Mach 3 is a 3D MHD Simulation program. Upgraded from a 2D code, Mach
2, by Uri Shumlak. [ Mach3 Fig. ]. It was written in FORTRAN.It is
a powerful simulation tool which
is capable of both Lagrangian (riding on a fluid element) and Eulerian (sitting in a fixed point
in space) views.
It solves the following equations:
- Ion Specific Internal Energy
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Axisymmetric plasma equilibria without flow are described by the
Grad-Shafranov equation: 
where the elliptic differential operator expressed in the cylindrical
coordinates R and Z is 
An equilibrium is described in terms of the flux function 
,
where 
, which is the poloidal flux per radian.
Note that the azimuthal angle Theta is ignored due to axisymmetry. Here 
is the plasma pressure and 
is 
times the poloidal current enclosed by the flux surface Phi. To solve this
nonlinear equation for Phi one must first choose 
, 
,
and the boundary conditions.
The EFIT code (Lao et. al., Nuclear Fusion 25 (11), 1985, pp. 1611-22)
was developed at General Atomics for use with the D-III tokamak device.
As input it uses various surface magnetic data, along with so-called 'global
parameters', for instance the total plasma current Ip and the excluded
toroidal flux 
.
The function and
are given assumed polynomial forms, where the number of parameters for
both is supposed to be less than or equal to the number of global parameters.
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The equilibrium is then reconstructed by a series of interleaved
iterations: each equilibrium calculation is followed by minimization, where
small modifications bring it closer to the experimental data, then the
equilibrium is re-calculated, and so on.
HIT-II experimental diagnostics can directly measure
for the open flux. Modifications to EFIT are underway that will use these
measurements directly as input, rather than merely a functional form for
Designed by
Trinh Phan.
Last modified: 24-June-1999
