Collisionless shocks heat electrons in the solar wind, interstellar blast waves, and hot gas permeating galaxy clusters. How much shock heating goes to electrons instead of ions, and what plasma physics controls electron heating? We simulate 2-D perpendicular shocks with a fully kinetic particle-in-cell code. For magnetosonic Mach number $\mathcal{M}_\mathrm{ms} \sim 1$-$10$ and plasma beta $β_\mathrm{p} \lesssim 4$, the post-shock electron/ion temperature ratio $T_\mathrm{e}/T_\mathrm{i}$ decreases from $1$ to $0.1$ with increasing $\mathcal{M}_\mathrm{ms}$. In a representative $\mathcal{M}_\mathrm{ms}=3.1$, $β_\mathrm{p}=0.25$ shock, electrons heat above adiabatic compression in two steps: ion-scale $E_\parallel = \vec{E} \cdot \hat{b}$ accelerates electrons into streams along $\vec{B}$, which then relax via two-stream-like instability. The $\vec{B}$-parallel heating is mostly induced by waves; $\vec{B}$-perpendicular heating is mostly adiabatic compression by quasi-static fields.
Solar wind ions are observed to be heated in the directions perpendicular to the large-scale magnetic field, with preferential heating given to heavy ions. In the solar corona, this heating may be responsible for the generation of the wind itself. It is likely that this heating results from the dissipation of plasma turbulence, but the specific kinetic mechanism that produces these preferential effects is not known. Solar wind turbulence at proton scales is often characterized in terms of highly oblique kinetic Alfvén waves (KAWs), which have been thought to dissipate through the Landau resona…
Minor ion (such as $He^{2+}$) heating via nonresonant interaction with spectra of linearly and circularly polarized Alfvén waves (LPAWs and CPAWs hereafter) is studied. The obtained analytic solutions are in good agreement with the simulation results, indicating that newborn ions are heated by low-frequency Alfvén waves with finite amplitude in low-beta plasmas such as the solar corona. The analytic solutions also reproduce the preferential heating of heavy ions in the solar wind. In the presence of parallel propagating Alfvén waves, turbulence-induced particle motion is clearly observed in th…
Based on Magnetospheric Multiscale (MMS) observations from the Earth's bow shock, we have identified two plasma heating processes that operate at quasi-perpendicular shocks. Ions are subject to stochastic heating in a process controlled by the heating function $χ_j = m_j q_j^{-1} B^{-2}\mathrm{div}(\mathbf{E}_\perp)$ for particles with mass $m_j$ and charge $q_j$ in the electric and magnetic fields $\mathbf{E}$ and $\mathbf{B}$. Test particle simulations are employed to identify the parameter ranges for bulk heating and stochastic acceleration of particles in the tail of the distribution funct…
We present a statistical analysis of 132 dayside (LT 0700-1700) bow shock crossings of the AMPTE/IRM spacecraft. We perform a superposed epoch analysis of plasma and magnetic field parameters as well as of low frequency magnetic power spectra some minutes upstream and downstream of the bow shock by dividing the events into categories depending on the angle between bow shock normal and interplanetary magnetic field and on the plasma-beta, i.e., the ratio of plasma to magnetic pressure. Downstream of the quasi-perpendicular low-beta (beta < 0.5) bow shock we find a dominance of the left-hand pol…
Seventy crossings of the Earths bow shock by the THEMIS satellites have been used to study thermal electron heating in collisionless, quasi-perpendicular shocks. It was found that the temperature increase of thermal electrons differed from the magnetic field increase by factors as great as three, that the parallel electron temperature increase was not produced by parallel electric fields, and that the parallel and perpendicular electron temperature increases were the same on the average. It was also found that the perpendicular and parallel electron heating occurred simultaneously so that the …
Seventy measurements of electron heating at the Earth's quasi-perpendicular bow shock are analyzed in terms of Maxwellian-temperatures obtained from fits to the core electrons that separate thermal heating from supra-thermal acceleration. The perpendicular temperatures are both greater and lesser than expected for adiabatic compression. The average parallel and perpendicular heating is the same. These results are explained because, over the electron gyroradius, $δB/B\sim 1$ and $eδϕ/T_e\sim 1$, so electron trajectories are more random and chaotic than adiabatic. Because density fluctuations ar…
