Non-relativistic Shocks Research Articles

Electron and ion acceleration in relativistic shocks with applications to GRB afterglows

We have modeled the simultaneous first-order Fermi shock acceleration of protons, electrons, and helium nuclei by relativistic shocks. By parameterizing the particle diffusion, our steady-state Monte Carlo simulation allows us to follow particles from particle injection at nonthermal thermal energies to above PeV energies, including the nonlinear smoothing of the shock structure due to cosmic-ray (CR) backpressure. We observe the mass-to-charge (A/Z) enhancement effect believed to occur in efficient Fermi acceleration in non-relativistic shocks and we parameterize the transfer of ion energy to electrons seen in particle-in-cell (PIC) simulations. For a given set of environmental and model parameters, the Monte Carlo simulation determines the absolute normalization of the particle distributions and the resulting synchrotron, inverse-Compton, and pion-decay emission in a largely self-consistent manner. The simulation is flexible and can be readily used with a wide range of parameters typical of gamma-ray burst (GRB) afterglows. We describe some preliminary results for photon emission from shocks of different Lorentz factors and outline how the Monte Carlo simulation can be generalized and coupled to hydrodynamic simulations of GRB blast waves. We assume Bohm diffusion for simplicity but emphasize that the nonlinear effects we describe stem mainly from an extended shock precursor where higher energy particles diffuse further upstream. Quantitative differences will occur with different diffusion models, particularly for the maximum CR energy and photon emission, but these nonlinear effects should be qualitatively similar as long as the scattering mean free path is an increasing function of momentum.

Gamma-ray novae as probes of relativistic particle acceleration at non-relativistic shocks

The Fermi LAT discovery that classical novae produce >100 MeV gamma-rays establishes that shocks and relativistic particle acceleration are key features of these events. These shocks are likely to be radiative due to the high densities of the nova ejecta at early times coincident with the gamma-ray emission. Thermal X-rays radiated behind the shock are absorbed by neutral gas and reprocessed into optical emission, similar to Type IIn (interacting) supernovae. Gamma-rays are produced by collisions between relativistic protons with the nova ejecta (hadronic scenario) or Inverse Compton/bremsstrahlung emission from relativistic electrons (leptonic scenario), where in both scenarios the efficiency for converting relativistic particle energy into LAT gamma-rays is at most a few tens of per cent. The ratio of gamma-ray and optical luminosities, L_gam/L_opt, thus sets a lower limit on the fraction of the shock power used to accelerate relativistic particles, e_nth. The measured values of L_gam/L_opt for two classical novae, V1324 Sco and V339 Del, constrains e_nth > 1e-2 and > 1e-3, respectively. Inverse Compton models for the gamma-ray emission are disfavored given the low electron acceleration efficiency, e_nth ~ 1e-4-1e-3, inferred from observations of Galactic cosmic rays and particle-in-cell (PIC) numerical simulations. A fraction > 100(0.01/e_nth) and > 10(0.01/e_nth) per cent of the optical luminosity is powered by shocks in V1324 Sco and V339 Del, respectively. Such high fractions challenge standard models that instead attribute all nova optical emission to the direct outwards transport of thermal energy released near the white dwarf surface.

On the origin of γ-ray emission in η Carina

Abstract η Car is the only colliding-wind binary for which high-energy γ rays are detected. Although the physical conditions in the shock region change on time-scales of hours to days, the variability seen at GeV energies is weak and on significantly longer time-scales. The γ-ray spectrum exhibits two features that can be interpreted as emission from the shocks on either side of the contact discontinuity. Here, we report on the first time-dependent modelling of the non-thermal emission in η Car. We find that emission from primary electrons is likely not responsible for the γ-ray emission, but accelerated protons interacting with the dense wind material can explain the observations. In our model, efficient acceleration is required at both shocks, with the primary side acting as a hadron calorimeter, whilst on the companion side acceleration is limited by the flow time out of the system, resulting in changing acceleration conditions. The system therefore represents a unique laboratory for the exploration of hadronic particle acceleration in non-relativistic shocks.

