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 Alfvénic 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.
Diffusive shock acceleration is the theory of particle acceleration through multiple shock crossings. In order for this process to proceed at a rate that can be reconciled with observations of high-energy electrons in the vicinity of the shock, and for cosmic rays protons to be accelerated to energies up to observed galactic values, significant magnetic field amplification is required. In this review we will discuss various theories on how magnetic field amplification can proceed in the presence of a cosmic ray population. On both short and long scales, cosmic ray streaming can induce instabil…
We have performed extensive two-dimensional magnetohydrodynamic simulations to study the amplification of magnetic fields when a supernova blast wave propagates into a turbulent interstellar plasma. The blast wave is driven by injecting high pressure in the simulation domain. The interstellar magnetic field can be amplified by two different processes, occurring in different regions. One is facilitated by the fluid vorticity generated by the ``rippled" shock front interacting with the background turbulence. The resulting turbulent flow keeps amplifying the magnetic field, consistent with earlie…
Supernova Remnants (SNRs) shocks are believed to accelerate charged particles and to generate strong turbulence in the post-shock flow. From high-energy observations in the past decade, a magnetic field at SNR shocks largely exceeding the shock-compressed interstellar field has been inferred. We outline how such a field amplification results from a small-scale dynamo process downstream of the shock, providing an explicit expression for the turbulence back-reaction to the fluid whirling. The spatial scale of the $X-$ray rims and the short time-variability can be obtained by using reasonable par…
We show that the energy required to turbulently amplify magnetic field during cosmic ray (CR) acceleration by shocks extracts energy from the CR and steepens the CR energy spectrum.
This research was motivated by the recent observations indicating very strong magnetic fields at some supernova remnant shocks, which suggests in-situ generation of magnetic turbulence. The dissertation presents a numerical model of collisionless shocks with strong amplification of stochastic magnetic fields, self-consistently coupled to efficient shock acceleration of charged particles. Based on a Monte Carlo simulation of particle transport and acceleration in nonlinear shocks, the model describes magnetic field amplification using the state-of-the-art analytic models of instabilities in mag…
(Abridged) X-ray observations of synchrotron rims in supernova remnant (SNR) shocks show evidence of strong magnetic field amplification (a factor of ~100 between the upstream and downstream medium). This amplification may be due to plasma instabilities driven by shock-accelerated cosmic rays (CRs). One candidate is the cosmic ray current-driven (CRCD) instability (Bell 2004), caused by the electric current of large Larmor radii CRs propagating parallel to the upstream magnetic field. Particle-in-cell (PIC) simulations have shown that the back-reaction of the amplified field on CRs would limit…
Dust-driven streaming instability and magnetic field amplification downstream of supernova remnant shocks
Université de Paris Cité（巴黎西岱大学）；CNRS（法国国家科学研究中心）；Center for Astrophysics（天体物理中心）；LUX（宇宙线与紫外实验室）；Observatoire de Paris（巴黎天文台）；Université PSL（巴黎文理研究大学）；Sorbonne Université（索邦大学）；Istituto Nazionale di Astrofisica – Osservatorio Astrofisico di Arcetri（意大利国家天体物理研究所-阿切特里天文台）；Institute of Nuclear Physics Polish Academy of Sciences（波兰科学院核物理研究所）；Université Paris-Saclay（巴黎萨克雷大学）；IJCLab（巴黎第十一大学宇宙射线与粒子物理实验室）
An extreme case of electron shock drift acceleration in low Mach number collisionless shocks is investigated as a plausible mechanism of initial acceleration of relativistic electrons in large-scale shocks in galaxy clusters where upstream plasma temperature is of the order of 10 keV and a degree of magnetization is not too small. One-dimensional electromagnetic full particle simulations reveal that, even though a shock is rather moderate, a part of thermal incoming electrons are accelerated and reflected through relativistic shock drift acceleration and form a local nonthermal population just…
In this paper, we study shock structures of collisionless shocks in partially ionized plasmas by means of two-dimensional hybrid simulations, where the shock is a perpendicular shock with shock velocity Vsh ~ 40 Va ~ 1333 km/s and the upstream ionization fraction is 0.5. We find that large density fluctuations and large magnetic fields fluctuations are generated both in the upstream and downstream regions. In addition, we find that the velocity distribution of downstream hydrogen atoms has three components. Observed shock structures suggest that diffusive shock acceleration can operate at perp…
