Equilibria and dynamics of temperature in a fusion reactor plasma
Abstract
Reactiondiffusion equations were studied by means of a new technique, the central expansion, which simultaneously accounts for the process of diffusion and the effects of sources, losses (represented by different powers of the temperature) as well as the effects of the boundaries. Various possibilities are discussed using new results from the central expansion analysis for describing the dynamics of complicated realistic systems. The procedure of how these results can be obtained by means of the central expansion is described in detail. It may be useful in this connection to consider the accompanying scheme of analysis. The starting point in the process of analysis is to construct a certain form of expansion, which for radially symmetric (or spatially symmetric onedimensional) profiles contains terms of increasing powers of the spatial variable squared, where the terms have timedependent coefficients. The expansion can be expressed as a product of the central value (amplitude) A(t) and a series in powers of chi squared. By proper account of the flux conditions at the boundary the effects of the boundary can be included directly in the form of the expansion. The next step is to introduce the expansion into the original reactiondiffusion equation, and to carry out the differentiations in space and time and the expansions of the powers in the source and loss terms. Matching separately the terms which do not depend on chi squared as well as the chi squared terms and the chi(exp 4) terms one obtains as a result of the three coupled nonlinear first order differential equations in time for the timedependent variables, as indicated in the scheme of analysis.
 Publication:

Plasma Physics and Controlled Nuclear Fusion. Nonlinear Phenomena in Fusion Plasmas: Theory and Computer Simulation
 Pub Date:
 April 1991
 Bibcode:
 1991ppcn.proc..198W
 Keywords:

 Differential Equations;
 Diffusion;
 Fusion Reactors;
 Nonlinear Equations;
 Plasmas (Physics);
 Thermodynamics;
 Time Dependence;
 Boundary Conditions;
 Losses;
 Mathematical Models;
 Time;
 Plasma Physics