Given the source rate of beam ions and the local plasma
densities and temperatures, *SNAP* solves the Fokker-Planck equation
in each radial shell for the distribution function of the thermalizing
beam-ion population as a function of energy and pitch-angle. The
source rate in a given shell is computed by the beam
neutral deposition routine, and is essentially a set of delta
functions in energy (one for each energy component of each beam
source) multiplied by narrow functions in . Here
represents the pitch-angle of the beam ions as they cross the
horizontal midplane. The equation solved is:

The charge-exchange lifetime is in the limit where the beam ion velocity *v*
is much greater than the average neutral velocity. Since in
supershots the neutral temperature--which is comparable to the local
ion temperature--can approach the third-component beam energy,
*SNAP* integrates the reaction rate over the neutral velocity
distribution, ,
where and are the relative energy
velocity between the beam ion and neutral.

Up to this point the beam charge-exchange is regarded as a complete
loss, i.e., the possibility of reionization of the beam neutral
before it leaves the plasma has not been considered (indeed, this is
probably not a bad assumption for a single shell, given its small
width--but it will ionize some neutrals born in other shells). As
discussed in section 3.4, *SNAP* includes a crude
correction for this reionization term: a fixed fraction of the
charge-exchange losses are considered to be reionized *locally*.
The fraction is selected by the user, and is constant in space,
energy, and pitch angle. This is done simply by increasing
by the factor where R is the
reionization fraction.

Note that electric field and trapping effects are neglected. The equation is solved by expanding in a series of Legendre polynomials: .

Fri Jul 11 15:18:44 EDT 1997