Whistler waves are thought to play an essential role in the dynamics of collisionless shocks. We use the magnetospheric multiscale (MMS) spacecraft to study whistler waves around the lower hybrid frequency, upstream of 11 quasi-perpendicular super-critical shocks. We apply the 4-spacecraft timing method to unambiguously determine the wave vector $\mathbf{k}$ of whistler waves. We find that the waves are oblique to the background magnetic field with a wave-normal angle between $20^{\circ}$ and $42^{\circ}$, a wavelength around 100 km which is close to the ion inertial length. We also find that $\mathbf{k}$ is predominantly in the same plane as the magnetic field and the normal to the shock. By combining this precise knowledge of $\mathbf{k}$ with high-resolution measurements of the 3D ion velocity distribution we show that a reflected ion beam is in resonance with the waves, opening up the possibility for wave-particle interaction between the reflected ions and the observed whistlers. The linear stability analysis of a system mimicking the observed distribution, suggests that such a system can produce the observed waves.
The structure of whistler precursor in a quasi-perpendicular shock is studied within two-fluid approach in one-dimensional case. The complete set of equations is reduced to the KdV equation, if no dissipation is included. With a phenomenological resistive dissipation the structure is described with the KdV-Burgers equation. The shock profile is intrinsically time dependent. For sufficiently strong dissipation, temporal evolution of a steepening profile results in generation of a stationary decaying whistler ahead of the shock front. With the decrease of the dissipation parameter whistler wavet…
The chaotic interaction between electrons and whistler mode waves has been shown to provide a mechanism for enhanced diffusion in phase space. Pitch angle diffusion is relevant for the scattering of electrons into the loss cones, thus providing a source for auroral precipitating electrons. A single whistler mode wave propagating parallel to the background magnetic field has resonance with the electrons but the process is not stochastic. The presence of a second, oppositely directed whistler wave has been shown previously to introduce stochasticity into the system, thus enhancing phase space di…
We studied the properties and occurrence of narrow band whistler waves and their interaction with strahl electrons observed between 0.17 and 0.26 au during the first encounter of Parker Solar Probe. We observe that occurrence of whistler waves is low, nearly 1.5% and less than 0.5% in the analyzed peak and average BPF data respectively. Whistlers occur highly intermittently and 80% of the whistlers appear continuously for less than 3 s. Occurrence rate of whistler waves was found to be anti-correlated with the solar wind bulk velocity. The study of the duration of the whistler intervals reveal…
A linear theory of whistler wave is developed wihtin the paradigm of a two dimensional incompressible electron magnetohydrodynamics model. Exact analytic wave solutions are obtained for a small amplitude whistler wave that exhibit magnetic field topological structures consistent with the observations and our simulations in linear regime. In agreement with experiment, we find that the parallel group velocity of the wave is large compared to its perpendicular counterpart. Numerical simulations of collisional interactions demonstrate that the wave magnetic field either coalesces or repels dependi…
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 consider the weak turbulence of whistler waves in the in low-β inner magnetosphere of the Earth. Whistler waves with frequencies, originating in the ionosphere, propagate radially outward and can trigger nonlinear induced scattering by thermal electrons provided the wave energy density is large enough. Nonlinear scattering can substantially change the direction of the wave vector of whistler waves and hence the direction of energy flux with only a small change in the frequency. A portion of whistler waves return to the ionosphere with a smaller perpendicular wave vector resulting in diminis…
We present waveform observations of electromagnetic lower hybrid and whistler waves with f_ci << f < f_ce downstream of four supercritical interplanetary (IP) shocks using the Wind search coil magnetometer. The whistler waves were observed to have a weak positive correlation between \partialB and normalized heat flux magnitude and an inverse correlation with T_eh/T_ec. All were observed simultaneous with electron distributions satisfying the whistler heat flux instability threshold and most with T_{perp,h}/T_{para,h} > 1.01. Thus, the whistler mode waves appear to be driven by a heat flux inst…
