Mirror Force Research Articles

Low-frequency Whistler Waves Modulate Electrons and Generate Higher-frequency Whistler Waves in the Solar Wind

Abstract The role of whistler-mode waves in the solar wind and the relationship between their electromagnetic fields and charged particles is a fundamental question in space physics. Using high-temporal-resolution electromagnetic field and plasma data from the Magnetospheric MultiScale spacecraft, we report observations of low-frequency whistler waves and associated electromagnetic fields and particle behavior in the Earth’s foreshock. The frequency of these whistler waves is close to half the lower-hybrid frequency (∼2 Hz), with their wavelength close to the ion gyroradius. The electron bulk flows are strongly modulated by these waves, with a modulation amplitude comparable to the solar wind velocity. At such a spatial scale, the electron flows are forcibly separated from the ion flows by the waves, resulting in strong electric currents and anisotropic ion distributions. Furthermore, we find that the low-frequency whistler wave propagates obliquely to the background magnetic field ( B 0), and results in spatially periodic magnetic gradients in the direction parallel to B 0. Under such conditions, large pitch-angle electrons are trapped in wave magnetic valleys by the magnetic mirror force, and may provide free perpendicular electron energy to excite higher-frequency whistler waves. This study offers important clues and new insights into wave–particle interactions, wave generation, and microscale energy conversion processes in the solar wind.

Ion temperature anisotropy in the tokamak scrape-off layer

Understanding tokamak exhaust-power heat loads on divertor plates depends critically on having a realistic model of the scrape-off layer (SOL) plasma. The Braginskii fluid model is often solved to understand the SOL plasma behavior. This model is based on the collisional limit for transport along the magnetic field . The ions and electron gyrofrequencies are assumed to be much larger than the Coulomb collision frequencies, which are nonetheless, sufficiently large to yield common parallel and perpendicular temperatures for each species, i.e. the temperatures are assumed to be isotropic. In certain circumstances such as encountered for the tokamak H-mode, the ion temperature can be quite anisotropic. In this work, the anisotropy effects are implemented in the two-dimensional (2D) transport code UEDGE. Various geometries (1D slab, 2D slab and a toroidal tokamak geometry) are used to study the 2D structure of ion temperature anisotropy and its effects on plasma transport in detail. Results show that the effects of ion temperature anisotropy on the plasma parallel transport are substantial near the magnetic X-point, which leads to different steady state density profiles in the divertor regions. The extra mirror force introduced by ion temperature anisotropy can be one of the main forces contributing to the plasma flow in the SOL.

Ultimate quantum limit for amplification: a single atom in front of a mirror

We investigate three types of amplification processes for light fields coupling to an atom near the end of a one-dimensional (1D) semi-infinite waveguide. We consider two setups where a drive creates population inversion in the bare or dressed basis of a three-level atom and one setup where the amplification is due to higher-order processes in a driven two-level atom. In all cases, the end of the waveguide acts as a mirror for the light. We find that this enhances the amplification in two ways compared to the same setups in an open waveguide. Firstly, the mirror forces all output from the atom to travel in one direction instead of being split up into two output channels. Secondly, interference due to the mirror enables tuning of the ratio of relaxation rates for different transitions in the atom to increase population inversion. We quantify the enhancement in amplification due to these factors and show that it can be demonstrated for standard parameters in experiments with superconducting quantum circuits.

The Polar Wind Modulated by the Spatial Inhomogeneity of the Strength of the Earth's Magnetic Field

AbstractWhen the geomagnetic field is weak, the small mirror force allows precipitating charged particles to deposit energy in the ionosphere. This leads to an increase in ionospheric outflow from the Earth's polar cap region, but such an effect has not been previously observed because the energies of the ions of the polar ionospheric outflow are too low, making it difficult to detect the low‐energy ions with a positively charged spacecraft. In this study, we found an anticorrelation between ionospheric outflow and the strength of the Earth's magnetic field. Our results suggest that the electron precipitation through the polar rain can be a main energy source of the polar wind during periods of high levels of solar activity. The decreased magnetic field due to spatial inhomogeneity of the Earth's magnetic field and its effect on outflow can be used to study the outflow in history when the magnetic field was at similar levels.

