Ion Gyroperiod Research Articles

Nightside magnetospheric current circuit: Time constants of the solar wind‐magnetosphere coupling

AbstractThis study addresses the characteristics of the nightside magnetospheric current system using the analogy of an electric circuit. The modeled circuit consists of the generator (V: solar wind), inductor (L: tail lobes), capacitor (C: plasma sheet convection), and resistor (R: particle energization). The electric circuit has three time constants: τCR(=CR), , and τL/R(=L/R). Here τCR is of the order of the ion gyroperiod in the plasma sheet, τLC is a global timescale (2πτLC is several tens of minutes), and τL/R is even longer (several hours). Despite uncertainty in the estimate of each circuit element, τCR ≪ τLC ≪ τL/R holds generally for the magnetosphere, which characterizes the electric circuit as overdamped. The following implications are obtained: (1) During the substorm growth phase the cross‐tail current increases continuously even if interplanetary magnetic field (IMF) BZ does not change after southward turning; (2) the magnetotail current weakens following northward turnings if the change of IMF BZ is comparable to the preceding southward IMF BZ; otherwise it may strengthen continuously if more gradually; (3) during the early main phase of magnetospheric storms the enhancement of the lobe magnetic energy is far more prominent than the enhancements of the kinematic and kinetic energies of the plasma sheet plasma; (4) The efficiency of the solar wind‐magnetosphere coupling changes on a timescale of several hours (τL/R) through the change of the tail flaring, and so does the cross polar‐cap potential; and (5) the magnetospheric current system does not resonate to an oscillatory external driver, and therefore, the periodicity of some magnetotail phenomena reflects that of their triggers.

Sequentially released tilted flux ropes in the Earth's magnetotail

On 14 July 2011, the two ARTEMIS spacecraft observed a chain of flux ropes generated by reconnection in the Earth's magnetotail. The flux ropes are found to extend more than 90 ion inertial lengths out of the reconnection plane. We analyze six of these flux ropes by employing a novel combination of two-spacecraft-timing for their global orientation and Grad–Shafranov reconstruction (GSR) for their local orientation. We find that their diameter was ∼10 ion inertial lengths, temporal separations ∼100 ion gyroperiods, and that their speed increased from ∼30% to ∼70% of the Alfvén velocity. Given their temporal and spatial separations, we can infer that they were produced sequentially via a secondary instability. All of the flux ropes were tilted in the current sheet plane, suggesting that the secondary instability grew along the X-line in the direction of the electron current (−YGSM). The first five had a tilt between −14° and −26°. Based on the GSR axes their shape became increasingly complex over a period of ∼300 gyroperiods indicating kinking. The sixth event was again rather linear, and had a larger tilt (−38°), cross-section and core magnetic field; these changes are most likely related to a change in the boundary conditions.

Nonlinear evolution of EMIC waves in a uniform magnetic field: 1. Hybrid simulations

We employ 2.5‐D electromagnetic, hybrid simulations that treat ions kinetically via particle‐in‐cell methods and electrons as a massless fluid to study the long‐term (hours) nonlinear evolution of electromagnetic ion cyclotron waves in the presence of multiple ion species in the outer magnetosphere. The source of the instability is a small population of hot (few keV) protons, representing plasma sheet ions at L = 9 with perpendicular temperature four times the parallel. In addition to the background population of cold protons the presence of minority, cold and heavy ions such as helium are also included. Both local (homogeneous) and nonlocal (finite‐sized source region) simulations with uniform magnetic field have been carried out. In the case of a homogeneous system, parallel propagating ion cyclotron waves are generated with amplitudes of a few percent of the background magnetic field (a few nT). After about 1000 ion gyroperiods (∼4 min) the wave amplitudes decrease by about 50% and remain nearly constant thereafter. The nonlinear evolution of the waves is associated with the gyrophase bunching of the cold protons and helium ions and reduction in the temperature anisotropy of the hot protons. In addition, parallel electrostatic waves with a wavelength half of that of the ion cyclotron waves are generated. These waves are subsequently absorbed and result in parallel heating of the cold ions. Throughout the run, both cold protons and heavy ions continue to gain energy primarily in the perpendicular direction while the hot protons reach isotropy followed by cooling in both parallel and perpendicular directions. In effect, the ion cyclotron waves continue to facilitate transfer of energy from the hot to cold ions. The results of simulations with localized hot protons show the simultaneous generation of ion cyclotron waves and expansion of the source region along the magnetic field. The nonlinear evolution of the waves is found to be similar to that seen in the homogeneous runs.

