On the electron-ion temperature ratio established by collisionless shocks

Shocks are ubiquitous in astrophysical environments and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration. It is believed that the CR pressure is important in the evolution of the interstellar medium of our galaxy and most of galactic CRs with energies up to eV are accelerated by supernova remnant shocks. In this contribution we have studied the CR acceleration at shocks through numerical simulation of 1D, quasi-parallel shocks for a wide range of shock Mach numbers and shock speeds. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies, and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number, and high Mach number shocks all evolve towards efficiencies , regardless of the injection rate and upstream CR pressure. We conclude that the injection rates in strong quasi-parallel shocks are sufficient to lead to significant nonlinear modifications to the shock structures, implying the importance of the CR acceleration at astrophysical shocks.

Shocks waves are a ubiquitous feature of many astrophysical plasma systems, and an important process for energy dissipation and transfer. The physics of these shock waves are frequently treated/modelled as a collisional, fluid magnetohydrodynamic (MHD) discontinuity, despite the fact that many shocks occur in the collisionless regime. In light of this, using fully kinetic, 3D simulations of non-relativistic, parallel propagating collisionless shocks comprised of electron-positron plasma, we detail the deviation of collisionless shocks form MHD predictions for varying magnetization/Alfvénic Mach numbers, with particular focus on systems with Alfénic Mach numbers much smaller than sonic Mach numbers. We show that the shock compression ratio decreases for sufficiently large upstream magnetic fields, in agreement with theoretical predictions from previous works. Additionally, we examine the role of magnetic field strength on the shock front width. This work reinforces a growing body of work that suggest that modelling many astrophysical systems with only a fluid plasma description omits potentially important physics.

Astrophysical shocks are often studied in the high Mach number limit but weakly compressive fast shocks can occur in magnetic reconnection outflows and are considered to be a site of particle energization in solar flares. Here we study the microphysics of such perpendicular, low Mach number collisionless shocks using two-dimensional particle-in-cell simulations with a reduced ion/electron mass ratio and employ a moving wall boundary method for initial generation of the shock. This moving wall method allows for more control of the shock speed, smaller simulation box sizes, and longer simulation times than the commonly used fixed wall, reflection method of shock formation. Our results, which are independent of the shock formation method, reveal the prevalence shock drift acceleration (SDA) of both electron and ions in a purely perpendicular shock with Alfvén Mach number MA=6.8 and ratio of thermal to magnetic pressure β=8. We determine the respective minimum energies required for electrons and ions to incur SDA. We derive a theoretical electron distribution via SDA that compares to the simulation results. We also show that a modified two-stream instability due to the incoming and reflecting ions in the shock transition region acts as the mechanism to generate collisionless plasma turbulence that sustains the shock.

Energy dissipation in collisionless shocks is a key mechanism in various astrophysical environments. Its nonlinear nature complicates analytical understanding and necessitates particle-in-cell (PIC) simulations. This study examines the impact of reducing the ion-to-electron mass ratio (m r ), to decrease computational cost, on energy partitioning in one spatial and three velocity-space dimension PIC simulations of strong, nonrelativistic, parallel electron–ion collisionless shocks using the SHARP code. We compare simulations with a reduced mass ratio (m r = 100) to those with a realistic mass ratio (m r = 1836) for shocks with high ( M A = 21.3 ) and low ( M A = 5.3 ) Alfvén Mach numbers. Our findings show that the mass ratio significantly affects particle acceleration and thermal energy dissipation. At high M A , a reduced mass ratio leads to more efficient electron acceleration and an unrealistically high ion flux at higher momentum. At low M A , it causes complete suppression of electron acceleration, whereas the realistic mass ratio enables efficient electron acceleration. The reduced mass ratio also results in excessive electron heating and lower heating in downstream ions at both Mach numbers, with slightly more magnetic field amplification at low M A . Consequently, the electron-to-ion temperature ratio is high at low M A due to reduced ion heating and remains high at high M A due to increased electron heating. In contrast, simulations with the realistic m r show that the ion-to-electron temperature ratio is independent of the upstream magnetic field, a result not observed in reduced m r simulations.

