Quasi-parallel Shock Research Articles

Intermittent turbulence in the heliosheath and the magnetosheath plasmas based on Voyager and THEMIS data

Abstract. Turbulence is complex behavior that is ubiquitous in space, including the environments of the heliosphere and the magnetosphere. Our studies on solar wind turbulence including the heliosheath, and even at the heliospheric boundaries, also beyond the ecliptic plane, have shown that turbulence is intermittent in the entire heliosphere. As is known, turbulence in space plasmas often exhibits substantial deviations from normal Gaussian distributions. Therefore, we analyze the fluctuations of plasma and magnetic field parameters also in the magnetosheath behind the Earth's bow shock. Based on THEMIS observations, we have already suggested that turbulence behind the quasi-perpendicular shock is more intermittent with larger kurtosis than that behind the quasi-parallel shocks. Following this study, we would like to present a detailed analysis of intermittent anisotropic turbulence in the magnetosheath depending on various characteristics of plasma behind the bow shock and now also near the magnetopause. In particular, for very high Alfvénic Mach numbers and high plasma beta we have clear non-Gaussian statistics in the directions perpendicular to the magnetic field. On the other hand, for directions parallel to this field the kurtosis is small and the plasma is close to equilibrium. However, the level of intermittency for the outgoing fluctuations seems to be similar to that for the ingoing fluctuations, which is consistent with approximate equipartition of energy between the oppositely propagating Alfvén waves. We hope that the difference in characteristic behavior of these fluctuations in various regions of space plasmas can help to detect some complex structures in space missions in the near future.

The Strongest Acceleration of >40 keV Electrons by ICME-driven Shocks at 1 au

Abstract We present two case studies of the in-situ electron acceleration during the 2000 February 11 shock and the 2004 July 22 shock, with the strongest electron flux enhancement at 40 keV across the shock, among all the quasi-perpendicular and quasi-parallel ICME-driven shocks observed by the WIND 3DP instrument from 1995 through 2014 at 1 au. We find that for this quasi-perpendicular (quasi-parallel) shock on 2000 February 11 (2004 July 22), the shocked electron differential fluxes at ∼0.4–50 keV in the downstream generally fit well to a double-power-law spectrum, J ∼ E −β , with an index of β ∼ 3.15 (4.0) at energies below a break at ∼3 keV (∼1 keV) and β ∼ 2.65 (2.6) at energies above. For both shock events, the downstream electron spectral indices appear to be similar for all pitch angles, which are significantly larger than the index prediction by diffusive shock acceleration. In addition, the downstream electron pitch-angle distributions show the anisotropic beams in the anti-sunward-traveling direction, while the ratio of the downstream over ambient fluxes appears to peak near 90° pitch angles, at all energies of ∼0.4–50 keV. These results suggest that in both shocks, shock drift acceleration likely plays an important role in accelerating electrons in situ at 1 au. Such ICME-driven shocks could contribute to the formation of solar wind halo electrons at energies ≲2 keV, as well as the production of solar wind superhalo electrons at energies ≳2 keV in interplanetary space.

The Acceleration of Thermal Ions at a Strong, Quasi-Parallel Interplanetary Shock: A Hybrid Simulation

Using a self-consistent hybrid simulation, with kinetic protons and fluid electrons, we investigate the acceleration of thermal protons and minor ions (alphas, 3He++, and C5+) by a quasi-parallel collisionless shock. The results are compared to spacecraft observations of a strong interplanetary shock seen by the Advanced Composition Explorer on DOY 94, 2001, which was associated with significant increases in the flux of > 50 keV/nuc ions. Our simulation uses similar plasma and shock parameters to those observed. The densities of minor ions for two of the species (alphas and C5+) were based on observations at thermal energies for this shock, and we used a nominal value for the density of 3He++, since no observations at thermal energies was available to us. Acceleration of the ions by the shock leads to a high-energy tail in the distribution in the post-shock plasma for all ion species. We find that by extrapolating the simulated tails to the higher energies measured by ACE/EPAM and ACE/ULEIS, the intensity matches well the observations for protons, alphas, and carbon. This suggests that thermal solar wind, accelerated directly at the shock, is a significant source of the observed high-energy protons and these minor ions.

