# Biblio

**Authors:**Birmingham Thomas J

**Title:**

__Convection Electric Fields and the Diffusion of Trapped Magnetospheric Radiation__

**Abstract**: We explore here the possible importance of time-dependent convection electric fields as an agent for diffusing trapped magnetospheric radiation inward toward the earth. By using a formalism (Birmingham, Northrop, and Fälthammar, 1967) based on first principles, and by adopting a simple model for the magnetosphere and its electric field, we succeed in deriving a one-dimensional diffusion equation to describe statistically the loss-free motion of mirroring particles with arbitrary but conserved values of the first two adiabatic invariants M and J. Solution of this equation bears out the fact that reasonable electric field strengths, correlated in time for no longer than the azimuthal drift period of an average particle, move particles toward the earth at a rate at least an order of magnitud. . .

**Date:**05/1969

**Publisher:**Journal of Geophysical Research

**Pages:**2169 - 2181

**DOI:**10.1029/JA074i009p02169

**Available at:**http://onlinelibrary.wiley.com/doi/10.1029/JA074i009p02169/abstract

*More Details***Authors:**Schulz Michael, and Eviatar Aharon

**Title:**

__Diffusion of Equatorial Particles in the Outer Radiation Zone__

**Abstract**: Expansions and contractions of the permanently compressed magnetosphere lead to the diffusion of equatorially trapped particles across drift shells. A general technique for obtaining the electric fields induced by these expansions and contractions is described and applied to the Mead geomagnetic field model. The resulting electric drifts are calculated and are superimposed upon the gradient drift executed by a particle that conserves its first (μ) and second (J = 0) adiabatic invariants. The noon-midnight asymmetry of the unperturbed drift trajectory (resulting from gradient drift alone) is approximated by means of a simple model. In this model the angular drift frequency is found to be the geometric mean of a particle's angular drift velocities at noon and midnight. The radial diffusion . . .

**Date:**05/1969

**Publisher:**Journal of Geophysical Research

**Pages:**2182 - 2192

**DOI:**10.1029/JA074i009p02182

**Available at:**http://onlinelibrary.wiley.com/doi/10.1029/JA074i009p02182/abstract

*More Details***Authors:**Vernov S N, Gorchakov E V, Kuznetsov S N, Logachev Yu. I, Sosnovets E N,

*et al.*

**Title:**

__Particle fluxes in the outer geomagnetic field__

**Abstract**: The outer geomagnetic field comprises the outer radiation belt, consisting of electrons with energies of 104–107 ev, and the unstable radiation zone. The outer radiation belt is bounded on its inner side by a gap, which is at various times located at a distance of 2.2–3.5 RE and in which a considerable precipitation of electrons from radiation belts occurs, possibly owing to a high intensity of electromagnetic waves. The boundary separating the outer radiation belt from the unstable radiation zone is at λ ∼ 71° and ∼9 RE in the equatorial plane on the sunlit side, and at 7–8 RE in the equatorial plane on the nightside. Beyond this, the unstable radiation zone extends out to the magnetosphere boundary and up to λ ∼ 77° on the sunlit side, and out to 14–15 RE on the nightsi. . .

**Date:**02/1969

**Publisher:**Reviews of Geophysics

**Pages:**257-280

**DOI:**10.1029/RG007i001p00257

**Available at:**http://onlinelibrary.wiley.com/doi/10.1029/RG007i001p00257/abstract

*More Details***Authors:**Farley Thomas A

**Title:**

__Radial Diffusion of Starfish Electrons__

**Abstract**: A study of the change in electron intensities in the Starfish electron belt from January 1, 1963, to November 3, 1965, indicates that radial diffusion, both inward and outward from L of 1.40, was a significant loss mechanism for these electrons during this period. For L values of 1.20 and below, the indicated steepening of the pitch-angle distributions during this period has been interpreted as the result of a radial diffusion source for each L shell concentrated near the geomagnetic equator. Since pitch-angle diffusion lifetimes are not well known for 1.20 < L < 1.65, a definitive radial diffusion coefficient cannot be computed from these data. A maximum reasonable diffusion coefficient (mean square displacement per unit time) computed for this range of L for this period has a minimum at . . .

**Date:**07/1969

**Publisher:**Journal of Geophysical Research

**Pages:**3591 - 3600

**DOI:**10.1029/JA074i014p03591

**Available at:**http://onlinelibrary.wiley.com/doi/10.1029/JA074i014p03591/abstract

*More Details***Authors:**Newkirk L L, and Walt M

**Title:**

__Radial Diffusion Coefficient for Electrons at 1.76 <__

*L*< 5**Abstract**: Radial diffusion by nonconservation of the third adiabatic invariant of particle motion is assumed in analyzing experiments in which electrons appeared to move across field lines. Time-dependent solutions of the Fokker-Planck diffusion equation are obtained numerically and fitted to the experimental results by adjusting the diffusion coefficient. Values deduced for the diffusion coefficient vary from 1.3 × 10−5 RE²/day at L = 1.76 to 0.10 RE²/day at L = 5. In the interval 2.6 < L < 5, the coefficient varies as L10±1. Assuming a constant electron source of arbitrary magnitude at L = 6 and the above diffusion coefficients, the equatorial equilibrium distribution is calculated for electrons with energies above 1.6 Mev. The calculation yields an outer belt of electrons whose radial distr. . .