Frequency Dependence of Very Low Frequency Chorus Poynting Flux in the Source Region: THEMIS Observations and a Model

AbstractUsing Poynting vector measurements of whistler mode chorus emissions detected by the THEMIS spacecraft within the source region, that is, close to the magnetic field minimum, we found both in individual events and statistically that chorus elements propagating equatorward had systematically higher frequencies and smaller amplitudes compared with simultaneously observed elements propagating away from the equator. We demonstrate similar features in the results of numerical simulations based on backward wave oscillator equations. It can be qualitatively explained by the nonlinear evolution of the energetic electron distribution function during wave generation. The motion of electrons from the equator is accompanied by a decrease in their velocity component along the magnetic field line due to both the adiabatic mirror force and nonlinear wave‐particle interactions. Thus, the frequency of the chorus elements generated by such electrons and propagating equatorward is higher compared with the elements propagating away from the equator.

Integration of kinetic ions in a three‐dimensional Monte‐Carlo neutral transport code

AbstractCharged particles of species different from the major constituents of a plasma might not reach local thermodynamic equilibrium during their lifespan. Such low collisional ions render the often‐used fluid description, assuming Maxwellian velocity distribution, as insufficient. Hence, kinetic treatment of such minorities becomes inevitable. The three‐dimensional kinetic neutral particle Monte‐Carlo code EIRENE [D. Reiter et al., Fusion Science and Technology, 47 (2), 172 (2005)] possesses a model for ion transport reduced in physics, consisting of field‐line tracing and energy relaxation of particles. The trajectory integration is now extended to account for first‐order particle drifts, anomalous cross‐field diffusion denoting for turbulence effects, and the consideration of the magnetic mirror force. The technical implementation, as well as the verification of the enhanced kinetic ion transport is being reported.

Turbulence in the Local Interstellar Medium and the IBEX Ribbon.

The effects of turbulence in the very local interstellar medium (VLISM) have been proposed by Giacalone & Jokipii (2015) to be important in determining the structure of the Interstellar Boundary Explorer (IBEX) ribbon via particle trapping by magnetic mirroring. We further explore this effect by simulating the motion of charged particles in a turbulent magnetic field superposed on a large-scale mean field, which we consider to be either spatially-uniform or a draped field derived from a 3D MHD simulation. We find that the ribbon is not double-peaked, in contrast to Giacalone & Jokipii (2015). However, the magnetic mirror force still plays an important role in trapping particles. Furthermore, the ribbon's thickness is considerably larger if the large-scale mean field is draped around the heliosphere. Voyager 1 observations in the VLISM show a turbulent field component that is stronger than previously thought, which we test in our simulation. We find that the inclusion of turbulent fluctuations at scales ≳100 au and power consistent with Voyager 1 observations produces a ribbon whose large-scale structure is inconsistent with IBEX observations. However, restricting fluctuations to <100 au produces a smoother ribbon structure similar to IBEX observations. Different turbulence realizations produce different small-scale features (≲10°) in the ribbon, but its large-scale structure is robust if the maximum fluctuation size is ≲50 au. This suggests that the magnetic field structure at scales ≲50 au is determined by the heliosphere-VLISM interaction and cannot entirely be represented by pristine interstellar turbulence.

