Engineering topics

Schulz, Michael

Publications and source records attributed to Schulz, Michael.

26 records · Page 2

NASA NTRS1993

Stormtime transport of ring current and radiation belt ions

A dynamical guiding-center simulation model is used to study the stormtime ion transport which leads to the formation of the ring current and diffusion in the radiation belts. Representative ions guiding-center motion in response to model storm-associated impulses in the convection electric field is traced for a range of ion mu values. The present numerical results are compared with previously formulated limiting idealization of particle transport in order to assess the limits of validity of these approximations. For ions having drift periods that exceed the duration of the main phase of the storm, their inward transport to form the stormtime ring current is appropriately described as direct convective access. For ions having drift periods comparable to the duration of the main phase of the storm, there is a transition between direct convective access and transport that resembles radial diffusion. Lower-energy ring-current ions at L of about 3 are freshly injected there from open adiabatic trajectories, whereas the higher-energy ring-current population consists of a mixture of freshly injected and previously trapped ions.

Chen, Margaret W.↗

NASA NTRS1992

Ion radial diffusion in an electrostatic impulse model for stormtime ring current formation

Guiding-center simulations of stormtime transport of ring-current and radiation-belt ions having first adiabatic invariants mu is approximately greater than 15 MeV/G (E is approximately greater than 165 keV at L is approximately 3) are surprisingly well described (typically within a factor of approximately less than 4) by the quasilinear theory of radial diffusion. This holds even for the case of an individual model storm characterized by substorm-associated impulses in the convection electric field, provided that the actual spectrum of the electric field is incorporated in the quasilinear theory. Correction of the quasilinear diffusion coefficient D(sub LL)(sup ql) for drift-resonance broadening (so as to define D(sub LL)(sup ql)) reduced the typical discrepancy with the diffusion coefficients D(sub LL)(sup sim) deduced from guiding-center simulations of representative-particle trajectories to a factor of approximately 3. The typical discrepancy was reduced to a factor of approximately 1.4 by averaging D(sub LL)(sup sim), D(sub LL)(sup ql), and D(sub LL)(sup rb) over an ensemble of model storms characterized by different (but statistically equivalent) sets of substorm-onset times.

Chen, Margaret W.↗

NASA NTRS1992

Ion radial diffusion in an electrostatic impulse model for stormtime ring current formation

Two refinements to the quasi-linear theory of ion radial diffusion are proposed and examined analytically with simulations of particle trajectories. The resonance-broadening correction by Dungey (1965) is applied to the quasi-linear diffusion theory by Faelthammar (1965) for an individual model storm. Quasi-linear theory is then applied to the mean diffusion coefficients resulting from simulations of particle trajectories in 20 model storms. The correction for drift-resonance broadening results in quasi-linear diffusion coefficients with discrepancies from the corresponding simulated values that are reduced by a factor of about 3. Further reductions in the discrepancies are noted following the averaging of the quasi-linear diffusion coefficients, the simulated coefficients, and the resonance-broadened coefficients for the 20 storms. Quasi-linear theory provides good descriptions of particle transport for a single storm but performs even better in conjunction with the present ensemble-averaging.

Chen, Margaret W.↗

NASA NTRS1991

The magnetic field and magnetospheric configuration of Uranus

A significant and unique planetary magnetic field discovered by Voyager 2 is presented. A large tilt of 58.6 deg of the magnetic-dipole axis from the rotation axis was found. Combined with a large offset of 0.3 RU of the magnetic dipole from the center of the planet, the moment of 0.23 gauss-RU3 leads to field magnitudes at the surface which vary widely between 0.1 and 1.0 gauss. A simple diagram illustrating the offset tilted dipole of Uranus and some field lines is shown. A more exact and accurate spherical-harmonic model of the planetary field, which includes both dipole and quadrupole moments, is derived. There exists a well-developed bipolar magnetic tail on the night side of the planet which rotates daily about the extended planet-sunline with Uranus because of the large obliquity of the Uranian rotation axis.

Ness, Norman F.↗

NASA NTRS1988

Eigenfunctions of the magnetospheric radial-diffusion operator

The applicability of eigenfunction methods to the theory of magnetospheric radial diffusion is investigated analytically, with a focus on the operator (Lambda) for radiation-belt and ring-current particles. It is shown that the eigenfunctions of Lambda can be expressed in terms of a linear combination of ordinary Bessel functions of the first and second kinds, and that the solution for the drift-averaged phase-space density can be expressed as the sum of a quasi-static solution and a time-dependent superposition of the eigenfunctions of Lambda. Results for illustrative and practical sample problems are presented in extensive tables and graphs and discussed in detail.

Schulz, Michael↗

NASA NTRS1988

Limiting energy spectrum of a saturated radiation belt

The condition for magnetospheric wave growth in the presence of anisotropic charged particle distributions is used to extend the Kennel-Petschek theory that traditionally imposes an upper bound on the integral flux of charged particles at energies above a certain threshold to provide a limit on the differential flux at any energy above this threshold. A closed-form expression is derived for the limiting energy spectrum consistent with marginal occurrence of a magnetospheric maser at all wave frequencies below a certain fraction of the electron or proton gyrofrequency. The bounded integral can be recast in such a way that repeated differentiations with respect to v(parallel) actually generate a closed expression for the limiting form of the velocity space distribution, and thus for the limiting energy spectrum of the corresponding particles, whenever the anisotropy parameter is an integer.

Schulz, Michael↗

NASA NTRS1987

Source-surface model of the magnetosphere

A new concept for modeling a planetary magnetosphere is implemented by juxtaposing the sunward portion of the magnetosphere (in which the magnetic field is expressed formally as an analytical expansion) and the tail region (in which field lines are constructed geometrically). The expansion coefficients for the sunward region are determined by means of a variational principle, according to which a user-specified linear combination of the mean-square normal component of the magnetic field on the prescribed magnetopause and the mean-square tangential component of the magnetic field on the innermost cross-magnetospheric surface normal to the tail field lines must be minimized. The contour of the vanishing normal component of the magnetic field on this latter surface corresponds to the inner edge of the neutral sheet in the planetary magnetotail. In its present form, the source-surface model accommodates an arbitrary angle of incidence between the solar-wind velocity and the planetary magnetic-dipole moment.

Schulz, Michael↗

NASA NTRS1986

Eigenfunction methods in magnetospheric radial-diffusion theory

Complete sets of orthonormal basis functions constructed according to a generalization of the quantum-mechanical WKB approximation can be used to generate a nearly-diagonal matrix representation of the radial-transport operator for ring-current ions in the presence of radial diffusion and charge exchange. The resulting eigenfunctions (constructed by weighting the basis functions in proportion to the respective components of the eigenvectors of the matrix representation) and eigenvalues provide a spatial and temporal description of the evolving phase-space density during and following a magnetospheric disturbance (e.g., a magnetic storm). A linear superposition of the basis functions can also be used to eliminate any discrepancy between the steady-state solution of the transport equation and the appropriate WKB approximation of this steady-state solution.

Schulz, Michael↗