Temperature Profiles and Decay Times of Conduction Dominated Nonlinear Heat Transport Equations

Abstract

An investigation is made of the heat transport equation T, = (l/r)(rKT,.)r where the thermal conductivity, K , is of the form K -rYTn (T being temperature and r radial coordinate). The analysis presents a systematic way to obtain analytic approximations for the radial temperature profile and the decay time of the temperature, in good agreement with numerical calculations. The results are applied to several thermal energy transport models for magnetically confined plasmas.

Analysis of a generalized nonlinear diffusion equation in fusion plasma physics

“…solutions for the profile as well as for the eigenvalue, following a procedure previously used for nonlinear diffusion equations where K oc r T n (Anderson et al 1981) and which, for that equation, yielded good agreement with numerical results.…”

“…From an analysis of the asymptotic solution of (37) for small x, we find the following approximate solution compatible with the boundary conditions and a finite flux at x = 1, (cf. Anderson et al 1981):…”

“…We finally consider the modification of (1) to a cylindrical situation, where also the diffusion coefficient is generalized to include an inhomogeneity in the form of a power of the radial co-ordinate, a complication present in several cases, (cf. Stott 1976;Anderson, Gustavsson & Lisak 1981). The diffusion equation then becomes…”

“…In two recent papers (Bhadra & Gross 1977;Anderson & Lisak 1979) the conductivity model corresponding to the current convective instability has been analysed in connexion with the possibility of using a cold turbulent plasma blanket to shield the container wall in a magnetic fusion reactor from highly energetic neutrals originating in the hot plasma core.…”