Engineering topics
Publications and source records attributed to Stern, D. P..
If the Hamiltonian for the motion of a charged particle in a magnetic field has one or more cyclic coordinates it may often be viewed as representing the motion of a particle subject to a potential V. The use of V provides qualitative insight about the motion even in some cases where a solution of the motion cannot be obtained. Several examples using this concept are reviewed and discussed.
Models of the main geomagnetic field are generally represented by a scalar potential gamma expanded in a finite number of spherical harmonics. Very accurate observations of F were used, but indications exist that the accuracy of models derived from them is considerably lower. One problem is that F does not always characterize gamma uniquely. It is not clear whether such ambiguity can be encountered in deriving gamma from F in geomagnetic surveys, but there exists a connection, due to the fact that the counterexamples of Backus are related to the dipole field, while the geomagnetic field is dominated by its dipole component. If the models are recovered with a finite error (i.e. they cannot completely fit the data and consequently have a small spurious component), this connection allows the error in certain sequences of harmonic terms in gamma to be enhanced without unduly large effects on the fit of F to the model.
Recently, Svalgaard and Heppner reported two separate features of the polar electromagnetic field that correlate with the dawn-dusk component of the interplanetary magnetic field. This work attempts to explain these findings in terms of properties of the open magnetosphere. The topology and qualitative properties of the open magnetosphere are first studied by means of a simple model, consisting of a dipole in a constant field. Many such properties are found to depend on the separation line, a curve connecting neutral points and separating different field line regimes. In the simple model it turns out that the electric field in the central polar cap tends to point from dawn to dusk for a wide variety of external fields, but, near the boundary of the polar cap, electric equipotentials are deformed into crescents.
It is shown that every field line velocity is associated with a set of Euler potentials (alpha prime, beta prime) such that particles moving with this velocity observe constant values of alpha prime and beta prime. The field line and flux preservation properties of the motion follow immediately, and a short independent proof of the Helmholtz-Zorawski criterion for field line preservation is also given. Arguments are given to show that in general it is not possible to single out one 'basic' field line velocity when only the time dependent magnetic field configuration is given.
The qualitative properties of an open magnetosphere and its electric field are examined and compared to a simple model of a dipole in a constant field and to actual observations. Many of these properties are found to depend on the separatrix, a curve connecting neutral points and separating different field-line regimes. In the simple model, the electric field in the central polar cap tends to point from dawn to dusk for a wide choice of external fields. Near the boundary of the polar cap electric equipotentials curve and become crescent-shaped, which may explain the correlation of polar magnetic variations with the azimuthal component of the interplanetary magnetic field, reported by Svalgaard. Modifications expected to occur in the actual magnetosphere are also investigated: in particular, it appears that bending of equipotentials may be reduced by cross-field flow during the merging of field lines and that open field lines connected to the polar caps emerge from a long and narrow slot extending along the tail.
At a tangential discontinuity between two constant magnetic fields a layer of trapped particles can exist, this work examines the conditions under which the current carried by such particles tends to maintain the discontinuity. Three cases are examined. If the discontinuity separates aligned vacuum fields, the only requirement is that they be antiparallel. With arbitrary relative orientations, the field must have equal intensities on both sides. Finally, with a guiding center plasma on both sides, the condition reduces to a relation which is also derivable from hydromagnetic theory. Arguments are presented for the occurrence of such trapped modes in the magnetopause and for the non-existence of specular particle reflection.
A theory is described for the production of electric currents in the magnetosphere and for the transfer of energy from the solar wind to the magnetosphere. Assuming that the magnetosheath has ohmic-type conduction properties, it is shown that unipolar induction can energize several current flows, explaining the correlation of the east-west component of the interplanetary magnetic field with polar electric fields and polar magnetic variations. In the tail region, unipolar induction can account for effects correlated with the north-south component of the interplanetary magnetic field.
Drift shells of trapped particles starting from a single field line in the earth's magnetic field may become separated owing to an electric field. By using the formalism of the shell-splitting function, this separation is calculated for an arbitrary curl-free time-independent electric field satisfying E.B = 0, with no limitation on the particle's longitudinal excursion. The effect of nondipole field components is also taken into account to the lowest order.
Kruskal transformation canonization of perturbed periodic systems with Hamiltonian
Classical Poincare-von Zeipel canonical perturbation theory extension to adiabatically perturbed systems with slow dependence on time or dynamic variables
The nonrelativistic guiding center motion of a charged particle in a static magnetic field is derived using the Hamiltonian formalism. By repeated application of first-order canonical perturbation theory, the first two adiabatic invariants and their averaged Hamiltonians are obtained, including the first-order correction terms. Other features of guiding center theory are also given, including lowest order drifts and the flux invariant.
Developmental history of adiabatic invariance including contributors to radiation energy transfer and celestial mechanics concepts
Drift shell splitting of trapped particles by earth magnetic field
Canonical perturbation theory formulation applied to Poincare-von Zeipel method
International geomagnetic reference field 1965 geomagnetic potential rate of change and transformation to dipole coordinates
Direct near identity canonical transformations
Adiabatic perturbation theory in celestial mechanics