The scattering of electrons by heat-flux-driven whistler waves is explored with a particle-in-cell (PIC) simulation relevant to the transport of energetic electrons in flares. The simulation is initiated with a large heat flux that is produced using a kappa distribution of electrons with positive velocity and a cold return current beam. This system represents energetic electrons escaping from a reconnection-driven energy release site. This heat flux system drives large amplitude oblique whistler waves propagating both along and against the heat flux, as well as electron acoustic waves. While t…
The role of solar wind expansion in generating whistler waves is investigated using the EB-iPic3D code, which models solar wind expansion self-consistently within a fully kinetic semi-implicit approach. The simulation is initialized with an electron velocity distribution function modeled after Parker Solar Probe observations during its first perihelion at 0.166 au, consisting of a dense core and an anti-sunward strahl. This distribution function is initially stable with respect to kinetic instabilities. Expansion drives the solar wind into successive regimes where whistler heat flux instabilit…
The 'Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun' (ARTEMIS) mission provides a unique opportunity to study the structure of interplanetary shocks and the associated generation of plasma waves with frequencies between ~50-8000 Hz due to its long duration electric and magnetic field burst waveform captures. We compare wave properties and occurrence rates at 11 quasi-perpendicular interplanetary shocks with burst data within 10 minutes (~3200 proton gyroradii upstream, ~1900 downstream) of the shock ramp. A perturbed shock is defined as posses…
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…
The SWEAP instrument suite on Parker Solar Probe (PSP) has detected numerous proton beams associated with coherent, circularly polarized, ion-scale waves observed by PSP's FIELDS instrument suite. Measurements during PSP Encounters 4-8 revealed pronounced complex shapes in the proton velocity distribution functions (VDFs), in which the tip of the beam undergoes strong perpendicular diffusion, resulting in VDF level contours that resemble a `hammerhead.' We refer to these proton beams, with their attendant `hammerhead' features, as the ion strahl. We present an example of these observations occ…
We present Wind spacecraft observations of ion distributions showing field-aligned beams (FABs) and large-amplitude magnetic fluctuations composed of a series of shocklets and short large-amplitude magnetic structures (SLAMS). We show that the SLAMS are acting like a local quasi-perpendicular shock reflecting ions to produce the FABs. Previous FAB observations reported the source as the quasi-perpendicular bow shock. The SLAMS exhibit a foot-like magnetic enhancement with a leading magnetosonic whistler train, consistent with previous observations. The FABs are found to have T_b ~ 80-850 eV, V…
Microinstabilities and waves excited at moderate-Mach-number perpendicular shocks in the near-Sun solar wind are investigated by full particle-in-cell (PIC) simulations. By analyzing the dispersion relation of fluctuating field components directly issued from the shock simulation, we obtain key findings concerning wave excitations at the shock front: (1) at the leading edge of the foot, two types of electrostatic (ES) waves are observed. The relative drift of the reflected ions versus the electrons triggers an electron cyclotron drift instability (ECDI) which excites the first ES wave. Because…
The anisotropy of turbulence in the fast solar wind, between the ion and electron gyroscales, is directly observed using a multispacecraft analysis technique. Second order structure functions are calculated at different angles to the local magnetic field, for magnetic fluctuations both perpendicular and parallel to the mean field. In both components, the structure function value at large angles to the field S_perp is greater than at small angles S_par: in the perpendicular component S_perp/S_par = 5 +- 1 and in the parallel component S_perp/S_par > 3, implying spatially anisotropic fluctuation…
A particle-in-cell code is used to examine contributions of the pickup ions (PIs) and the solar wind ions (SWs) to the cross shock electric field at the supercritical, perpendicular shocks. The code treats the pickup ions self-consistently as a third component. Herein, two different runs with relative pickup ion density of 25% and 55% are presented in this paper. Present preliminary results show that: (1) in the low percentage (25%) pickup ion case, the shock front is nonstationary. During the evolution of this perpendicular shock, a nonstationary foot resulting from the reflected solar wind i…
