Mirror Mode Research Articles

Entanglement and Gaussian interferometric power dynamics in an optomechanical system with radiation pressure

We investigate the non-classical correlations existing in the mixed bipartite state consisting of the reflected optical 1 mode and the mechanical mode (movable mirror). The covariance matrix is calculated when the state of each mode is initially in a vacuum. We consider the criterion of positivity of the partially transposed state (PPT criterion) to quantify the dynamical evolution of the entanglement between the reflected optical 1 and the movable mirror modes using the smallest symplectic eigenvalue. Then we use Gaussian quantum steering to measure the steerability between the two modes. We also consider the Gaussian interferometric power to quantify the quantum correlations that exist beyond entanglement.

Radial evolution of the solar wind in pure high-speed streams: HELIOS revised observations

Spacecraft observations have shown that the proton temperature in the solar wind falls off with radial distance more slowly than expected for an adiabatic prediction. Usually, previous studies have been focused on the evolution of the solar-wind plasma by using the bulk speed as an order parameter to discriminate different regimes. In contrast, here, we study the radial evolution of pure and homogeneous fast streams (i.e. well-defined streams of coronal-hole plasma that maintain their identity during several solar rotations) by means of re-processed particle data, from the HELIOS satellites between 0.3 and 1 AU. We have identified 16 intervals of unperturbed high-speed coronal hole plasma, from three different sources and measured at different radial distances. The observations show that, for all three streams, (i) the proton density decreases as expected for a radially expanding plasma, unlike previous analysis that found a slower decrease; (ii) the magnetic field deviates from the Parker prediction, with the radial and tangential components decreasing more slowly and quickly than expected, respectively; (iii) the double-adiabatic invariants are violated and an increase of entropy is observed; (iv) the proton-core temperature anisotropy is constrained by mirror mode instability; (v) the collisional frequency is not constant, but decreases as the plasma travels away from the Sun. The present work provides an insight into the heating problem in pure fast solar wind, fitting in the context of the next solar missions, and, especially for Parker Solar Probe, it enables us to predict the high-speed solar-wind environment much closer to the Sun.

Electron mirror branch: observational evidence from “historical” AMPTE-IRM and Equator-S measurements

Abstract. Based on now “historical” magnetic observations, supported by few available plasma data, and wave spectra from the AMPTE-IRM spacecraft, and also on “historical” Equator-S high-cadence magnetic field observations of mirror modes in the magnetosheath near the dayside magnetopause, we present observational evidence for a recent theoretical evaluation by Noreen et al. (2017) of the contribution of a global (bulk) electron temperature anisotropy to the evolution of mirror modes, giving rise to a separate electron mirror branch. We also refer to related low-frequency lion roars (whistlers) excited by the trapped resonant electron component in the high-temperature anisotropic collisionless plasma of the magnetosheath. These old data most probably indicate that signatures of the anisotropic electron effect on mirror modes had indeed already been observed long ago in magnetic and wave data, though they had not been recognised as such. Unfortunately either poor time resolution or complete lack of plasma data would have inhibited the confirmation of the required pressure balance in the electron branch for unambiguous confirmation of a separate electron mirror mode. If confirmed by future high-resolution observations (like those provided by the MMS mission), in both cases the large mirror mode amplitudes suggest that mirror modes escape quasilinear saturation, being in a state of weak kinetic plasma turbulence. As a side product, this casts as erroneous the frequent claim that the excitation of lion roars (whistlers) would eventually saturate the mirror instability by depleting the bulk temperature anisotropy. Whistlers, excited in mirror modes, just flatten the anisotropy of the small population of resonant electrons responsible for them, without having any effect on the global electron-pressure anisotropy, which causes the electron branch and by no means at all on the ion-mirror instability. For the confirmation of both the electron mirror branch and its responsibility for trapping of electrons and resonantly exciting high-frequency whistlers, also known as lion roars, high time- and energy-resolution observations of electrons (as provided for instance by MMS) are required.

All-in-fiber SESAM based comb oscillator with an intra-cavity electro-optic modulator for coherent high bandwidth stabilization.