Localized enhancements of energetic particles at oblique collisionless shocks

We investigate the spatial distribution of charged particles accelerated by non-relativistic oblique fast collisionless shocks using three-dimensional test-particle simulations. We find that the density of low-energy particles exhibit a localised enhancement at the shock, resembling the "spike" measured at interplanetary shocks. In contrast to previous results based on numerical solutions to the focused transport equation, we find a shock spike for any magnetic obliquity, from quasi-perpendicular to parallel. We compare the pitch-angle distribution with respect to the local magnetic field and the momentum distribution far downstream and very near the shock within the spike; our findings are compatible with predictions from the scatter-free shock drift acceleration (SDA) limit in these regions. The enhancement of low-energy particles measured by Voyager 1 at solar termination shock is comparable with our profiles. Our simulations allow for predictions of supra-thermal protons at interplanetary shocks within ten solar radii to be tested by Solar Probe Mission. They also have implications for the interpretation of ions accelerated at supernova remnant shocks.

Simultaneous acceleration of protons and electrons at nonrelativistic quasiparallel collisionless shocks.

We study diffusive shock acceleration (DSA) of protons and electrons at nonrelativistic, high Mach number, quasiparallel, collisionless shocks by means of self-consistent 1D particle-in-cell simulations. For the first time, both species are found to develop power-law distributions with the universal spectral index -4 in momentum space, in agreement with the prediction of DSA. We find that scattering of both protons and electrons is mediated by right-handed circularly polarized waves excited by the current of energetic protons via nonresonant hybrid (Bell) instability. Protons are injected into DSA after a few gyrocycles of shock drift acceleration (SDA), while electrons are first preheated via SDA, then energized via a hybrid acceleration process that involves both SDA and Fermi-like acceleration mediated by Bell waves, before eventual injection into DSA. Using the simulations we can measure the electron-proton ratio in accelerated particles, which is of paramount importance for explaining the cosmic ray fluxes measured on Earth and the multiwavelength emission of astrophysical objects such as supernova remnants, radio supernovae, and galaxy clusters. We find the normalization of the electron power law is ≲10^{-2} of the protons for strong nonrelativistic shocks.

Plasma physics. Stochastic electron acceleration during spontaneous turbulent reconnection in a strong shock wave.

Explosive phenomena such as supernova remnant shocks and solar flares have demonstrated evidence for the production of relativistic particles. Interest has therefore been renewed in collisionless shock waves and magnetic reconnection as a means to achieve such energies. Although ions can be energized during such phenomena, the relativistic energy of the electrons remains a puzzle for theory. We present supercomputer simulations showing that efficient electron energization can occur during turbulent magnetic reconnection arising from a strong collisionless shock. Upstream electrons undergo first-order Fermi acceleration by colliding with reconnection jets and magnetic islands, giving rise to a nonthermal relativistic population downstream. These results shed new light on magnetic reconnection as an agent of energy dissipation and particle acceleration in strong shock waves.

Shocking! Particle accelerators in space

Plasma Physics The acceleration of charged particles to high energies has been a major mystery, with a number of competing theories based on plasma physics. Many include the concept of turbulence, but with different roles. For example, shock-based theories emphasize the importance of turbulence developed from an unstable shock layer, whereas turbulent reconnection theories emphasize interactions of multiple reconnection sites. Matsumoto et al. present results of a large particle-in-cell simulation and examine how electrons are accelerated in the transition layer of a fast nonrelativistic shock (see the Perspective by Ji and Zweibel). Surprisingly, they find that when the shock is strong enough, charged particles (electrons in this case) are efficiently accelerated by turbulent reconnection within a turbulent shock layer containing multiscale structures. Science , this issue p. [974][1]; see also p. [944][2] [1]: /lookup/doi/10.1126/science.1260168 [2]: /lookup/doi/10.1126/science.aaa3036

SIMULATIONS AND THEORY OF ION INJECTION AT NON-RELATIVISTIC COLLISIONLESS SHOCKS

We use kinetic hybrid simulations (kinetic ions - fluid electrons) to characterize the fraction of ions that are accelerated to non-thermal energies at non-relativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasi-parallel shocks) reform quasi-periodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. This is a necessary condition for being injected, but it is not sufficient. Also by following the trajectories of reflected ions, we calculate the minimum energy needed for injection into diffusive shock acceleration, as a function of the shock inclination. We construct a minimal model that accounts for the ion reflection from quasi-periodic shock barrier, for the fraction of injected ions, and for the ion spectrum throughout the transition from thermal to non-thermal energies. This model captures the physics relevant for ion injection at non-relativistic astrophysical shocks with arbitrary strengths and magnetic inclinations, and represents a crucial ingredient for understanding the diffusive shock acceleration of cosmic rays.