An in situ Comparison of Electron Acceleration at Collisionless Shocks under Differing Upstream Magnetic Field Orientations

Abstract A leading explanation for the origin of Galactic cosmic rays is acceleration at high-Mach number shock waves in the collisionless plasma surrounding young supernova remnants. Evidence for this is provided by multi-wavelength non-thermal emission thought to be associated with ultrarelativistic electrons at these shocks. However, the dependence of the electron acceleration process on the orientation of the upstream magnetic field with respect to the local normal to the shock front (quasi-parallel/quasi-perpendicular) is debated. Cassini spacecraft observations at Saturn’s bow shock have revealed examples of electron acceleration under quasi-perpendicular conditions, and the first in situ evidence of electron acceleration at a quasi-parallel shock. Here we use Cassini data to make the first comparison between energy spectra of locally accelerated electrons under these differing upstream magnetic field regimes. We present data taken during a quasi-perpendicular shock crossing on 2008 March 8 and during a quasi-parallel shock crossing on 2007 February 3, highlighting that both were associated with electron acceleration to at least MeV energies. The magnetic signature of the quasi-perpendicular crossing has a relatively sharp upstream–downstream transition, and energetic electrons were detected close to the transition and immediately downstream. The magnetic transition at the quasi-parallel crossing is less clear, energetic electrons were encountered upstream and downstream, and the electron energy spectrum is harder above ∼100 keV. We discuss whether the acceleration is consistent with diffusive shock acceleration theory in each case, and suggest that the quasi-parallel spectral break is due to an energy-dependent interaction between the electrons and short, large-amplitude magnetic structures.

Temperature variations in the dayside magnetosheath and their dependence on ion‐scale magnetic structures: THEMIS statistics and measurements by MMS

AbstractThe magnetosheath contains an array of waves, instabilities, and nonlinear magnetic structures which modify global plasma properties by means of various wave‐particle interactions. The present work demonstrates that ion‐scale magnetic field structures (∼0.2–0.5 Hz) observed in the dayside magnetosheath are statistically correlated to ion temperature changes on orders 10–20% of the background value. In addition, our statistical analysis implies that larger temperature changes are in equipartition to larger amplitude magnetic structures. This effect was more pronounced behind the quasi‐parallel bow shock and during faster solar wind speeds. The study of two separate intervals suggests that this effect can result from both local and external drivers. This manuscript presents two separate case studies, one from using THEMIS (Time History of Events and Macroscale Interactions during Substorms) data and another from Magnetospheric Multiscale; these measurements are then supported by extensive THEMIS statistical observations. These results could partly explain the 10–20% dawn‐favored asymmetry of the magnetosheath ion temperature seed population and contribute to the dawn‐favored asymmetry of cold component ions in the cold dense plasma sheet.

Which Bow Shock Theory, Gasdynamic or Magnetohydrodynamic, Better Explains CME Stand-off Distance Ratios from LASCO-C2 Observations ?

Abstract It is generally believed that fast coronal mass ejections (CMEs) can generate their associated shocks, which are characterized by faint structures ahead of CMEs in white-light coronagraph images. In this study, we examine whether the observational stand-off distance ratio, defined as the CME stand-off distance divided by its radius, can be explained by bow shock theories. Of 535 SOHO/LASCO CMEs (from 1996 to 2015) with speeds greater than 1000 km s−1 and angular widths wider than 60°, we select 18 limb CMEs with the following conditions: (1) their Alfvénic Mach numbers are greater than one under Mann’s magnetic field and Saito’s density distributions; and (2) the shock structures ahead of the CMEs are well identified. We determine observational CME stand-off distance ratios by using brightness profiles from LASCO-C2 observations. We compare our estimates with theoretical stand-off distance ratios from gasdynamic (GD) and magnetohydrodynamic (MHD) theories. The main results are as follows. Under the GD theory, 39% (7/18) of the CMEs are explained in the acceptable ranges of adiabatic gamma (γ) and CME geometry. Under the MHD theory, all the events are well explained when we consider quasi-parallel MHD shocks with γ = 5/3. When we use polarized brightness (pB) measurements for coronal density distributions, we also find similar results: 8% (1/12) under GD theory and 100% (12/12) under MHD theory. Our results demonstrate that the bow shock relationships based on MHD theory are more suitable than those based on GD theory for analyzing CME-driven shock signatures.

