Instabilities And Growth Rate of Guiding Center Diffuse Pinches
Instabilities And Growth Rate of Guiding Center Diffuse Pinches
Young Ping Pao
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B)]F ^ (6) where the subscript v denotes differentiation with respect to V, K is the magnetic field curvature, T = P'[(VP/p) + - (VP/p)-] (7) + and the constants a is given by a- = (e/M)7f(e/M)+- (e/M)"], (8) + + where e and M are respectively the charge (signed) and the mass of the ions and electrons. Following the nonnal-mode method, we consider the perturbations F = F° +f exp(ie), (9) ^1, 2 = Pl, 2+Pl, 2 e^P(iS) ' (10) B = B° +b exp(i9), (11) U = U exp(i9), p =3 p°+p^ exp(i0), (12) -6- where... 9 = (-cot + kz +mVn) S> ^-i^d u . We can then solve these equations for y], p, and p^ in terms of g and u . This result then enables us to express p, and Pp in terms of linear combinations of g and u . If these expressions are used in (l8) for x and C, we can then write T = K^g + {lG, )-\n^, (32) C = L^g + (icD)"%u^ . (33) The coefficients K-, Kp, L and Lp can be expressed in a convenient form if we introduce the functions ! jr, which may be written in full as i/^)'^^^ - K^ ] "- ^^^b2(v/v)2
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