An approximate expression for the maximum pellet displacement can be derived as follows. In Reduced MHD, the equilibrium condition is

Approximate this equation by

where is the pellet pressure,
is the pellet radius,
and measures the extent of the pellet cloud
in the toroidal angle
The factor the component of the *R* unit vector
along the outward normal to the magnetic surface,
accounts for the relative direction of the shift.
The equilibrium at the pellet is
approximately

Combining these approximations, one finds that

where and is the backgound pressure. Plugging in and gives

The data from Fig.5, Fig.10 and Fig.15 is collected in Fig.16, which plots the maximum shift as a function of Included are other runs with with as well as with and Several cases were initialized with a simple non adiabatic model, in which the temperature was not modified to give an invariant pressure profile. The maximum displacement (16) is proportional to In the adiabatic case is given by (10), and in the nonadiabatic case by The adiabatic case is marked by filled circles in Fig.16, and the simple case by open circles. The data is consistent with a straight line fit to the dotted line given by (17). The left most point from Fig.10, the inboard injection case, has the maximum possible deviation the pellet having penetrated to the center.

It may be useful to express (16) in terms of a pellet displacement the total pellet particle number and the background particle number Taking and gives

The result (18) shows that sufficiently massive and localized pellets can have large excursions.

Wed Jan 7 14:23:34 EST 1998