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General Fokker-Planck equation for geomagnetically trapped electron distribution as function of longitude, time, energy, and mirror point field intensity
Fokker-Planck equation describing distribution of geomagnetically trapped electrons as function of longitude, time, energy, and mirror point field intensity
Cu-Ni diffusion couples voids and edges effect on concentration gradients measurement by electron probe microanalysis
A steady-state model of Jupiter's electron radiation belt is developed. The model includes injection from the solar wind, radial diffusion, energy degradation by synchrotron radiation, and absorption at Jupiter's surface. A diffusion coefficient of the form D sub RR/R sub J squared = k times R to the m-th power is assumed, and then observed data on synchrotron radiation are used to fit the model. The free parameters determined from this fit are m = 1.95 plus or minus 0.5, k = 1.7 plus or minus 0.5 x 10 to the 9th power per sec, and the magnetic moment of injected particles equals 770 plus or minus 300 MeV/G. The value of m shows quite clearly that the diffusion is not caused by magnetic pumping by a variable solar wind or by a fluctuating convection electric field. The process might be field line exchange driven by atmospheric-ionospheric winds; our diffusion coefficient has roughly the same radial dependence but is considerably smaller in magnitude than the upper bound diffusion coefficients recently suggested for this process by Brice and McDonough (1973) and Jacques and Davis (1972).
Fokker-Planck equation for geomagnetically trapped electron distribution as function of longitude, time, energy and mirror-point field intensity
The relativistic motion of electrons in an intense electromagnetic wave packet propagating obliquely to a uniform magnetic field is analytically studied on the basis of the Fokker-Planck-Kolmogorov (FPK) approach. The wavepacket consists of circularly polarized electron-cyclotron waves. The dynamical system in question is shown to be reducible to one with three degrees of freedom. Within the framework of the Hamiltonian analysis the nonlinear diffusion tensor is derived, and it is shown that this tensor can be separated into zeroth-, first-, and second-order parts with respect to the relative bandwidth. The zeroth-order part describes diffusive acceleration along lines of constant unperturbed Hamiltonian. The second-order part, which corresponds to the longest time scale, describes diffusion across those lines. A possible transport theory is outlined on the basis of this separation of the time scales.
The radio synchrotron emission from relativistic electrons in shell supernova remnants (SNRs) provides a unique opportunity to probe the energy distribution of energetic electrons at their acceleration site (SNR shock fronts). This information provides insight into the acceleration mechanism(s). The implications of these observations for the diffusive (first-order Fermi) acceleration of electrons at the SNR shock fronts are discussed.
The dissipation mechanism of magnetic reconnection remains a subject of intense scientific interest. On one hand, one set of recent studies have shown that particle inertia-based processes, which include thermal and bulk inertial effects, provide the reconnection electric field in the diffusion region. On the other hand, a second set of studies emphasizes the role of wave-particle interactions in providing anomalous resistivity in the diffusion region. In this presentation, we present analytical theory results, as well as PIC simulations of guide-field magnetic reconnection. We will show that the thermal electron inertia-based dissipation mechanism, expressed through nongyrotropic electron pressure tensors, remains viable in three dimensions. We will demonstrate the thermal inertia effect through studies of electron distribution functions. Furthermore, we will show that the reconnection electric field provides a transient acceleration on particles traversing the inner reconnection region. This inertia1 effect can be described as a diffusion-like term of the current density, which matches key features of electron distribution functions.
The dissipation mechanism of magnetic reconnection remains a subject of intense scientific interest. On one hand, one set of recent studies have shown that particle inertia-based processes, which include thermal and bulk inertial effects, provide the reconnection electric field in the diffusion region. On the other hand, a second set of studies emphasizes the role of wave-particle interactions in providing anomalous resistivity in the diffusion region. In this presentation, we present analytical theory results, as well as PIC simulations of guide-field magnetic reconnection. We will show that the thermal electron inertia-based dissipation mechanism, expressed through nongyrotropic electron pressure tensors, remains viable in three dimensions. We will demonstrate the thermal inertia effect through studies of electron distribution functions. Furthermore, we will show that the reconnection electric field provides a transient acceleration on particles traversing the inner reconnection region. This inertial effect can be described as a diffusion-like term of the current density, which matches key features of electron distribution functions.
The use of a hollow cathode in place of an oxide cathode to increase thruster operating lifetimes requires, among other things, the addition of a baffle to restrict the flow of electrons from the hollow cathode. A theoretical model is developed which relates the baffle aperture area of a hollow-cathode thruster to the magnetic flux density and plasma properties in the aperture region, with the result that this model could be used as an aid in thruster design. Extensive Langmuir probing is undertaken to verify the validity of the model and demonstrate its capability. It is shown that the model can be used to calculate the aperture area required to effect discharge operation at a specified discharge voltage and arc current.
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