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VII. Pellet Displacement

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 tex2html_wrap_inline1021 is the pellet pressure, tex2html_wrap_inline1023 is the pellet radius, and tex2html_wrap_inline1025 measures the extent of the pellet cloud in the toroidal angle tex2html_wrap_inline1027 The factor tex2html_wrap_inline1029 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 tex2html_wrap_inline765 at the pellet is approximately


Combining these approximations, one finds that


where tex2html_wrap_inline1037 and tex2html_wrap_inline1039 is the backgound pressure. Plugging in tex2html_wrap_inline1041 and tex2html_wrap_inline1043 gives


The data from Fig.5, Fig.10 and Fig.15 is collected in Fig.16, which plots the maximum shift tex2html_wrap_inline815 as a function of tex2html_wrap_inline1047 Included are other runs with tex2html_wrap_inline1049 with tex2html_wrap_inline1051 as well as with tex2html_wrap_inline1053 and tex2html_wrap_inline1055 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 tex2html_wrap_inline1057 In the adiabatic case tex2html_wrap_inline1021 is given by (10), and in the nonadiabatic case by tex2html_wrap_inline1061 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 tex2html_wrap_inline1063 the pellet having penetrated to the center.

It may be useful to express (16) in terms of a pellet displacement tex2html_wrap_inline1065 the total pellet particle number tex2html_wrap_inline1067 and the background particle number tex2html_wrap_inline1069 Taking tex2html_wrap_inline1071 and tex2html_wrap_inline1073 gives


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

next up previous
Next: VIII. Conclusion Up: MHD Effects on Previous: VI. Intermediate Injection

Hank Strauss
Wed Jan 7 14:23:34 EST 1998