We have performed magnetohydrodynamical simulations to study the amplification of magnetic fields in the precursors of shock waves. Strong magnetic fields are required in the precursors of the strong shocks that occur in supernova remnants. Observations also suggest that magnetic field amplification takes place in the weak shocks that occur in galaxy clusters and that produce so-called radio relics. Here, we extend the study of magnetic field amplification by cosmic-ray driven turbulence to weak shocks. The amplification is driven by turbulence that is produced by the cosmic-ray pressure actin…
This review presents the fundamentals of the particle acceleration processes active in interstellar medium (ISM), which are essentially based on the so-called Fermi mechanism theory. More specifically, the review presents here in more details the first order Fermi acceleration process -- also known as diffusive shock acceleration (DSA) mechanism. In this case, acceleration is induced by the interstellar (IS) shock waves. These IS shocks are mainly associated with emission nebulae (HII regions, planetary nebulae and supernova remnants). Among all types of emission nebulae, the strongest shocks …
We present an interpretation of the time variability of the $X$-ray flux recently reported from a multi-epoch campaign of $15$ years observations of the supernova remnant Cassiopeia A by {\it Chandra}. We show for the first time quantitatively that the $[4.2-6]$ keV non-thermal flux increase up to $50\%$ traces the growth of the magnetic field due to vortical amplification mechanism at a reflection inward shock colliding with inner overdensities. The fast synchrotron cooling as compared with shock-acceleration time scale qualitatively supports the flux decrease.
We study the acceleration of cosmic rays by collisionless structure formation shocks with ENZO grid simulations. Data from the FERMI satellite enable the use of galaxy clusters as a testbed for particle acceleration models. Based on advanced cosmological simulations that include different prescriptions for gas and cosmic rays physics, we use the predicted γ-ray emission to constrain the shock acceleration efficiency. We infer that the efficiency must be on average <0.1% for cosmic shocks, particularly for the 2<M<5 merger shocks that are mostly responsible for the thermalisation of the intracl…
We investigate the observability, by direct and indirect means, of a shock precursor arising from magnetic field amplification by cosmic rays. We estimate the depth of such a precursor under conditions of nonresonant amplification, which can provide magnetic field strengths comparable to those inferred for supernova remnants. Magnetic field generation occurs as the streaming cosmic rays induce a plasma return current, and may be quenched either by nonresonant or resonant channels. In the case of nonresonant saturation, the cosmic rays become magnetized and amplification saturates at higher mag…
We have investigated via two-dimensional relativistic MHD simulations the long-term evolution of turbulence created by a relativistic shock propagating through an inhomogeneous medium. In the postshock region, magnetic field is strongly amplified by turbulent motions triggered by preshock density inhomogeneities. Using a long-simulation box we have followed the magnetic-field amplification until it is fully developed and saturated. The turbulent velocity is sub-relativistic even for a strong shock. Magnetic-field amplification is controled by the turbulent motion and saturation occurs when the…
We perform two-dimensional relativistic magnetohydrodynamic simulations of a mildly relativistic shock propagating through an inhomogeneous medium. We show that the postshock region becomes turbulent owing to preshock density inhomogeneity, and the magnetic field is strongly amplified due to the stretching and folding of field lines in the turbulent velocity field. The amplified magnetic field evolves into a filamentary structure in two-dimensional simulations. The magnetic energy spectrum is flatter than the Kolmogorov spectrum and indicates that a so-called small-scale dynamo is occurring in…
Turbulent dynamo field amplification has often been invoked to explain the strong field strengths in thin rims in supernova shocks ($\sim 100 \, μ$G) and in radio relics in galaxy clusters ($\sim μ$G). We present high resolution MHD simulations of the interaction between pre-shock turbulence, clumping and shocks, to quantify the conditions under which turbulent dynamo amplification can be significant. We demonstrate numerically converged field amplification which scales with Alfvén Mach number, $B/B_0 \propto {\mathcal M}_{\rm A}$, up to ${\mathcal M}_{\rm A} \sim 150$. This implies that the p…
We present simulations of magnetized astrophysical shocks taking into account the interplay between the thermal plasma of the shock and supra-thermal particles. Such interaction is depicted by combining a grid-based magneto-hydrodynamics description of the thermal fluid with particle in cell techniques devoted to the dynamics of supra-thermal particles. This approach, which incorporates the use of adaptive mesh refinement features, is potentially a key to simulate astrophysical systems on spatial scales that are beyond the reach of pure particle-in-cell simulations. We consider in this study n…