In this review we discuss some observational aspects and theoretical models of astrophysical collisionless shocks in partly ionized plasma with the presence of non-thermal components. A specific feature of fast strong collisionless shocks is their ability to accelerate energetic particles that can modify the shock upstream flow and form the shock precursors. We discuss the effects of energetic particle acceleration and associated magnetic field amplification and decay in the extended shock precursors on the line and continuum multi-wavelength emission spectra of the shocks. Both Balmer-type and radiative astrophysical shocks are discussed in connection to supernova remnants interacting with partially neutral clouds. Quantitative models described in the review predict a number of observable line-like emission features that can be used to reveal the physical state of the matter in the shock precursors and the character of nonthermal processes in the shocks. Implications of recent progress of gamma-ray observations of supernova remnants in molecular clouds are highlighted.

This paper discusses the sound generated when an inhomogeneity in density is convected in a low Mach number steady flow through a contraction in a duct of infinite extent, and also when the inhomogeneity exhausts through a nozzle into free space. The analyses of Candel (1972) and Marble (1973) for the case of duct flow were based on a frequency decomposition of the incident inhomogeneity and cannot adequately deal with sharp-fronted inhomogeneities and entropy spots. However, the practical difficulties of this earlier work can be avoided at low flow Mach numbers by conducting the analysis in terms of an approximate expression for the acoustic Green's function in the manner described by Howe (1975). This method also permits a considerable extension of the range of the earlier investigations to the determination of the sound generated when the inhomogeneity is swept out of a nozzle orifice into free space. It is shown that the acoustic pressure perturbations developed in a duct at a contraction are in general proportional to the fractional difference between the density of the inhomogeneity and that of the mean flow times a typical mean flow pressure level, and are due principally to the fluctuation in thrust accompanying the passage of the inhomogeneity through the region of variable pressure gradient. The pressure waves generated at a nozzle orifice and radiated into free space are O(M0) smaller, where M0 is a mean flow Mach number based on the speed of sound in the jet.

The electron heating and the electrostatic potential jump across collisionless shocks play an important, if not dominant, role in the electron momentum balance. We present here a survey of these two quantities over a large sample of fast mode collisionless shocks. Results for estimates of the electrostatic potential (as measured in the de Hoffmann‐Teller reference frame) based on an estimate of the jump in electron enthalpy and on Liouville's theorem correlate well with each other, although the latter are consistently higher, perhaps due to irreversible processes affecting the shock electron dynamics. The size of the potential does not appear to be strongly controlled by any of the various upstream parameters (shock geometry, Mach number, etc.) and represents approximately 12% of the incident ion ram kinetic energy, this figure showing some tendency to decrease with increasing Mach number. The electron contribution to the total (ion plus electron) heating across the shock varies systematically from 50% or more at subcritical Mach numbers to less than 10% at the highest Mach number shocks in the sample. The electron heating shows only modest, but systematic, departure from that which would result by preserving the ratio of the perpendicular temperature to the magnetic field strength.

Nonthermal radiation from supernova remnants (SNRs) provides observational evidence and constraints on the diffusive shock acceleration (DSA) hypothesis for the origins of Galactic cosmic rays (CRs). Recently it has been recognized that a variety of plasma wave-particle interactions operate at astrophysical shocks and the detailed outcomes of DSA are governed by their complex and nonlinear interrelationships. Here we calculate the energy spectra of CR protons and electrons accelerated at Type Ia SNRs, using time-dependent, DSA simulations with phenomenological models for magnetic field amplification due to CR streaming instabilities, Alf<TEX>$\acute{e}$</TEX>enic drift, and free escape boundary. We show that, if scattering centers drift with the Alf<TEX>$\acute{e}$</TEX>en speed in the amplified magnetic fields, the CR energy spectrum is steepened and the acceleration efficiency is significantly reduced at strong CR modified SNR shocks. Even with fast Afv<TEX>$\acute{e}$</TEX>nic drift, DSA can still be efficient enough to develop a substantial shock precursor due to CR pressure feedback and convert about 20-30% of the SN explosion energy into CRs. Since the high energy end of the CR proton spectrum is composed of the particles that are injected in the early stages, in order to predict nonthermal emissions, especially in X-ray and <TEX>${\gamma}-ray$</TEX> bands, it is important to follow the time dependent evolution of the shock dynamics, CR injection process, magnetic field amplification, and particle escape. Thus it is crucial to understand the details of these plasma interactions associated with collisionless shocks in successful modeling of nonlinear DSA.

