Pullback scheme implementation in ORB5

Abstract

The pullback scheme is implemented in the global gyrokinetic particle-incell code ORB5 [S. Jolliet et al, Comp. Phys. Comm., 177, 409 (2007)] to mitigate the cancellation problem in electromagnetic simulations. The equations and the discretisation used by the code are described. Numerical simulations of the Toroidal Alfvén Eigenmodes are performed in linear and nonlinear regimes to verify the scheme. A considerable improvement in the code efficiency is observed. For the internal kink mode, it is shown that the pullback mitigation efficiently cures a numerical instability which would make the simulation more costly otherwise.

Orb5: A global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry

“…A further development of the mitigation schemes is given in Refs. [68,69], the so-called pullback mitigation based on the mixed-variable formulation [70] of the gyrokinetic theory, has also been implemented in Orb5 [37]. Mitigation of the cancellation problem made possible the Orb5 electromagnetic simulations described in Refs.…”

“…drift-kinetic electron dynamics, electromagnetic (EM) perturbations [26], multiple gyrokinetic ion species, inter and intraspecies collisions [27], hybrid electron model [28,29], removal of the long wavelength approximation [30], various heating sources [31,32] and strong flows [33], and the numerical side with e.g. the enhanced control variate [34,35,36], and, more recently, the mixedrepresentation "pullback" scheme [37] resolving the so-called cancellation problem for EM simulations, various noise control operators (generalized moment-conserving Krook operator [31], coarse graining [38], and quadtree [39]), and a thorough refactoring with multithreading using OpenMP and OpenACC which will be detailed in a separate publication. The aim of this paper is to review these improvements, and present the current status of the code and illustrate its performance and capabilities with a few significant results.…”

Gyrokinetic investigation of the damping channels of Alfvén modes in ASDEX Upgrade

“…The quasineutrality and Ampère equations are solved using the Galerkin methods and the perturbed fields are discretized through cubic B-splines finite elements defined on a grid (N s , N χ , N φ ). Finally it is important to mention that from the numerical side, recently the mixed-representation ("pullback" scheme [14]) has solved the so-called "cancellation problem" for electromagnetic simulations.…”

“…(14) Equation14 proves that the shear Alfvén waves are local plasma oscillations, having a frequency spectrum that varies continuously throughout the plasma radial direction. Due to the hypothesis…”

Effect of the electron redistribution on the nonlinear saturation of Alfvén eigenmodes and the excitation of zonal flows

“…The resolution of the Vlasov-Maxwell set of equations in a p formulation (also known as Hamiltonian formulation) with a δf (perturbed distribution function) particle-in-cell code is found to be affected by the cancellation problem, which can be mitigated with a control variate method, or with a pull-back scheme (Mishchenko, Hatzky & Könies 2004;Hatzky, Könies & Mishchenko 2007;Mishchenko et al 2017). The recent inclusion of the pull-back scheme greatly improved the efficiency of ORB5 (Mishchenko et al 2019), making these simulations feasible.…”