M. Gedalin

Relativistic Plasma Emission and Pulsar Radio Emission: A Critique

Relativistic plasma emission due to a beam instability in the polar cap regions is examined critically as a pulsar radio emission mechanism. Wave dispersion in the pulsar plasma is discussed, based on the use of a relativistic plasma dispersion function. The growth rate for the beam instability is estimated in the rest frame of the plasma for parallel Langmuir waves, L-O mode waves, and oblique Alfven waves. The first two of these imply frequencies that are much higher than the observed frequencies for plausible parameters, suggesting that they are not viable as pulsar radio emission mechanisms. Growth of Alfven waves requires that the beam speed equal the phase speed of the Alfven waves, and this condition cannot be satisfied within the light cylinder, except for an extremely high energy beam. It is suggested that either the plasma parameters in the source region are quite different from what is currently considered plausible or the emission mechanism does not involve a beam instability. Alternative pulsar radio emission mechanisms should be explored further.

The ramp widths of high‐Mach‐number, quasi‐perpendicular collisionless shocks

The shock ramp is traditionally defined as the narrow region over which the magnetic field primarily jumps from upstream to downstream conditions. Although narrow in comparison to other features in the shock profile, the ramp plays the most important role in providing the necessary dissipation of the incident solar wind flow. However, its features are not well understood, particularly for shocks observed when the upstream solar wind has a high Mach number and high plasma β. Using the ISEE 1 and 2 spacecraft to measure the spatial scales in supercritical, quasi-perpendicular bow shock profiles, we examine the scale size of the ramp and pay particular attention to features found within the ramp. It is shown that the ramp can usually be characterized by two different scales: (1) a large scale (or global ramp width) within which the main transition from the upstream to downstream magnetic field occurs and (2) a thinner subramp scale which contains steep jumps in the magnetic field magnitude with amplitudes comparable to the overall change in magnetic field at the shock. It is shown that both scales are characteristic of the quasi-stationary shock profile (and are stationary within an ion gyroperiod), which allows for a reliable conversion from measured temporal durations to spatial lengths in the shock profile. In most shocks the global ramp width is 0.4–1 ion inertial lengths (c/ωpi), and the subramp scale is about 0.1–0.2 c/ωpi We argue that presence of these small-scale, large-amplitude, quasi-stationary structures in the ramp may be important for ion dynamics. An oscillatory behavior of the ramp is also observed in some shocks. Also, the global ramp width and subramp scales show little dependence on upstream parameters: The global ramp scale thins as θBn approaches 90°, but not as much as predicted, and there is little overall correlation between ramp scales and either Mach number or β. Future multispacecraft observations of the bow shock will require high-temporal-resolution measurements and close spatial separations to address the problem of shock structure. Present plans for the Cluster mission will provide little data at the close separations needed for such a study.

Venus Express observes a new type of shock with pure kinematic relaxation

[1] Collisionless shocks are present in the vicinity of many astrophysical objects such as supernova remnants, space jets, stars and planets immersed in the supersonic flow of stellar winds. Understanding the shock structure is crucial for understanding the processes of the redistribution of the upstream flow energy into accelerated particles and formation of downstream thermalized distribution. We report first observations (by Venus Express) of subcritical shocks that do not fit into the well-established classical structure classification. It is shown that its abnormal structure is due to kinematical collisionless relaxation of downstream ions. The spatial gyrophase mixing leads to formation of a downstream thermalized distribution, instead of various instabilities. This type of subcritical shock with kinematic relaxation has never been discussed before in theoretical models (e.g., C. F. Kennel et al., 1985).

Ion reflection at the shock front revisited

We study the process of ion reflection at the structured perpendicular shock front, in which ions cross the ramp, proceed to the overshoot, turn back to the ramp, and cross it again, being observed in the upstream region as reflected-gyrating ions. We derive analytically the reflection condition which depends on the potential, magnetic compression ratio and increase of the vector potential across the foot and ramp. The theoretical developments are illustrated by direct numerical analysis of ion trajectories in a model structured shock front. The parameters of the model shock are chosen close to the parameters of the observed high-Mach number supercritical shock with βi ∼ 1. The analysis shows that the foot length differs substantially from the value predicted by the specular reflection model and depends on βi as well. The foot length found for the model shock with βi ∼ 1 is in a good agreement with observations and simulations of shocks with similar parameters. It is also shown that the reflected ion velocities at the outer edge of the foot and downstream agree with measurements within the limits of the observational errors.

