By R. Blandford, K. Thorne
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Additional info for Applications of Classical Physics
Clearly, Eq. 68) remains the same as before, and Eq. 75) where Dan is the anomalous-diffusion coefficient. It is known from experiment that Dan is much larger than the neoclassical diffusion coefficient everywhere except in a narrow region near, -+ 0 (if, of course, the field Bo is not too weak). 75) that the density profile ceases to depend on the field Bo. This makes it possible to separate the equations for the density and for the magnetic field, and obtain as a consequence a reasonable radial distribution of the field Bo.
I. Kolesnichenko, V. V. Parail, and G. V. 73), assuming S = const, that the poloidal magnetic field increases exponentially along the radius. Let us consider the most interesting case of a weak priming current, when Bo(' = '0) « Bo(a). From this inequality and from the condition that Bo increases exponentially it follows directly that the bootstrap current, and with it the poloidal magnetic field, is localized mainly on the periphery of the plasma filament, a situation hardly acceptable for a reactor.
V. Parail, and G. V. Pereverzev In the axial region of interest to us the particle motion is essentially non-one-dimensional in the 1/J, 8 plane, since the effect of the drift on the shapes of the orbits is not smaller than that of the particle displacement along the field. One can therefore not solve the kinetic equation by the known procedure based on the use of the smallness of the ratio Vd/V I' To operate not with two coordinates (1/J, 8) but with only one of them (1/J), we use the conservation of the component of the generalized momentum of the particle along the magnetic axis of the torus.
Applications of Classical Physics by R. Blandford, K. Thorne