It is shown that in low-beta, weakly collisional plasmas, such as the solar corona, some instances of the solar wind, the aurora, inner regions of accretion discs, their coronae, and some laboratory plasmas, Alfvénic fluctuations produce no ion heating within the gyrokinetic approximation, i.e., as long as their amplitudes (at the Larmor scale) are small and their frequencies stay below the ion Larmor frequency (even as their spatial scales can be above or below the ion Larmor scale). Thus, all low-frequency ion heating in such plasmas is due to compressive fluctuations ("slow modes"). Because…
Perpendicular ion heating in turbulence and reconnection: magnetic moment breaking by coherent fluctuations
University of California, Berkeley（加州大学伯克利分校）；Lunar and Planetary Laboratory, University of Arizona（亚利桑那大学）；Space Science Center and Department of Physics, University of New Hampshire（新罕布什尔大学）；Department of Physics, University of California, Berkeley（加州大学伯克利分校）
Recent theoretical studies argue that the rate of stochastic ion heating in low-frequency Alfvén-wave turbulence is given by $Q_\perp = c_1 [(δu)^3 /ρ] \exp(-c_2/ε)$, where $δu$ is the rms turbulent velocity at the scale of the ion gyroradius $ρ$, $ε= δu/v_{\perp \rm i}$, $v_{\perp \rm i}$ is the perpendicular ion thermal speed, and $c_1$ and $c_2$ are dimensionless constants. We test this theoretical result by numerically simulating test particles interacting with strong reduced magnetohydrodynamic (RMHD) turbulence. The heating rates in our simulations are well fit by this formula. The best-…
Enhancement of minor ions such as $^3$He and heavy ions in flare-associated solar energetic particle (SEP) events remains one of the major puzzles in heliophysics. In this work, we use 3D hybrid simulations (kinetic protons and fluid electrons) to investigate particle energization in a turbulent low-beta environment similar to solar flares. It is shown that in this regime the injected large-amplitude Alfvén waves develop into compressible and anisotropic turbulence, which efficiently heats thermal ions of different species. We find that temperature increase of heavy ions is inversely proportio…
The solar wind undergoes significant heating as it propagates away from the Sun; the exact mechanisms responsible for this heating are not yet fully understood. We present for the first time a statistical test for one of the proposed mechanisms, stochastic ion heating. We use the amplitude of magnetic field fluctuations near the proton gyroscale as a proxy for the ratio of gyroscale velocity fluctuations to perpendicular (with respect to the magnetic field) proton thermal speed, defined as $ε_p$. Enhanced proton temperatures are observed when $ε_p$ is larger than a critical value ($\sim 0.019 …
Spacecraft measurements show that protons undergo substantial perpendicular heating during their transit from the Sun to the outer heliosphere. In this paper, we use {\em Helios~2} measurements to investigate whether stochastic heating by low-frequency turbulence is capable of explaining this perpendicular heating. We analyze {\em Helios~2} magnetic-field measurements in low-$β$ fast-solar-wind streams between heliocentric distances $r=0.29$ AU and $r=0.64$ AU to determine the rms amplitude of the fluctuating magnetic field, $δB_{\rm p}$, near the proton gyroradius scale $ρ_{\rm p}$. We then e…
How ions are energized and heated is a fundamental problem in the study of energy dissipation in magnetized plasmas. In particular, the heating of heavy ions (including ${}^{4}\mathrm{He}^{2+}$, ${}^{3}\mathrm{He}^{2+}$ and others) has been a constant concern for understanding the microphysics of impulsive solar flares. In this article, via two-dimensional hybrid-kinetic Particle-in-Cell simulations, we study the heating of Helium ions (${}^{4}\mathrm{He}^{2+}$) by turbulence driven by cascading waves launched at large scales from the left-handed polarized Helium ion cyclotron wave branch of a…
We consider the radial evolution of perpendicular ion heating due to the violation of magnetic moment conservation caused by Alfven and kinetic Alfven wave turbulence. This process, referred to as stochastic heating, can be quantified by the ratio between the average velocity fluctuations at the ion gyroradius and the perpendicular ion thermal speed $ε\equiv δv / v_{t\perp}$. Using 17 years of Helios observations, we constrain how much energy could be dissipated by this mechanism between 0.29 and 0.98 au. We find that stochastic heating likely operates throughout the entire inner heliosphere, …
A minimal model for magnetic reconnection and, generally, low-frequency dynamics in low-beta plasmas is proposed. The model combines analytical and computational simplicity with physical realizability: it is a rigorous limit of gyrokinetics for plasma beta of order the electron-ion mass ratio. The model contains collisions and can be used both in the collisional and collisionless reconnection regimes. It includes gyrokinetic ions (not assumed cold) and allows for the topological rearrangement of the magnetic field lines by either resistivity or electron inertia, whichever predominates. The two…