Gyrofluid modeling of magnetosphere in feedback instability

Feedback instability occurs in a coupling system of the magnetosphere and the ionosphere, and is a theoretical model explaining spontaneous development of the quiet aurora. In this study, we extend a model of the magnetosphere in the feedback instability to the gyrofluid model. This extension makes it possible to properly discuss kinetic effects, such as the finite Larmor radius effect, the Landau damping, and the mirror force, on the feedback instability in a framework of a fluid model. The derived model is applied to linear stability analysis of the low-frequency feedback instability in the absence of the mirror force. An analytical expression of the parallel electron momentum diffusion coefficient associated with the electron Landau damping is obtained by considering a Landau-fluid closure model. It is found that high-wavenumber modes are strongly affected by the finite ion Larmor radius effect and the electron Landau damping. In particular, a stabilizing effect of the electron Landau damping is dominant and stronger for high-parallel-wavenumber modes. This result indicates that the lowest-parallel-wavenumber mode primarily grows during the spontaneous development of the quiet aurora.

Low Electron Temperatures Observed at Mars by MAVEN on Dayside Crustal Magnetic Field Lines

AbstractThe ionospheric electron temperature is important for determining the neutral/photochemical escape rate from the Martian atmosphere via the dissociative recombination of O2+. The Langmuir Probe and Waves instrument onboard MAVEN (Mars Atmosphere and Volatile EvolutioN) measures electron temperatures in the ionosphere. The current paper studies electron temperatures in the dayside for two regions where (1) crustal magnetic fields are dominant and (2) draped magnetic fields are dominant. Overall, the electron temperature is lower in the crustal‐field regions, namely, the strong magnetic field region, which is due to a transport of cold electrons along magnetic field lines from the lower to upper atmosphere. The electron temperature is also greater for high solar extreme ultraviolet conditions, which is associated with the local extreme ultraviolet energy deposition. The current models underestimate the electron temperature above 250‐km altitude in the crustal‐field region. Electron heat conduction associated with a photoelectron transport in the crustal‐field regions is altered due to kinetic effects, such the magnetic mirror and/or ambipolar electric field because the electron mean free path exceeds the relevant length scale for electron temperature. The mirror force can affect the electron and heat transport between low altitudes, where the neutral density and related electron cooling rates are the greatest, and high altitudes, while the ambipolar electric field decelerates the electron's upward motion. These effects have not been included in current models of the electron energetics, and consideration of such effects on the electron temperature in the crustal‐field region should be considered for future numerical simulations.

Electron Energization by Parallel Electric Fields in Poloidal Standing Waves

AbstractA hybrid gyrofluid‐kinetic electron model is adapted and used to simulate poloidal standing modes for different electron temperatures and azimuthal mode numbers. As in previous studies of toroidal standing modes, mirror force effects lead to increased parallel potential drops, monoenergetic electron energization, and wave energy dissipation as the ambient electron temperature is increased. A similar trend is also observed when the electron temperature is held fixed and the azimuthal mode number increased—owing to the narrowing of the azimuthal flux tube width, which necessitates more electron energization to carry the increased parallel current density. In both cases, the increase in electron energization eventually leads to more rapid decreases in the parallel current with time because of the dissipation of wave energy.

Particle Energy Diffusion in Linear Magnetohydrodynamic Waves

Abstract In high-energy astronomical phenomena, the stochastic particle acceleration by turbulences is one of the promising processes to generate nonthermal particles. In this paper, we investigate the energy-diffusion efficiency of relativistic particles in a temporally evolving wave ensemble that consists of a single mode (Alfvén, fast or slow) of linear magnetohydrodynamic waves. In addition to the gyroresonance with waves, the transit-time damping (TTD) also contributes to the energy diffusion for fast and slow-mode waves. While the resonance condition with the TTD has been considered to be fulfilled by a very small fraction of particles, our simulations show that a significant fraction of particles are in the TTD resonance owing to the resonance broadening by the mirror force, which nonresonantly diffuses the pitch angle of particles. When the cutoff scale in the turbulence spectrum is smaller than the Larmor radius of a particle, the gyroresonance is the main acceleration mechanism for all the three wave modes. For the fast mode, the coexistence of the gyroresonance and TTD resonance leads to anomalous energy diffusion. For a particle with its Larmor radius smaller than the cutoff scale, the gyroresonance is negligible, and the TTD becomes the dominant mechanism to diffuse its energy. The energy diffusion by the TTD-only resonance with fast-mode waves agrees with the hard-sphere-like acceleration suggested in some high-energy astronomical phenomena.