A two-dimensional particle-in-cell simulation is performed to investigate weakly magnetized perpendicular shocks with a magnetization parameter of 6 x 10^-5, which is equivalent to a high Alfvén Mach number M_A of ~130. It is shown that current filaments form in the foot region of the shock due to the ion-beam--Weibel instability (or the ion filamentation instability) and that they generate a strong magnetic field there. In the downstream region, these current filaments also generate a tangled magnetic field that is typically 15 times stronger than the upstream magnetic field. The thermal ener…
European Space Agency (ESA)（欧洲航天局）；European Space Astronomy Centre (ESAC)（欧洲空间天文中心）；Swedish Institute of Space Physics（瑞典空间物理研究所）；Uppsala University（乌普萨拉大学）
We present STEREO observations within 1500 proton gyroradii of 12 interplanetary shocks, with long-duration burst mode electric field acquisition by S/WAVES enabling observation of the evolution of waves throughout the entire ramp of interplanetary shocks. The shocks are low Mach number ($M_{f} \sim $1--5), quasi-perpendicular ($θ_{Bn} \geq 45^{\circ}$), with beta ($β$) $\sim $0.2--1.8. High variability in frequency, amplitude, and wave mode is observed upstream, downstream, and in shock ramps. Observations in every region include ion acoustic-like waves, electron cyclotron drift instability d…
Collisionless shocks play an important role in space and astrophysical plasmas by irreversibly converting the energy of the incoming supersonic plasma flows into other forms, including plasma heat, particle acceleration, and electromagnetic field energy. Here we present the application of the field-particle correlation technique to an idealized perpendicular magnetized collisionless shock to understand the transfer of energy from the incoming flow into ion and electron energy through the structure of the shock. The connection between a Lagrangian perspective following particle trajectories, an…
Shock parameters at Earth's bow shock in rare instances can approach the Mach numbers predicted at supernova remnants. We present our analysis of a high Alfvén Mach number ($M_A= 27$) shock utilizing multipoint measurements from the Magnetospheric Multiscale (MMS) spacecraft during a crossing of Earth's quasi-perpendicular bow shock. We find that the shock dynamics are mostly driven by reflected ions, perturbations that they generate, and nonlinear amplification of the perturbations. Our analyses show that reflected ions create modest magnetic enhancements upstream of the shock which evolve in…
In this paper, by performing a two-dimensional particle-in-cell simulation, we investigate magnetic reconnection in the downstream of a quasi-perpendicular shock. The shock is nonstationary, and experiences a cyclic reformation. At the beginning of reformation process, the shock front is relatively flat, and part of upstream ions are reflected by the shock front. The reflected ions move upward in the action of Lorentz force, which leads to the upward bending of magnetic field lines at the foot of the shock front, and then a current sheet is formed due to the squeezing of the bending magnetic f…
Supercritical collisionless perpendicular shocks have an average macrostructure determined primarily by the dynamics of ions specularly reflected at the magnetic ramp. Within the overall macrostructure, instabilities, both linear and nonlinear, generate fluctuations and microstructure. To identify the sources of such microstructure, high-resolution two- and three-dimensional simulations have been carried out using the hybrid method, wherein the ions are treated as particles and the electron response is modelled as a massless fluid. We confirm the results of earlier 2-D simulations showing both…
The magnetization $|Ω_{\mathrm e}|/ω_{\mathrm{e}}$ is an important parameter in plasma astrophysics, where $Ω_{\mathrm e}$ and $ω_{\mathrm{e}}$ are the electron gyro-frequency and electron plasma frequency, respectively. It only depends on the mass ratio $m_{\mathrm i}/m_{\mathrm e}$ and the light-to-Alfvén speed ratio $c/v_{\mathrm{Ai}}$, where $m_{\mathrm i}$ ($m_{\mathrm e}$) is the ion (electron) mass, $c$ is the speed of light, and $v_{\mathrm{Ai}}$ is the ion Alfvén speed. Nonlinear numerical plasma models such as particle-in-cell simulations must often assume unrealistic values for $m_{…