Ion heating in oblique low‐Mach number shocks

The contribution of the directly transmitted ions to ion heating in the low-Mach number oblique shock is determined analytically. We derive approximate expressions for the pressure tensor inside the ramp of a low-Mach number low-β shock. In the thin shock limit the ion state equation p ∝ n³ is recovered within the ramp, which corresponds to the complete demagnetization of ions and effective one-dimensional behavior. We derive the estimate for the maximum downstream temperature of the heated ion distribution, which depends only on the magnetic compression ratio and cross-shock potential, and may be verified observationally.

Nonlinear wave conversion in electron-positron plasmas

Wave conversion mechanisms causing large-frequency shifts are considered for an electron-positron plasma in a strong magnetic field. In particular, we discuss the effects of the nonlinear Čerenkov as well as the cyclotron resonances in order to associate pulsar radio-emissions with our present model for nonlinear conversion of high-frequency radiation into the low-frequency region.

Kinematic mechanism of electron heating in shocks: Theory vs observations

Shock electron heating due to breakdown of adiabaticity in a small-scale quasistationary electrostatic field in the shock ramp is analyzed analytically and numerically and compared with experimental data. We derive statistical dependencies of the heating on the shock parameters. Relations obtained numerically are in good agreement with experiment.

Noncoplanar magnetic field in the collisionless shock front

General expression for the noncoplanar component of the magnetic field in the front of the quasi-perpendicular fast collisionless shock is derived from the two-fluid hydrodynamics in the assumptions of (1) stationarity, (2) one-dimensionality, and (3) quasi-neutrality of the shock. The tensorial structure of ion and electron pressure is taken into account. Limits of validity of previously proposed phenomenological expressions are found.

Transmitted ions and ion heating in nearly perpendicular low-Mach number shocks

Nonadiabatic ion heating in low-Mach number shocks is only partially due to reflected ions. Directly transmitted ions contribute significantly into the downstream ion temperature and can be responsible for the whole heating even in the absence of reflected ions, due to insufficient and inhomogeneous deceleration in the cross-shock potential. As a result, the average ion velocity at the downstream edge of the shock ramp is significantly greater than the velocity required by the Rankine-Hugoniot relations, and the ion distribution gyrates as a whole. Because of the nonlinear dependence of the deceleration on the cross-shock potential and initial ion velocity, the gyrating ion distribution is also much more dispersed than the upstream distribution. Additional dispersion is caused by the increase of the vector potential across the shock ramp. The heating depends not only on the bulk shock parameters, as Mach number and β, but also on the field profile. The ion distribution which leaves the ramp is gyrophase-bunched. Further downstream, strong spatially periodic heating occurs, because the initially gyrophase bunched ions become periodically gyrophase dispersed due to nonlinear dependence of the ion gyrophase on its coordinate and velocity.

Quasi-linear theory of the Jeans instability in disk-shaped galaxies

We analyse the reaction between almost aperiodically growing Jeans-unstable gravity perturbations and stars of a rotating and spatially inhomogeneous disk of flat galaxies. A mathematical formalism in the approx- imation of weak turbulence (a quasi-linearization of the Boltzmann collisionless kinetic equation) is developed. A diusion equation in conguration space is derived which describes the change in the main body of equilibrium distribution of stars. The distortion in phase space resulting from such a wave{star interaction is studied. The theory, applied to the Solar neighborhood, accounts for the observed Schwarzschild shape of the velocity ellipsoid, the increase in the random stellar velocities with age, and the essential radial migration of the Sun from its birth-place in the inner part of the Galaxy outwards during its lifetime.