Combining electromagnetic gyro-kinetic particle-in-cell simulations with collisions

Abstract

It has been an open question whether for electromagnetic gyro-kinetic particle-in-cell (PIC) simulations pitch-angle collisions and the recently introduced pullback transformation scheme [A. Mishchenko et al., Physics of Plasmas 21, 092110 (2014) and R. Kleiber et al., Physics of Plasmas 23, 032501 (2016)] are consistent. This question is positively answered by comparing the PIC code EUTERPE with an approach based on an expansion of the perturbed distribution function in eigenfunctions of the pitchangle collision operator (Legendre polynomials) to solve the electromagnetic drift-kinetic equation with collisions in slab geometry. It is shown how both approaches yield the same results for the frequency and damping rate of a kinetic Alfvén wave and how the perturbed distribution function is substantially changed by the presence of pitch-angle collisions.

Effects of collisions on the saturation dynamics of TAEs in tokamaks and stellarators

“…We used N p = 10 6 numerical marker particles in the standard runs. It has been reported before that for the particular collisional scheme used in EUTERPE the time step is more critical than the number of markers [27]. Nevertheless, the relative deviations in the linear growth rate (compared with the standard resolution) are well below 1%, which is very acceptable.…”

“…Being a PIC code, EUTERPE is very well suited to compute the collisions between the fast ions. The implementation of collisions into the electromagnetic version of EUTERPE has been benchmarked recently [27]. This reference also serves as a brief introduction to the EUTERPE code.…”

On non-linear frequency chirping in connection with collisions

“…The implementation of the pitch-angle collision operator into EUTERPE is described in detail in Refs. [9,36]. Furthermore, going back to Eq.…”

“…In the code, an operator splitting is employed. The pitch-angle part can be treated in the way described in [9,36]. The drag part, which contains only a first-order derivative with respect to velocity, can be incorporated into the regular equations of motion, i.e.…”