Transient growth in stable linearized Vlasov–Maxwell plasmas

Large amplitude transient growth of kinetic scale perturbations in stable collisionless magnetized plasmas has recently been demonstrated using a linearized Landau fluid model. Initial perturbations with lengthscales of the order of the ion gyroradius were shown to have transient timescales that in some cases were long compared to the ion gyroperiod, Ωit⪢1. Moreover, it was suggested that such perturbations are not rare but instead form a large class within the set of all possible initial conditions. For collisionless plasmas, the Vlasov–Maxwell equations provide a more complete description of kinetic physics and the existence of transient growth of solutions for the linearized Vlasov–Maxwell system is an interesting question. The existence of transient growth of solutions is demonstrated here for a special case of the Vlasov–Maxwell equations, namely, the one dimensional Vlasov–Poisson system. The analysis is different from the standard approach of nonmodal analysis since the initial value problem is described by a Volterra integral equation of the second kind, reflecting the fact that the time evolution of the system depends on the memory of the state from time zero through time t. For the case of a thermal equilibrium plasma, it is shown how initial conditions may be constructed to obtain solutions that grow linearly in time; the duration of this growth is the time required for a thermal electron to traverse the wavelength of the initial perturbation, a timescale that can last for many plasma periods 2π/ωpe, thus demonstrating the existence of transient growth of solutions for the linearized Vlasov–Poisson system. The results suggest that the phenomenon of transient growth may be a common feature of the linearized Vlasov–Maxwell system as well as for Landau fluid models.

Shock Formation in a Collision of Two Plasmas with Their Relative Velocity Oblique to the Magnetic Field

Shock formation processes arising from a collision of two plasmas in an external magnetic field B 0 are studied with electromagnetic particle simulations, for the case in which one plasma (exploding plasma) has a high velocity v 0 while the other (surrounding plasma) is at rest with a lower density; the ion gyroradius for the speed v 0 is much greater than the width of the shock transition region. The ion motion across B 0 induces strong electric field in the direction - v 0 × B 0 , which accelerates the surrounding ions in this direction in the early phase. Then, the change in the velocities of the two groups of ions due to the magnetic force leads to the formation of two pulses near the front of the exploding ions, which evolve into forward and reverse shock waves. The effect of the angle θ between v 0 and B 0 on plasma behavior is examined. The two pulses appear in time of the order of the ion gyroperiod. As θ decreases from 90°, however, it takes a longer time for the two pulses to form.

Analysis of the H + ring velocity distribution function near the Martian and Venusian bow shocks by an analytical model

We have studied the H + velocity distribution function at Mars and Venus near the bow shock both in the solar wind and in the magnetosheath by a simple analytical one-dimensional model. We found that over half of the ions in the ring velocity distribution which moved towards the magnetosheath were scattered back into the bow shock. The original ring distribution is destroyed in less than an ion gyro period. Ions contained in the magnetosphere which hit the bow shock bounce back into the solar wind with a maximum energy exceeding twice the energy of solar wind protons. The ions finite gyroradius causes an asymmetric flow in the magnetosheath with respect to the direction of the convective electric field, which can be observed already a few ion gyroradius downstream of the bow shock.

Three-dimensional current systems generated by plasmas colliding in a background magnetoplasma

Results are presented from an experiment in which two plasmas, initially far denser than a background magnetoplasma, collide as they move across the magnetic field. The dense plasmas are formed when laser beams, nearly orthogonal to the background magnetic field, strike two targets. The merging plasmas are observed to carry large diamagnetic currents. A reconnection event is triggered by the collision and the electric field induced in this event generates a field-aligned current, which is the first step in the development of a fully three-dimensional current system. After several ion gyroperiods, the current systems become those of shear Alfvén waves. As local currents move, small reconnection “flares” occur at many locations throughout the volume, but they do not seem to affect the overall system dynamics. The data clearly show that the induced electric field is carried though the system by shear Alfvén waves. The wave electric fields as well as local magnetic helicity are discussed.