Large-scale altitude distribution profile of auroral parallel electric potentials: A statistical analysis of Cluster data

It is generally believed that the heart of the Auroral Acceleration Region (AAR) is located between 5000 and 8000 km altitude above the auroral oval. Various altitude distribution profiles are suggested by different theories, including the transition layer model, which predicts that the strongest electric fields can be found at about 1 RE, and can vary depending on the plasma and geomagnetic conditions. However, there have been no specific experimental results that cover regions both below and well above such altitude. This paper presents a method for obtaining such a profile from AAR satellite crossings, applies it to a data set gathered from 116 Cluster spacecraft encounters with acceleration potential structures, and discusses the results. The crossings cover an altitude range between 0.63 RE and 2.9 RE. The outcome is the first empirical altitude distribution profile of the auroral acceleration potentials. The results suggest that the region within the altitude range of 0.9245 RE and 1.158 RE statistically contains 30% of the total potential, which is the largest fraction of the parallel potentials among all altitude segments of the same size. The altitude which equally divides the distribution of acceleration potentials was found at 1.076 RE (6863 km). The obtained parallel potential distribution is in agreement with both the magnetic mirror force theory and the transition layer model, and can hence provide a proper baseline for future missions to the AAR.

Effect of Kinetic Alfvén Waves on Electron Transport in an Ion-Scale Flux Rope**Supported by the National Natural Science Foundation of China under Grant Nos 41474145, 41574159, 41731070 and 41504114, the Frontier Science Foundation of the Chinese Academy of Sciences under Grant No QYZDJ-SSW-JSC028, the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No XDA15052500, and the

At the Earth’s magnetopause, the electron transport due to kinetic Alfvén waves (KAWs) is investigated in an ion-scale flux rope by the Magnetospheric Multiscale mission. Clear electron dropout around 90° pitch angle is observed throughout the flux rope, where intense KAWs are identified. The KAWs can effectively trap electrons by the wave parallel electric field and the magnetic mirror force, allowing electrons to undergo Landau resonance and be transported into more field-aligned directions. The pitch angle range for the trapped electrons is estimated from the wave analysis, which is in good agreement with direct pitch angle measurements of the electron distributions. The newly formed beam-like electron distribution is unstable and excites whistler waves, as revealed in the observations. We suggest that KAWs could be responsible for the plasma depletion inside a flux rope by this transport process, and thus be responsible for the formation of a typical flux rope.

The Role of Pickup Ion Dynamics Outside of the Heliopause in the Limit of Weak Pitch Angle Scattering: Implications for the Source of the IBEX Ribbon.

We present a new model of the Interstellar Boundary Explorer (IBEX) ribbon based on the secondary energetic neutral atom (ENA) mechanism, under the assumption that there is negligible pitch angle scattering of pickup ions (PUIs) outside the heliopause. Using the results of an MHD-plasma/kinetic-neutral simulation of the heliosphere, we generate PUIs in the outer heliosheath, solve their transport using guiding center theory, and compute ribbon ENA fluxes at 1 AU. We implement several aspects of the PUI dynamics, including (1) parallel motion along the local interstellar magnetic field (ISMF), (2) advective transport with the interstellar plasma, (3) the mirror force acting on PUIs propagating along the ISMF, and (4) betatron acceleration of PUIs as they are advected within an increasing magnetic field towards the heliopause. We find that ENA fluxes at 1 AU are reduced when PUIs are allowed to move along the ISMF, and ENA fluxes are reduced even more by the inclusion of the mirror force, which pushes particles away from IBEX lines-of-sight. Inclusion of advection and betatron acceleration do not result in any significant change in the ribbon. Interestingly, the mirror force reduces the ENA fluxes from the inner edge of the ribbon more than its outer edge, effectively reducing the ribbon's width by ∼6° and increasing its radius projected on the sky. This is caused by the asymmetric draping of the ISMF around the heliopause, such that ENAs from the ribbon's inner edge originate closer to the heliopause, where the mirror force is strongest.

