Propagation of solar cosmic rays in the interplanetary magnetic field
Diffusion-convection theory for solar cosmic ray propagation in interplanetary magnetic field
Roelof, E. C.↗
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Foundation of the theory of cosmic-ray transport in random magnetic fields
Cosmic ray transport in random magnetic fields, deriving coupled integrodifferential equations for radiant intensity and flux
Klimas, A. J.↗
Cross correlation between cosmic-ray fluctuations and interplanetary magnetic-field fluctuations
Study of the cross-correlation between cosmic-ray intensity fluctuations and the interplanetary magnetic field, using the low-frequency limit of the theory of the interplanetary scintillations of cosmic rays. Cross-spectral analysis of the flux of the Alert neutron monitor and simultaneous values of the interplanetary magnetic field components are presented which support the theory. A model of cosmic-ray fluctuations is described, with effects of gradients and interplanetary sector structure dominating for very low frequencies (less than or about equal to .000005 Hz) and magnetic-field induced interplanetary scintillations of cosmic rays dominating for higher frequencies.
Jokipii, J. R.↗
Cosmic ray scintillations. II - General theory of interplanetary scintillations
The motion of charged particles in a stochastic magnetic field with nonzero mean is considered via a generalized quasi-linear expansion of Liouville's equation. The general result is an equation relating cosmic ray scintillations to magnetic fluctuations and to cosmic ray gradients. The resonant interaction between particles and the random magnetic field is considered in detail, and the effect of nonlinear terms in the equations is considered. The nonlinear terms are important in damping out initial conditions and in determining conditions near cyclotron resonances. The application of the theory to the propagation of cosmic rays during quiet times in interplanetary space is considered. It is concluded that cosmic ray scintillations in interplanetary space may provide useful information about interplanetary particles and fields and also about nonlinear plasma interactions.
Owens, A. J.↗
Stability of the interstellar gas and field including rotation.
Stability of interstellar gas to perturbations in gas pressure, magnetic field and cosmic ray pressure from hydromagnetic viewpoint taking rotation into account
INTERSTELLAR MAGNETIC FIELD↗
Cosmic ray diffusion: Report of the Workshop in Cosmic Ray Diffusion Theory
A workshop in cosmic ray diffusion theory was held at Goddard Space Flight Center on May 16-17, 1974. Topics discussed and summarized are: (1) cosmic ray measurements as related to diffusion theory; (2) quasi-linear theory, nonlinear theory, and computer simulation of cosmic ray pitch-angle diffusion; and (3) magnetic field fluctuation measurements as related to diffusion theory.
Birmingham, T. J.↗
A time-averaged cosmic ray propagation theory
An argument is presented, which casts doubt on our ability to choose an appropriate magnetic field ensemble for computing the average behavior of cosmic ray particles. An alternate procedure, using time-averages rather than ensemble-averages, is presented.
Klimas, A. J.↗
The Fokker-Planck coefficient for pitch-angle scattering of cosmic rays
For the case of homogeneous, isotropic magnetic field fluctuations, it is shown that most theories which are based on the quasi-linear and adiabatic approximation yield the same integral for the Fokker-Planck coefficient for the pitch angle scattering of cosmic rays. For example, despite apparent differences, the theories due to Jokipii and to Klimas and Sandri yield the same integral. It is also shown, however, that this integral in most cases has been evaluated incorrectly in the past. For large pitch angles these errors become significant, and for pitch angles of 90 deg the actual Fokker-Planck coefficient contains a delta function. The implications for these corrections relating cosmic ray diffusion coefficients to observed properties of the interplanetary magnetic field are discussed.
Fisk, L. A.↗
The Fokker-Planck coefficient for pitch-angle scattering of cosmic rays
For the case of homogeneous, isotropic magnetic field fluctuations, it is shown that most theories which are based on the quasi-linear and adiabatic approximations yield the same integral for the Fokker-Planck coefficient for the pitch-angle scattering of cosmic rays. For example, despite apparent differences, the theories due to Jokipii and to Klimas and Sandri yield the same integral. It is also shown, however, that this integral in most cases has been evaluated incorrectly in the past. For small pitch angles, the errors in previous evaluations are fortuitously of minor importance. For large pitch angles, however, these errors become more significant; and for pitch angles of 90 deg, the actual Fokker-Planck coefficient contains a delta function which has been overlooked in the past. The implications of these corrections on the possibility of relating cosmic-ray diffusion coefficients to observed properties of the interplanetary magnetic field are discussed.
Fisk, L. A.↗
New approach to cosmic-ray diffusion theory.
We have investigated a new approach to deriving a diffusion equation for charged particles in a static, random magnetic field. Our method incorporates essential effects of the magnetic fluctuations in the lowest order particle orbits. Significant corrections to the usual quasilinear diffusion coefficient for cosmic rays with pitch angles near 90 deg are a consequence. Monte Carlo results bear out the validity of our theory.