Micro-vortex generators (μVGs) have the ability to alter the near-wall structure of compressible turbulent boundary layers to provide increased mixing of high speed fluid such that the boundary layer remains healthy even with some disturbance imparted to the flow. Due to their small size, μVGs are embedded in the boundary layer and may provide reduced drag when compared to traditional vortex generators. In particular, micro-ramps are of significant interest as they are cost-effective, physically robust, and do not require a power source. To examine their potential, a detailed computational study of micro-ramps in a supersonic boundary layer at M=1.4, 2.2 and 3.0 was undertaken. The moderate Reynolds number of 3,800 allowed the computations to use monotone integrated Large Eddy Simulations (MILES) which generally reproduced the experimentally obtained mean velocity profiles, although some differences were found with respect to grid resolution. The MILES results indicate that micro-ramps have greater impact at lower Mach number near the device where its influence decays faster than that for the higher Mach number cases. This may be due to the reduced aspect ratio of the turbulent structure at the lower Mach number such that their coherency is easily lost yielding the streamwise vorticity and the turbulent kinetic energy to decay quickly. The normal distance between the vortex core and the wall had similar growth indicating weak correlation with the Mach number; however, the spanwise distance between the two counter-rotating cores further increases with lower Mach number.

Asymptotic and numerical analysis of an inviscid bounded vortex flow at low Mach number

The paper suggests a modification of AUSMPW+ scheme designed to low Mach number. For Mach number vanishing, AUSMPW+ scheme has an excessive numerical dissipation to result in the incorrect scaling of pressure and density fluctuations. The modification rescales all velocity components in the numerical flux by the local Mach number. The improved method reduces the dissipation and recovers the correct scaling of pressure and density fluctuations, which is proved by low Mach number cases. In addition, the improved scheme performs the stronger independence than AUSMPW+ in terms of grid, reconstruction method, and Mach number at low speeds.

Shock waves propagating in collisionless heliospheric and astrophysical plasmas have been studied extensively over the decades. One prime motivation is to understand the nonthermal particle acceleration at shocks. Although the theory of diffusive shock acceleration (DSA) has long been the standard for cosmic-ray acceleration at shocks, plasma physical understanding of particle acceleration remains elusive. In this review, we discuss nonthermal electron acceleration mechanisms at quasi-perpendicular shocks, for which substantial progress has been made in recent years. The discussion presented in this review is restricted to the following three specific topics: The first is stochastic shock drift acceleration (SSDA), which is a relatively new mechanism for electron injection into DSA. The basic mechanism, related in-situ observations and kinetic simulations results, and how it is connected with DSA will be discussed. Second, we discuss shock surfing acceleration (SSA) at very high Mach number shocks relevant to young supernova remnants (SNRs). While the original proposal under the one-dimensional assumption is unrealistic, SSA has now been proven efficient by a fully three-dimensional kinetic simulation. We discuss the multidimensional nature of SSA and its role in electron injection. Finally, we discuss the current understanding of the magnetized Weibel-dominated shock. It is essentially a magnetized shock in which the reflected-gyrating ions dominate the formation of the shock structure but with a substantial magnetic field amplification by the ion-Weibel instability. Spontaneous magnetic reconnection of self-generated current sheets within the shock structure is an interesting consequence of Weibel-generated strong magnetic turbulence. Although the exact condition for active magnetic reconnection has not been clarified, we argue that high Mach number shocks with both Alfvén and sound Mach numbers exceeding 20–40 will likely behave as a Weibel-dominated shock. Despite a number of interesting recent findings, the relative roles of SSDA, SSA, and magnetic reconnection for electron acceleration at collisionless shocks and how the dominant particle acceleration mechanisms change depending on shock parameters remain to be answered.

