Limit on stably trapped particle fluxes determined theoretically and compared with data from Explorer satellites

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Limit on stably trapped particle fluxes

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 particles by fluctuating electric potential fields have a formal similarity to the so-called stochastic mode of acceleration in synchrocyclotrons. In the magnetosphere, the rate of displacement of trapped particles is found to depend on the spectral power density of the fluctuating electric fields at the azimuthal drift frequency and its harmonics. Which of these frequencies is most important depends on the spatial structure of the fluctuations. The observational data needed for numerical evaluation of the rate of transport are still lacking, but the formulas derived serve the purpose of indicating what properties of the fields are important and ought to be measured experimentally. The effects of magnetic time variations, which have been discussed in the literature under special assumptions, are considered in a more general way. A first-order result is given, which applies not only to initial phases of magnetic storms but also to other types of magnetic time variations.

Effects of time‐dependent electric fields on geomagnetically trapped radiation

This paper is a continuation of the review (Shabansky, 1968), which is quoted here as I. This paper considers the problems related to the processes of the interaction of charged particles with the geomagnetic field, and also contains the original results obtained by the author (1, 2.1; 2.2; 2.3.4; 2.4; 3.1; 3.2; 3.3; 3.4.3). The problems under discussion in the Sections 1; 2.1; 2.2 were partly dealt with in the end of paper I. However, the equations of motion for the two-and three-component plasma shortly represented in 1.1, 1.2, take into account the inertial terms in distinction to paper I. The ionospheric current induction (1.4), the transition layer (2.1) and the magnetotail rotation (2.2) are considered in more detail than in I.

Some processes in the magnetosphere

This paper presents fundamental properties of the storm-time ring current on the basis of the numerical simulations. This simulation model solves spatial and temporal evolution of the ion distribution in the magnetosphere by tracing the bounce-averaged drift trajectories. The tracing is performed under the dipole magnetic field and the time-dependent Volland-Stern-type convection field. After tracing particles, we calculate the differential flux, the plasma pressure, and the current density. The magnetic disturbance induced by the ring current is directly calculated from the Biot-Savart integral over the whole three-dimensional distribution of the calculated current density. We examined following subjects during the magnetic storms; the causes of the ring current buildup, the electric current distribution, the causes of the ring current decay, the energy composition of the plasma pressure, the response time of the plasma sheet density to the solar wind density, and the diamagnetic effect. This simulation suggests the following results: (1) The major variation of corrected Dst is mainly due to the changes in both the convection electric field and the plasma sheet density. (2) The Dessler-Parker-Sckopke relation overestimates the corrected Dst by a factor of 2.5–4. (3) The storm-time ring current buildup is insensitive to the plasma sheet temperature for the temperature above 3 keV. (4) The ions with energies around 15–40 keV at L ∼4–6 in the dusk region mostly contribute to the perpendicular pressure. (5) The equatorial magnetic fields are dramatically distorted by the diamagnetic effect. The grad-B drift trajectories under the distorted equatorial magnetic field can be classified into four patterns.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999JA900493

Simulation study on fundamental properties of the storm‐time ring current

[1] Three-dimensional simulations of the dynamics of outer radiation belt electrons with the recently developed Versatile Electron Radiation Belt (VERB) code are presented. Simulations are preformed for an idealized storm with geomagnetic activity–dependent wave amplitudes that are parameterized as a function of the level of geomagnetic activity. Numerical experiments using the VERB code with various scattering processes (pitch angle diffusion, radial diffusion, and energy diffusion) indicate that diffusive processes are strongly coupled with each other and that they all should be included in realistic simulations of the radiation belts. We show that during storms, inward radial diffusion can produce significant accelerations to relativistic energies, while pitch angle scattering and energy diffusion produce a decrease and an increase in fluxes, respectively. We show that in the presence of high-latitude and low-latitude chorus, peaks in the radial profile of phase space density are formed between L of 4 and 6 during the recovery phase of a storm and are later smoothed by radial diffusion. Sensitivity experiments show that geomagnetic control of wave intensities plays a controlling role in the dynamics of radiation belt electrons. Numerical simulations indicate that electrons of 10–100 keV near geosynchronous orbit can reach MeV energies in the heart of the radiation belts by combined radial diffusion and in situ acceleration. We present two scenarios of acceleration of the plasma sheet electrons: (1) in the range of hundreds of keV by means of radial diffusion and (2) in the range of tens of keV by means of radial diffusion combined with local acceleration.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2008JA013784

Evolution of electron fluxes in the outer radiation belt computed with the VERB code

The effect of large-scale geomagnetic fluctuations on Van Allen belt particles with mirror points near the geomagnetic equatorial plane is studied in a model where a dipole field is perturbed by the sudden approach and adiabatic withdrawal of a perfectly conducting plane. The Fokker-Planck equation for the particle density is obtained by following the motions of the particle guiding centers, assuming that the first and second adiabatic invariants, but not the third, remain valid during the approach. Steady-state and transient solutions for several cases are obtained. The steady-state solution for the density of particles with a particular nonrelativistic energy E, due to a source producing the density KE−(8+1) at an intermediate radius with sinks at very large and very small radii, varies with radius r approximately as r−4−38 inside the source region and as r-11−38 outside it. The equations resemble, but are not identical with, those of Parker for the same problem, corresponding solutions differing in that his density at small radii is less.

On the effect of geomagnetic fluctuations on trapped particles

Synchrotron radiation as the source of jupiter's polarized decimeter radiation

Amplified Whistlers as the Source of Jupiter's Sporadic Decameter Radiation.

Two-dimensional Stokes parameters for synchrotron radiation from ultrarelativistic electrons in dipole field

David B. Chang

Papers

On the effect of geomagnetic fluctuations on trapped particles

Synchrotron radiation as the source of jupiter's polarized decimeter radiation

Amplified Whistlers as the Source of Jupiter's Sporadic Decameter Radiation.

Synchrotron radiation from a dipole field