We demonstrate the stabilization of an all-in-fiber polarization maintaining semi-conductor saturable absorber mirror (SESAM) mode locked frequency comb oscillator with an intra-cavity waveguide electro-optic phase modulator (EOM) to a narrow linewidth HeNe laser over 46 hours. The high feedback bandwidth of the EOM allows a coherent optical lock with an in-loop integrated phase noise of 1.12 rad (integrated from 10 Hz to 3 MHz) from the carrier signal. No piezo fiber stretcher was required to guarantee long-term stabilization, preventing mechanical degradation of the optical fibers and enabling a long lifetime of the oscillator. As an application a hybrid stabilization scheme is presented, where a comb tooth is phase locked to a longitudinal mode of the large ring laser "G" located at the Geodatic Observatory Wettzell. The hybrid stabilization scheme describes the optical lock of the frequency comb to the G laser and the simultaneous compensation of the ring laser frequency drift by comparing the comb repetition rate against an active H-maser reference. In this context the ring laser reached a fractional Allan deviation of 5 · 10-16 at an integration time of 16384 s.

Nature of Magnetic Holes above Ion Scales: A Mixture of Stable Slow Magnetosonic and Unstable Mirror Modes in a Double-polytropic Scenario?

Abstract Magnetic holes are common features with a prominent dip of magnetic field strength in space plasma turbulence. As to their nature, there exists a dispute of explanations among discontinuities, magnetic reconnection, solitons, kinetic-scale electron vortexes, slow waves, and mirror-mode instability. As magnetic holes are often accompanied by thermal anisotropy, at magnetohydrodynamic scales double-polytropic equations can serve as an appropriate description. The reason for the long-lasting dispute lies in the fact that both mirror-mode structures and oblique slow-mode waves are characterized with anticorrelation between plasma density (or temperature) and magnetic field strength, which, as often used in preceding works, is also the characteristic feature of magnetic holes. Therefore, to finally and unambiguously diagnose the nature of magnetic holes above ion scales, we propose to resort to other features, among which v ∥ and its phase relation with and n behave differently between mirror-mode structures and slow-mode waves. Herewith we establish a model with superposition of both slow and mirror modes to reproduce the observed types of behaviors . This model inspires new understanding of the nature of magnetic holes: the magnetic hole in reality is not solely contributed by only one mode, but a mixture of the two modes with an adjustable amplitude ratio.

The mirror mode: a “superconducting” space plasma analogue

Abstract. We examine the physics of the magnetic mirror mode in its final state of saturation, the thermodynamic equilibrium, to demonstrate that the mirror mode is the analogue of a superconducting effect in a classical anisotropic-pressure space plasma. Two different spatial scales are identified which control the behaviour of its evolution. These are the ion inertial scale λim(τ) based on the excess density Nm(τ) generated in the mirror mode, and the Debye scale λD(τ). The Debye length plays the role of the correlation length in superconductivity. Their dependence on the temperature ratio τ=T‖/T⟂<1 is given, with T⟂ the reference temperature at the critical magnetic field. The mirror-mode equilibrium structure under saturation is determined by the Landau–Ginzburg ratio κD=λim/λD, or κρ=λim/ρ, depending on whether the Debye length or the thermal-ion gyroradius ρ – or possibly also an undefined turbulent correlation length ℓturb – serve as correlation lengths. Since in all space plasmas κD≫1, plasmas with λD as the relevant correlation length always behave like type II superconductors, naturally giving rise to chains of local depletions of the magnetic field of the kind observed in the mirror mode. In this way they would provide the plasma with a short-scale magnetic bubble texture. The problem becomes more subtle when ρ is taken as correlation length. In this case the evolution of mirror modes is more restricted. Their existence as chains or trains of larger-scale mirror bubbles implies that another threshold, VA>υ⟂th, is exceeded. Finally, in case the correlation length ℓturb instead results from low-frequency magnetic/magnetohydrodynamic turbulence, the observation of mirror bubbles and the measurement of their spatial scales sets an upper limit on the turbulent correlation length. This might be important in the study of magnetic turbulence in plasmas.

