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Henrad's (1982) method, which is based on an extension of the theory of adiabatic invariants, is presently applied to a simplified analytic derivation of the capture probabilities for the j + 1 : j and j + 2 : j orbital resonances. The results originally obtained by Yoder (1979) are thereby recovered.
An analysis is made of interplanetary tangential and rotational solar wind discontinuities (TD and RD) and comparisons are made between the features of RDs and TDs. An ISEE 3 field and positive ion data set from 1978 includes high time resolution magnetometer data and is used for the comparisons, as are data from a positive ion analyzer. The field magnitude of RDs remains constant as the field rotates, while that of a TD passes through a local minimum. First and second adiabatic invariants for protons and He abundances are usually also conserved for RDs but not for TDs. The velocity change for an RD across a discontinuity is smaller than that predicted by MHD theory. Finally, plasma conditions at a discontinuity more closely resemble RDs than TDs.
Currents in the earth's magnetotail are detected with the plasma instrumentation on board the ISEE-1 spacecraft. Field-aligned currents directed into and out of the ionosphere are found in the boundary layer of the plasma sheet. Typical current densities are in the range of 5 x 10-9 to 5 x 10-8 A/m2. These currents are associated with the Region 1 current system that is observed previously at low altitudes. An intense current sheet is shown to exist at a discontinuity in convection electric fields during a period of great magnetic activity. Electron acceleration, similar to that for electron inverted-V precipitation regions at low altitudes, occurs in this current sheet. Examination of the plasma velocity distributions at a neutral-sheet crossing reveals that the neutral sheet current is carried by electrons and protons. The relative directions for the bulk flows of the proton and electron plasmas indicate that the first adiabatic invariant is not conserved for the protons, and quite possibly for the electrons also. These letter findings are in substantial agreement with a neutral sheet model for acceleration of charged particles in the presence of a weak electric field.
Energetic-ion phase-space density profiles are strikingly similar in the inner magnetospheres of earth, Jupiter, and Saturn for ions of first adiabatic invariant near 100 MeV/G and small mirror latitudes. Losses occur inside L approximately equal to 7 for Jupiter and Saturn and inside L approximately equal to 5 at earth. At these L values there exist steep plasma-density gradients at all three planets, associated with the Io plasma torus at Jupiter, the Rhea-Dione-Tethys torus at Saturn, and the plasmasphere at earth. Measurements of ion flux-tube contents at Jupiter and Saturn by the low-energy charged-particle experiment show that these are similar (for O ions at L = 5-9) to those at earth (for protons at L = 2-6). Furthermore, the thermal-ion flux-tube contents from Voyager plasma-science data at Jupiter and Saturn are also very nearly equal, and again similar to those at earth, differing by less than a factor of 3 at the respective L values. The near equality of energetic and thermal ion flux-tube contents at earth, Jupiter, and Saturn suggests the possibility of strong physical analogies in the interaction between plasma and energetic particles at the plasma tori/plasma sheets of Jupiter and Saturn and the plasmasphere of earth.
The general case of acoustic-radiation stress associated with quasi-compressional and quasi-shear waves propagating in infinite and semiinfinite lossless solids of arbitrary crystalline symmetry is studied. The Boussinesq radiation stress is defined and found to depend directly on an acoustic nonlinearity parameter which characterizes the radiation-induced static strain, a stress-generalized nonlinearity parameter which characterizes the stress nonlinearity, and the energy density of the propagating wave. Application of the Boltzmann-Ehrenfest principle of adiabatic invariance to a self-constrained system described by the nonlinear equations of motion allows the acoustic-radiation-induced static strain to be identified with a self-constrained variation in the time-averaged product of the internal energy density and displacement gradient. The time-averaged product is scaled by the acoustic nonlinearity parameter and represents the first-order nonlinearity in the virial theorem. Finally, the relationship between the Boussinesq and the Cauchy radiation stress is obtained in a closed three-dimensional form.
The large-scale peculiar velocity field and the large- and intermediate-angular scale anisotropy of the cosmic microwave background are studied in inflationary cosmological models of critical density and containing primordial scale-invariant adiabatic density perturbations. Comparison with recent observations by de Vaucouleurs and Peters Provides tentative support for a cold dark matter scenario in which the dark matter is not appreciably less clustered than the luminous galaxy distribution.
Models are presented for particle distributions, electric fields and currents in an adiabatic treatment of auroral electrostatic potential distributions in order to describe the quiet-time evening auroral arcs featuring both upward and return currents. The models are consistent with current continuity and charge balance requirements for particle populations controlled by adiabatic invariants and quasi-neutrality in the magnetosphere. The effective energy of the cool electron population is demonstrated to have a significant effect on the latitudinal breadth of the auroral electrostatic potential structure and the extent of the penetration of the accelerating potential into the ionosphere. Another finding is that the energy of any parallel potential drop in the lowest few thousand kilometers of the field line is of the same order of magnitude as the thermal energy of the cool electrons. Additional predictions include density cavities along field lines that support large potential drops, and density enhancements along field lines at the edge of an inverted V with a small potential drop.
A model is presented for the possible diurnal modulation of outer radiation belt electron precipitation by considering the effect of the convection electric field on geomagnetically trapped electrons. The modulation flux is the flux due to electrons in the drift loss cone, i.e., those which drift into the bounce loss cone. The electron flux in the drift loss cone is related to the time allowable for diffusion from the stably trapped population to the drift loss cone for precipitation at a specific geographic location. This time, which is termed the maximum L-shell lifetime, is obtained by computing electron trajectories, using a realistic magnetic field model and a simple model for the electric field. The maximum L-shell lifetimes are taken to be the times between successive entries into the bounce loss cone. Conservation of the first two adiabatic invariants, as electrons are slowly energized by the convection electric field, leads to variations in pitch angle, maximum L-shell lifetimes, and, consequently, to changes in the electron flux in the drift loss cone. These results are compared with observations of precipitating electrons made with sounding rocket payloads.
