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DIII-D, #89943, t=1.7 sec

DIII-D, #89943, t=1.7 sec. 1. The first critical gradient.

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DIII-D, #89943, t=1.7 sec

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  1. DIII-D, #89943, t=1.7 sec

  2. 1. The first critical gradient We find the first critical gradient by the canonical profiles theory. The canonical profile for the function  = 1/q(denoted below as с) can be found by the solution of the Euler equation for the free plasma energy functional [1] 2Gc2/ + (/2) / ((1/ V) (VGc)) = Cc/V.(1) Here:indexSmeans the plasma boundary, iс = 1/V/(G Vс)is the dimensionless current density, Vis the plasma volume,V= V/, G = R2<(grad )2/r2>is the metric coefficient.

  3. The solution of Eq. (1) and the constants Сandare determined by the following four boundary conditions: c(0) = 0 ~ 1, c(0) = 0,c(max) = S, X [ic/(2Gc)]S = G(a)1/2S/0 (2) The first dimensionless critical gradientsfor the temperature and density are following: Tc = R/LTc -RTc/Tc = - 2/3 Ric/ic, nc -Rnc/n = - 1/3Ric/ic. (3)

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