Homa Karimabadi

Fully kinetic simulations of undriven magnetic reconnection with open boundary conditions

Kinetic simulations of magnetic reconnection typically employ periodic boundary conditions that limit the duration in which the results are physically meaningful. To address this issue, a new model is proposed that is open with respect to particles, magnetic flux, and electromagnetic radiation. The model is used to examine undriven reconnection in a neutral sheet initialized with a single x-point. While at early times the results are in excellent agreement with previous periodic studies, the evolution over longer intervals is entirely different. In particular, the length of the electron diffusion region is observed to increase with time resulting in the formation of an extended electron current sheet. As a consequence, the electron diffusion region forms a bottleneck and the reconnection rate is substantially reduced. Periodically, the electron layer becomes unstable and produces a secondary island, breaking the diffusion region into two shorter segments. After growing for some period, the island is eject...

Coherent structures, intermittent turbulence, and dissipation in high-temperature plasmas

An unsolved problem in plasma turbulence is how energy is dissipated at small scales. Particle collisions are too infrequent in hot plasmas to provide the necessary dissipation. Simulations either treat the fluid scales and impose an ad hoc form of dissipation (e.g., resistivity) or consider dissipation arising from resonant damping of small amplitude disturbances where damping rates are found to be comparable to that predicted from linear theory. Here, we report kinetic simulations that span the macroscopic fluid scales down to the motion of electrons. We find that turbulent cascade leads to generation of coherent structures in the form of current sheets that steepen to electron scales, triggering strong localized heating of the plasma. The dominant heating mechanism is due to parallel electric fields associated with the current sheets, leading to anisotropic electron and ion distributions which can be measured with NASAs upcoming Magnetospheric Multiscale mission. The motion of coherent structures also generates waves that are emitted into the ambient plasma in form of highly oblique compressional and shear Alfven modes. In 3D, modes propagating at other angles can also be generated. This indicates that intermittent plasma turbulence will in general consist of both coherent structures and waves. However, the current sheet heating is found to be locally several orders of magnitude more efficient than wave damping and is sufficient to explain the observed heating rates in the solar wind.

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.

The link between shocks, turbulence, and magnetic reconnection in collisionless plasmas

Global hybrid (electron fluid, kinetic ions) and fully kinetic simulations of the magnetosphere have been used to show surprising interconnection between shocks, turbulence, and magnetic reconnection. In particular, collisionless shocks with their reflected ions that can get upstream before retransmission can generate previously unforeseen phenomena in the post shocked flows: (i) formation of reconnecting current sheets and magnetic islands with sizes up to tens of ion inertial length. (ii) Generation of large scale low frequency electromagnetic waves that are compressed and amplified as they cross the shock. These “wavefronts” maintain their integrity for tens of ion cyclotron times but eventually disrupt and dissipate their energy. (iii) Rippling of the shock front, which can in turn lead to formation of fast collimated jets extending to hundreds of ion inertial lengths downstream of the shock. The jets, which have high dynamical pressure, “stir” the downstream region, creating large scale disturbances ...

INTERMITTENT HEATING IN SOLAR WIND AND KINETIC SIMULATIONS

Low-density astrophysical plasmas may be described by magnetohydrodynamics at large scales, but require kinetic description at ion scales in order to include dissipative processes that terminate the cascade. Here kinetic plasma simulations and high-resolution spacecraft observations are compared to facilitate the interpretation of signatures of various dissipation mechanisms. Kurtosis of increments indicates that kinetic scale coherent structures are present, with some suggestion of incoherent activity near ion scales. Conditioned proton temperature distributions suggest heating associated with coherent structures. The results reinforce the association of intermittent turbulence, coherent structures, and plasma dissipation.

On the energy principle and ion tearing in the magnetotail

We re-examine the use of the energy principle as applied to the tearing instability in the magnetotail. We demonstrate that when a magnetic field component normal to the current sheet is present, electron pitch-angle diffusion (PAD) either by micro-turbulence or by chaotic orbits cannot remove the strong stabilization of the tearing mode caused by electron compressibility. We find that our conclusions are in agreement with those of Pellat et al. [1991], who argued on the basis of canonical Py conservation that the stabilization of the ion tearing mode cannot be removed by the introduction of PAD. Our results are at variance with those of Kuznetsova and Zelenyi [1991], who argued that the application of the energy principle used by Pellat et al. [1991] is incorrect, and that tearing is in fact unstable in the limit of strong PAD. We show that the disagreement between these two studies can be traced to an incorrect orbit evaluation first introduced by Coroniti [1980] and subsequently used by Kuznetsova and Zelenyi [1991].

