D. L. Holland

Self‐consistent current sheet structures in the quiet‐time magnetotail

The structure of the quiet-time magnetotail is studied using a test particle simulation. Vlasov equilibria are obtained in the regime where υD = Ey c/Bz is much less than the ion thermal velocity and are self-consistent in that the current and magnetic field satisfy Ampere’s law. Force balance between the plasma and magnetic field is satisfied everywhere. The global structure of the current sheet is found to be critically dependent on the source distribution function. The pressure tensor is nondiagonal in the current sheet with anisotropic temperature. A kinetic mechanism is proposed whereby changes in the source distribution results in a thinning of the current sheet.

Sheath structure in a magnetized plasma

The sheath formed between a magnetized plasma and a particle absorbing wall is examined for the case in which the magnetic field intercepts the wall at a small angle 0°<e≲9°, where sin e=B⋅n/‖B‖, and n is the unit normal to the wall. The model is time‐independent and one‐dimensional (1‐D) with all functions varying only in the direction normal to the wall. The ions are modeled by a Maxwellian velocity distribution which is modified by the condition that ions, which would have hit the wall, are absent. For the electrons a fluid description is used, including the effects of electron–neutral collisions. The transport of particles due to turbulent electrostatic fluctuations is modeled by a constant electric field perpendicular to both B and n. It is found that in the range of angles under consideration, there are two distinct regimes of sheath formation. If e≲ν=ν/Ωe (grazing incidence), where ν is the electron–neutral collision frequency and Ωe is the electron cyclotron frequency, then the properties of t...

Effects of a constant cross‐tail magnetic field on the particle dynamics in the magnetotail

The effects of a constant cross-tail magnetic field B y on the phase space structures and the observational signatures of nonlinear particle dynamics in the quiet time magnetotail are examined. The separation of phase space into dynamically distinct regions (transient, stochastic and integrable) is found to persist, albeit with considerable complications. In addition, it is shown that if |B y | is less than the B z component, the resonant coherent chaotic scattering of particles and the resulting distribution function features persist. If |B y |≥ B z , on the other hand, the majority of the particles are forward scattered through the current sheet, and there is no discernible signature of the resonance in the distribution function. This is significant in that the presence or absence of the resonance effect in observed distribution functions can constrain the magnitude of B y .

Effects of collisions on the nonlinear particle dynamics in the magnetotail

The effects of collisional processes on the non-linear particle dynamics in the magnetotail are considered. A simple collision operator is developed to model the effects of pitch-angle and energy scattering. It is found that the phase space partition persists for up to moderate scattering amplitudes in pitch-angle and energy, and that certain distribution function features are robust even in the presence of large amplitude collisions. It is shown that if the collisions are due to short scale length electrostatic fields, excessively large field amplitudes are required to significantly alter the phase space structures and the resulting distribution function features.

Particle energization near an X line in the magnetotail based on global MHD fields

Particle acceleration near an X line in the magnetotail and the resulting ion distribution functions in the central plasma sheet are studied by using 2½-dimensional test particle simulations. The electric and magnetic fields are taken from a three-dimensional global magnetohydrodynamic (MHD) simulation model describing the solar wind-magnetosphere interaction. A southward interplanetary magnetic field is chosen as the input solar wind condition. Test particles are generated from a model ion source distribution consistent with the macroscopic MHD parameters in the lobe region. The particles are calculated earthward and tailward of the X line. It is found that ion distributions consist of two main components: a low-energy population similar to the input distribution and a high-energy population. The former corresponds to particles that do not cross the region in which the Bχ field reverses direction, while the latter consists of particles which cross the midplane, gaining energies on the order of keV. The spatial dependence of the relative population of low-energy versus high-energy components is discussed. The details of the acceleration process are determined from the motion of test particles in the simulation.

On chaotic conductivity in the magnetotail

The concept of chaotic conductivity and the acceleration of particles due to a constant dawn dusk electric field are studied in a magnetotail-like magnetic field. A test particle simulation is used including the full nonlinear dynamics. It is found that the acceleration process can be understood without invoking chaos and that the cross tail current is determined by the particle dynamics and distributions. We conclude that in general there is no simple relationship between the electric field and the current, i.e. J ≠ σ·E.

Signatures of nonlinear charged particle dynamics in Geotail comprehensive plasma instrument observations

In this paper we present simulation results and observational data from the Geotail comprehensive plasma instrument of an ion distribution function signature which arises due to nonlinear particle dynamics in the quiet time magnetotail. The signature manifests itself as peaks and valleys in the ion distribution function whose separation scales as the fourth root of the particle energy. The Geotail observations represent the first independent corroboration of this signature since it was seen in ISEE 1 data by Chen et al. [1990]. The simulations demonstrate that the signature is present in the pitch-angle-resolved distribution even in the case of perfectly symmetric particle sources in the northern and southern hemispheres. When combined with magnetometer data, we show how the peaks and valleys may be used to determine the current sheet thickness using a single satellite. The current sheet thickness determined in this fashion is less than but consistent with other measurements of the current sheet.

Determination of the quiet time current sheet thickness using Geotail CPI data and nonlinear dynamics modeling

[1] In this paper we present a survey of the quiet (Kp < 1+) current sheet thickness for X GSE between -20 R E and -80 R E as determined from an ion distribution function signature of nonlinear particle dynamics in current sheet-like magnetic fields. The signature manifests itself as a series of peaks in the ion distribution function whose separation depend on the fourth root of the energy and parameters that describe the current sheet structure. We have found clear evidence of the distribution function signature throughout the entire region of interest. Analysis of the data shows that the current sheet thickness is remarkably uniform in the region under study with an average thickness of 0.76 ± 0.56 R E . This result is consistent with measurements of the quiet time current sheet thickness made using other techniques.

Analytic boundary for resistive ballooning stability in the tokamak second‐stable regime

Analytical expressions for the marginal stability boundary for resistive ballooning modes at high beta are obtained in the limits of both large and small global shear. These results confirm the recent numerical finding of Sykes et al. [Plasma Phys. Controlled Fusion 29, 719 (1987)] that resistive ballooning modes are stable throughout most of the regime corresponding to ideal ballooning ‘‘second stability’’ in high‐beta tokamaks.

Correction to ''Signatures of nonlinear charged particle dynamics in Geotail comprehensive plasma instrument observations''

[1] During the preparation of an article in which we exploit the methodology presented in the paper ‘‘Signatures of nonlinear charged particle dynamics in Geotail comprehensive plasma instrument observations’’ by D. L. Holland, W. R. Paterson, L. A. Frank, S. Kokubun, and Y. Yamamoto (Journal of Geophysical Research, 104, 2479, 1999), we came across two errors. Neither of them undermines the basic conclusion that the ion energy resonance signature allows one to infer a lot of information about the mesoscale current sheet structure. It is, however, important to correct the errors since they directly affect the application of the technique. [2] The first error concerns the derivation of equation used for inferring current sheet topology from the resonance peak. The proper derivation is as follows. In their original paper describing the energy resonance phenomena, Burkhart and Chen [1991] followed an source distribution of particles through the modified Harris magnetic field