Hybrid Simulations of Particle Acceleration at Shocks

We present the results of large hybrid (kinetic ions – fluid electrons) simulations of particle acceleration at non-relativistic collisionless shocks. Ion acceleration efficiency and magnetic field amplification are investigated in detail as a function of shock inclination and strength, and compared with predictions of diffusive shock acceleration theory, for shocks with Mach number up to 100. Moreover, we discuss the relative importance of resonant and Bell's instability in the shock precursor, and show that diffusion in the self-generated turbulence can be effectively parametrized as Bohm diffusion in the amplified magnetic field.

SIMULATIONS OF ION ACCELERATION AT NON-RELATIVISTIC SHOCKS. II. MAGNETIC FIELD AMPLIFICATION

We use large hybrid simulations to study ion acceleration and generation of magnetic turbulence due to the streaming of particles that are self-consistently accelerated at non-relativistic shocks. When acceleration is efficient, we find that the upstream magnetic field is significantly amplified. The total amplification factor is larger than 10 for shocks with Alfv\'enic Mach number $M=100$, and scales with the square root of $M$. The spectral energy density of excited magnetic turbulence is determined by the energy distribution of accelerated particles, and for moderately-strong shocks ($M\lesssim30$) agrees well with the prediction of resonant streaming instability, in the framework of quasilinear theory of diffusive shock acceleration. For $M\gtrsim30$, instead, Bell's non-resonant hybrid (NRH) instability is predicted and found to grow faster than resonant instability. NRH modes are excited far upstream by escaping particles, and initially grow without disrupting the current, their typical wavelengths being much shorter than the current ions' gyroradii. Then, in the nonlinear stage, most unstable modes migrate to larger and larger wavelengths, eventually becoming resonant in wavelength with the driving ions, which start diffuse. Ahead of strong shocks we distinguish two regions, separated by the free-escape boundary: the far upstream, where field amplification is provided by the current of escaping ions via NRH instability, and the shock precursor, where energetic particles are effectively magnetized, and field amplification is provided by the current in diffusing ions. The presented scalings of magnetic field amplification enable the inclusion of self-consistent microphysics into phenomenological models of ion acceleration at non-relativistic shocks.

Ultrafast ignition with relativistic shock waves induced by high power lasers

Abstract In this paper we consider laser intensities greater than $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}10^{16}\ \mathrm{W\ cm}^{-2}$ where the ablation pressure is negligible in comparison with the radiation pressure. The radiation pressure is caused by the ponderomotive force acting mainly on the electrons that are separated from the ions to create a double layer (DL). This DL is accelerated into the target, like a piston that pushes the matter in such a way that a shock wave is created. Here we discuss two novel ideas. Firstly, the transition domain between the relativistic and non-relativistic laser-induced shock waves. Our solution is based on relativistic hydrodynamics also for the above transition domain. The relativistic shock wave parameters, such as compression, pressure, shock wave and particle flow velocities, sound velocity and rarefaction wave velocity in the compressed target, and temperature are calculated. Secondly, we would like to use this transition domain for shock-wave-induced ultrafast ignition of a pre-compressed target. The laser parameters for these purposes are calculated and the main advantages of this scheme are described. If this scheme is successful a new source of energy in large quantities may become feasible.