Low-frequency Alfven-wave turbulence causes ion trajectories to become chaotic, or "stochastic," when the turbulence amplitude is sufficiently large. Stochastic orbits enable ions to absorb energy from the turbulence, increasing the perpendicular ion temperature even when the fluctuation frequencies are too small for a cyclotron resonance to occur. In this paper, an analytic expression for the stochastic heating rate is used in conjunction with an observationally constrained turbulence model to obtain an analytic formula for the perpendicular ion temperature as a function of heliocentric dista…
We study the effects of plasma \b{eta} (ratio of plasma pressure to magnetic pressure) on the evolution of kinetic plasma turbulence using fully kinetic particle-in-cell simulations of decaying turbulence. We find that the plasma \b{eta} systematically affects spectra, measures of intermittency, decay rates of turbulence fluctuations, and partitioning over different channels of energy exchange More specifically, an increase in plasma \b{eta} leads to greater total heating, with proton heating preferentially more than electrons. Implications for achieving magnetosheath like temperature ratios a…
Remote sensing observations of coronal holes show that heavy ions are hotter than protons and their temperature is anisotropic. In-situ observations of fast solar wind streams provide direct evidence for turbulent Alfvén wave spectrum, left-hand polarized ion-cyclotron waves, and He$^{++}$ -- proton drift in the solar wind plasma, which can produce temperature anisotropies by resonant absorption and perpendicular heating of the ions. Furthermore, the solar wind is expected to be inhomogeneous on decreasing scales approaching the Sun. We study the heating of solar wind ions in inhomogeneous pla…
The fast solar wind emerging from coronal holes is likely heated and accelerated by the dissipation of magnetohydrodynamic turbulence, but the specific kinetic mechanism resulting in the perpendicular ion heating required by observations is not understood. A promising mechanism has been proposed by Chandran et al. (2010), which in this paper we call "magnetic moment breaking" (MMB). As currently formulated, MMB dissipation operates only on the ion perpendicular motion, and does not influence their parallel temperature. Thus, the MMB mechanism acting by itself produces coronal hole proton distr…
We investigate mechanisms of wave-particle heating of ionospheric O$^{+}$ ions resulting from broadband extremely low frequency (BBELF) waves using numerical test particle simulations that take into account ion-neutral collisions, in order to explain observations from the Enhanced Polar Outflow Probe (e-POP) satellite at low altitudes ($\sim$400 km)[Shen et al., 2018]. We argue that in order to reproduce ion temperatures observed at e-POP altitudes, the most effective ion heating mechanism is through cyclotron acceleration by short-scale electrostatic ion cyclotron (EIC) waves with perpendicul…
The parametric decay of finite-size Alfvén waves in nonperiodic low-beta plasmas is investigated using one-dimensional hybrid simulations. Compared with the usual small periodic system, a wave packet in a large system under the absorption boundary condition shows different decay dynamics, including reduced energy transfer and localized density cavitation and ion heating. The resulting Alfvén wave dynamics are influenced by several factors of the instability including the growth rate, central wave frequency, and unstable bandwidth. A final steady state of the wave packet may be achieved when th…
Low Mach number, high beta fast mode shocks can occur in the magnetic reconnection outflows of solar flares. These shocks, which occur above flare loop tops, may provide the electron energization responsible for some of the observed hard X-rays and contemporaneous radio emission. Here we present new 2D particle-in-cell simulations of low Mach number/high beta quasi-perpendicular shocks. The simulations show that electrons above a certain energy threshold experience shock-drift-acceleration. The transition energy between the thermal and non-thermal spectrum and the spectral index from the simul…
We revisit the theory of stochastic heating of ions and investigate its phase-space signatures in kinetic turbulence of relevance to low-$β$ portions of the solar wind. We retain a full scale-dependent approach in our treatment, and consider the case in which electric-field fluctuations can be described by a generalized Ohm's law that includes Hall and thermo-electric effects. These two electric-field terms provide the dominant contributions to stochastic ion heating when the ion-Larmor scale is much smaller than the ion skin depth, $ρ_{\mathrm{i}}\ll d_{\mathrm{i}}$, which is the case at $β{\…
