Critical Mach
-------------

This IDL code can be used to calculate critical Mach numbers for
collisionless shocks as described in Kennel et al. 1985. It was
written in 2009 by Marc Pulupa (pulupa AT ssl.berkeley.edu).

This code is free for anyone to use or improve upon. It should work
simply by placing the relevant files in your IDL path. If you use this
code to calculate critical Mach numbers for publications, please cite
the original papers by Kennel et al. or Edmiston and Kennel. However,
I would be grateful if you let me know that you found this code
useful.


Included files:
---------------

crit_mf.pro - solves the Rankine-Hugoniot equations for various types
of critical Mach numbers. Outputs the critical value.

crit_mf_plot.pro - makes contour or surface plots of the critical Mach
number as a function of theta_bn and beta.

crit_mf_fig.crib - example file showing how to use crit_mf_plot to
replicate the plots in Kennel et al. 1985 and Edmiston and Kennel
1984.

critmach.pdf - gives a little background and explains the algebra
behind solving for the critical Mach number.

genarr.pro - IDL utility to generate evenly spaced 1D or 2D arrays of
numbers.

README.text - this file.


Dependencies not included in this package:
------------------------------------------

The plotting program uses TeXtoIDL code, available from:

http://physics.mnstate.edu/mcraig/textoidl/

The solver uses the ZBRENT procedure, which is part of the IDLASTRO
code:

http://idlastro.gsfc.nasa.gov/

The commands in crit_mf_fig.crib to open and close plots are available
as part of TDAS:

http://themis.ssl.berkeley.edu/software.shtml

If I have missed anything on this list (and if you get any errors when
trying to run the code, this is the most likely explanation) then send
me an email with the error message from IDL and I will gladly try to
help.


- Marc Pulupa, June 2012