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Neutral Density Model

Neutral hydrogen atoms and deuterium atoms created at the limiter surface through recycling of plasma ions or desorption of trapped gas penetrate only a few centimeters before they become ionized, either through charge-exchange with a plasma ion or through direct ionization by thermal electrons or ions. These are the cold wall neutrals, so-named because they have a very low energy, a few to a few 10's of eV. Their density decreases exponentially with increasing distance into the plasma, typically by many orders of magnitude, because the charge-exchange and ionization cross sections are large at low energy.

If a neutral's life is terminated by a charge-exchange event, it is effectively reincarnated as a new neutral (possibly of a different ion species, but that is a detail) whose energy is comparable to the local ion temperature, moving in an arbitrary direction. This warm neutral will also move a few centimeters before suffering a subsequent charge-exchange or ionization event, but its mean-free-path is likely to be greater than that of the original cold wall neutral, since its energy is higher. If its life is terminated by an ionization, the family tree of the original cold wall neutral is terminated. But if it charge-exchanges with yet another thermal ion, a new generation of neutral is born. If the neutral's trajectory was toward the plasma center, the next generation is likely to have still higher energy, and therefore a still larger mean free path.

Each generation of warm neutral (note the singular: a charge-exchange event can produce only one neutral for each incident neutral) has some probability of charge-exchanging, and some probability of terminating the chain through ionization. Thus, the density of warm neutrals also decreases with increasing distance into the plasma, but more slowly than the cold wall neutral population, because it has a higher temperature and a larger mean free path.

There is an additional source of neutrals in the plasma, arising from charge-exchange of incident beam neutrals with thermal ions. This creates a population of halo neutrals with a source profile roughly similar to the beam deposition profile, and with a neutral temperature close to the local ion temperature. The physics of this neutral population is governed by the same principles: the neutrals travel on average one mean free path before being ionized or charge-exchanging on other thermal ions, creating successive (but successively smaller) generations of halo neutrals.

The density of both the wall neutral population (cold and warm) and the halo neutral population is calculated in SNAP with a routine adapted from S. Tamor's ANTIC [] code.

The source term for the halo population is provided by the beam deposition routines. For the wall neutral population, we require a boundary condition: the edge neutral density (an edge temperature, effectively the temperature of the cold wall neutrals, is also specified by the user through the SNAP.DAT file).

Obviously, given some value for the edge neutral density, the neutrals code can calculate the neutral density profile as a function of radius. It can then integrate the ionization rate over the entire plasma to determine the total rate of ionization events from wall neutrals (which will be heavily dominated by the contribution from near the plasma edge). Since the mechanism is linear--doubling the edge neutral density will double the neutral population everywhere and will double the total integrated ionization source--only one calculation is required to determine the ratio between edge neutral density and total ionization source.

An experimental estimate of the total ionization source is obtained by measuring the intensity of H emission along 5 viewing sightlines in a poloidal plane, which strike the inner bumper limiter at 4 roughly equally spaced locations (the fifth sightline passes above the inner bumper limiter and generally sees little signal). Some of the H emission originates from outside the last closed flux surface, and therefore is not associated with a particle source that fuels the plasma. By comparing the poloidal distribution of the H light to Monte-Carlo simulations using the DEGAS code [], it is possible to characterize transport in the edge region roughly and to obtain, with factor-of-2 accuracy, an estimate of the total ionization source rate.

A number of such studies with DEGAS found that the ratio of total ionization source rate to summed H intensity from the 5 viewing chords is roughly a constant. This is the so-called magic number which is used in SNAPIN to convert from H measurements to total ionization source rate. The value of this multiplicative scaling factor can be changed in the recycling submenu of the impurities menu in SNAPIN, should you wish to.

next up previous contents index
Next: Plasma Density Up: Physics of SNAP Previous: RF models

Marilee Thompson
Fri Jul 11 15:18:44 EDT 1997