D. Krauss-Varban

Large‐scale hybrid simulations of the magnetotail during reconnection

Large-scale, 2-D hybrid simulations are used to investigate the ion kinetic physics associated with quasi steady-state reconnection in the magnetotail. The simulations encompass a significant portion (20 × 120 RE) of the tail. After formation of transient plasmoids, the results show the features of fast Petschek-type reconnection. There are two pairs of thin transition layers attached to the x-point which divert and accelerate the flow within a few ion inertial lengths. These transition layers do not quite conform to the properties of the expected slow shocks. The reason for this appears to be the fact that the ion dissipation scale is comparable to the thickness of the developing plasma sheet. As a result, we find signatures of only partially thermalized, counterstreaming ions in what resembles the plasma sheet boundary layer. A fast ion beam forms immediately upstream of the boundary layer. The results are consistent with the notion that slow shocks or similar transition layers are responsible for the heating and formation of the central plasma sheet and for the ion beams observed in the plasma sheet boundary layer.

Magnetic structure of the reconnection layer and core field generation in plasmoids

Plasmoids/flux ropes have been observed both at Earths magnetopause as well as in the magnetotail. Magnetic field measurements of such structures often reveal that rather than a minimum in field strength at their centers as expected from a simple O-type neutral line picture, they exhibit a strong core field. To address this issue, two-dimensional (2-D) and 3-D hybrid simulations are used to investigate the magnetic structure of reconnection layer in general and the formation of the core field within plasmoids in particular. The reconnection layer in the magnetotail is found to be unstable to the fire hose instability. As a result, the region between the lobe and the central plasma sheet is nearly at the marginal fire hose condition. The magnetic signatures of single and multiple X line geometries are contrasted, and it is shown that the interaction of outflowing jets from neighboring X lines leads in general to a highly complex magnetic structure within a plasmoid. The large observed core fields are explained in terms of Hall-generated currents which can naturally lead to core field strengths that even exceed the ambient lobe field in magnitude. Ion beta and the presence of a preexisting guide field are two important factors controlling the Hall-generated fields. In particular, it is shown that the presence of the small ubiquitous cross-tail field component in the magnetotail can under certain conditions lead to a strong unipolar plasmoid core field. There exist significant differences between core fields associated with plasmoids at the magnetopause and those in the tail. This is due to (1) high plasma beta in the magnetosheath and (2) the asymmetry in plasma density across the magnetopause. The former leads to smaller core fields at the magnetopause, whereas the latter leads to differences in the polarity and structure of core fields within magnetopause and magnetotail plasmoids. Such differences are illustrated through examples.

Damping and spectral formation of upstream whistlers

Previous studies have indicated that damping rates of upstream whistlers strongly depend on the details of the electron distribution function. Moreover, detailed analysis of Doppler shift and the whistler dispersion relation indicate that upstream whistlers propagate obliquely in a finite band of frequencies. In this paper we present results of a kinetic calculation of damping lengths of wideband whistlers using the sum of seven drifting bi-Maxwellian electron distributions as a best fit to the ISEE 1 electron data. For two cases, when upstream whistlers are observed, convective damping lengths derived from ISEE magnetic field and ephemeris data are compared with theoretical results. We find that the calculated convective damping lengths are consistent with the data and that upstream whistlers remain marginally stable. We also show that the slope of plasma frame spectra of upstream whistlers, obtained by direct fitting of the observed spectra, is between 5 and 7. The overall spectral, wave, and particle characteristics, proximity to the shock, as well as propagation and damping properties indicate that these waves cannot be generated locally. Instead, the observed upstream whistlers arise in the shock ramp, most likely by a variety of cross-field drift and/or anisotropy driven instabilities.

