CERN Accelerating science

The Monte Carlo technique allows the solution of the transport equations to be independent of the series expansions in Legendre Polynomials or Spherical Harmonics required by analytic solutions of the Boltzmann equations. The technique lends itself easily to use by non-experts since the only inputs now required are the electric and magnetic fields, the angle between the fields, the temperature and pressure and the fractional composition of the gases. The program now has the option of calculating its own electron energy integration range: this option is enabled if the energy integration range is set to 0.0.

Intermediate output at six equally spaced integration intervals allows the accuracy of the solution to be monitored. An accuracy of better than 1 % for the drift velocity and 2 % on the diffusion coefficients can usually be guaranteed for a number of collisions given by the setting the input parameter NMAX = 10. It is possible however in very weakly quenched noble gas mixtures with less than 5 % molecular quencher that the solution will require a higher value of NMAX.

In pure noble gases at low electric fields below the ionisation region where only elastic collisions occur it is recommended that Magboltz 1 is used. The analytic solution Magboltz 1 in the elastic limit is an exact solution and the computation time is reduced in this case.

Experience with the new program shows that the accuracy with magnetic fields is much improved. This is primarily because the solution is more accurate than the Legendre expansion technique and is equivalent to the Spherical Harmonics expansion solution of Ness and Robson (see e.g. Phys. Rev. 47 E (1993) 327). A typical accuracy equal to measurement accuracy of about 1 ° can now be obtained for very large Lorentz angles (see first reference).

The program is available as a Fortran listing and includes some comments and instructions in the listing. The external requirements are only an efficient real*8 random number generator. The RNDM2 generator from the CERN library is used in the program. The typical execution time on an DEC Alpha is about 10 seconds for a better than 1 % calculation accuracy. There is an extensive list of about 30 gases covered by the program and mixtures of up to any four of them can be simulated.

The author can be contacted at sfb@hep.ph.liv.ac.uk for further information.