Gyrofluid Model of Plasma Expansion in a Diverging Magnetic Field

The gyrofluid equations for electrons and for ions are used to model the acceleration of plasma from a source region of high magnetic field to a region of lower field. The model includes a source term for plasma generation, a self-consistent electric field, nonzero ion temperature, plasma acceleration by the mirror force, and the reduction in density from the diverging flow. The model is applicable to plasma experiments with helicon sources, ion engines for spacecraft, and some plasma processing configurations. The ion flux from the source region is found to be approximately the Bohm flux and the downstream ion flux density scales with the magnetic field. The downstream flow is determined by the conversion of upstream thermal energy in both electrons and ions into kinetic energy in flow speed. For large expansion ratios, the final speed approaches 1.5 times the ion sound speed.

Ion Heating in the Martian Ionosphere

AbstractEnergetic O+ and O ions with energies of up to a few hundred eV are observed in the Martian ionosphere. Corresponding ion velocity distributions show ion conics, suggesting that the observed ion populations have been heated perpendicular to the local magnetic field before experiencing a magnetic mirror force. Magnetic field observations support these interpretations: wave power at the local O+ and O gyrofrequencies in the spacecraft frame is observed coincident with the energetic ions, within an apparent magnetic field bottle‐like topology. Analysis of the observed ion conics leads to estimates of ion temperatures of 10–30 eV. We suggest that the ion populations are initially heated perpendicular to the local magnetic field by wave power propagating inward from the Mars‐solar wind interaction. The local magnetic field “balloons out” in response to these enhanced ion temperatures and pressures. The resultant magnetic field topology is bottle like; the transversely heated ions would subsequently experience a magnetic mirror force in the converging field regions, agreeing with the reported observations. Such strong heating events that significantly increase the ion temperature and pressure, thereby decreasing the net magnetic field, are rare and seem to occur under specific interplanetary magnetic field orientations. Events were observed to span the upper exobase region and just above, a region characterized by significant ion densities in an increasingly collisionless domain. Ion heating in this region has the potential to drive significant ion outflows, thus contributing to atmospheric loss from the planet.

The Relationship between Long-Duration Gamma-Ray Flares and Solar Cosmic Rays

AbstractA characteristic pattern of solar hard X-ray emission, first identified in SOL1969-03-30 by Frost &amp; Dennis (1971), turns out to have a close association with the prolonged high-energy gamma-ray emission originally observed by Forrestet al.(1985). This identification has become clear via the observations of long-duration γ-ray flares by theFermi/LAT experiment, for example in the event SOL2014-09-01. The distinctive features of these events include flat hard X-ray spectra extending well above 100 keV, a characteristic pattern of time development, low-frequency gyrosynchrotron peaks, CME association, and gamma-rays identifiable with pion decay originating in GeV ions. The identification of these events with otherwise known solar structures nevertheless remains elusive, in spite of the wealth of EUV imagery available from SDO/AIA. The quandary is that these events have a clear association with SEPs in the high corona, and yet the gamma-ray production implicates the photosphere itself, despite the strong mirror force that should focus the particlesawayfrom the Sun We discuss the morphology of these phenomena and propose a solution to this problem.