**Date:**12/1968

**Publisher:**Journal of Geophysical Research

**Pages:**7231 - 7236

**DOI:**10.1029/JA073i023p07231

**Available at:**http://onlinelibrary.wiley.com/doi/10.1029/JA073i023p07231/abstract

*More Details***Authors:**Newkirk L L, and Walt M

**Title:**

__Radial Diffusion Coefficient for Electrons at Low__

*L*Values**Abstract**: An empirical evaluation of the diffusion coefficient for trapped electrons diffusing across low L shells is obtained by adjusting the coefficient to account for the observed radial profile and the long-term decay rate of the trapped electron flux. The diffusion mechanism is not identified, but it is assumed that the adiabatic invariants µ and J are conserved. The average value of the coefficient for electrons > 1.6 Mev energy is found to decrease monotonically from ∼4 × 10−6 RE²/day at L = 1.16 to ∼2 × 10−7 RE²/day at L = 1.20.

**Date:**02/1968

**Publisher:**Journal of Geophysical Research

**Pages:**1013 - 1017

**DOI:**10.1029/JA073i003p01013

**Available at:**http://onlinelibrary.wiley.com/doi/10.1029/JA073i003p01013/abstract

*More Details***Authors:**Kennel C, and Petschek H

**Title:**

__Limit on Stably Trapped Particle Fluxes__

**Abstract**: Whistler mode noise leads to electron pitch angle diffusion. Similarly, ion cyclotron noise couples to ions. This diffusion results in particle precipitation into the ionosphere and creates a pitch angle distributon of trapped particles that is unstable to further wave growth. Since excessive wave growth leads to rapid diffusion and particle loss, the requirement that the growth rate be limited to the rate at which wave energy is depleted by wave propagation permits an estimate of an upper limit to the trapped equatorial particle flux. Electron fluxes >40 kev and proton fluxes >120 kev observed on Explorers 14 and 12, respectively, obey this limit with occasional exceptions. Beyond L = 4, the fluxes are just below their limit, indicating that an unspecified acceleration source, sufficient . . .

**Date:**01/1966

**Publisher:**Journal Geophysical Research

**Pages:**1-28

**DOI:**10.1029/JZ071i001p00001

**Available at:**http://onlinelibrary.wiley.com/doi/10.1029/JZ071i001p00001/full

*More Details***Authors:**Kennel C F

**Title:**

__Velocity Space Diffusion from Weak Plasma Turbulence in a Magnetic Field__

**Abstract**: The quasi‐linear velocity space diffusion is considered for waves of any oscillation branch propagating at an arbitrary angle to a uniform magnetic field in a spatially uniform plasma. The space‐averaged distribution function is assumed to change slowly compared to a gyroperiod and characteristic times of the wave motion. Nonlinear mode coupling is neglected. An H‐like theorem shows that both resonant and nonresonant quasi‐linear diffusion force the particle distributions towards marginal stablity. Creation of the marginally stable state in the presence of a sufficiently broad wave spectrum in general involves diffusing particles to infinite energies, and so the marginally stable plateau is not accessible physically, except in special cases. Resonant particles with velocities much . . .

**Date:**12/1966

**Publisher:**Physics of Fluids

**Pages:**2377

**DOI:**10.1063/1.1761629

**Available at:**http://scitation.aip.org/content/aip/journal/pof1/9/12/10.1063/1.1761629

*More Details***Authors:**Falthammar C -G

**Title:**

__Effects of time-dependent electric fields on geomagnetically trapped radiation.__

**Abstract**: Large-scale electric potential fields in the magnetosphere are generally invoked in theories of the aurora. It is shown in the present article that irregular fluctuations of such fields cause a random radial motion of trapped energetic particles by violating the third adiabatic invariant. When the first and second invariants are conserved, any radial motion of the particles is associated with a corresponding energy change. Some particles move outward and others inward; but, if there is a source in the outer magnetosphere and a sink farther in, there will be a net inward transport and an associated net energy gain. This mechanism supplements that of particle transport by magnetic disturbances, which has already been discussed in the literature. The transport and acceleration of energetic pa. . .

**Date:**06/1965

**Publisher:**Journal of Geophysical Research

**Pages:**2503–2516

**DOI:**10.1029/JZ070i011p02503

**Available at:**http://onlinelibrary.wiley.com/doi/10.1029/JZ070i011p02503/full

*More Details*