Large parallel ($\leq$ 100 mV/m) and perpendicular ($\leq$ 600 mV/m) electric fields were measured in the Earth's bow shock by the vector electric field experiment on the Polar satellite. These are the first reported direct measurements of parallel electric fields in a collisionless shock. These fields exist on spatial scales comparable to or less than the electron skin depth (a few kilometers) and correspond to magnetic field-aligned potentials of tens of volts and perpendicular potentials up to a kilovolt. The perpendicular fields are amongst the largest ever measured in space, with energy d…
The kinetic evolution of the Orszag-Tang vortex is studied using collisionless hybrid simulations. In the magnetohydrodynamic regime this vortex leads rapidly to broadband turbulence. Significant differences from MHD arise at small scales, where the fluid scale energy dissipates into heat almost exclusively through the magnetic field because the protons are decoupled from the magnetic field. Although cyclotron resonance is absent, the protons heat preferentially in the plane perpendicular to the mean field, as in the corona and solar wind. Effective transport coefficients are calculated.
We report analytical and numerical investigations of sub-ion-scale turbulence in low-beta plasmas, focusing on the spectral properties of the fluctuations and electron heating. In the isothermal limit, the numerical results strongly support a description of the turbulence as a critically-balanced Kolmogorov-like cascade of kinetic Alfvén wave fluctuations, as amended by Boldyrev & Perez (Astrophys. J. Lett. 758, L44 (2012)) to include intermittent effects. When the constraint of isothermality is removed (i.e., with the inclusion of electron kinetic physics), the energy spectrum is found to ste…
Evolution of the parametric decay instability (PDI) of a circularly polarized Aflvén wave in a turbulent low-beta plasma background is investigated using 3D hybrid simulations. It is shown that the turbulence reduces the growth rate of PDI as compared to the linear theory predictions, but PDI can still exist. Interestingly, the damping rate of ion acoustic mode (as the product of PDI) is also reduced as compared to the linear Vlasov predictions. Nonetheless, significant heating of ions in the direction parallel to the background magnetic field is observed due to resonant Landau damping of the …
Using the field-particle correlation technique, we examine the particle energization in a 1D-2V continuum Vlasov--Maxwell simulation of a perpendicular magnetized collisionless shock. The combination of the field-particle correlation technique with the high fidelity representation of the particle distribution function provided by a direct discretization of the Vlasov equation allows us to ascertain the details of the exchange of energy between the electromagnetic fields and the particles in phase space. We identify the velocity-space signatures of shock-drift acceleration of the ions and adiab…
It is shown that the dispersion relation for whistler waves is identical for a high or low beta plasma. Furthermore in the high-beta solar wind plasma whistler waves meet the Landau resonance with electrons for velocities less than the thermal speed, and consequently the electric force is small compared to the mirror force. As whistlers propagate through the inhomogeneous solar wind, the perpendicular wave number increases through refraction, increasing the Landau damping rate. However, the whistlers can survive because the background kinetic Alfven wave turbulence creates a plateau by quasili…
We simulate decaying turbulence in a homogeneous pair plasma using three dimensional electromagnetic particle-in-cell (PIC) method. A uniform background magnetic field permeates the plasma such that the magnetic pressure is three times larger than the thermal pressure and the turbulence is generated by counter-propagating shear Alfvén waves. The energy predominately cascades transverse to the background magnetic field, rendering the turbulence anisotropic at smaller scales. We simultaneously move several ion species of varying charge to mass ratios in our simulation and show that the particles…
The analysis of the wave content inside a perpendicular bow shock indicates that heating of ions is related to the Lower-Hybrid-Drift (LHD) instability, and heating of electrons to the Electron-Cyclotron-Drift (ECD) instability. Both processes represent stochastic acceleration caused by the electric field gradients on the electron gyroradius scales, produced by the two instabilities. Stochastic heating is a single particle mechanism where large gradients break adiabatic invariants and expose particles to direct acceleration by the DC- and wave-fields. The acceleration is controlled by function…