Despite the presence of several large, ice moons within the Uranian magnetosphere, the Voyager 2 spacecraft did not detect any heavy ion plasma. This paper estimates the heavy ion density that would be consistent with a heavy neutral torus formed by photosputtering, charged particle sputtering, and micrometeoroid impact vaporization of icy surfaces on the moons, taking into account the large 60 deg angle between the satellite orbit plane and the magnetic equator. The expected heavy ion density is unobservably small. The observed proton plasma of the inner magnetosphere can be maintained by ionization of the atomic hydrogen corona and by the ionospheric proton source driven by photoelectron escape, for a plasma residence time of about 30 days. These two proton sources are comparable near L = 5. The same 30-day residence time for energetic protons implies an upper limit of 0.00001 on the fraction of incident solar wind protons that enter the magnetosphere and penetrate to within L less than 6 while conserving their first adiabatic invariants.
Expressions are derived for the mirror point, the bounce period, the second adiabatic invariant, and the bounce-averaged azimuthal drift velocity as functions of equatorial pitch angle for a charged particle in a dipole magnetic field in the presence of centrifugal, gravitational, and Coriolis forces. These expressions are evaluated numerically, and the results are displayed graphically. The average azimuthal drift speed for a flux tube containing a thermal equilibrium plasma distribution is also evaluated.
The generalized first adiabatic invariant, an extension of the magnetic moment for regions of large field gradients, has been applied to the study of particles in the magnetotail current sheet. Boundaries in phase space are obtained which form a generalized loss cone and separate particles drifting into and out of the layer from particles trapped within the layer, and the boundaries can be employed in the moment integrals for densities and currents when the drifting particles differ in temperature. It is shown that the parallel pressure of the drifting particles must exceed the transverse pressure for self-consistent solutions to exist. Fully self-consistent solutions are obtained using bi-Maxwellian ion and Maxwellian electron distributions.
Equilibrium position and orientation of acoustically-levitated weightless object determined by calibration technique on Earth. From calibration data, possible to calculate equilibrium position and orientation in presence of Earth gravitation. Sample not levitated acoustically during calibration. Technique relies on Boltzmann-Ehrenfest adiabatic-invariance principle. One converts resonant-frequency-shift data into data on normalized acoustical potential energy. Minimum of energy occurs at equilibrium point. From gradients of acoustical potential energy, one calculates acoustical restoring force or torque on objects as function of deviation from equilibrium position or orientation.
The Boltzmann-Ehrenfest principle of adiabatic invariance relates the acoustic potential acting on a sample positioned in a single-mode cavity to the shift in resonant frequency caused by the presence of this sample. This general and simple relation applies to samples and cavities of arbitrary shape, dimension, and compressibility. Positioning forces and torques can, therefore, be determined from straightforward measurements of frequency shifts. Applications to the Rayleigh disk phenomenon and levitated cylinders are presented.
Shock-drift acceleration at relativistic shock fronts is investigated using a fully relativistic treatment of both the microphysics of the shock-drift acceleration and the macrophysics of the shock front. By explicitly tracing particle trajectories across shocks, it is shown how the adiabatic invariance of a particle's magnetic moment breaks down as the upstream shock speed becomes relativistic, and is recovered at subrelativistic velocities. These calculations enable the mean increase in energy of a particle which encounters the shock with a given pitch angle to be calculated. The results are used to construct the downstream electron distribution function in terms of the incident distribution function and the bulk properties of the shock. The synchrotron emissivity of the transmitted distribution is calculated, and it is demonstrated that amplification factors are easily obtained which are more than adequate to explain the observed constrasts in surface brightness between jets and hot spots.
The nonadiabatic acceleration of plasma sheet ions during the expansion phase of substorms is examined by means of single-particle codes. It is shown that, in the near-earth plasma sheet, the gyration phase at substorm onset controls the net ion energization, as the gyro-period is locally comparable to the field variation time scale. This can yield a particularly significant decrease of the particle magnetic moment. It is accordingly argued that, via adiabatic invariant violation, the dipolarization of magnetospheric field lines can induce a 'de-trapping' of inner plasma sheet populations and, hence, give rise to short-lived precipitation enhancements over the auroral zone. As this effect depends upon cyclotron frequency, it is expected to occur at distinct latitudes for different ion species. This contrasts with nonadiabatic ion behavior further out into the geotail, which is characterized by intense perpendicular heating and a likely collective trapping.
The motion of charged particles is studied numerically and analytically using a test particle approach. Acceleration near the X-type neutral line is described in terms of adiabatic invariants and separatrix crossings. The relation between regular and chaotic properties of the process is discussed for a realistic source in the plasma mantle.
Based on its ionic composition, the magnetosphere of Uranus appears to contain little plasma of solar wind origin. If the plasma source is the atmosphere of the planet, both adiabatic convection with uniform losses and radial diffusion would imply negative radial gradients of the distribution function at fixed first and second adiabatic invariants. The analysis of LECP data in the outer magnetosphere reveals different gradients. Evidence is presented that ions may have been non-adiabaticaly heated during the fourth plasma sheet immersion although this is not unambiguously distinguishable from a source at large down tail distance.
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.