Parametric study of density cavities caused by ion outflow in the topside ionosphere

Plasma density cavities are correlated with heavy ion outflow where ions are heated transversely by wave particle interactions (WPIs). This paper presents the first result of a 3D ionospheric fluid model that incorporates plasma temperature anisotropies and a phenomenological treatment of WPIs, leading to transversely accelerated ions (TAIs). It is demonstrated that O+ outflow can generate density cavities in the topside ionosphere. With the empirical heating rate applied in a designated heating region on the dayside, the O+ species in the heating region is accelerated upward by the mirror force. The O+ species below the heating region upflows under the parallel pressure gradient force and the parallel electric force. As the O+ species flows upward, the plasma is eroded both below and inside the heating region. Parametric modeling studies show that the depth of density cavities in the upper ionosphere increases as the heating rate increases. The percent change in the density of the cavity relative to the local background density is practically independent of the low-altitude cutoff of the heating region, but the altitude of the relative density minimum moves upward with the increasing altitude of cutoff. The O+ flux is insensitive to the change of the heating rate, while depends strongly on the altitude of cutoff. Using empirical values of the initial heating rate and the height of the low-altitude boundary as input, the ranges of the modeled electron density and the O+ outflow moments are in reasonable agreement with observations of a storm-time density cavity observed by the FAST satellite. The 3D ionospheric model has the potential to be coupled to magnetospheric models for magnetosphere-ionosphere (MI) coupling.

Direct measurement of the plasma loss width in an optimized, high ionization fraction, magnetic multi-dipole ring cusp

The loss width of plasma in the WiPAL multi-dipole magnetic ring cusp [Cooper et al., Phys. Plasmas 21, 13505 (2014); Forest et al., J. Plasma Phys. 81, 345810501 (2015)] has been directly measured using a novel array of probes embedded in the insulating plasma limiters. The large plasma volume (∼10 m3), small loss area associated with strong rare earth permanent magnets (Bo∼2.23 kG at face), and large heating power (≤200 kW) produces a broad range of electron temperatures (2&amp;lt;Te&amp;lt;15 eV), ion temperatures (0.03&amp;lt;Ti&amp;lt;2 eV), plasma densities (3×1010&amp;lt;ne&amp;lt;2×1012 cm−3), and ionization fractions (0.05&amp;lt;ne/(ne+nn)&amp;lt;1), in both argon and helium, all of which were accurately measured. This plasma regime, accessible with high magnetic fields, differs from previous devices: the cusp loss width is much larger than the Debye length and electron gyroradius and comparable to the collision length. Plasma parameters measured at the surface of ceramic limiter tiles covering the magnets and along radial chords in the cusp magnetic field indicate that electron density and temperature are nearly constant on magnetic field lines and that the mirror forces play little role in confining the plasma other than to constrict the loss area. Particle balance modeling is used to determine the cross field diffusion coefficient base on the measured losses to the limiters. The experimentally determined cross field diffusion coefficient (which determines the cusp loss width) is consistent with ambipolar diffusion across five orders of magnitude. The ambipolar diffusion across a given field line is set primarily by the electron-neutral collisions in the region where the magnetic field is the weakest, even though these plasmas can have ionization fractions near 1.

Upper limit of electron fluxes generated by kinetic Alfvén waves in Maxwellian plasma

AbstractWe consider electron acceleration by kinetic Alfvén waves in the equatorial inner magnetosphere and plasma sheet boundary layer. The competition between the accelerating effect of the wave parallel electric field and mirror force acting on particles in an inhomogeneous background magnetic field generates an effective potential well where electrons can be trapped and accelerated. We compare energy variations of trapped and transient resonant electrons and show that these variations almost compensate each other. Thus, energy provided to waves by transient particles is transferred to trapped particles. This effect allows waves accelerate trapped electrons without being significantly damped. Using energy balance equations, we estimate the maximum flux of electrons accelerated via trapping into Landau resonance with kinetic Alfvén waves. For a wide range of system parameters (i.e., ion to electron temperature ratio, magnetic field amplitude, and wave number and wave frequency), acceleration of trapped electrons can generate fluxes with amplitude about 5–25% of the background thermal fluxes. We determine parametric regions for the most efficient acceleration.