Kinetic structure of rotational discontinuities: Implications for the magnetopause

Magnetic field rotations in the high ion beta magnetosheath that are part of the magnetopause structure are expected to have only a small normal component. We have studied the properties of rotational discontinuities (RDs) under these conditions, viewed as the limit of weak intermediate shocks (ISs), by performing hybrid simulations with a reflecting wall boundary condition (piston method). With this dynamic formation, the sense and size of rotation are not arbitrarily predetermined, but rather evolve from the given upstream (magnetosheath) and downstream (magnetospheric) boundary conditions, similar to what takes place at the magnetopause. This work focuses on several aspects: the observed minimum shear of RDs, their width, their internal signature, and their relation to ISs in isotropic plasmas. Our simulation results are in agreement with the minimum shear observations, that is, the RDs choose the sense of rotation that corresponds to the minimum angle between the upstream and downstream field vector. The RDs are stable, with a unique scale size. Typical gradient scale half widths are one to four ion inertial lengths with a total width up to ten times of that, in agreement with magnetopause observations. We develop a generalized fluid theory of RDs and discuss the characteristic internal signatures of the rotational layer, comparing the kinetic simulation results to predictions from the generalized fluid theory. The results show that ion inertia, anisotropic pressure, finite Larmor radius effects, nonzero ion heat flux, and reflected ions all contribute to the signatures of RDs on kinetic scales. The RDs may have upstream or downstream wave trains, which become weak for high ion beta and small normal components of the magnetic field. We explain the presence and direction of wave trains in terms of the kinetic properties of the Alfven/ion-cyclotron mode. Away from the RD limit there is a smooth transition to weak intermediate shocks, which have small jumps close to expected Rankine-Hugoniot values. Apart from that, there are few kinetic plasma signatures that distinguish RDs from their neighboring ISs. However, noncoplanar ISs evolve in time into thin RDs. Using the properties of RDs and ISs, we make specific suggestions how these discontinuities can be distinguished observationally in the case of an isotropic plasma.

Electron dynamics and whistler waves at quasi‐perpendicular shocks

The collisionless, supercritical, quasi-perpendicular fast shock is investigated on sub-ion scales using an implicit, two-dimensional (2-D) full particle code. For the first time, simulations are carried out with realistic characteristic frequencies and sufficiently high mass ratio between the protons and electrons. As a result, there is relatively little scattering of the electrons, i.e., they behave largely adiabatically as previously suggested based on spacecraft observations at the Earths bow shock. The large mass ratio also allows for a realistic description of the whistler mode dispersion. Phase-standing whistlers with propagation along the shock normal appear as transients. The dominant whistlers found at late times in the simulations have upstream directed group velocity but propagate at oblique direction between the shock normal and the ambient magnetic field. Their properties match those of the ubiquitous observed upstream whistlers (“one-Hertz waves”).

Sources of magnetosheath waves and turbulence

Abstract In this paper the possible sources of waves and turbulence in the magnetosheath are discussed. In particular, three separate sources resulting in different types of waves are identified. One is the quasi-parallel portion of the bow shock which contains large amplitude magnetosonic waves generated at or upstream of the shock. Due to their small group velocity these waves are convected back into downstream. It is suggested that the convected wave energy results in the generation of Alfven waves through a linear mode conversion process. Another source is the quasi-perpendicular portion of the shock which results in an anisotropic plasma downstream of the shock. This temperature anisotropy is unstable to the excitation of both Alfven and mirror waves with the former having a larger growth rate. The competition between these two wave modes is discussed and it is shown that the mirror mode can be excited despite its lower growth rate. Finally, it is shown that the magnetopause itself can generate slow magnetosonic waves in the magnetosheath. It is suggested that these waves can be thought of as part of the overall magnetopause structure, as are dispersive whistlers associated with low Mach number shocks.

Two‐dimensional structure of the co‐planar and non‐coplanar magnetopause during reconnection

The two-dimensional (2-D) magnetopause transition during reconnection is investigated with large-scale hybrid simulations. Contrary to previous studies, but in agreement with observations, the two discontinuities that form are not an intermediate shock or a slow shock. A 2-D reconnection configuration develops with jumps that do not satisfy Rankine-Hugoniot conditions of known discontinuities. All plasma quantities are fairly constant between the discontinuities. This region is characterized by a nearly unchanged sheath density, slight temperature enhancement, and significant magnetic field depression and thus resembles the “Sheath Transition Layer” of Song et al. [1989]. For a non-coplanar magnetic field Bzo, the plasma β attains very high values on the outflow side where Bzo and the Hall-generated field cancel, and the jet becomes unstable. In this case, the magnetosheath-side discontinuity resembles the often-observed rotational discontinuity.