THE INTERACTION OF TURBULENCE WITH PARALLEL AND PERPENDICULAR SHOCKS: THEORY AND OBSERVATIONS AT 1 au

ABSTRACT Shocks are thought to be responsible for the amplification of turbulence as well as for generating turbulence throughout the heliosphere. We study the interaction of turbulence with parallel and perpendicular shock waves using the six-coupled-equation turbulence transport model of Zank et al. We model a 1D stationary shock wave using a hyperbolic tangent function and the Rankine–Hugoniot conditions for both a reduced model with four coupled equations and the full model. Eight quasi-parallel and five quasi-perpendicular events in the WIND spacecraft data sets are identified, and we compute the fluctuating magnetic and kinetic energy, the energy in forward and backward propagating modes, the total turbulent energy, the normalized residual energy, and the normalized cross helicity upstream and downstream of the observed shocks. We compare the observed fitted values upstream and downstream of the shock with numerical solutions to our model equations. The comparison shows that our theoretical results are in reasonable agreement with observations for both quasi-parallel and perpendicular shocks. We find that (1) the total turbulent energy, the energy in forward and backward propagating modes, and the normalized residual energy increase across the shock, (2) the normalized cross helicity increases or decreases across the shock, and (3) the correlation length increases upstream and downstream of the shock, and slightly flattens or decreases across the shock.

Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.

We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.

Studying the Effect of Shock Obliquity on the γ-ray and Diffuse Radio Emission in Galaxy Clusters

Observations of diffuse radio emission in galaxy clusters indicate that cosmic-ray electrons are accelerated on ∼ Mpc scales. However, protons appear to be accelerated less efficiently since their associated hadronic γ-ray emission has not yet been detected. Inspired by recent particle-in-cell simulations, we study the cosmic-ray production and its signatures under the hypothesis that the efficiency of shock acceleration depends on the Mach number and on the shock obliquity. For this purpose, we combine ENZO cosmological magneto-hydrodynamical simulations with a Lagrangian tracer code to follow the properties of the cosmic rays. Our simulations suggest that the distribution of obliquities in galaxy clusters is random to first order. Quasi-perpendicular shocks are able to accelerate cosmic-ray electrons to the energies needed to produce observable radio emission. However, the γ-ray emission is lowered by a factor of a few, ∼3 , if cosmic-ray protons are only accelerated by quasi-parallel shocks, reducing (yet not entirely solving) the tension with the non-detection of hadronic γ-ray emission by the Fermi-satellite.

Testing cosmic ray acceleration with radio relics: a high-resolution study using MHD and tracers

Weak shocks in the intracluster medium may accelerate cosmic-ray protons and cosmic-ray electrons differently depending on the angle between the upstream magnetic field and the shock normal. In this work, we investigate how shock obliquity affects the production of cosmic rays in high-resolution simulations of galaxy clusters. For this purpose, we performed a magnetohydrodynamical simulation of a galaxy cluster using the mesh refinement code ENZO. We use Lagrangian tracers to follow the properties of the thermal gas, the cosmic rays and the magnetic fields over time. We tested a number of different acceleration scenarios by varying the obliquity-dependent acceleration efficiencies of protons and electrons, and by examining the resulting hadronic γ-ray and radio emission. We find that the radio emission does not change significantly if only quasi-perpendicular shocks are able to accelerate cosmic-ray electrons. Our analysis suggests that radio-emitting electrons found in relics have been typically shocked many times before z = 0. On the other hand, the hadronic γ-ray emission from clusters is found to decrease significantly if only quasi-parallel shocks are allowed to accelerate cosmic ray protons. This might reduce the tension with the low upper limits on γ-ray emission from clusters set by the Fermi satellite.