Ion Pickup by Finite Amplitude Parallel Propagating Alfvén Waves

Two scenarios of possible ion heating due to finite amplitude parallel propagating Alfven waves in the solar atmosphere are investigated using a one-dimensional test particle approach. (1) A finite amplitude Alfven wave is instantly introduced into a plasma (or equivalently, new ions are instantly created). (2) New ions are constantly created. In both scenarios, ions will be picked up by the Alfven wave. In case 1, the wave scatters ions in the transverse direction leading to a randomization (or heating) process. This process is complete when a phase shift of ±π in the ion gyrospeed is produced between particles with characteristic parallel thermal speed and particles with zero parallel speed. This corresponds to t = π/kvth (k is the wavenumber, and vth is the ion thermal speed). A ring velocity distribution can be produced for a large wave amplitude. The process yields a mass-proportional heating in the transverse direction, a temperature anisotropy, and a bulk flow along the background magnetic field. In case 2, continuous ion creation represents a continuing phase shift in the ion gyrospeed leading to heating. New particles are picked up by the Alfven wave within one ion gyroperiod. It is speculated that the mechanism may operate in the chromosphere and active regions where transient events may generate finite amplitude Alfven waves.

Nonstationarity and reformation of high‐Mach‐number quasiperpendicular shocks: Cluster observations

A set of experimental data is presented for a high‐Mach‐number (Mf = 5) quasiperpendicular (θBn = 81°) bow shock layer crossed by Cluster spacecraft on 24 January 2001 at 07:05–07:09 UT. The measurements of magnetic field, spectra of electric field fluctuations, and ion distributions reveal that the shock is highly nonstationary. In particular, the magnetic field profiles measured aboard different spacecraft differ considerably from each other. The mean frequency of downshifted waves observed upstream of the shock ramp oscillates with a characteristic time comparable with the proton gyroperiod. In addition, the reflection of ions from the shock is bursty and a characteristic time for this process is also comparable with the ion gyroperiod. All of these features in conjunction are the first convincing experimental evidence in favor of the shock front reformation.

On microinstabilities in the foot of high Mach number perpendicular shocks

Microinstabilities excited in the foot of a supercritical perpendicular shock wave are investigated. A two‐dimensional full particle simulation with periodic boundary conditions in both directions using the physical ion to electron mass ratio is performed as a proxy for the foot region where incoming and specularly reflected ions overlap. The simulation shows that six types of different instabilities are excited in a time period shorter than ion gyroperiod of the reflected ions. The most dominant instability is the modified two‐stream instability, which leads to strong parallel electron heating through a so‐called two step instability and to ion phase space holes.

Vortex formation in an electron plasma with a sheared flow

The formation of vortex structures in an electron plasma with a sheared flow is investigated. The electron fluid is drifting in a self-electric field generated by an unshielded electron population. This setting is linearly unstable and an instability of diocotron (slipping-stream) type occurs. The time scale of the dynamics is assumed to be much shorter than the ion plasma and ion gyroperiods. Consequently, the ions do not respond to the wave potential and serve only as a neutralizing background. An equation determining the nonlinear evolution of the electrostatic potential in a plane perpendicular to an external magnetic field is derived within the drift approximation. The governing equation is then analyzed for the case with a localized shear in the electron fluid velocity. Possible final states of the diocotron instability are investigated analytically and solutions in the form of a tripolar vortex, a zonal flow, and a vortex street are found. The nonlinear time evolution of the diocotron instability is investigated by solving the governing equation numerically. In particular, the dynamics of nonlinearly saturated states and the formation of such states are discussed. Numerical solutions show a vortex street structure in a saturated state. The relevance of our investigation for space and laboratory plasmas is discussed.

Diffusive Shock Acceleration of High Energy Cosmic Rays

The process of diffusive acceleration of charged particles in shocked plasmas is widely invoked in astrophysics to account for the ubiquitous presence of signatures of non-thermal relativistic electrons and ions in the universe. A key characteristic of this statistical energization mechanism is the absence of a momentum scale; astrophysical systems generally only impose scales at the injection (low energy) and loss (high energy) ends of the particle spectrum. The existence of structure in the cosmic ray spectrum (the "knee") at around 3000 TeV has promoted contentions that there are at least two origins for cosmic rays, a galactic one supplying those up to the knee, and even beyond, and perhaps an extragalactic one that can explain even the ultra-high energy cosmic rays (UHECRs) seen at 1-300 EeV. Accounting for the UHECRs with familiar astrophysical sites of acceleration has historically proven difficult due to the need to assume high magnetic fields in order to reduce the shortest diffusive acceleration timescale, the ion gyroperiod, to meaningful values. Yet active galaxies and gamma-ray bursts remain strong and interesting candidate sources for UHECRs, turning the theoretical focus to relativistic shocks. This review summarizes properties of diffusive shock acceleration that are salient to the issue of UHECR generation. These include spectral indices, acceleration efficencies and timescales, as functions of the shock speed and mean field orientation, and also the nature of the field turbulence. The interpretation of these characteristics in the context of gamma-ray burst models for the production of UHECRs is also examined.

