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Stephen Biagi , Department of Physics, University of Liverpool
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
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
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
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.
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
The author can be contacted at
for further information.
For matters related to this article please contact the author.Cnl.Editor@cern.ch