TRANSPORT OF SOLAR WIND H+ AND He++ IONS ACROSS EARTH’S BOW SHOCK

ABSTRACT We have investigated the dependence of mass, energy, and charge of solar wind (SW) transport across Earth’s bow shock. An examination of 111 crossings during quiet SW in both quasi-perpendicular and quasi-parallel shock regions shows that 64 crossings had various degrees of heating and thermalization of SW. We found 22 crossings where the SW speed was <400 km s−1. The shock potential of a typical supercritical quasi-perpendicular shock estimated from deceleration of the SW and cutoff energy of electron flat top distribution is ∼50 Volts. We find that the temperatures of H+ and He++ beams that penetrate the shock can sometimes be nearly the same in the upstream and downstream regions, indicating little or no heating had occurred crossing the bow shock. None of the models predict that the SW can cross the bow shock without heating. Our observations are important constraints for new models of collisionless shocks.

Isolated magnetic field structures in Mercury's magnetosheath as possible analogues for terrestrial magnetosheath plasmoids and jets

We have investigated MESSENGER magnetic field data from the Mercury magnetosheath and near solar wind, to identify isolated magnetic field structures (defined as clear, isolated changes in the field magnitude). Their properties are studied in order to determine if they may be considered as analogues to plasmoids and jets known to exist in Earth's magnetosheath. Both isolated decreases of the magnetic field absolute value (‘negative magnetic field structures’) and increases (‘positive structures’) are found in the magnetosheath, whereas only negative structures are found in the solar wind. The similar properties of the solar wind and magnetosheath negative magnetic field structures suggests that they are analogous to diamagnetic plasmoids found in Earth's magnetosheath and near solar wind. The latter have earlier been identified with solar wind magnetic holes. Positive magnetic field structures are only found in the magnetosheath, concentrated to a region relatively close to the magnetopause. Their proximity to the magnetopause, their scale sizes, and the association of a majority of the structures with bipolar magnetic field signatures identify them as flux transfer events (which generally are associated with a decrease of plasma density in the magnetosheath). The positive magnetic field structures are therefore not likely to be analogous to terrestrial paramagnetic plasmoids but possibly to a sub-population of magnetosheath jets. At Earth, a majority of magnetosheath jets are associated with the quasi-parallel bow shock. We discuss some consequences of the findings of the present investigation pertaining to the different nature of the quasi-parallel bow shock at Mercury and Earth.

ION DYNAMICS AT A RIPPLED QUASI-PARALLEL SHOCK: 2D HYBRID SIMULATIONS

ABSTRACT In this paper, two-dimensional hybrid simulations are performed to investigate ion dynamics at a rippled quasi-parallel shock. The results show that the ripples around the shock front are inherent structures of a quasi-parallel shock, and the re-formation of the shock is not synchronous along the surface of the shock front. By following the trajectories of the upstream ions, we find that these ions behave differently when they interact with the shock front at different positions along the shock surface. The upstream particles are transmitted more easily through the upper part of a ripple, and the corresponding bulk velocity downstream is larger, where a high-speed jet is formed. In the lower part of the ripple, the upstream particles tend to be reflected by the shock. Ions reflected by the shock may suffer multiple-stage acceleration when moving along the shock surface or trapped between the upstream waves and the shock front. Finally, these ions may escape further upstream or move downstream; therefore, superthermal ions can be found both upstream and downstream.

TURBULENCE-GENERATED PROTON-SCALE STRUCTURES IN THE TERRESTRIAL MAGNETOSHEATH

ABSTRACT Recent results of numerical magnetohydrodynamic simulations suggest that in collisionless space plasmas, turbulence can spontaneously generate thin current sheets. These coherent structures can partially explain the intermittency and the non-homogenous distribution of localized plasma heating in turbulence. In this Letter, Cluster multi-point observations are used to investigate the distribution of magnetic field discontinuities and the associated small-scale current sheets in the terrestrial magnetosheath downstream of a quasi-parallel bow shock. It is shown experimentally, for the first time, that the strongest turbulence-generated current sheets occupy the long tails of probability distribution functions associated with extremal values of magnetic field partial derivatives. During the analyzed one-hour time interval, about a hundred strong discontinuities, possibly proton-scale current sheets, were observed.

