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At low reduced electric fields the electron energy distribution function inheavy noble gases can take two distinct shapes. This "bistability effect" - inwhich electron-electron (Coulomb) collisions play an essential role - isanalyzed here for Xe with a Boltzmann equation approach and with a firstprinciples particle simulation method. The solution of the Boltzmann equationadopts the usual approximations of (i) searching for the distribution functionin the form of two terms ("two-term approximation"), (ii) neglecting theCoulomb part of the collision integral for the anisotropic part of thedistribution function, (iii) treating Coulomb collisions as binary events, and(iv) truncating the range of the electron-electron interaction beyond acharacteristic distance. The particle-based simulation method avoids theseapproximations: the many-body interactions within the electron gas with a true(un- truncated) Coulomb potential are described by a Molecular Dynamicsalgorithm, while the collisions between electrons and the background gas atomsare treated with Monte Carlo simulation. We find a good general agreementbetween the results of the two techniques, which confirms, to a certain extent,the approximations used in the solution of the Boltzmann equation. Thedifferences observed between the results are believed to originate from theseapproximations and from the presence of statistical noise in the particlesimulations.

Bistable solutions for the electron energy distribution function in  electron swarms in xenon via Boltzmann equation analysis and particle  simulations