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Birmingham, T. J.

Publications and source records attributed to Birmingham, T. J..

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Cosmic rays in a random magnetic field: Breakdown of the quasilinear derivation of the kinetic equation

The problem of deriving a kinetic equation for the cosmic ray distribution function in a random magnetic field is considered. A model is adopted which is mathematically simple but which contains the essential physics. The perturbation expansion upon which the quasi-linear treatment is based is investigated. The existence of resonant particles causes the breakdown of the adiabatic approximation frequently used in this theory. Resonant particles cause a general secular growth of higher order terms in the expansion which invalidates the entire perturbative approach.

Kaiser, T. B.↗
NASA NTRS1972

Field line motion in the presence of finite conductivity.

The relation of plasma motion to field line motion is determined in the case where the conductivity is imperfect. The imperfect conductivity may result from collisions between plasma particles and neutrals, as in the case of the earth's ionosphere, or from the scattering of charged particles by the enhanced field fluctuations which characterize a turbulent plasma. A magnetic field is assumed which is a given, known function of space and time, and it is further assumed that all field lines intersect an ideally conducting surface and are identified by their points of intersection. It is shown that the relative displacement between drifting particles and moving field lines has significance only when compared with some other pertinent length such as the total particle drift distance. In such a comparison, when the latter quantity is much larger than the first, the particles can be followed by tracing field lines.

Birmingham, T. J.↗
NASA NTRS1972

Resonant diffusion in strongly turbulent plasmas.

The effect of turbulent fluctuations on plasma particles is considered, and equations are derived which describe the evolution of macroscopic properties such as temperature and flow speed of the turbulent plasma. Initially, a diffusion equation for a single-particle distribution function averaged over an ensemble of plasmas is derived for an unmagnetized plasma. For the resonant diffusion in strongly turbulent plasmas, an ensemble of three-dimensional plasmas is considered with an approximately homogeneous and stationary distribution of random electromagnetic fluctuations. For each realization, the single-particle distribution function satisfies the Vlasov equation.

Birmingham, T. J.↗
NASA NTRS1971

Resonant diffusion in the presence of strong plasma turbulence

The diffusion equation which describes the evolution of the average one particle distribution function for an ensemble of strongly turbulent plasmas is derived. The diffusion tensor is a time integral of the autocorrelation tensor of the fluctuations as observed by particles moving along statistically distributed orbits. These orbits contain the effects of fluctuations and thus differ from those encountered in weak turbulence theory. The plasma trajectory equations are used to relate each to the diffusion tensor itself when the turbulence is electrostatic. The diffusion tensor is explicity evaluated for a strongly turbulent unmagnetized plasma.

Birmingham, T. J.↗
NASA NTRS1971

Propagators in strong plasma turbulence.

Straightforward relationships between Weinstock's (1969) propagator, U sub A, the Vlasov propagator, U, and the ensemble average Vlasov propagator, U (in carets) are derived. It is shown that U and U (in carets) are related to the characteristic trajectories of the Vlasov equation, and that U (in carets) can be related to various statistical correlations of the turbulent fields.

Birmingham, T. J.↗
NASA NTRS1971

Wave growth in a strongly turbulent plasma

An equation is derived for the average nonlinear growth (damping) rate of an electrostatic mode with wave vector k for an ensemble of electrostatically turbulent, unmagnetized plasmas. Strong turbulence alters particle orbits during the course of wave growth and hence brings particles in and out of resonance with the wave. The wave growth rate in a strongly turbulent plasma therefore depends on the initial velocity distribution of particles not only at the wave speed, but in the vicinity of this speed as well. Two orbital effects are considered: turbulence modification of ensemble average orbits and turbulence-produced orbital dispersion about the average orbits. Both contribute to a resonance broadening.

Birmingham, T. J.↗