Computing the reconnection rate in turbulent kinetic layers by using electron mixing to identify topology

Three-dimensional kinetic simulations of magnetic reconnection for parameter regimes relevant to the magnetopause current layer feature the development of turbulence, driven by the magnetic and velocity shear, and dominated by coherent structures including flux ropes, current sheets, and flow vortices. Here, we propose a new approach for computing the global reconnection rate in the presence of this complexity. The mixing of electrons originating from separate sides of the magnetopause layer is used as a proxy to rapidly identify the magnetic topology and track the evolution of magnetic flux. The details of this method are illustrated for an asymmetric current layer relevant to the subsolar magnetopause and for a flow shear dominated layer relevant to the lower latitude magnetopause. While the three-dimensional reconnection rates show a number of interesting differences relative to the corresponding two-dimensional simulations, the time scale for the energy conversion remains very similar. These results suggest that the mixing of field lines between topologies is more easily influenced by kinetic turbulence than the physics responsible for the energy conversion.

Hybrid Simulation Codes: Past, Present and Future—A Tutorial

Hybrid codes, in which the ions are treated kinetically and the electrons are assumed to be a massless fluid, have been widely used in space physics over the past two decades. These codes are used to model phenomena on ion inertial and gyro-radius scales, which fall between longer scales obtained by magnetohydrodynamic simulations and shorter scales attainable by full particle simulations. In this tutorial, the assump- tions and equations of the hybrid model are described along with some most commonly used numerical implementations. Modifications to include finite electron mass are also briefly discussed. Examples of results of two-dimensional hybrid simulations are used to illustrate the method, to indicate some of the tradeoffs that need to be addressed in a realistic calculation, and to demonstrate the utility of the technique for problems of contemporary interest. Some speculation about the future direction of space physics research using hybrid codes is also provided.

A new approach to the linear theory of single-species tearing in two-dimensional quasi-neutral sheets

We have developed the linear theory of collisionless ion tearing in a two-dimensional magnetotail equilibrium for a single resonant species. We have solved the normal mode problem for tearing instability by an algorithm that employs particle-in-cell simulation to calculate the orbit integrals in the Maxwell-Vlasov eigenmode equation. The results of our single-species tearing analysis can be applied to ion tearing where electron effects are not included. We have calculated the tearing growth rate as a function of the magnetic field component Bn normal to the current sheet for thick and thin current sheets, and we show that marginal stability occurs when the normal gyrofrequency Ωn is comparable to the Harris neutral sheet growth rate. A cross-tail By component has little effect on the growth rate for By ≃ Bn. Even in the limit By ≫ Bn, the mode is strongly stabilized by Bn. We report that random pitch angle scattering can overcome the stabilizing effect of Bn and drive the growth rate up toward the Harris neutral sheet (Bn = 0) value when the pitch angle diffusion rate is comparable to Ωn.

Consequences of particle conservation along a flux surface for magnetotail tearing

The energy principle for magnetotail tearing is reexamined using conservation of electron particle number along a flux surface as a means of calculating the volume-integrated perturbed number density 〈 n1 〉, where n1 is the perturbed electron number density and the angle brackets denote integration along a field line. It is shown that if the electron response is magnetohydrodynamic, then 〈 n1 〉 can be calculated as a function of the perturbation vector potential component A1y (assuming magnetotail coordinates) independent of the potential components A1x and A1z and independent of the scalar potential ϕ. This result holds as long as the equilibrium and the tearing perturbations are two-dimensional, independent of the y coordinate. In the case of a parabolic field model, the resulting 〈 n1 〉 exactly matches the results obtained previously by Lembege and Pellat [1982], who used the kinetic drift equation to calculate the electron response. Thus the compressional stabilization of the tearing mode is a direct consequence of, and can be completely calculated from, the conservation of electron particle number along the field line. Further, it is shown that 〈 n1 〉 is independent of By, the guide component of the magnetic field, so the inclusion of a guide field does not alter the tearing stabilization condition.