A KINETIC APPROACH TO COLLISION PROCESSES IN GASES. I. SMALL AMPLITUDE PROCESSES IN CHARGES AND NEUTRAL ONE COMPONENT SYSTEMS
Abstract
This approach appears adequate for the unified treatment of the dynamic properties of gases over a continuous range pressures from the Knudsen limit to the high-pressure limit where the aerodynamic equations are valid. Alterations are made in the collision terms of the Boltzmann equation; each collision conserves particle number, momentum, and energy; persistence of velocities angular dependence may be included. The approach illustrates a technique for a simple model involving the assumption of a collision time independent of velocity; this model is applied to the study of small amplitude oscillations of 1-component ionized and neutral gases. The initial value problem for unbounded space is solved by performing a Fourier transformation of the space variable and Laplace transformation on the time variable. For uncharged gases there results the correct adiabatic limiting law for sound-wave propagation at high pressures. For ionized gases the difference in the nature of the organization in the low-pressure plasma oscillations and in high-pressure sound type oscillations is studied. Two important cases are distinguished. If the wave length of the oscillations is long compared to either the Debye length or the mean free path, a small change in frequency is obtained as the collision frequency varies from zero to infinity. The accompanying absorption is small and reaches its maximum value when the collion frequency equals the plasma frequency. the other case refers to waves shorter than both the Debye length and the mean free path; these waves are characterized by a very heavy absorption.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1953
- Accession Number
- AD0017744
Entities
People
- E. P. Gross
- M. Krook
- P. L. Bhatnager
Organizations
- Harvard College Observatory