ION INJECTION AT QUASI-PARALLEL SHOCKS SEEN BY THE CLUSTER SPACECRAFT

ABSTRACT Collisionless shocks in space plasma are known to be capable of accelerating ions to very high energies through diffusive shock acceleration (DSA). This process requires an injection of suprathermal ions, but the mechanisms producing such a suprathermal ion seed population are still not fully understood. We study acceleration of solar wind ions resulting from reflection off short large-amplitude magnetic structures (SLAMSs) in the quasi-parallel bow shock of Earth using in situ data from the four Cluster spacecraft. Nearly specularly reflected solar wind ions are observed just upstream of a SLAMS. The reflected ions are undergoing shock drift acceleration (SDA) and obtain energies higher than the solar wind energy upstream of the SLAMS. Our test particle simulations show that solar wind ions with lower energy are more likely to be reflected off the SLAMS, while high-energy ions pass through the SLAMS, which is consistent with the observations. The process of SDA at SLAMSs can provide an effective way of accelerating solar wind ions to suprathermal energies. Therefore, this could be a mechanism of ion injection into DSA in astrophysical plasmas.

Statistical study of the ULF Pc4–Pc5 range fluctuations in the vicinity of Earth’s magnetopause and correlation with the Low Latitude Boundary Layer thickness

The main generation mechanisms for the Earth’s Low Latitude Boundary Layer (LLBL) are considered to be magnetic reconnection, viscous interactions such as Kelvin–Helmholtz instability and associated plasma mixing and diffusion. We have performed a statistical study of the Ultra Low Frequency (ULF) fluctuation power at the Pc4–Pc5 range using ≈6years of THEMIS measurements of the plasma velocity and magnetic field. The results reveal a clear dawn–dusk asymmetry showing that the fluctuation power is typically more enhanced in the vicinity of the magnetopause downstream of the quasi-parallel shock. The statistical study of the Vx-component of the plasma velocity indicates that the LLBL is also thicker on the dawn-sector. These results may suggest that the physical mechanisms that provide power in the Pc4–Pc5 range are more effective on the dawn-sector and provide a means for a more effective LLBL generation.

Self-consistent Monte Carlo simulations of proton acceleration in coronal shocks: Effect of anisotropic pitch-angle scattering of particles

Context. Solar energetic particles observed in association with coronal mass ejections (CMEs) are produced by the CME-driven shock waves. The acceleration of particles is considered to be due to diffusive shock acceleration (DSA). Aims. We aim at a better understanding of DSA in the case of quasi-parallel shocks, in which self-generated turbulence in the shock vicinity plays a key role. Methods. We have developed and applied a new Monte Carlo simulation code for acceleration of protons in parallel coronal shocks. The code performs a self-consistent calculation of resonant interactions of particles with Alfv\'en waves based on the quasi-linear theory. In contrast to the existing Monte Carlo codes of DSA, the new code features the full quasi-linear resonance condition of particle pitch-angle scattering. This allows us to take anisotropy of particle pitch-angle scattering into account, while the older codes implement an approximate resonance condition leading to isotropic scattering.We performed simulations with the new code and with an old code, applying the same initial and boundary conditions, and have compared the results provided by both codes with each other, and with the predictions of the steady-state theory. Results. We have found that anisotropic pitch-angle scattering leads to less efficient acceleration of particles than isotropic. However, extrapolations to particle injection rates higher than those we were able to use suggest the capability of DSA to produce relativistic particles. The particle and wave distributions in the foreshock as well as their time evolution, provided by our new simulation code, are significantly different from the previous results and from the steady-state theory. Specifically, the mean free path in the simulations with the new code is increasing with energy, in contrast to the theoretical result.