Magnetosheath dynamics downstream of low Mach number shocks

The dissipation of the flow kinetic energy of solar wind ions at the quasi-perpendicular bow shock results in the formation of ion distributions that have large perpendicular temperature anisotropies. These anisotropies provide free energy for the growth of Alfven ion cyclotron (A/IC) and mirror waves. The waves then make the ion distributions gyrotropic and substantially reduce their anisotropy. Although differences exist, many of the mechanisms governing wave generation and particle isotropization operate at both high and low Mach number shocks. These mechanisms are easier to study at low Mach number shocks because they proceed relatively slowly and the turbulence level is lower. Also, in general, the plasma beta is lower at the low Mach number bow shock, allowing for situations in which minority ion species like He ++ can suppress proton cyclotron waves and thus play a larger role in sheath dynamics than they do at high Mach number shocks. For these reasons, we use two-dimensional hybrid simulations to model the heating of H + and He ++ ions at the low Mach number bow shock and examine wave excitation and ion isotropization in the magnetosheath downstream. In agreement with observations and theory and in contrast to high Mach numbers, we find that the magnetosheath turbulence mostly consists of A/IC waves. Without helium ions, the A/IC wave activity is dominated by parallel propagating proton cyclotron waves. When helium ions are included at a low density, they tend to absorb these waves, leaving obliquely-propagating A/IC waves dominant, though at a lower intensity level. Proton heating at the shock is dominated by bulk perpendicular heating of the core, while the helium ions are heated only slightly. Instead, initially they gyrate around field lines downstream as a coherent, nongyrotropic bunch. Downstream, the protons are slowly isotropized through pitch-angle scattering by A/IC waves. The helium ions undergo perpendicular heating through absorption of proton waves and become more gyrotropic. The perpendicular heating drives the growth of helium cyclotron waves, which in turn reduce the anisotropy of the helium ions. Far downstream of the shock, obliquely-propagating helium cyclotron waves dominate the sheath turbulence.

Waves associated with quasi-parallel shocks: Generation, mode conversion and implications

Ions that are energized at quasi-parallel collisionless shocks and move back upstream generate low-frequency waves, largely on the fast/magnetosonic branch. At sufficient Mach number, the waves are convected back into the shock, lead to shock re-formation, and are mode-converted into downstream (magnetosheath) Alfvenic turbulence. Other waves are generated more locally at the interface of the incoming solar wind and the partially thermalized plasma. This paper reviews how recent simulation studies of collisionless shocks in conjunction with linear kinetic theory and proper wave diagnostics have aided in our understanding of the upstream and magnetosheath waves.

A test of the Hall-MHD Model: Application to low-frequency upstream waves at Venus

Early studies suggested that in the range of parameter space where the wave angular frequency is less than the proton gyrofrequency and the plasma beta, the ratio of the thermal to magnetic pressure, is less than 1 magnetohydrodynamics provides an adequate description of the propagating modes in a plasma. However, recently, Lacombe et al. [1992] have reported significant differences between basic wave characteristics of the specific propagation modes derived from linear Vlasov and Hall-MHD theories even when the waves are only weakly damped. In this paper we compare the magnetic polarization and normalization magnetic compression ratio of ULF upstream waves at Venus with magnetic polarization and normalized magnetic compression ratio derived from both theories. We find that while the “kinetic” approach gives magnetic polarization and normalized magnetic compression ratio consistent with the data in the analyzed range of beta (0.5 < beta < 5) for the fast magnetosonic mode, the same wave characteristics derived from the Hall-MHD model strongly depend on beta arid are consistent with the data only at low beta for the fast mode and at high beta for the intermediate mode.