ENTROPY PRINCIPLE FOR TOKAMAK PROFILES
It is shown that experimental temperature and density profiles are consistent with the assumption that they relax towards profiles related by gamma = 5/3 = adiabatic constant, a>or=-(gamma-1)n-min/n-o independent of x; in most cases one has n-min-O. Cases of incomplete relaxation are exceptions, e.g. pellet injection in which the temperature profiles are too flat compared with the corresponding density profiles. Relation (1) follows from the entropy principle proposed here. According to it tokamak plasmas should relax towards states described by relations T = T(n(x)), in which the total entropy of the plasma does not change when the plasma performs arbitrary internal motions slow enough so as not to alter the relation between T and n. a = 1 corresponds to the profiles obtained by Biskamp and Kadomtsev from an energy principle assuming the electrical conductivity being given by Spitzer's law o = const. T(x)**3/2. To get agreement with experimental profiles, however, a value ranging from 0 to 3 are required. Tokamak equilibria are usually describable in terms of two arbitrary functions of the poloidal flux psi. For resistive plasmas with Spitzer's formula valid one can choose the temperature and the density as these functions. Equation (1) reduces this freedom to the free choice of one function, say T(psi), and of a special value of the parameter a. This is a feature that can be related to what is called "profile consistency". Examples are presented for cylindrical plasmas with circular cross- sections.
Bibliographic Reference: WRITE TO MAX-PLANCK-INSTITUT FUER PLASMAPHYSIK, 8046 GARCHING BEI MUENCHEN (GERMANY), MENTIONING REPORT IPP 6/263, 1986
Record Number: 1989125023800 / Last updated on: 1987-02-01
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