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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Effect of magnetic helicity upon rectilinear propagation of charged particles in random magnetic fields

When charged particles spiral along a large constant magnetic field, their trajectories are scattered by any random field components that are superposed on the guiding field. If the random field configuration embodies helicity, the scattering is asymmetrical with respect to a plane perpendicular to the guiding field, for particles moving into the forward hemisphere are scattered at different rates from those moving into the backward hemisphere. This asymmetry gives rise to new terms in the transport equations that describe propagation of charged particles. Helicity has virtually no impact on qualitative features of the diffusive mode of propagation. However, characteristic velocities of the coherent modes that appear after a highly anisotropic injection exhibit an asymmetry related to helicity. Explicit formulas, which embody the effects of helicity, are given for the anisotropies, the coefficient diffusion, and the coherent velocities. Predictions derived from these expressions are in good agreement with Monte Carlo simulations of particle transport, but the simulations reveal certain phenomena whose explanation calls for further analytical work.

Earl, James A.↗
NASA NTRS1972

Random walk study of electron motion in helium in crossed electromagnetic fields

Random walk theory, previously adapted to electron motion in the presence of an electric field, is extended to include a transverse magnetic field. In principle, the random walk approach avoids mathematical complexity and concomitant simplifying assumptions and permits determination of energy distributions and transport coefficients within the accuracy of available collisional cross section data. Application is made to a weakly ionized helium gas. Time of relaxation of electron energy distribution, determined by the random walk, is described by simple expressions based on energy exchange between the electron and an effective electric field. The restrictive effect of the magnetic field on electron motion, which increases the required number of collisions per walk to reach a terminal steady state condition, as well as the effect of the magnetic field on electron transport coefficients and mean energy can be quite adequately described by expressions involving only the Hall parameter.

Englert, G. W.↗
NASA NTRS1976

The effect of adiabatic focusing upon charged-particle propagation in random magnetic fields

The charged particles considered are scattered by random fields while they propagate along the diverging lines of force of a spatially inhomogeneous guiding field. Their longitudinal transport is described in terms of the eigenfunctions of a Sturm-Liouville operator which incorporates the effect of adiabatic focusing along with that of scattering. The relaxation times and characteristic velocities which appear in this matrix formulation of the transport problem are graphed and tabulated. Explicit formulas which describe the particle-density profile that results from a localized impulsive injection are derived for two different regimes. In the first regime, where focusing is relatively weak, a diffusive mode of propagation is dominant, but coherent modes are also present, and they become prominent as the intensity of focusing increases. In the second regime, where focusing is strong and where diffusion does not occur, the propagation is purely coherent. The existence of this supercoherent mode of particle transport opens up many possibilities for the interpretation of astrophysical phenomena.

Earl, J. A.↗
NASA NTRS1992

Effective diffusion equation in a random velocity field

The effects are studied of assumed random velocity fields on diffusion in a binary fluid. Random velocity fields can result, for example, from the high-frequency components of residual accelerations onboard spacecraft (often called g-jitter). An effective diffusion equation is derived for an average concentration which includes spatial and temporal correlations induced by the fluctuating velocity fields assumed to be Gaussianly distributed. The resulting equation becomes nonlocal, and if correlations between different components of the velocity field exist, it is also anisotropic. The simple limiting case of short correlation times is discussed and an effective diffusivity is obtained which reflects the enhanced mixing caused by the velocity fields. The results obtained in the limit of short correlation times are valid even if the probability distribution of the velocity field is not Gaussian.

Vinals, Jorge↗
NASA NTRS1973

The parallel diffusion of cosmic rays in a random magnetic field.

Within the quasi-linear approximation, the existence of the parallel diffusion coefficient for cosmic rays in a random magnetic field (homogeneous, isotropic), despite the slow decay of the interaction between particles and random field, is demonstrated. As an example, the results of a numerical calculation of the parallel diffusion coefficient for a Gaussian random-field correlation function are presented. The numerical results are corroborated by asymptotic analysis and are compared to those of other theories.

