F a s t H e n r y   3 . 0 w r
                       -----------------------------
                                 10-21-2001

Modifications by:        Stephen R. Whiteley  ([email protected])
                         Whitleley Research Inc.

** This is the fasthenry-3.0-12Nov96 distribution with the following
   changes:

  1) Support for superconductive elements has been added.  This release
     is the successor to fasthenry-2.0S.

  2) All references to "malloc.h" in the source code have been changed
     to "stdlib.h" to avoid a cascade of warnings during compilation.

  3) A long expression in mutual.c which triggered a compiler bug in
     Red Hat Linux 6.0 has been altered to avoid the bug.

  4) This version of fasthenry returns status 0 if there are no
     errors, nonzero if an error occurs.  The original version had
     undefined return status.

  5) The latex files for the manual have been eliminated, since they
     are useless without the figures.  The master's thesis has been
     included instead (in the doc directory).

  6) Two superconducting example files, sline1.inp and sline2.inp
     have been added to the examples directory.

  7) Added declarations of static functions in sparse matrix package
     to avoid annoying compiler warnings.

  8) Ported to Microsoft Windows using the mingw (www.mingw.org)
     version of gcc.  To build under mingw, use "config mingw".  The
     source code was made sensitive to the following defines, which
     are all necessary for mingw.

     a) NO_SBRK            The library lacks the sbrk() function.
     b) NO_ATANH           Substitute for missing atanh() and asinh()
                           functions.
     c) NO_ISNAN           The library lacks isnan() and finite()
                           functions.

** 4-25-2001 Bug Fix:  .default lambda=xxx should work now

** 6-19-2001 Bug Fix:  Error in resistance computation fixed

** 10-21-2001 Changes:

  1) For segments with no sigma/rho/lambda defined with no explicit
     defaults, sigma now defaults to copper (5.8e7).  Previously this
     was a fatal error.

  2) When files are opened for writing, binary files are now opened
     in "wb" mode rather than "w" mode.  This is only important under
     Microsoft Windows, where binary data can be corrupted if file
     pointers are not explicitly opened in binary mode.

** 4-27-2004 Changes:

  Added #include "sparse/spMatrix" in Preconfig.c for declaration of
  spGetElement.  This is critical when ints and pointers are of different
  widths.

  Commented out redundant spGetElement declaration in newPreconfig.c.

  Declaration of umalloc added to mulGlobal.h in zbuf, for int/pointer
  width difference.

  All programs compile without warnings on 64-bit sparc gcc-3.x
  (Solaris 8) using CC = gcc and CFLAGS = -O -m64 -DFOUR.

** 1-11-2009 Changes:

  Misc. code tweeks to avoid compiler warnings when using newer
  compilers, e.g., gcc-4.2.


--------------------- Superconductivity Support -------------------------

This version of fasthenry has been modified to support superconducting
segments and ground planes.  The analysis used is based on the London
equations and the two-fluid model.  Both reactive and lossy components
of the superconductor complex conductivity are employed in obtaining
the impedance matrix.

Theory
------
 *
 *    In normal metal:     (1)  del X del X H = -i*omega*mu*sigma * H
 *    In superconductor:   (2)  del X del X H = (1/lambda)^2 * H
 *
 *    In fasthenry, (1) is solved, so the game is to replace sigma in
 *    (1) with a complex variable that includes and reduces to (2).
 *    We choose
 *
 *      sigma_prime = sigma + i/(omega*mu*lambda^2)
 *
 *    Then, using sigma_prime in (1) rather than sigma, one obtains
 *    an expression that reduces to (2) as omega -> 0,  yet retains
 *    properties of (1).  This is the two-fluid model, where the
 *    sigma in sigma_prime represents the conductivity due to unpaired
 *    electrons.
 *
 *    Since sigma_prime blows up at omega = 0, we work with the
 *    impedance, which we take as z = r1 + i*omega*r2 = i/sigma_prime.
 *    The r1 and r2 variables are thus
 *
 *           (3) r1 =    sigma*(omega*mu*lambda^2)^2
 *                    --------------------------------
 *                    (sigma*omega*mu*lambda^2)^2 + 1
 *
 *           (4) r2 =           mu*lambda^2
 *                    --------------------------------
 *                    (sigma*omega*mu*lambda^2)^2 + 1


Operation
---------

The input and output formats of fasthenry are unchanged, with the
exception of a new input parameter "lambda".  The lambda parameter is
the London penetration depth specified in the units in use, and can
appear in segment or ground plane specification lines, and .default
lines.  When lambda is given and nonzero, the element is analyzed as a
superconductor, and the sigma parameter defaults to zero (not the
conductivity of copper, as in the normal case).

If, however, a default sigma is specified, or a sigma specification
appears in the segment or ground plane line, that sigma will be used. 
The proper value for sigma is the sigma 1 from the two-fluid model,
which is the normal sigma times the ratio of the quasiparticle and
total carrier densities, a temperature dependent quantity.  For most
applications, the loss is small enough to be considered negligible, so
sigma need not be specified.

To obtain accurate results, a sufficient number of filaments must
exist in regions of high field gradient.  Although the ground plane
construct is supported, experience has shown that its use often leads
to inaccurate results presumably due to insufficient filamentation. 
Some of the new fasthenry-3.0 features may solve this problem, but
this has not been tested.  It may prove necessary to implement ground
planes with segments.

The large filament count consumes much memory.  This program benefits
from cpu power and memory.  Despite its name, be prepared to wait for
results.

Compilation is as described in the fasthenry documentation.  If for
some reason the superconductivity support is to be deleted, the
mulGlobal.h file should be edited to set "SUPERCON" to "OFF".


Interpretation of Results
-------------------------

Fasthenry computes an impedance matrix, which is written to a file
named "Zc.mat" when the run is complete.  This gives the inductance
values indirectly, through the imaginary parts divided by the radian
frequency (2PI times the value given for ".freq").  In order to
compute inductance, the specified frequency, i.e., the value provided
for the ".freq" parameter in the input file, must be nonzero.  For
superconductors, with sigma equal to zero, the inductances should be
independent of frequency, so the actual frequency chosen is not
important.  If the frequency is set to zero, FastHenry will compute
the resistance of the conductors only, which will be zero for
superconductors.