Anisotropic pressure and finite hot-electron Larmor-radius effects on ring stability Page: 17 of 22
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-13-
To evaluate I2h ' I4h , and T5h , we first note that
h = w*h - (vih/aih)2(1 A)wbh '
where the wbh term is obtained by keeping E,u constant in the spatial gradient
of Fh , and A = Ah . In the limit wl < lw*h. ' lbhl , we haveand
I2h (h 4 + A - 1 .,
I4h 2 * + 2(A - 1)
I5h wh + 3(A - 1)]The integral
because the lowest
pressure balance.
I3h = (1
bhI3h has to be evaluated to higher order in E and w/wbh
order terms cancel in D3 due to the equilibrium perpendicular
Evaluating I3h to higher order yields
)w +h- 1 + c + (A - 1) (2- .Using the preceding approximations, Di , D2 , and D3 can be rewritten as
D = 2 + iC e - bh[1 + + (A - 1)(2 + 1h11
D2 =wb.{E1 - C -pc + bh + AEbh[1 - 'h(A - 1)] (
J (26)
and
b1 ) - 1i+ h)
03= - C +bh+S c(1 + W' -
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Tsang, K. T.; Lee, X. S. & Catto, P. J. Anisotropic pressure and finite hot-electron Larmor-radius effects on ring stability, report, September 1, 1982; United States. (https://digital.library.unt.edu/ark:/67531/metadc1183030/m1/17/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.