Observations of lower hybrid cavities in the inner magnetosphere by the Cluster and Viking satellites

Abstract. Observations by the Viking and Cluster satellites at altitudes up to 35000km show that Lower Hybrid Cavities (LHCs) are common in the inner magnetosphere. LHCs are density depletions filled with waves in the lower hybrid frequency range. The LHCs have, until recently, only been found at altitudes up to 2000km. Statistics of the locations and general shape of the LHCs is performed to obtain an overview of some of their properties. In total, we have observed 166 LHCs on Viking during 27h of data, and 535 LHCs on Cluster during 87h of data. These LHCs are found at invariant latitudes from the auroral region to the plasmapause. A comparison with lower altitude observations shows that the LHC occurrence frequency does not scale with the flux tube radius, so that the LHCs are moderately rarer at high altitudes. This indicates that the individual LHCs do not reach from the ionosphere to 35000km altitude, which gives an upper bound for their length. The width of the LHCs perpendicular to the geomagnetic field at high altitudes is a few times the ion gyroradius, consistent with observations at low altitudes. The estimated depth of the density depletions vary with altitude, being larger at altitudes of 20000-35000km (Cluster, 10-20%), smaller around 1500-13000km (Viking and previous Freja results, a few percent) and again larger around 1000km (previous sounding rocket observations, 10-20%). The LHCs in the inner magnetosphere are situated in regions with background electrostatic hiss in the lower hybrid frequency range, consistent with investigations at low altitudes. Individual LHCs observed at high altitudes are stable at least on time scales of 0.2s (about the ion gyro period), which is consistent with previous results at lower altitudes, and observations by the four Cluster satellites show that the occurrence of LHCs in a region in space is a stable phenomenon, at least on time scales of an hour.

Full particle simulations of short large‐amplitude magnetic structures (SLAMS) in quasi‐parallel shocks

Dynamics of SLAMS (short large‐amplitude magnetic structures) is investigated by the use of one‐dimensional, full particle electromagnetic simulations. As previous hybrid simulations and analysis of experimental observations suggested, present results confirm that the SLAMS patterns result from the steepening of long wavelength magnetosonic waves which are excited by diffuse ions (representing the field‐aligned reflected ion beam) interacting with the upstream ambient plasma. Five successive phases have been identified in the SLAMS dynamics: ULF wave growth and symmetric, asymmetric, spiky, and late SLAMS. The present accessibility to high‐resolution (electron) scales leads to the following new features: (1) the leading edge of the SLAMS steepens over a spatial scale from which a large‐amplitude whistler precursor is emitted; (2) this whistler departs from the SLAMS edge and behaves as a new shock front; (3) the spiky SLAMS phase is characterized by the build‐up of a strong spiky electrostatic field (its width is about 0.5 ion inertial length) within the whistler precursor and is intermittent with a lifetime less than one inverse ion gyroperiod; (4) the new shock front suffers a local self‐reformation typical of a quasi‐perpendicular shock in supercritical regime during the late‐SLAMS phase. The features of the spiky SLAMS phase can be used as a typical signature in the time history of the SLAMS dynamics. Spatial/time scales of SLAMS have been measured throughout the different phases and are found in good agreement with results issued from previous hybrid simulations and with experimental measurements made by AMPTE UKS/IRM satellites; these are also compared with recent results from Cluster‐2 space mission.

