Relativistic effects in nuclear fusion power
Effects of correcting the Lawson-type of fusion reactor feasibility for errors arising from the use of the first Born approximation and the nonrelativistic approximation are investigated. This is done for the D(50%) + T(50%) cycle, the D(100%) cycle, and the H(50%) + /sup 11/B(50%) cycle. In order to accomplish this goal, an expression for the Maxwell-Boltzmann distribution is derived while avoiding the use of any nonrelativistic approximation. The mean kinetic energy and most probable kinetic energy of this distribution are evaluated and found to be significantly larger in the high temperature limit than that which would have been predicted by using the conventional nonrelativistic solution. Furthermore, Heitler's nonrelativistic approximation and relativistic expressions for the cross-section of the bremsstrahlung reaction are corrected for the error incurred, as a result of assuming the validity of Born's first approximation, through the use of the Elwert factor. In this manner, (and, in the case of the relativistic cross-section, through the use of the relativistic Maxwell-Boltzmann distribution introduced by this work), the conventional solution for the bremsstrahlung radiative power density is corrected; first, for effect of the first Born approximation such that a valid nonrelativistic solution is obtained; and second, for the effect of nonrelativistic approximation so that a correct solution may be obtained. The bremsstrahlung is analyzed in the electron kinetic temperature range (10/sup -1/, 10/sup 5/) keV. The maximum possible effect of the first Born approximation correction is shown to be limited to about a 38.63% increase in the radiative power density.
- Research Organization:
- Kansas State Univ., Manhattan (USA)
- OSTI ID:
- 5928567
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
700105 -- Fusion Energy-- Plasma Research-- Plasma Kinetics-Theoretical-- (-1987)
700200* -- Fusion Energy-- Fusion Power Plant Technology
BOLTZMANN EQUATION
BORN APPROXIMATION
DIFFERENTIAL EQUATIONS
EQUATIONS
ERRORS
FEASIBILITY STUDIES
FUELS
KINETIC EQUATIONS
LAWSON CRITERION
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
POWER DENSITY
RELATIVISTIC PLASMA
THERMONUCLEAR FUELS
THERMONUCLEAR REACTORS