ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
The stability of a Migma disk is reexamined to determine the threshold to the interchange instability. It is shown that a previous calculation [Z. Naturforsch. Teil A 42, 1208 (1987)], which assumes a rigid mode eigenfunction, is inaccurate at the predicted particle number for marginal stability. As a result the integral equation for the system must be solved. A variational method of solution is developed and is shown to give good agreement with a direct numerical solution. The threshold for instability is found to be sensitive to the details of the distribution function. For highly focused systems, where all ions pass close to the axis, the threshold particle number (Nu1) for instability is substantially below that predicted by rigid mode theory (Nrigid) (by a factor ∼8ε2, where ε=r1/rL, r1 is the spread in the distance of closest approach to the axis, and rL the ion Larmor radius). At a higher density, a second band of stability appears that again destabilizes at yet a higher particle number (Nu2). If ε(very-much-less-than)1, Nu2 is substantially below the rigid mode prediction, while for 0.2〈ε〈0.3, Nu2 is comparable to the rigid mode prediction. At moderate values of ε (ε≈0.3–0.4) the second stability band disappears and the instability particle number threshold varies from the rigid stability threshold by a factor of 0.4ε, when ε=0.4, to 0.7ε when ε is about unity. The stability criteria would be consistent with the observed particle storage number obtained in experimental configurations if the spread in ε is sufficiently large.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.859008
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