Numerical heating of electrons in particle-in-cell simulations of fully magnetized plasmas

Abstract

The role of spatial resolution of the electron gyroradius in electrostatic particle-in-cell (PIC) simulations is studied. It is demonstrated that resolving the gyroradius is crucial for simulations of strongly magnetized plasmas and that nonresolving it results in substantial anisotropic heating of electrons. The numerical heating can, in some cases, be suppressed by the higher-order weighting to the grid, but it cannot be avoided. Possible mechanisms behind this numerical heating are discussed. The study is carried out with a fully three dimensional electrostatic PIC code with an external magnetic and electric fields.

Electron energy distribution function in a low-power Hall thruster discharge and near-field plume

“…The amplitudes of the high-energy peaks on the computed EEDFs are smaller with respect to those found on the experimental EEDF; however, their amplitude is well above the noise level that occurs in our PIC simulations. 36 Hence, the fast electron groups on the EEDFs estimated experimentally correspond to the electrons emitted by the cathode and accelerated by the difference between the cathode and the plasma potential almost without collisions with the ions in the plasma plume. The PIC model yielded also the spectrum of potential fluctuations.…”

“…The first order weighting is sufficient to maintain a numerical stability in such simulations where the electron gyroradius is well resolved on the grid. 36 The code as well as its tests with regard to numerical noise is described in more detail in the previous publications. [37][38][39] For our simulations, we used Cartesian coordinate system and periodic boundary conditions, which means that the values of electric potential generated by particles were the same on the opposite sides and edges of simulation box.…”

Dispersion chain of quantum mechanics equations

“…In applied problems of plasma physics [19,21,22], astrophysics [23][24][25][26][27][28], statistical physics [29][30][31], solid state physics [32][33][34], accelerator physics [35][36][37] the best known is the Vlasov equation for the function f 1,2 = f 1,2 (⃗ r,⃗ v, t), which is obtained as a result of chain cut-off in the second equation using the approximation m ⃗ v 1,2…”

On the validity of quasilinear theory applied to the electron bump-on-tail instability

“…Many numerical studies have been done comparing quasilinear analysis to solutions of the Vlasov equation using particle-in-cell (PIC) method [15][16][17] . Yet it is well-known that PIC methods are prone to errors due to statistically sampling the sensitive trajectories of the continuous distribution [18][19][20] , so it is worthwhile to explore alternative kinetic modeling methods. In one such alternative the equation for the continuous distribution is solved by a demonstrably convergent and conservative finite element discretization of phase space, using for example discontinuous Galerkin methods [21][22][23] .…”