SIMULATIONS OF ION ACCELERATION AT NON-RELATIVISTIC SHOCKS. I. ACCELERATION EFFICIENCY

We use 2D and 3D hybrid (kinetic ions - fluid electrons) simulations to investigate particle acceleration and magnetic field amplification at non-relativistic astrophysical shocks. We show that diffusive shock acceleration operates for quasi-parallel configurations (i.e., when the background magnetic field is almost aligned with the shock normal) and, for large sonic and Alfv\'enic Mach numbers, produces universal power-law spectra proportional to p^(-4), where p is the particle momentum. The maximum energy of accelerated ions increases with time, and it is only limited by finite box size and run time. Acceleration is mainly efficient for parallel and quasi-parallel strong shocks, where 10-20% of the bulk kinetic energy can be converted to energetic particles, and becomes ineffective for quasi-perpendicular shocks. Also, the generation of magnetic turbulence correlates with efficient ion acceleration, and vanishes for quasi-perpendicular configurations. At very oblique shocks, ions can be accelerated via shock drift acceleration, but they only gain a factor of a few in momentum, and their maximum energy does not increase with time. These findings are consistent with the degree of polarization and the morphology of the radio and X-ray synchrotron emission observed, for instance, in the remnant of SN 1006. We also discuss the transition from thermal to non-thermal particles in the ion spectrum (supra-thermal region), and we identify two dynamical signatures peculiar of efficient particle acceleration, namely the formation of an upstream precursor and the alteration of standard shock jump conditions.

Electron Acceleration in a Nonrelativistic Shock with Very High Alfvén Mach Number

Electron acceleration associated with various plasma kinetic instabilities in a nonrelativistic shock with very high Alfvén Mach number (M(A)~45) is revealed by means of a two-dimensional fully kinetic particle-in-cell simulation. Electromagnetic (ion Weibel) and electrostatic (ion-acoustic and Buneman) instabilities are strongly activated at the same time in different regions of the two-dimensional shock structure. Relativistic electrons are quickly produced predominantly by the shock surfing mechanism with the Buneman instability at the leading edge of the foot. The energy spectrum has a high-energy tail exceeding the upstream ion kinetic energy accompanying the main thermal population. This gives a favorable condition for the ion-acoustic instability at the shock front, which in turn results in additional energization. The large-amplitude ion Weibel instability generates current sheets in the foot, implying another dissipation mechanism via magnetic reconnection in a three-dimensional shock structure in the very-high-M(A) regime.

MONTE CARLO SIMULATIONS OF NONLINEAR PARTICLE ACCELERATION IN PARALLEL TRANS-RELATIVISTIC SHOCKS

We present results from a Monte Carlo simulation of a parallel collisionless shock undergoing particle acceleration. Our simulation, which contains parameterized scattering and a particular thermal leakage injection model, calculates the feedback between accelerated particles ahead of the shock, which influence the shock precursor and "smooth" the shock, and thermal particle injection. We show that there is a transition between nonrelativistic shocks, where the acceleration efficiency can be extremely high and the nonlinear compression ratio can be substantially greater than the Rankine-Hugoniot value, and fully relativistic shocks, where diffusive shock acceleration is less efficient and the compression ratio remains at the Rankine-Hugoniot value. This transition occurs in the trans-relativistic regime and, for the particular parameters we use, occurs around a shock Lorentz factor = 1.5. We also find that nonlinear shock smoothing dramatically reduces the acceleration efficiency presumed to occur with large-angle scattering in ultra-relativistic shocks. Our ability to seamlessly treat the transition from ultra-relativistic to trans-relativistic to nonrelativistic shocks may be important for evolving relativistic systems, such as gamma-ray bursts and type Ibc supernovae. We expect a substantial evolution of shock accelerated spectra during this transition from soft early on to much harder when the blast-wave shock becomes nonrelativistic.

Parametric study of non-relativistic electrostatic shocks and the structure of their transition layer

Nonrelativistic electrostatic unmagnetized shocks are frequently observed in laboratory plasmas and they are likely to exist in astrophysical plasmas. Their maximum speed, expressed in units of the ion acoustic speed far upstream of the shock, depends only on the electron-to-ion temperature ratio if binary collisions are absent. The formation and evolution of such shocks is examined here for a wide range of shock speeds with particle-in-cell simulations. The initial temperatures of the electrons and the 400 times heavier ions are equal. Shocks form on electron time scales at Mach numbers between 1.7 and 2.2. Shocks with Mach numbers up to 2.5 form after tens of inverse ion plasma frequencies. The density of the shock-reflected ion beam increases and the number of ions crossing the shock thus decreases with an increasing Mach number, causing a slower expansion of the downstream region in its rest frame. The interval occupied by this ion beam is on a positive potential relative to the far upstream. This potential pre-heats the electrons ahead of the shock even in the absence of beam instabilities and decouples the electron temperature in the foreshock ahead of the shock from the one in the far upstream plasma. The effective Mach number of the shock is reduced by this electron heating. This effect can potentially stabilize nonrelativistic electrostatic shocks moving as fast as supernova remnant shocks.

