A simple neoclassical point model is presented for the ELMO Bump¥ Torus experiment. Solutions for steady state are derived. Comparison with experimental observations is made and reasonable agreement is obtained. * Work supported by Energy Research and Development Administration under Contract W-7405-eng-26 with Union Carbide Corporation, Contract EY-76-C-03-0167, Project 38 with General Atomic Company, and Contr~ct AT-04-3-1018 with Science Applications, Incorporat~d.
High-beta, hot-electron plasmas have been produced by electron-cyclotron heating in the SM-1 axisymmetric mirror using closely-spaced multiple frequencies. The relativistic electrons produce annular distributions (ELMO rings) with as much as ten times more stored energy than with single-frequency heating. While larger frequency separations (Δf/f∼0.1) provide some control of the ring size, the dominant effects are associated with an improvement in heating efficiency which persists to very small frequency separations (Δf/f∼10−3). Details of the reconstruction of the ring distribution (both in steady state and during build-up), the influence of multiple frequency heating on fluctuations, axial electron losses, and a scaling of these effects with power are presented.
equation was the dominant nonlinearity (with adiabatic electrons).The maximum diffusion coefficient obtained from Eq. (9) occurs for b =6 0 = (1 + rfr m2^P B ml 9where the nonlinear and linear shear damping become comparable. Here, A PB = (L S /L n ) 3 (m e /m { ) is of order unity for tokamakSo The mode width A#~ (r 3 A PB L s /L n ) l/2 {l +r)" 2^ 1, which justifies the use of the differential Eq. (7). The diffusion coefficient which results from maximizing D rr with respect to b is D rr = 15A PB 3/2 r 5/2 [0.5(l + r)]-9/2 p s 2 c S A s>where c s = (T e /m { ) l/2 and p s 2 =TP, 2 . The associated electron thermal conduction coefficient is K e «fz) yr . If EXB electrostatic turbulence is the dominant scattering mechanism for these modes, then Eqs. (5) and (10) indicate a density fluctuation level at saturation, fl/n =A Pfl (p 5 /L n ) for r =1, in the strong-turbulence limit o> c^c o'. The coefficient in Eq. (10) is of the correct order of magnitude to account for electron heat transport in tokamaks outside the q = 1 surface, with a fluctuation level of several percent.In conclusion, destabilization and saturation of the drift mode in a sheared field have been shown to result from a resonance broadening mechanism that dominantly affects electrons. This contrasts with previous turbulence theories in a shearless field, 4 where nonlinear ion damping led to saturation and the electron dynamics were linear. The present theory predicts saturation at modest fluctuation levels. Measurements of the energy confinement time r E in the ISX-A (Impurity Study Experiment) tokamak are interpreted theoretically using a one-dimensional time-dependent transport code. The maximum T B observed as the plasma density is varied over a wide range occurs at that density above which anomalous electron thermal conductivity leads to a smaller energy flux than neoclassical ion thermal conductivity.One of the most striking features of recent experiments in the ISX-A (Impurity Study Experiment) tokamak 1 is the apparent saturation of the energy confinement time r E with increasing plasma density as shown in Fig. 1. Effective impurity control in the ISX-A, as in the earlier Alcator experiments, 2 permitted operation over a comparatively wide range of plasma density under circumstances such that radiation was not a dominant energy-loss mechanism in the interior of the plasma. Since anomalous heat losses decrease with density, while neoclassical losses
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