Glenn Bateman, Arnold H. Kritz

Lehigh University Physics Department

16 Memorial Drive East, Bethlehem PA 18015

bateman@plasma.physics.lehigh.edu

kritz@plasma.physics.lehigh.edu

This file documents a subroutine called `mmm95`, which computes
plasma transport coefficients using the Multi-Mode transport model
which has been held fixed since 1995. A complete derivation of the
MMM95 model is given in reference [1]. Note, the mmm95
subroutine has been tested and used when compiled with flags such that
double precision is used. Note also, if this module is used in
another code, the minimum dimension required for cswitch is 23,
the minimum dimension for lswitch is 5 and fig, frb, and fkb
must all be dimensioned to a minimum of 4.

When sbrtn mmm95 is used in the BALDUR transport code to compute particle and thermal fluxes, smoothing of the gradients is normally needed for numerical stability. Note that the lower bounds of the gradient scale lengths are limited by the poloidal ion Larmor radius (zlarpo) in sbrtn mmm95.

The full matrix form of anomalous transport has the form

Note that all the diffusivities are in units of m/sec while the convective velocities and vfluxes are in units of m/sec.

WARNING: Do not add separate convective transport terms to this
anomalous transport model. All the anomalous transport
predicted by this Multi-Mode model is contained
in the diffusion coefficients `difthi` and `velthi` given
above.

We then enter a loop over the spatial zones, and establish local variables for all the input arrays for more compact notation.

To complete the rest of the calculation we then compute various
quantities needed for the transport flux formulas (as in Table 1 of
the Comments paper, from which
was inadvertantly omitted).
To begin with, we compute only quantities
which do not involve scale heights.
In the order in which they are computed, algebraic notation for
these quantities is:

The corresponding coding is:

Our formulas for the shear begin with

computed earlier in this subroutine. The minimum prescribed shear is

where =

The relevant coding for the calculations just described is: