MAGBOLTZ

The MAGBOLTZ program computes drift gas properties by "numerically integrating the Boltzmann transport equation"-- i.e., simulating an electron bouncing around inside a gas. By tracking how far the virtual electron propagates, the program can compute the drift velocity. By including a magnetic field, the program can also calculate the Lorentz angle. It can just as easily compute transverse diffusion coefficients, electron mobilities and other parameters, but since our apparatus does not measure those quantities, they are not included in our database's plots.

In order to find macroscopic parameters like the drift velocity, MAGBOLTZ needs to know about the microscopic nature of each gas under study. The most important quantities are the scattering cross sections, which measure how likely collisions are to occur, and the energy loss per collision. In some cases, such as the noble gas helium, the excitation energies are so high that over our experimental range, the drifting electrons lack the energy to excite the atoms, thus making all collisions elastic hard-sphere interactions. Other gases, like the organic quenchers CO₂, CH₄, etc., have vibrational and translational modes which the program must also take into account.

The article by Fraser and Matheison (cited below) provides a good introduction to the algorithms MAGBOLTZ contains for implementing various types of scattering. I recommend keeping this paper at hand while examining the MAGBOLTZ source code.

The program's author may be reached through the following:

Dr. S. F. Biagi,
Physics Department,
University of Liverpool,
Liverpool,
U.K.

For more information, please see the following web sites:

• Unofficial Magboltz Homepage
• Magboltz 2 page at CERN
• Listing of cross sections (somewhat outdated)

• S.F. Biagi, Nucl. Instr. and Meth. A 421 (1999) 234-240
  A description of the Magboltz program, with results compared to experiment.
• G.W. Fraser, E. Matheison, Nucl. Instr. and Meth. A 247 (1986) 544
  A more detailed article on Monte Carlo integration, as applied to electron motion.
• H.R. Skullerud, Brit. J. Appl. Phys. (J. Phys. D) 1 (1968) 1567
  Cited by both articles above, this communication describes how to stochastically choose the time increment used in the Monte Carlo simulation.

Finally, the following thesis contains an implementation of the electron-motion Monte Carlo algorithm in C, which may be easier to follow (or useful for comparison purposes). This paper and the references therein also discuss analytic approximations which can, in some circumstances, deliver results more rapidly than executing a long Monte-Carlo run.

• B. Stacey, Relation of Electron Scattering Cross-Sections to Drift Measurements in Noble Gases, 2005.