We present a nonlinear Monte Carlo model of efficient diffusive shock acceleration (DSA) where the magnetic turbulence responsible for particle diffusion is calculated self-consistently from the resonant cosmic-ray (CR) streaming instability, together with non-resonant short- and long-wavelength CR-current-driven instabilities. We include the backpressure from CRs interacting with the strongly amplified magnetic turbulence which decelerates and heats the super-alfvenic flow in the extended shock precursor. Uniquely, in our plane-parallel, steady-state, multi-scale model, the full range of part…
Collisionless shocks are ubiquitous in the Universe and often associated with strong magnetic field. Here we use large-scale particle-in-cell simulations of non-relativistic perpendicular shocks in the high-Mach-number regime to study the amplification of magnetic field within shocks. The magnetic field is amplified at the shock transition due to the ion-ion two-stream Weibel instability. The normalized magnetic-field strength strongly correlates with the Alfvénic Mach number. Mock spacecraft measurements derived from PIC simulations are fully consistent with those taken in-situ at Saturn's bo…
We derive analytically the vorticity generated downstream of a two-dimensional rippled hydromagnetic shock neglecting fluid viscosity and resistivity. The growth of the turbulent component of the downstream magnetic field is driven by the vortical eddies motion. We determine an analytic time-evolution of the magnetic field amplification at shocks, so far described only numerically, until saturation occurs due to seed-field reaction to field lines whirling. The explicit expression of the amplification growth rate and of the non-linear field back-reaction in terms of the parameters of shock and …
Cosmic-ray streaming instabilities at supernova shocks are discussed in the quasilinear diffusion formalism which takes into account the feedback effect of wave growth on the cosmic ray streaming motion. In particular, the nonresonant instability that leads to magnetic field amplification in the short wavelength regime is considered. The linear growth rate is calculated using kinetic theory for a streaming distribution. We show that the nonresonant instability is actually driven by a compensating current in the background plasma. The nonresonant instability can develop into a nonlinear regime …
We explore electron pre-acceleration at high Mach-number nonrelativistic perpendicular shocks at, e.g., young supernova remnants, which are a prerequisite of further acceleration to very high energies via diffusive shock acceleration. Using fully kinetic particle-in-cell simulations of shocks and electron dynamics in them, we investigate the influence of shock-surfing acceleration at the shock foot on the nonthermal population of electrons downstream of the shock. The shock-surfing acceleration is followed by further energization at the shock ramp where the Weibel instability spawns a type of …
Using observations from the literature, we show that the non-thermal radio luminosity (L) of supernova remnants (SNRs) is a strong function of the average gas surface density (Sigma) of the galaxy in which the remnants reside, from normal spirals to luminous starbursts. We combine a simple theory for electron cooling in SNRs with the observed radio luminosities to estimate the remnant magnetic field strength (B_SNR): the correlation between L and Sigma implies that B_SNR also increases with Sigma. We explore two interpretations of this correlation: (1) B_SNR is generated by post-shock magnetic…
Delayed radio flares of optical tidal disruption events (TDEs) indicate the existence of non-relativistic outflows accompanying TDEs. The interaction of TDE outflows with the surrounding circumnuclear medium creates quasi-perpendicular shocks in the presence of toroidal magnetic fields. Because of the large shock obliquity and large outflow velocity, we find that the shock acceleration induced by TDE outflows generally leads to a steep particle energy spectrum, with the power-law index significantly larger than the "universal" index for a parallel shock. The measured synchrotron spectral indic…
We investigated electromagnetic precursor wave emission in relativistic shocks by using two-dimensional particle-in-cell simulations. We found that the wave amplitude is significantly enhanced by a positive feedback process associated with ion-electron coupling through the wakefields for high magnetization. The wakefields collapse during the nonlinear process of the parametric decay instability in the near-upstream region, where nonthermal electrons and ions are generated. The intense coherent emission and the particle acceleration may opperate in high-energy astrophysical objects.
