Construction and analysis of guiding center distributions for tokamak plasmas with ambient radial electric field

Abstract

The contribution of a time-independent toroidally-symmetric radial electric field $E_r$ is implemented in VisualStart (Bierwage et al. (2022) [21]), a code whose purposes include the construction of guiding center (GC) drift orbit databases for the study of plasma instabilities in tokamaks. $E_r$ alters the transit frequencies and orbit shapes of charged particles, and it shifts the trapped-passing boundary, especially in the thermal part of the velocity distribution. $E_r$ can also affect fast particle resonances in the kHz frequency range. Here, KSTAR, JT-60U and ITER tokamak cases are used as working examples to test our methods. In the course of our detailed consistency checks, we unravel how nonuniformities in the moments of a GC distribution emerge from the collection of individual GC orbits. We also discuss technical and practical issues connected with $E_r$, two of which shall be emphasized here: First, the GC orbit space is sampled in the magnetic midplane as before, and we find that, in the presence of $E_r$, midplane-based coordinates are not only equivalent but superior to conventional constants of motion, allowing to attain high numerical accuracy and efficiency with a relatively simple mesh. Second, the periodic parallel acceleration and deceleration of GCs via the mirror force is modulated by $E_r$. Although its poloidal transit (bounce) average is zero, this parallel electric acceleration gives rise to a reference point bias: When measured at fixed GC launch coordinates, the toroidal transit frequency of passing orbits acquires an apparent $E_r$-dependence, which can cause confusion.