Klimas, A.↗
NASA NTRS1985

The dispersive evolution of charged-particle bunches in random magnetic fields

Shortly after a strongly anisotropic beam of charged particles is injected along a guiding magnetic field on which is superimposed a small random conponent, the particle density can be represented by a Gaussian profile whose center moves with the coherent velocity and whose width increases with time at a rate controlled by the coefficient of dispersion. Both parameters depend upon the mean free path, which characterizes scattering by the random fields, and the focusing length, which characterizes spatial variations of the guiding field. These dependencies are known explicitly for the coherent velocity. Formulae for coefficient of dispersion are available only in the limits of very weak and very strong focusing. A new expression for coefficient of dispersion, which spans this gap, is presented.

Earl, J. A.↗
NASA NTRS1989

The effect of dispersion upon charged particle transport in random magnetic fields

Shortly after a strongly anisotropic beam is injected along a guiding magnetic field on which is superposed a small random component, the charged-particle density can be represented by a Gaussian profile whose center moves with the coherent velocity and whose width increases with time at a rate controlled by the coefficient of dispersion. Both parameters of this coherent mode of propagation depend upon the mean free path, which characterizes scattering by the random fields, and the focusing length, which characterizes spatial variations of the guiding field. These dependences are known explicitly for the coherent velocity, but expressions for the coefficient of dispersion are available only in the limits of very weak and very strong focusing. To span this gap, a more comprehensive analytic description of focused transport has been developed. This description includes dispersion and is valid for arbitrary spatial dependences of both the scattering mean free path and the focusing length.

Earl, James A.↗
NASA NTRS1975

The effect of adiabatic focusing upon charged particle propagation in random magnetic fields

Charged particles propagating along the diverging lines of force of a spatially inhomogeneous guiding field were considered as they are scattered by random fields. Their longitudinal transport is described in terms of the eigenfunctions of a Sturm-Liouville operator incorporating the effect of adiabatic focussing along with that of scattering. The relaxation times and characteristic velocities are graphed and tabulated. The particle density is evaluated as a function of space and time for two different regimes. In the first regime (relatively weak focussing), a diffusive mode of propagation is dominant but coherent modes are also dominant. In the second regime (strong focussing), diffusion does not occur and the propagation is purely coherent. This supercoherent mode corresponds exactly to the so-called scatter-free propagation of kilovolt solar flare electrons. On a larger scale, focussed transport provides an interpretation of many observed characteristics of extragalactic radio sources.

Earl, J. A.↗
NASA NTRS1973

Coherent Propagation of Charged Particle Bunches in Random Magnetic Fields

Cosmic ray particle transport in random magnetic fields is analyzed. Data cover particle transport in which q is greater than or equal to 2, and density inhomogeneities propagate in a wavelike fashion with very little dispersion. Physical interpretations rather than mathematical proofs are emphasized.

Earl, J. A.↗
NASA NTRS1972

Diffusion of charged particles in a random magnetic field

When charged particles move in a random magnetic field superimposed upon a relatively large constant field, their pitch angle distribution can be calculated to any desired precision by an iterative approximation procedure. Improved knowledge of the pitch angle distribution and of the characteristic time for relaxation of anisotropy leads to an accurate expression for the coefficient of diffusion parallel to the mean field.

Earl, J. A.↗
NASA NTRS1973

Diffusion of charged particles in a random magnetic field.

When charged particles move in a random magnetic field superposed upon a relatively large constant field, their pitch-angle distribution can be calculated to any desired precision by an iterative approximation procedure. Improved knowledge of the pitch-angle distribution and of the characteristic time for relaxation of anisotropy leads to an accurate expression for the coefficient of diffusion parallel to the mean field.

Earl, J. A.↗
NASA NTRS1975

The effect of adiabatic focusing upon charged particle propagation in random magnetic fields

This paper describes the effects of strong adiabatic focusing in terms of eigenfunctions of an operator which incorporates both scattering by random fields and focusing by a spatially inhomogeneous guiding field. It is found that focused transport differs from rectilinear transport in the following ways: (1) the coherent velocity toward stronger fields is larger than that toward weaker fields; (2) coherent effects are more prominent relative to diffusive effects when focusing is present; and (3) initial anisotropies at injection have a minimal influence upon rectilinear transport but they have a pronounced effect on focused transport. These features explain certain well-known discrepancies between the diffusive picture and the observed profiles of solar particle events. In particular, they explain the so-called scatter-free propagation of kilovolt flare electrons.

Earl, J. A.↗