Jones, F. C.↗
Theory of streaming of cosmic rays and the diurnal variation.
Charged particle motion in magnetic field investigated to understand net streaming of cosmic rays through interplanetary space leading to diurnal variation
PARTICLE MOTION↗
An examination of the adiabatic approximation in cosmic ray propagation theory
A theory for the pitch-angle scattering of cosmic rays in a turbulent magnetic field can be derived from first principles by applying both the quasi-linear and adiabatic approximations to the master equation for the ensemble averaged distribution function. A proof of the failure of these approximations, taken together, is given. Some predictions of the quasi-linear theory, are given. New wave-like propagation modes have been discovered.
Scudder, J.↗
The effect of corotating interaction regions on the propagation of relativistic cosmic rays in the heliosphere
This paper questions the validity of modulation theories that ignore the presence of large regions of enhanced magnetic field in the heliosphere. The scatter-free and diffusive motion of relativistic cosmic rays is simulated in models of the heliospheric magnetic field, which include compressed field structures representing the corotating interaction regions that are believed to be present in the interplanetary medium throughout most of the solar cycle. It is found that the strong field gradients associated with these regions greatly perturb the drift pattern anticipated for simple Parkerian fields, and thus the expected streaming of cosmic rays from over the poles or along the current sheet, during consecutive solar cycles, no longer holds.
Thomas, B. T.↗
Propagation of cosmic rays in the solar wind
Cosmic rays propagation in solar wind, presenting statistical theory of interplanetary magnetic field effect on charged particles transport
Jokipii, J. R.↗
Geomagnetic Cutoff Rigidity Computer Program: Theory, Software Description and Example
The access of charged particles to the earth from space through the geomagnetic field has been of interest since the discovery of the cosmic radiation. The early cosmic ray measurements found that cosmic ray intensity was ordered by the magnetic latitude and the concept of cutoff rigidity was developed. The pioneering work of Stoermer resulted in the theory of particle motion in the geomagnetic field, but the fundamental mathematical equations developed have 'no solution in closed form'. This difficulty has forced researchers to use the 'brute force' technique of numerical integration of individual trajectories to ascertain the behavior of trajectory families or groups. This requires that many of the trajectories must be traced in order to determine what energy (or rigidity) a charged particle must have to penetrate the magnetic field and arrive at a specified position. It turned out the cutoff rigidity was not a simple quantity but had many unanticipated complexities that required many hundreds if not thousands of individual trajectory calculations to solve. The accurate calculation of particle trajectories in the earth's magnetic field is a fundamental problem that limited the efficient utilization of cosmic ray measurements during the early years of cosmic ray research. As the power of computers has improved over the decades, the numerical integration procedure has grown more tractable, and magnetic field models of increasing accuracy and complexity have been utilized. This report is documentation of a general FORTRAN computer program to trace the trajectory of a charged particle of a specified rigidity from a specified position and direction through a model of the geomagnetic field.
Smart, D. F.↗
A quasi-linear kinetic equation for cosmic rays in the interplanetary medium
A kinetic equation for interplanetary cosmic rays is set up with the aid of weak-plasma-turbulence theory for an idealized radially symmetric model of the interplanetary magnetic field. As a starting point, this treatment invokes the Vlasov equation instead of the traditional Fokker-Planck equation. Quasi-linear theory is applied to obtain a momentum diffusion equation for the heliocentric frame of reference which describes the interaction of cosmic rays with convecting magnetic irregularities in the solar-wind plasma. Under restricted conditions, the well-known equation of solar modulation can be obtained from this kinetic equation.
Luhmann, J. G.↗
Particle acceleration, transport and turbulence in cosmic and heliospheric physics
In this progress report, the long term goals, recent scientific progress, and organizational activities are described. The scientific focus of this annual report is in three areas: first, the physics of particle acceleration and transport, including heliospheric modulation and transport, shock acceleration and galactic propagation and reacceleration of cosmic rays; second, the development of theories of the interaction of turbulence and large scale plasma and magnetic field structures, as in winds and shocks; third, the elucidation of the nature of magnetohydrodynamic turbulence processes and the role such turbulence processes might play in heliospheric, galactic, cosmic ray physics, and other space physics applications.
Matthaeus, W.↗
A relation between cosmic-ray fluctuations, gradient, and diffusion coefficient
The motion of charged particles in a stochastic magnetic field is considered via a generalized quasi-linear expansion of Liouville's equation. The result is an equation relating cosmic-ray scintillations to particle gradients and to magnetic-field fluctuations (or diffusion coefficient). The resulting theory may be regarded as an example of a fluctuation-dissipation phenomenon, in which the diffusion coefficient plays the role of the dissipative parameter. The resonant interaction between particles and the random interplanetary magnetic field is considered explicitly, and it is shown that observed scintillations of high-energy (about 1 GeV) cosmic rays may be reasonably explained by the model.
Owens, A. J.↗