We design and analyse a first-order accurate implicit–explicit (IMEX) scheme for the two-dimensional wave equation system in the low Mach number limit. It has been shown by Dellacherie [S. Dellacherie, Analysis of Godunov-type schemes applied to the compressible Euler system at low Mach number. J. Comput. Phys., 229(4): 978–1016, 2010, [1]] that the standard Godunov-type numerical schemes suffer from a severe loss of accuracy at low Mach numbers. This inaccuracy arises due to the inability of schemes to preserve the incompressible space of constant densities and divergence-free velocities. Guided by this principle, we design an IMEX scheme which possess the invariance property, and analyse its stability. The proposed scheme has been shown to be stable under a usual CFL-like condition, independent of the Mach number. The results of numerical experiments confirm the accuracy and stability of the new scheme when applied to low Mach number problems.

The increasing demand for the wide-range aircraft technique requires the ground test facilities with continuous variation of the Mach number. Owing to the rigorous aerodynamic foundation and simple operation, the single-jack flexible nozzle is widely used. However, there are still some problems in the original single-jack flexible nozzle, such as low Mach number and insufficient flow uniformity. This paper presents a novel design of the single-jack flexible nozzle with high flow uniformity and continuous variable Mach number, adopting flow field inverse design and elasticity inverse design. The new nozzle adopts a three-order transonic asymptotic solution and a B-spline axial velocity distribution, designed by the method of characteristics. By comparing with the original nozzle, the new nozzle no longer requires the conical flow assumption, and the flow fields are more uniform. Another improvement is the continuous contour curvature to ensure the coincidence of the aerodynamic profile and the elastic profile, avoiding the negative Mach waves generated by the curvature discontinuity. In addition, the new nozzle has the advantage of two Mach number design points. Similar to the squeeze theorem, the flow fields are uniform at the non-design points between two design points. The numerical results show that the new nozzle eliminates the Mach waves at different Mach number cases. Within the design range of Mach 2.0–4.0, the flow angle's maximum deviations do not exceed 0.2°, and the average deviations do not exceed 0.1°, meeting the national standard of 0.3°. The Mach number's maximum deviations are around 0.5% of Ma¯, the average deviations are less than 0.2% of Ma¯, and the standard deviations meet the national advanced standard. Even at Mach 1.5 and Mach 4.5 outside the design range, the new nozzle still performs well. The evaluation results validate the feasibility of the novel design, supporting the future construction of the variable Mach number facility.

A new method to quickly generate hypersonic waverider forebody configurations has been developed. The new method is an extension of the analysis method and power law method.and is called “Osculating analysis Method”. In this new method the constraint of creating only one attached wave shock in the forebody design by analysis or power law method is removed. More than one attached forebody shock waves can be created in the new method. For the purpose to integrate with ramjet or scramjet, a hypersonic forebody integrated with inlet was designed. The design objective is that the hypersonic forebody has three attached shock waves in the design flight condition. To better understand the forebody performance, three dimensional flow field calculation of the design waverider forebody (designed by osculating analysis method) integrated with hypersonic inlet and two comparative reference waverider forebodies(designed by analysis method and power law method, respectively) integrated with hypersonic inlet in the design and off design conditions were conducted. The computational results show that the performance of design waverider with three attached shock wave is great better than that of two comparative reference waveriders. Compared with two comparative reference models, the flow coefficient is increased by 10.38%, 8.2%; the recovery coefficient of total pressure is increased by 9.38%, 7%, respectively; the uniformity coefficient of inlet exit is increased by 8.8%,6.2%. Three waverider forebodies integrated with hypersonic inlet show better perforemance in high Mach number and attack angle than that in low mach number and negative attack angle. CFD predictions show that the design mach number of waverider forebody should be great than the real flight mach number and the design attack angle should be less than that of real flight condition. Test of the design waverider forebody integrated with hypersonic inlet was performed at a 500-mm-diameter hypersonic tunnel. Experimental results were obtained for a range of conditions, including the on-design Mach number and off-design Mach number. The experimental results were greatly agreed with those of simulation predictions. Vapor screen results for the model indicate three attached (or very nearly attached, within the limits of observation) shock waves along the entire leading edge. Simulation predictions generally agree with the measured pressure distribution.