact that the statistical error affects only the term discretized with markers (first term in Eq.…”

Global particle-in-cell simulations of fast-particle effects on shear Alfvén waves

“…A detailed description of the discretization procedure can be found in Refs. [26][27][28][29][30]. We apply the so-called phase factor transform [26] to all perturbed quantities in the code.…”

“…Fig. 14, we study the convergence of our simulations with respect to the number of iterations [30] used to achieve the cancellation in Ampére's law [27,33]. In all our simulations shown above, we have used N iter = 4.…”

Global particle-in-cell simulations of Alfvénic modes

“…In the past, electromagnetic PIC simulations have wrestled with stringent numerical constraints associated with the so-called cancellation problem [3,4]. This problem has been solved recently [3][4][5][6][7]. The key point to its solution is a careful balance between the adiabatic current computed with the markers and the so-called skin terms in Ampére's law discretized on the spatial grid.…”

“…We use the linear two-dimensional δ f PIC-code GYGLES [4][5][6][7][8][9][10][11]. The code allows for electromagnetic perturbations and treats all particle species (ions and electrons) on the same footing (kinetically).…”