Statistical analysis of mirror mode waves in sheath regions driven by interplanetary coronal mass ejection

Abstract. We present a comprehensive statistical analysis of mirror mode waves and the properties of their plasma surroundings in sheath regions driven by interplanetary coronal mass ejection (ICME). We have constructed a semi-automated method to identify mirror modes from the magnetic field data. We analyze 91 ICME sheath regions from January 1997 to April 2015 using data from the Wind spacecraft. The results imply that similarly to planetary magnetosheaths, mirror modes are also common structures in ICME sheaths. However, they occur almost exclusively as dip-like structures and in mirror stable plasma. We observe mirror modes throughout the sheath, from the bow shock to the ICME leading edge, but their amplitudes are largest closest to the shock. We also find that the shock strength (measured by Alfvén Mach number) is the most important parameter in controlling the occurrence of mirror modes. Our findings suggest that in ICME sheaths the dominant source of free energy for mirror mode generation is the shock compression. We also suggest that mirror modes that are found deeper in the sheath are remnants from earlier times of the sheath evolution, generated also in the vicinity of the shock. Keywords. Interplanetary physics (plasma waves and turbulence; solar wind plasma) – space plasma physics (waves and instabilities)

Electron Heating in Low Mach Number Perpendicular Shocks. II. Dependence on the Pre-shock Conditions

Abstract Recent X-ray observations of merger shocks in galaxy clusters have shown that the post-shock plasma is two-temperature, with the protons being hotter than the electrons. In this work, the second of a series, we investigate the efficiency of irreversible electron heating in perpendicular low Mach number shocks, by means of two-dimensional particle-in-cell simulations. We consider values of plasma beta (the ratio of thermal and magnetic pressures) in the range 4 ≲ β p0 ≲ 32, and sonic Mach number (the ratio of shock speed to pre-shock sound speed) in the range 2 ≲ M s ≲ 5, as appropriate for galaxy cluster shocks. As shown in Paper I, magnetic field amplification—induced by shock compression of the pre-shock field, or by strong proton cyclotron and mirror modes accompanying the relaxation of proton temperature anisotropy—can drive the electron temperature anisotropy beyond the threshold of the electron whistler instability. The growth of whistler waves breaks the electron adiabatic invariance, and allows for efficient entropy production. We find that the post-shock electron temperature T e2 exceeds the adiabatic expectation by an amount (here, T e0 is the pre-shock temperature), which depends only weakly on the plasma beta over the range 4 ≲ β p0 ≲ 32 that we have explored, as well as on the proton-to-electron mass ratio (the coefficient of ≃0.044 is measured for our fiducial , and we estimate that it will decrease to ≃0.03 for the realistic mass ratio). Our results have important implications for current and future observations of galaxy cluster shocks in the radio band (synchrotron emission and Sunyaev–Zel’dovich effect) and at X-ray frequencies.

Two-dimensional Nonlinear Simulations of Temperature-anisotropy Instabilities with a Proton-alpha Drift

Abstract We present two-dimensional hybrid simulations of proton-cyclotron and mirror instabilities in a proton-alpha plasma with particle-in-cell ions and a neutralizing electron fluid. The instabilities are driven by the protons with temperature perpendicular to the background magnetic field larger than the parallel temperature. The alpha particles with initially isotropic temperature have a nonzero drift speed with respect to the protons. The minor ions are known to influence the relative effect of the proton-cyclotron and mirror instabilities. In this paper, we show that the mirror mode can dominate the power spectrum at the nonlinear stage even if its linear growth rate is significantly lower than that of the proton-cyclotron mode. The proton-cyclotron instability combined with the alpha-proton drift is a possible cause of the nonzero magnetic helicity observed in the solar wind for fluctuations propagating nearly parallel to the magnetic field. Our simulations generally confirm this concept but reveal a complex helicity spectrum that is not anticipated from the linear theory of the instability.

Compressible Magnetohydrodynamic Turbulence in the Earth's Magnetosheath: Estimation of the Energy Cascade Rate Using insitu Spacecraft Data.

