Part IV, Problems 5.1 to 5.5

Axisymmetric linear mean-field dynamo models
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The files you have grabbed are:

   sphdyn_eig.f  --> Fortran-77 source code
   butterfly.idl --> IDL source code, to make butterfly diagram
		     (as Fig. IV.5.4 in notes)
   medplane.idl  --> IDL source code, to display solutions
		     in meridional planes (as Fig. IV.5.2 in notes)

To facilitate use, nothing very fancy has been done in terms
of Input/Output. The fortran code is fully self-contained
(does not need to be linked to anything), and produces a
single unformatted output file, to be read by the IDL graphics codes.

Likewise, the IDL codes are set up to be fully self-contained,
and read the output file produced by the fortran code every time
they are run.

If you are an experienced Fortran and/or IDL user, feel free
to tailor the I/O to your tastes (but don't come and bug me
if the codes no longer work...)

The following gives a few bits of information on running fortran
and IDL codes, as well as useful hints for some of the problems.

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1. Running the Fortran code

   Under most Unix operating systems, compiling a self-contained
   fortran code will involve a command such as

   f77 code.f

   which will produce an executable usually called a.out
   Running the code is carried out by simply typing

   a.out

   And that's it. The input parameter values (C_alpha, C_omega, etc.)
   as well as the output filename are set in the code itself, so
   every time you want to change these you must recompile the code.
   Not elegant, but simple and it works.

   Note that the code is standard fortran-77, which means that it
   can be compiled using a fortran-90 compiler.

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2. Running the IDL postprocessing codes

   To run the IDL postprocessing codes you must first start IDL, which
   on Unix systems usually means typing

   idl

   you will then get the idl prompt

   IDL>

   To compile and run the IDL postprocessing codes, simply type

   IDL> .run medplane.idl

   which should produce output to the screen. To plot different
   output files you need to edit the IDL codes and change the name
   of the variable solfile near the top of the source code.
   Again not elegant, but simple and it works.

   To produce printable postscript, you need to type the sequence

   IDL> set_plot,'ps'
   IDL> device,filename='outputfile.ps'
   IDL> device,/portrait,yoffset=2,xsize=18,ysize=14
   IDL> .run medplane.idl
   IDL> device,/close

   This will produce an output file called outputfile.ps, which
   you can send to your favorite postscript printer. The various
   size specification (third IDL> input line) ensure that your
   plot will have the aspect ratio needed so that your spherical
   quadrants do not turn out oblate or prolate.

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3. Continuation schemes [ problems 5.3 and 5.5 ]

   In constructing sequences of solution it is a good idea
   to proceed as follows; the hardest thing to do will be to
   obtain your first solution, for a given dynamo number.
   This will involve some trial-and-error until the code
   converges to a solution. Call the corresponding dynamo
   number and solution eigenvalue D_1 and s_1. Your sequence
   of N solutions can be constructed as follow:

   for n=2,N do begin
      set: D_n  = D_n-1 *delta
      set: mu_n = s_n-1
      inverse iteration yields: s_n
   enddo

   where delta is some multiplicative increment in dynamo number
   (1.5 to 2 seems to work well), and mu is the trial eigenvalue
   needed by the inverse iteration. The idea is that for small
   enough delta, s_n-1 will always be a good guess for s_n.
   In this way it is relatively straigntforward to construct
   sequences of eigensolutions where one of the input parameters
   (for example C_alpha) is varying.