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THE WEAK-FIELD LORENTZ GAS AND A PERTURBATION THEORY OF APPROXIMATE SOLUTION TO THE BOLTZMANN EQUATION
RAYTHEON CO WAYLAND MASS
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The Lorentz gas model of the Boltzmann equation is solved in closed form for conditions approximating weak external field effects, and proximity to equilibrium. General methods of perturbation theory are devised to obtain bounds for the validity of the approximation in terms related to errors in derived expectation values due to the use of the approximate distribution function. The zero-field solution is derived exactly in closed form and serves in a modified and specific manner as the weak-field approximation. The weak-field solution is shown to portray on the average the property of decay to equilibrium expected for a perturbation of the zero-field distribution function. Quantitative upper bounds are established on the field magnitudes in terms of number density of neutral atomic scatters, and time duration for weakfield effects. An example is given of the approximation technique applied to an initially Maxwellian distribution. Author
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