The first estimation of the energy cascade rate |ε_{C}| of magnetosheath turbulence is obtained using the Cluster and THEMIS spacecraft data and an exact law of compressible isothermal magnetohydrodynamics turbulence. The mean value of |ε_{C}| is found to be close to 10^{-13} J m^{-3} s^{-1}, at least 2 orders of magnitude larger than its value in the solar wind (∼10^{-16} J m^{-3} s^{-1} in the fast wind). Two types of turbulence are evidenced and shown to be dominated either by incompressible Alfvénic or compressible magnetosoniclike fluctuations. Density fluctuations are shown to amplify the cascade rate and its spatial anisotropy in comparison with incompressible Alfvénic turbulence. Furthermore, for compressible magnetosonic fluctuations, large cascade rates are found to lie mostly near the linear kinetic instability of the mirror mode. New empirical power-laws relating |ε_{C}| to the turbulent Mach number and to the internal energy are evidenced. These new findings have potential applications in distant astrophysical plasmas that are not accessible to insitu measurements.

Magnetospheric Multiscale Observations of Electron Scale Magnetic Peak

AbstractThe sudden enhancements of magnetic strength, named magnetic peaks (MPs), are often observed in the magnetosheath of magnetized planets. They are usually identified as flux ropes (FRs) or magnetic mirror mode structures. Previous studies of MPs are mostly on the magnetohydrodynamics (MHD) scale. In this study, an electron scale MP is reported in the Earth magnetosheath. We present a typical case with a scale of ~7 electron gyroradii and a duration of ~0.18 s. A strong magnetic disturbance and associated electrical current are detected. Electron vortex is found perpendicular to the magnetic field line and is self‐consist with the peak. We use multipoint spacecraft techniques to determine the propagation velocity of the MP structure and find that the magnetic peak does propagate relative to the plasma (ion) flow. This is very different from the magnetic mirror mode that does not propagate relative to the plasma flow. Furthermore, we developed an efficient method that can effectively distinguish “magnetic bottle like” and “FRs like” structures. The MP presented in this study is identified as magnetic bottle like type. The mechanism to generate the electron scale magnetic bottle like structure is still unclear, suggesting that new theory needs to be developed to understand such small‐scale phenomena.

Contributions of Mirror and Ion Bernstein Instabilities to the Scattering of Pickup Ions in the Outer Heliosheath

Abstract Maintaining the stability of pickup ions in the outer heliosheath is a critical element for the secondary energetic neutral atom (ENA) mechanism, a theory put forth to explain the nearly annular band of ENA emission observed by the Interstellar Boundary EXplorer. A recent study showed that a pickup ion ring can remain stable to the Alfvén/ion cyclotron (AC) instability at propagation parallel to the background magnetic field when the parallel thermal spread of the ring is comparable to that of a background population. This study investigates the potential role that the mirror or ion Bernstein (IB) instabilities can play in the stability of pickup ions when conditions are such that the AC instability is suppressed. Linear Vlasov theory predicts relatively fast mirror and IB instability growth even though AC instability growth is suppressed. For a few such cases, two-dimensional hybrid and macroscopic quasi-linear simulations are carried out to examine how the unstable mirror and IB modes evolve and affect the pickup ion ring beyond the linear theory picture. For the parameters used, the mirror mode dominates initially and leads to a rapid parallel heating of the pickup ions in excess of the parallel temperature of the background protons. The heated pickup ions subsequently trigger onset of the AC mode, which grows sufficiently large to be the dominant pitch angle scattering agent after the mirror mode has decayed away. The present results indicate that the pickup ion stability needed may not be guaranteed once the mirror and IB instabilities are taken into account.

The Properties of Lion Roars and Electron Dynamics in Mirror Mode Waves Observed by the Magnetospheric MultiScale Mission

AbstractMirror mode waves are ubiquitous in the Earth's magnetosheath, in particular behind the quasi‐perpendicular shock. Embedded in these nonlinear structures, intense lion roars are often observed. Lion roars are characterized by whistler wave packets at a frequency ∼100 Hz, which are thought to be generated in the magnetic field minima. In this study, we make use of the high time resolution instruments on board the Magnetospheric MultiScale mission to investigate these waves and the associated electron dynamics in the quasi‐perpendicular magnetosheath on 22 January 2016. We show that despite a core electron parallel anisotropy, lion roars can be generated locally in the range 0.05–0.2fce by the perpendicular anisotropy of electrons in a particular energy range. We also show that intense lion roars can be observed up to higher frequencies due to the sharp nonlinear peaks of the signal, which appear as sharp spikes in the dynamic spectra. As a result, a high sampling rate is needed to estimate correctly their amplitude, and the latter might have been underestimated in previous studies using lower time resolution instruments. We also present for the first‐time 3‐D high time resolution electron velocity distribution functions in mirror modes. We demonstrate that the dynamics of electrons trapped in the mirror mode structures are consistent with the Kivelson and Southwood (1996) model. However, these electrons can also interact with the embedded lion roars: first signatures of electron quasi‐linear pitch angle diffusion and possible signatures of nonlinear interaction with high‐amplitude wave packets are presented. These processes can lead to electron untrapping from mirror modes.