Using test particle simulations we study electron acceleration at collisionless shocks with a two-component model turbulent magnetic field with slab component including dissipation range. We investigate the importance of shock normal angle $θ_{Bn}$, magnetic turbulence level $\left(b/B_0\right)^2$, and shock thickness on the acceleration efficiency of electrons. It is shown that at perpendicular shocks the electron acceleration efficiency is enhanced with the decreasing of $\left(b/B_0\right)^2$, and at $\left(b/B_0\right)^2=0.01$ the acceleration becomes significant due to strong drift electr…
We investigate shock structure and particle acceleration in relativistic magnetized collisionless pair shocks by means of 2.5D and 3D particle-in-cell simulations. We explore a range of inclination angles between the pre-shock magnetic field and the shock normal. We find that only magnetic inclinations corresponding to "subluminal" shocks, where relativistic particles following the magnetic field can escape ahead of the shock, lead to particle acceleration. The downstream spectrum in such shocks consists of a relativistic Maxwellian and a high-energy power-law tail with exponential cutoff. For…
We explore how wave-particle interactions affect diffusive shock acceleration (DSA) at astrophysical shocks by performing time-dependent kinetic simulations, in which phenomenological models for magnetic field amplification (MFA), Alfvenic drift, thermal leakage injection, Bohm-like diffusion, and a free escape boundary are implemented. If the injection fraction of cosmic-ray (CR) particles is greater than 2x10^{-4}, for the shock parameters relevant for young supernova remnants, DSA is efficient enough to develop a significant shock precursor due to CR feedback, and magnetic field can be ampl…
Radio relics could be generated by multiple shocks induced in the turbulent intracluster medium during galaxy mergers. Kang (2021) demonstrated that the re-acceleration of cosmic ray (CR) protons via diffusive shock acceleration (DSA) by multiple shocks could enhance the acceleration efficiency and flatten the CR spectrum, compared to a single episode of DSA. Here we examine the CR electron acceleration through multiple re-acceleration by considering energy losses and decompression of the particle distribution and magnetic fields in the postshock region between consecutive shock passages. We f…
Electron acceleration to non-thermal energies in low Mach number (M<5) shocks is revealed by radio and X-ray observations of galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Diffusive shock acceleration, also known as first-order Fermi acceleration, cannot be directly invoked to explain the acceleration of electrons. Rather, an additional mechanism is required to pre-accelerate the electrons from thermal to supra-thermal energies, so they can then participate in the Fermi process. In this work, we use two- and three-dimensional particle-in-ce…
We model the multi-wavelength emission in the southern hotspot of the radio quasar 4C74.26. The synchrotron radio emission is resolved near the shock with the MERLIN radio-interferometer, and the rapid decay of this emission behind the shock is interpreted as the decay of the amplified downstream magnetic field as expected for small scale turbulence. Electrons are accelerated to only 0.3 TeV, consistent with a diffusion coefficient many orders of magnitude greater than in the Bohm regime. If the same diffusion coefficient applies to the protons, their maximum energy is only ~100 TeV.