Plasma ions heating (especially minor heavy ions preferential heating) in fast solar wind and solar corona is an open question in space physics. However, Alfvén waves have been always considered as a candidate of energy source for corona heating. In this paper, by using a two-dimensional (2-D) hybrid simulation model in a low beta electron-proton-alpha plasma system, we have investigated the relationships between plasma ions heating and power spectra evolution of density and magnetic field fluctuations excited from the parametric instabilities of initial pump Alfvén waves with an incoherent sp…
We develop a 1D solar-wind model that includes separate energy equations for the electrons and protons, proton temperature anisotropy, collisional and collisionless heat flux, and an analytical treatment of low-frequency, reflection-driven, Alfven-wave turbulence. To partition the turbulent heating between electron heating, parallel proton heating, and perpendicular proton heating, we employ results from the theories of linear wave damping and nonlinear stochastic heating. We account for mirror and oblique firehose instabilities by increasing the proton pitch-angle scattering rate when the pro…
We present measurements from the ESA/NASA Cluster mission that show in situ acceleration of ions to energies of 1 MeV outside the bow shock. The observed heating can be associated with the presence of electromagnetic structures with strong spatial gradients of the electric field that lead to ion gyro-phase breaking and to the onset of chaos in ion trajectories. It results in rapid, stochastic acceleration of ions in the direction perpendicular to the ambient magnetic field. The electric potential of the structures can be compared to a field of moguls on a ski slope, capable of accelerating and…
Collisionless shocks play an important role in space and astrophysical plasmas by irreversibly converting the energy of the incoming supersonic plasma flows into other forms, including plasma heat, particle acceleration, and electromagnetic field energy. Here we present the application of the field-particle correlation technique to an idealized perpendicular magnetized collisionless shock to understand the transfer of energy from the incoming flow into ion and electron energy through the structure of the shock. The connection between a Lagrangian perspective following particle trajectories, an…
Electron bulk heating during magnetic reconnection with symmetric inflow conditions is examined using kinetic particle-in-cell (PIC) simulations. The degree of electron heating is well correlated with the inflowing Alfvén speed $c_{Ar}$ based on the reconnecting magnetic field through the relation $ΔT_e = 0.033 \,m_i\,c_{Ar}^2$, where $ΔT_{e}$ is the increase in electron temperature. For the range of simulations performed, the heating shows almost no correlation with inflow total temperature $T_{tot} = T_i + T_e$ or plasma $β$. An out-of-plane (guide) magnetic field of similar magnitude to the…
Using one-dimensional hybrid expanding box model we investigate properties of the solar wind in the outer heliosphere. We assume a proton-electron plasma with a strictly transverse ambient magnetic field and, beside the expansion, we take into account influence of a continuous injection of cold pick-up protons through the charge-exchange process between the solar wind protons and hydrogen of interstellar origin. The injected cold pick-up protons form a ring distribution function that rapidly becomes unstable and generate Alfvén cyclotron waves. The Alfvén cyclotron waves scatter pick-up proton…
Heavy (O+) ion energization and field-aligned motion in and near the ionosphere are still not well understood. Based on observations from the CASSIOPE Enhanced Polar Outflow Probe (e-POP) at altitudes between 325 km and 730 km over one year, we present a statistical study (24 events) of ion heating and its relation to field-aligned ion bulk flow velocity, low-frequency waves and field-aligned currents (FACs). The ion temperature and field-aligned bulk flow velocity are derived from 2-D ion velocity distribution functions measured by the suprathermal electron imager (SEI) instrument. Consistent…
Stochastic heating refers to an increase in the average magnetic moment of charged particles interacting with electromagnetic fluctuations whose frequencies are smaller than the particles' cyclotron frequencies. This type of heating arises when the amplitude of the gyroscale fluctuations exceeds a certain threshold, causing particle orbits in the plane perpendicular to the magnetic field to become stochastic rather than nearly periodic. We consider the stochastic heating of protons by Alfvén-wave (AW) and kinetic-Alfvén-wave (KAW) turbulence, which may make an important contribution to the hea…