Unsteady propagation of collisionless trans‐Alfvénic shocks at large timescales

In a collisional plasma, fast and slow shocks are time stationary. They evolve in such a way that the flow variations remain small under the action of a small perturbation. By contrast, in the case of a trans‐Alfvénic shock wave (TASW), at which the flow velocity passes over the Alfvén velocity, the small perturbation generates finite variation of the initial flow. As a result, the shock disintegrates or transforms into some other unsteady state. In the present paper, the problem of shock propagation is considered for a collisionless plasma with anisotropic pressure. Using a kinetic theory, it is shown that the transition of the flow velocity over the Alfvén velocity at a shock is crucial for its evolution. Namely, the small perturbation makes collisionless TASWs unsteady at timescales large enough compared to the ion gyroperiod. This conclusion is valid for both ordinary TASWs at which the Alfvén Mach number decreases and anomalous TASWs at which it increases. Possible manifestations of unsteady propagation of planetary bow shocks are discussed.

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.

Observation of Simultaneous Axial and Transverse Classical Heat Transport in a Magnetized Plasma

The transport of heat deposited by a small low-voltage electron beam in a strongly magnetized plasma is studied for a time interval in excess of two thousand ion-gyro periods. Electron temperatures are observed to evolve along and across the magnetic field at the classically predicted rates up to times approaching one thousand gyro periods. At later times the onset of low-frequency fluctuations (below one-tenth the ion gyrofrequency) coincides with departures from classical behavior.

Current disruption in the Earth's magnetosphere: Observations and models

Observations and models of current disruption in the Earth's magnetosphere are briefly reviewed. At the approach of current disruption onset, the cross‐tail current sheet shows a rapid growth in the current density, a large upsurge in the duskward ion bulk speed to nearly the ion thermal speed, an increase in the plasma pressure and its isotropy, a rise in the plasma beta, and a decrease in the current sheet thickness to a length scale comparable to the thermal ion gyroradius. During current disruption, there are (1) large changes in the local magnetic and electric fields, (2) significant magnetic and electric fluctuations over a broad frequency range, (3) magnetic field‐aligned counterstreaming electron beams, (4) ion energization perpendicular to the magnetic field, and (5) reduction in the cross‐tail current by an amount similar to that built up during the growth phase. Observations further indicate that regions of local reversal of the north‐south magnetic field component are not necessarily sites of intense particle energization. Remote sensing of disruption activities shows that at least some current disruptions are not caused by a disturbance propagating earthward from the tail beyond 10 RE downstream. The timescale involved is comparable to or shorter than the ion gyroperiod. Current disruption thus has spatial and temporal scales outside the MHD regime. Several models for current disruption are briefly discussed. Two roles are considered for the cross‐field current instability proposed for current disruption. It can provide anomalous resistivity for magnetic reconnection as advocated by the traditional viewpoint or act singly to instigate global changes of the magnetosphere during the initial substorrn expansion phase. The latter role is elaborated by showing that the instability may modify significantly the local current density and any such process will alter the force equilibrium in the current sheet and give rise to an efficient plasma and energy transport on a global scale. Furthermore, such a process can generate field‐aligned current with intensity comparable to those associated with an auroral breakup arc at substorrn expansion onset. This scenario leads to a new emphasis that in addition to magnetic reconnection, rapid conversion of magnetic energy into particle energy in magnetotail systems may take place without a magnetic X line or separatrix playing the key role in energy conversion.

Fast formation of a plateau on the electron distribution function during the early phase of the ion‐ion stability

Numerical simulations of the ion‐ion instability carried out with parameters suitable to the description of the plasma in the high‐altitude auroral region of the Earth show a very fast evolution of the electron distribution function that cannot be explained by the quasi‐linear theory. A detailed analysis of this phenomenon has been carried on. A model based on the reflection of electrons against potential structures created during the linear phase of the ion‐ion instability is discussed. The lifetime of the potential structures, which is longer than one ion gyroperiod, can be explained by the linear theory of the ion‐ion instability. A simple statistical model of these potential structures enables us to reproduce accurately the evolution of the electron distribution function.

Induction response of plasma in nonadiabatic magnetic compression heating

Fast magnetic compression, where the compression time is shorter than the ion gyroperiod, is illustrated by a simple model. In this model the Vlasov–Ampère equation gives a Bernstein–Greene–Kruskal (BGK) stationary state at the so-called zero-β limit. It is possible to achieve hundreds of keV ion energy by the fast compression heating, because there is very little shielding from the plasma currents in the heating phase. Strong shielding appears when the compression has generated strongly phase-correlated oscillations of the ion orbits. Thresholds of plasma β for the appearance of ion stochasticity and ion trapping are estimated. Parameters in a 500 keV ion energy case are presented.