Alternating Dimension Plasma Transport in Three Dimensions
Alternating Dimension Plasma Transport in Three Dimensions
Harold Grad
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4) first with J, then with B, and then average, to obtain = -^| + (4. 6) d * dt = -|l + P, ' f 1^2V 14 = (4. 7) = ip' (£±0-2 ~ f 2 a l^ It remains to evaluate the periods f, and f_. Taking the jump of (4. 3) across either E, or £», = [Va] || - V* [|£] + [Vf] . Note that only the projection of [Va] is zero for a surface potential a. First take a = a. And the indicated jump across Z~ where [a. ]_= 1 [cf. (2. 8)]. This implies that [Va, ]- = and [3a /at], = 0, hence [f]y = c, (t) . Similarly, ...for a = a~, [g], = -c-(t). The remaining period of f or g can then be eliminated between (4. 6) and (4. 7) giving dip. Dip. 2 dl. Ip! 2 I! (4 - 8) dt 1 = ' diT + d^ " c i= " p^ + p^ - Ci These are the two averaged flux conservation equations. They reduce to the conventional equations in the case of an ignorable coordinate (two dimensions, axial symmetry, helical symmetry), These equations could be used, in principle, to advance \p . In time, since the right side is known in terms of a given, instantaneous equilibrium state, Vp = J*b.
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