We investigate effects of upstream density fluctuations on the diffusive shock acceleration by Monte Carlo simulations. The simulations show that particles are reaccelerated in the shock downstream region by a sound wave generated at the shock front. The time scale of turbulent acceleration by the sound wave is estimated. We propose a new back reaction of particles accelerated around the shock front. The accelerated particles generate the upstream density fluctuations by the Drury instability, which are converted to the downstream sound waves by the shock. The downstream sound waves modify the…
The intracluster medium (ICM) is expected to experience on average about three passages of weak shocks with low sonic Mach numbers, $M\lesssim 3$, during the formation of galaxy clusters. Both protons and electrons could be accelerated to become high energy cosmic rays (CRs) at such ICM shocks via diffusive shock acceleration (DSA). We examine the effects of DSA by multiple shocks on the spectrum of accelerated CRs by including {\it in situ} injection/acceleration at each shock, followed by repeated re-acceleration at successive shocks in the test-particle regime. For simplicity, the accelerat…
Electron acceleration to non-thermal energies is known to occur in low Mach number (M<5) shocks in galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Using two-dimensional (2D) particle-in-cell (PIC) plasma simulations, we showed in Paper I that electrons are efficiently accelerated in low Mach number (M=3) quasi-perpendicular shocks via a Fermi-like process. The electrons bounce between the upstream region and the shock front, with each reflection at the shock resulting in energy gain via shock drift acceleration. The upstream scattering is pr…
Strong downstream magnetic fields of order of $\sim 1$G, with large correlation lengths, are believed to cause the large synchrotron emission at the afterglow phase of gamma ray bursts (GRBs). Despite of the recent theoretical efforts, models have failed to fully explain the amplification of the magnetic field, particularly in a matter dominated scenario. We revisit the problem by considering the synchrotron emission to occur at the expanding shock front of a weakly magnetized relativistic jet over a magnetized surrounding medium. Analytical estimates and a number of high resolution 2D relativ…
We present a three-dimensional hybrid simulation of a collisionless perpendicular shock in a partially ionized plasma for the first time. In this simulation, the shock velocity and the upstream ionization fraction are Vsh ~ 1333 km/s and fi ~ 0.5, that are typical values for isolated young supernova remnants in the interstellar medium. We confirm previous two-dimensional simulation results that downstream hydrogen atoms leak into the upstream region, they are accelerated by the pickup process in the upstream region, and large magnetic field fluctuations are generated both in the upstream and d…
Synchrotron radio emission from non-relativistic jets powered by massive protostars has been reported, indicating the presence of relativistic electrons and magnetic fields of strength ~0.3-5 mG. We study diffusive shock acceleration and magnetic field amplification in protostellar jets with speeds between 300 and 1500 km/s. We show that the magnetic field in the synchrotron emitter can be amplified by the non-resonant hybrid (Bell) instability excited by the cosmic-ray streaming. By combining the synchrotron data with basic theory of Bell instability we estimate the magnetic field in the sync…
Relativistic particle acceleration in collisionless shocks of supernova remnants is accompanied by magnetic field amplification from cosmic ray (CR) driven plasma instabilities. Bell's fast CR-current instability is predicted to produce turbulence with a non-zero mean electric field in the shock precursor. We present a Monte Carlo model of Fermi shock acceleration explicitly taking into account an effective mean upstream electric field. Our model is nonlinear and includes the backreaction effects of efficient Fermi acceleration on the shock structure.