Electron Heating in Low-Mach-number Perpendicular Shocks. I. Heating Mechanism

Abstract Recent X-ray observations of merger shocks in galaxy clusters have shown that the postshock plasma has two temperatures, with the protons hotter than the electrons. By means of two-dimensional particle-in-cell simulations, we study the physics of electron irreversible heating in low-Mach-number perpendicular shocks, for a representative case with sonic Mach number of 3 and plasma beta of 16. We find that two basic ingredients are needed for electron entropy production: (1) an electron temperature anisotropy, induced by field amplification coupled to adiabatic invariance; and (2) a mechanism to break the electron adiabatic invariance itself. In shocks, field amplification occurs at two major sites: at the shock ramp, where density compression leads to an increase of the frozen-in field; and farther downstream, where the shock-driven proton temperature anisotropy generates strong proton cyclotron and mirror modes. The electron temperature anisotropy induced by field amplification exceeds the threshold of the electron whistler instability. The growth of whistler waves breaks the electron adiabatic invariance and allows for efficient entropy production. For our reference run, the postshock electron temperature exceeds the adiabatic expectation by , resulting in an electron-to-proton temperature ratio of . We find that the electron heating efficiency displays only a weak dependence on mass ratio (less than drop, as we increase the mass ratio from up to ). We develop an analytical model of electron irreversible heating and show that it is in excellent agreement with our simulation results.

Simulation of magnetic holes formation in the magnetosheath

Magnetic holes have been frequently observed in the Earth's magnetosheath and are believed to be the consequence of the nonlinear evolution of the mirror instability. Mirror mode perturbations mainly form as magnetic holes in regions where the plasma is marginally mirror stable with respect to the linear instability criterion. We present an expanding box particle-in-cell simulation to mimic the changing conditions in the magnetosheath as the plasma is convected through it that produces mirror mode magnetic holes. We show that in the initial nonlinear evolution, where the plasma conditions are mirror unstable, the magnetic peaks are dominant, while later, as the plasma relaxes toward marginal stability, the fluctuations evolve into deep magnetic holes. While the averaged plasma parameters in the simulation remain close to the mirror instability threshold, the local plasma in the magnetic holes is highly unstable to mirror instability and locally mirror stable in the magnetic peaks.

Reprint of Low-energy electron potentiometry

In a lot of systems, charge transport is governed by local features rather than being a global property as suggested by extracting a single resistance value. Consequently, techniques that resolve local structure in the electronic potential are crucial for a detailed understanding of electronic transport in realistic devices. Recently, we have introduced a new potentiometry method based on low-energy electron microscopy (LEEM) that utilizes characteristic features in the reflectivity spectra of layered materials [1]. Performing potentiometry experiments in LEEM has the advantage of being fast, offering a large field of view and the option to zoom in and out easily, and of being non-invasive compared to scanning-probe methods. However, not all materials show clear features in their reflectivity spectra. Here we, therefore, focus on a different version of low-energy electron potentiometry (LEEP) that uses the mirror mode transition, i.e. the drop in electron reflectivity around zero electron landing energy when they start to interact with the sample rather than being reflected in front of it. This transition is universal and sensitive to the local electrostatic surface potential (either workfunction or applied potential). It can consequently be used to perform LEEP experiments on a broader range of material compared to the method described in Ref[1]. We provide a detailed description of the experimental setup and demonstrate LEEP on workfunction-related intrinsic potential variations on the Si(111) surface and for a metal-semiconductor-metal junction with external bias applied. In the latter, we visualize the Schottky effect at the metal-semiconductor interface. Finally, we compare how robust the two LEEP techniques discussed above are against image distortions due to sample inhomogeneities or contamination.