Statistical mapping of ULF Pc3 velocity fluctuations in the Earth’s dayside magnetosheath as a function of solar wind conditions

In this paper, we present the results of a statistical study of Pc3 velocity fluctuations in the Earth’s dayside magnetosheath. There exists a notable dawn–dusk asymmetry, such that velocity fluctuations generally exhibit enhanced spectral power in the magnetosheath downstream of the quasi-parallel shock. The fluctuations in the central magnetosheath and close to bow shock tend to dampen with increasing tail-ward distance while the opposite trend is observed close to the magnetopause. This strongly suggests that velocity shear driven processes such as the Kelvin–Helmholtz instability drive Pc3 flow variations close to the magnetopause as the velocity shear increases with increasing tail-ward distance. We also show strong evidence that Pc3 velocity fluctuations are significantly enhanced during intervals of faster solar wind speeds. We see negligible differences between data collected during northward and southward IMF orientations, but in general, a dawn-favoured asymmetry persists.

Superdiffusive transport in laboratory and astrophysical plasmas

In the last few years it has been demonstrated, both by data analysis and by numerical simulations, that the transport of energetic particles in the presence of magnetic turbulence can be superdiffusive rather than normal diffusive (Gaussian). The term ‘superdiffusive’ refers to the mean square displacement of particle positions growing superlinearly with time, as compared to the normal linear growth. The so-called anomalous transport, which in general comprises both subdiffusion and superdiffusion, has gained growing attention during the last two decades in many fields including laboratory plasma physics, and recently in astrophysics and space physics. Here we show a number of examples, both from laboratory and from astrophysical plasmas, where superdiffusive transport has been identified, with a focus on what could be the main influence of superdiffusion on fundamental processes like diffusive shock acceleration and heliospheric energetic particle propagation. For laboratory plasmas, superdiffusion appears to be due to the presence of electrostatic turbulence which creates long-range correlations and convoluted structures in perpendicular transport: this corresponds to a similar phenomenon in the propagation of solar energetic particles (SEPs) which leads to SEP dropouts. For the propagation of energetic particles accelerated at interplanetary shocks in the solar wind, parallel superdiffusion seems to be prevailing; this is based on a pitch-angle scattering process different from that envisaged by quasi-linear theory, and this emphasizes the importance of nonlinear interactions and trapping effects. In the case of supernova remnant shocks, parallel superdiffusion is possible at quasi-parallel shocks, as occurring in the interplanetary space, and perpendicular superdiffusion is possible at quasi-perpendicular shocks, as corresponding to Richardson diffusion: therefore, cosmic ray acceleration at supernova remnant shocks should be formulated in terms of superdiffusion. The possible relations among anomalous transport in laboratory, heliospheric, and astrophysical plasmas will be indicated.

Relativistic Shocks: Particle Acceleration and Magnetization

We review the physics of relativistic shocks, which are often invoked as the sources of non-thermal particles in pulsar wind nebulae (PWNe), gamma-ray bursts (GRBs), and active galactic nuclei (AGN) jets, and as possible sources of ultra-high energy cosmic-rays. We focus on particle acceleration and magnetic field generation, and describe the recent progress in the field driven by theory advances and by the rapid development of particle-in-cell (PIC) simulations. In weakly magnetized or quasi parallel-shocks (where the magnetic field is nearly aligned with the flow), particle acceleration is efficient. The accelerated particles stream ahead of the shock, where they generate strong magnetic waves which in turn scatter the particles back and forth across the shock, mediating their acceleration. In contrast, in strongly magnetized quasi-perpendicular shocks, the efficiencies of both particle acceleration and magnetic field generation are suppressed. Particle acceleration, when efficient, modifies the turbulence around the shock on a long time scale, and the accelerated particles have a characteristic energy spectral index of ~ 2.2 in the ultra-relativistic limit. We discuss how this novel understanding of particle acceleration and magnetic field generation in relativistic shocks can be applied to high-energy astrophysical phenomena, with an emphasis on PWNe and GRB afterglows.