Laser experiments are becoming established as a new tool for astronomical research that complements observations and theoretical modeling. Localized strong magnetic fields have been observed at a shock front of supernova explosions. Experimental confirmation and identification of the physical mechanism for this observation are of great importance in understanding the evolution of the interstellar medium. However, it has been challenging to treat the interaction between hydrodynamic instabilities and an ambient magnetic field in the laboratory. Here, we developed an experimental platform to exa…
We show that the diffusion approximation breaks down for particle acceleration at oblique shocks with velocities typical of young supernova remnants. Higher order anisotropies flatten the spectral index at quasi-parallel shocks and steepen the spectral index at quasi-perpendicular shocks. We compare the theory with observed spectral indices.
Using large-scale fully-kinetic two-dimensional particle-in-cell simulations, we investigate the effects of shock rippling on electron acceleration at low-Mach-number shocks propagating in high-$β$ plasmas, in application to merger shocks in galaxy clusters. We find that the electron acceleration rate increases considerably when the rippling modes appear. The main acceleration mechanism is stochastic shock-drift acceleration, in which electrons are confined at the shock by pitch-angle scattering off turbulence and gain energy from the motional electric field. The presence of multi-scale magnet…
We examine limits to the energy to which cosmic rays can be accelerated by relativistic shocks, showing that acceleration of light ions as high as 100 EeV is unlikely. The implication of our estimates is that if ultra-high energy cosmic rays are accelerated by shocks, then those shocks are probably not relativistic.
Plasma streaming instabilities play an important role in magnetic field amplification and particle acceleration in relativistic shocks and their environments. However, in the far shock precursor region where accelerated particles constitute a highly relativistic and dilute beam, streaming instabilities typically become inefficient and operate at very small scales when compared to the gyroradii of the beam particles. We report on a plasma cavitation instability that is driven by dilute relativistic beams and can increase both the magnetic field strength and coherence scale by orders of magnitud…
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 di…
Collisionless shocks with low sonic Mach numbers, $M_{\rm s} \lesssim 4$, are expected to accelerate cosmic ray (CR) protons via diffusive shock acceleration (DSA) in the intracluster medium (ICM). However, observational evidence for CR protons in the ICM has yet to be established. Performing particle-in-cell simulations, we study the injection of protons into DSA and the early development of a nonthermal particle population in weak shocks in high $β$ ($\approx 100$) plasmas. Reflection of incident protons, self-excitation of plasma waves via CR-driven instabilities, and multiple cycles of sho…
We study diffusive shock acceleration (DSA) of electrons in non-relativistic quasi-perpendicular shocks using self-consistent one-dimensional particle-in-cell (PIC) simulations. By exploring the parameter space of sonic and Alfvénic Mach numbers we find that high Mach number quasi-perpendicular shocks can efficiently accelerate electrons to power-law downstream spectra with slopes consistent with DSA prediction. Electrons are reflected by magnetic mirroring at the shock and drive non-resonant waves in the upstream. Reflected electrons are trapped between the shock front and upstream waves and …
Fast collisionless shocks in cosmic plasmas convert their kinetic energy flow into the hot downstream thermal plasma with a substantial fraction of energy going into a broad spectrum of superthermal charged particles and magnetic fluctuations. The superthermal particles can penetrate into the shock upstream region producing an extended shock precursor. The cold upstream plasma flow is decelerated by the force provided by the superthermal particle pressure gradient. In high Mach number collisionless shocks, efficient particle acceleration is likely coupled with turbulent magnetic field amplific…
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 Alfvénic 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 ru…
A new numerical model of the nonlinear diffusive shock acceleration is presented. It is used for modeling of particle acceleration in supernova remnants. The model contains coupled spherically symmetric hydrodynamic equations and the transport equations for energetic protons, ions and electrons. The forward and reverse shocks are included in the consideration. The spectra of cosmic rays released into interstellar medium from a supernova remnant are determined. The role of the reverse shock in the production of CR ions and positrons is discussed.