COSMIC-RAY-INDUCED FILAMENTATION INSTABILITY IN COLLISIONLESS SHOCKS

We used unprecedentedly large 2D and 3D hybrid (kinetic ions - fluid electrons) simulations of non-relativistic collisionless strong shocks in order to investigate the effects of self-consistently accelerated ions on the overall shock dynamics. The current driven by suprathermal particles streaming ahead of the shock excites modes transverse to the background magnetic field. The Lorentz force induced by these self-amplified fields tends to excavate tubular, underdense, magnetic-field-depleted cavities that are advected with the fluid and perturb the shock surface, triggering downstream turbulent motions. These motions further amplify the magnetic field, up to factors of 50-100 in knot-like structures. Once downstream, the cavities tend to be filled by hot plasma plumes that compress and stretch the magnetic fields in elongated filaments; this effect is particularly evident if the shock propagates parallel to the background field. Highly-magnetized knots and filaments may provide explanations for the rapid X-ray variability observed in RX J1713.7-3946 and for the regular pattern of X-ray bright stripes detected in Tycho's supernova remnant.

Distilled shock conditions for ideal magneto-acoustic shock waves in an optically thick medium

AbstractThe shock waves are important features in the analysis of transonic magnetohydrodynamical (MHD) flows where thermal radiation could also be significant. In this paper the effects of black-body radiation on non-relativistic shock waves in an ideal radiation MHD model for the optically thick case are discussed. Distilled shock conditions were derived and discussed for the case of a fixed ratio of specific heats of an ideal gas (γ) and ratio of gas to total pressure (b). The special case, when jumps in γ and/or b are allowed, was also considered.

Laboratory investigations on the origins of cosmic rays

We report our recent efforts on the experimental investigations related to the origins of cosmic rays. The origins of cosmic rays are long standing open issues in astrophysics. The galactic and extragalactic cosmic rays are considered to be accelerated in non-relativistic and relativistic collisionless shocks in the universe, respectively. However, the acceleration and transport processes of the cosmic rays are not well understood, and how the collisionless shocks are created is still under investigation. Recent high-power and high-intensity laser technologies allow us to simulate astrophysical phenomena in laboratories. We present our experimental results of collisionless shock formations in laser-produced plasmas.

NONRELATIVISTIC PARALLEL SHOCKS IN UNMAGNETIZED AND WEAKLY MAGNETIZED PLASMAS

We present results of 2D3V particle-in-cell simulations of non-relativistic plasma collisions with absent or parallel large-scale magnetic field for parameters applicable to the conditions at young supernova remnants. We study the collision of plasma slabs of different density, leading to two different shocks and a contact discontinuity. Electron dynamics play an important role in the development of the system. While non-relativistic shocks in both unmagnetized and magnetized plasmas can be mediated by Weibel-type instabilities, the efficiency of shock-formation processes is higher when a large-scale magnetic field is present. The electron distributions downstream of the forward and reverse shocks are generally isotropic, whereas that is not always the case for the ions. We do not see any significant evidence of pre-acceleration, neither in the electron population nor in the ion distribution.

Diffuse Galactic Gamma Rays from Shock-Accelerated Cosmic Rays

A shock-accelerated particle flux is proportional to p(-s), where p is the particle momentum, follows from simple theoretical considerations of cosmic-ray acceleration at nonrelativistic shocks followed by rigidity-dependent escape into the Galactic halo. A flux of shock-accelerated cosmic-ray protons with s≈2.8 provides an adequate fit to the Fermi Large Area Telescope γ-ray emission spectra of high-latitude and molecular cloud gas when uncertainties in nuclear production models are considered. A break in the spectrum of cosmic-ray protons claimed by Neronov, Semikoz, and Taylor [Phys. Rev. Lett. 108, 051105 (2012)] when fitting the γ-ray spectra of high-latitude molecular clouds is a consequence of using a cosmic-ray proton flux described by a power law in kinetic energy.