BOLSIG+ is a free and user-friendly computer program for the numerical solution of the Boltzmann equation for electrons in weakly ionized gases in uniform electric fields, conditions which occur in swarm experiments and in various types of gas discharges and collisional low-temperature plasmas. Under these conditions the electron distribution function is non-Maxwellian and determined by an equilibrium between electric acceleration and momentum and energy losses in collisions with neutral gas particles.

The main utility of BOLSIG+ is to obtain electron transport coefficients and collision rate coefficients from more fundamental cross section data, which can then be used as input for fluid models.

The principles of BOLSIG+ can be summarized as follows:

  • Electron-neutral collision cross sections versus electron energy are read from input files.
  • It is assumed that the electric field and collision probabilities are constant in space and time and that there are no boundaries.
  • Angular dependence of the electron velocity distribution is approximated by two-term Legendre expansion.
  • Electron production/loss due to ionization/attachment is assumed to result in exponential growth/decay of the electron number density.
  • Under the above assumptions, the Boltzmann equation reduces to a convection-diffusion equation with non-local source term in energy space, which is then discretized by an exponential scheme and solved for the electron energy distribution function by a standard matrix inversion technique.
  • Various electron transport coefficients and rate coefficients are calculated and accessible in different numerical/graphical forms and output file formats.
  • Additional options are provided for AC electric fields, crossed electric and magnetic fields, electron-electron and electron-ion collisions, …

Developed by Gerjan Hagelaar of the LAPLACE laboratory in Toulouse in France, BOLSIG+ was first released in 2005 as a replacement for the earlier BOLSIG solver developed by Leanne Pitchford, Jean-Pierre Boeuf and Lowell Morgan.