The early acceleration of protons and electrons in the nonrelativistic collisionless shocks with three obliquities are investigated through 1D particle-in-cell simulations. In the simulations, the charged particles possessing a velocity of $0.2\, c$ flow towards a reflecting boundary, and the shocks with a sonic Mach number of $13.4$ and a Alfven Mach number of $16.5$ in the downstream shock frame are generated. In these quasi-parallel shocks with the obliquity angles $θ= 15^\circ$, $30^\circ$, and $45^\circ$, some of the protons and the electrons can be injected into the acceleration processe…
The shock waves produce relativistic particles via the diffusive shock acceleration (DSA) mechanism. Among various circumstances, fast acceleration has been expected for perpendicular shocks. We investigate the acceleration time and the energy spectrum of particles accelerated at a perpendicular shock. In our model, the upstream perpendicular magnetic field has no fluctuation, and the downstream region is highly turbulent. Then, the particle motion is the gyration in the upstream region and Bohm-like diffusion downstream. Under this situation, we derive an analytical form of the acceleration t…
We present results of semi-analytic calculations which show clear evidence for changes in the non-equilibrium ionization behind a supernova remnant forward shock undergoing efficient diffusive shock acceleration (DSA). The efficient acceleration of particles (i.e., cosmic rays) lowers the shock temperature and raises the density of the shocked gas, thus altering the ionization state of the plasma in comparison to the test particle approximation where cosmic rays gain an insignificant fraction of the shock energy. The differences between the test particle and efficient acceleration cases are su…
Plasma processes close to SNR shocks result in the amplification of magnetic fields and in the acceleration of electrons, injecting them into the diffusive acceleration mechanism. The acceleration of electrons and the B field amplification by the collision of two plasma clouds, each consisting of electrons and ions, at a speed of 0.5c is investigated. A quasi-parallel guiding magnetic field, a cloud density ratio of 10 and a plasma temperature of 25 keV are considered. A quasi-planar shock forms at the front of the dense plasma cloud. It is mediated by a circularly left-hand polarized electrom…
It has been suggested that relativistic shocks in extragalactic sources may accelerate the most energetic cosmic rays. However, recent theoretical advances indicating that relativistic shocks are probably unable to accelerate particles to energies much larger than a PeV cast doubt on this. In the present contribution we model the radio to X-ray emission in the southern hotspot of the quasar 4C74.26. The synchrotron radio emission is resolved near the shock with the MERLIN radio-interferometer, and the rapid decay of this emission behind the shock is interpreted as the decay of the downstream m…
We study cosmic-ray acceleration in young Type Ia Supernova Remnants (SNRs) by means of test-particle diffusive shock acceleration theory and 1-D hydrodynamical simulations of their evolution. In addition to acceleration at the forward shock, we explore the particle acceleration at the reverse shock in the presence of a possible substantial magnetic field, and consequently the impact of this acceleration on the particle spectra in the remnant. We investigate the time evolution of the spectra for various time-dependent profiles of the magnetic field in the shocked region of the remnant. We test…
We modeled the radio non-detection of two Type Ia supernovae (SNe) 2011fe and 2014J considering synchrotron emission from the interaction between SN ejecta and the circumstellar medium. For an ejecta with the outer part having a power law density structure we compare synchrotron emission with radio observations. Assuming that 20$\%$ of the bulk shock energy is being shared equally between electrons and magnetic fields we found a very low density medium around both the SNe. A less tenuous medium with particle density $\sim$ 1 $\rm cm^{-3}$, which could be expected around both SNe, can be estima…
We propose semi-analytic models for the electron momentum distribution in weak shocks that accounts for both in situ acceleration and re-acceleration through diffusive shock acceleration (DSA). In the former case, a small fraction of incoming electrons are assumed to be reflected at the shock ramp and pre-accelerated to the so-called injection momentum, $p_{\rm inj}$, above which particles can diffuse across the shock transition and participate in the DSA process. This leads to the DSA power-law distribution extending from the smallest momentum of reflected electrons, $p_{\rm ref}$, all the wa…