Ultra low frequency waves at Venus: Observations by the Venus Express spacecraft

The generation of waves with low frequencies (below 100 mHz) has been observed in the environment of most bodies in the solar system and well studied at Earth. These waves can be generated either upstream of the body in the solar wind by ionization of planetary exospheres or ions reflected from a bow shock or in the magnetosheath closer to the magnetic barrier. For Mars and Venus the waves may have special importance since they can contribute to the erosion of the ionopause and by that enhance atmospheric escape. While over the past years many case studies on wave phenomena observed at Venus have been published most statistical studies have been based on magnetic observations only. On the other hand the generation mechanisms and transport of these waves through the magnetosphere can only be quantified using both magnetic and particle observations. We use the long time observations of Venus Express (2006–2014) to determine the predominant processes and transport parameters. First we demonstrate the analysis methods in four case studies, then we present a statistical analysis by determining transport ratios from the complete Venus Express dataset. We find that Alfvenic waves are very dominant (>80%) in the solar wind and in the core magnetosheath. Fast waves are observed mainly at the bow shock (around 40%) but also at the magnetic barrier where they may be most important for the energy transfer into the ionosphere. Their occurrence in the magnetotail may be an artifact of the detection of individual plasma jets in this region. Slow mode waves are rarely dominating but occur with probability of about 10% at the bow shock and in the pile-up-region. Mirror mode waves have probability <20% in the magnetosheath slightly increasing towards the pile-up-boundary.

The Interaction of Coronal Mass Ejections with Alfvénic Turbulence

We provide a first attempt to understand the interaction between Alfvén wave turbulence, kinetic instabilities and temperature anisotropies in the environment of a fast coronal mass ejection (CME) near the Sun. The impact of a fast CME on the solar corona causes turbulent energy, thermal energy and dissipative heating to increase by orders of magnitude, and produces conditions suitable for a host of kinetic instabilities. We study these CME-induced effects with the recently developed Alfvén Wave Solar Model, with which we are able to self-consistently simulate the turbulent energy transport and dissipation as well as isotropic electron heating and anisotropic proton heating. Furthermore, the model also offers the capability to address the effects of fire hose, mirror mode, and cyclotron kinetic instabilities on proton energy partitioning all in a global-scale numerical simulation. We find amplified turbulent energy in the CME sheath, along with strong wave reflection at the shock combine to cause wave dissipation rates to increase by more than a factor of 100. In contrast, wave energy is greatly diminished by adiabatic expansion in the flux rope. Finally, we find proton temperature anisotropies are limited by kinetic instabilities to a level consistent with solar wind observations.

Proton velocity ring‐driven instabilities and their dependence on the ring speed: Linear theory

AbstractLinear dispersion theory is used to study the Alfvén‐cyclotron, mirror and ion Bernstein instabilities driven by a tenuous (1%) warm proton ring velocity distribution with a ring speed, vr, varying between 2vA and 10vA, where vA is the Alfvén speed. Relatively cool background protons and electrons are assumed. The modeled ring velocity distributions are unstable to both the Alfvén‐cyclotron and ion Bernstein instabilities whose maximum growth rates are roughly a linear function of the ring speed. The mirror mode, which has real frequency ωr=0, becomes the fastest growing mode for sufficiently large vr/vA. The mirror and Bernstein instabilities have maximum growth at propagation oblique to the background magnetic field and become more field‐aligned with an increasing ring speed. Considering its largest growth rate, the mirror mode, in addition to the Alfvén‐cyclotron mode, can cause pitch angle diffusion of the ring protons when the ring speed becomes sufficiently large. Moreover, because the parallel phase speed, v∥ph, becomes sufficiently small relative to vr, the low‐frequency Bernstein waves can also aid the pitch angle scattering of the ring protons for large vr. Potential implications of including these two instabilities at oblique propagation on heliospheric pickup ion dynamics are discussed.

Fluxgate magnetometer offset vector determination by the 3D mirror mode method

Fluxgate magnetometer offset vector determination by the 3D mirror mode method