Non-resonant Streaming Instability Research Articles

Laboratory evidence of the nonresonant streaming instability in the formation of quasiparallel collisionless shocks at high Alfvénic Mach number.

We present an experimental investigation of the formation stage of a collisionless shock when the flow velocity is aligned with an ambient magnetic field utilizing laser-driven, super-Alfvénic plasma flows. As the flows interact, electromagnetic streaming instabilities develop. Proton deflectometry is used to visualize these electromagnetic fluctuations indicating the development of the ion-Weibel instability and the nonresonant instability. Hybrid simulations also show growth of the nonresonant instability and suggest that it provides an efficient source of dissipation for a shock.

Interplay between the non-resonant streaming instability and self-generated pressure anisotropies

ABSTRACT The non-thermal particles escaping from collision-less shocks into the surrounding medium can trigger a non-resonant streaming instability that converts parts of their drift kinetic energy into large amplitude magnetic field perturbations, and promote the confinement and acceleration of high energy cosmic rays. We present simulations of the instability using an hybrid-Particle-in-Cell approach including Monte Carlo collisions, and demonstrate that the development of the non-resonant mode is associated with important ion pressure anisotropies in the background plasma. Depending on the initial conditions, the anisotropies may act on the instability by lowering its growth and trigger secondary micro-instabilities. Introducing collisions with neutrals yield a strong reduction of the magnetic field amplification as predicted by linear fluid theory. In contrast, Coulomb collisions in fully ionized plasmas are found to mitigate the self-generated pressure anisotropies and promote the growth of the magnetic field.

Modeling the Saturation of the Bell Instability Using Hybrid Simulations

The nonresonant streaming instability (Bell instability) plays a pivotal role in the acceleration and confinement of cosmic rays (CRs), yet the exact mechanism responsible for its saturation and the magnitude of the final amplified magnetic field have not been assessed from first principles. Using a survey of hybrid simulations (with kinetic ions and fluid electrons), we study the evolution of the Bell instability as a function of the parameters of the CR population. We find that at saturation, the magnetic pressure in the amplified field is comparable with the initial CR anisotropic pressure, rather than with the CR energy flux, as previously argued. These results provide a predictive prescription for the total magnetic field amplification expected in the many astrophysical environments where the Bell instability is important.

Microphysics of Diffusive Shock Acceleration: Impact on the Spectrum of Accelerated Particles

Diffusive shock acceleration at collisionless shocks remains the most likely process for accelerating particles in a variety of astrophysical sources. While the standard prediction for strong shocks is that the spectrum of accelerated particles is universal, f(p) ∝ p −4, numerous phenomena affect this simple conclusion. In general, the nonlinear dynamical reaction of accelerated particles leads to a concave spectrum, steeper than p −4 at momenta below a few tens of GeV c −1 and harder than the standard prediction at high energies. However, the nonlinear effects become important in the presence of magnetic field amplification, which in turn leads to higher values of the maximum momentum p max. It was recently discovered that the self-generated perturbations that enhance particle scattering, when advected downstream, move in the same direction as the background plasma, so that the effective compression factor at the shock decreases and the spectrum becomes steeper. We investigate the implications of the excitation of the non-resonant streaming instability on these spectral deformations, the dependence of the spectral steepening on the shock velocity, and the role played by the injection momentum.

Enhancement of the Nonresonant Streaming Instability by Particle Collisions.

Streaming cosmic rays can power the exponential growth of a seed magnetic field by exciting a nonresonant instability that feeds on their bulk kinetic energy. By generating the necessary turbulent magnetic field, it is thought to play a key role in the confinement and acceleration of cosmic rays at shocks. In this Letter we present hybrid-particle-in-cell simulations of the nonresonant mode including MonteCarlo collisions, and investigate the interplay between the pressure anisotropies produced by the instability and particle collisions in the background plasma. Simulations of poorly ionized plasmas confirm the rapid damping of the instability by proton-neutral collisions predicted by linear fluid theory calculations. In contrast we find that Coulomb collisions in fully ionized plasmas do not oppose the growth of the magnetic field, but under certain conditions suppress the pressure anisotropies and actually enhance the magnetic field amplification.

Lepton-driven Nonresonant Streaming Instability

Abstract A strong super-Alfvénic drift of energetic particles (or cosmic rays) in a magnetized plasma can amplify the magnetic field significantly through nonresonant streaming instability (NRSI). While the traditional analysis is done for an ion current, here we use kinetic particle-in-cell simulations to study how the NRSI behaves when it is driven by electrons or by a mixture of electrons and positrons. In particular, we characterize the growth rate, spectrum, and helicity of the unstable modes, as well the level of the magnetic field at saturation. Our results are potentially relevant for several space/astrophysical environments (e.g., electron strahl in the solar wind, at oblique nonrelativistic shocks, around pulsar wind nebulae), and also in laboratory experiments.

Direct Numerical Simulations of Cosmic-ray Acceleration at Dense Circumstellar Medium: Magnetic-field Amplification and Maximum Energy

Abstract Galactic cosmic rays are believed to be accelerated at supernova remnants. However, whether supernova remnants can be PeV is still very unclear. In this work we argue that PeV cosmic rays can be accelerated during the early phase of a supernova blast-wave expansion in dense red supergiant winds. We solve in spherical geometry a system combining a diffusive–convection equation that treats cosmic-ray dynamics coupled to magnetohydrodynamics to follow gas dynamics. A fast shock expanding in a dense ionized wind is able to trigger fast, non-resonant streaming instability over day timescales and energizes cosmic rays even under the effect of p–p losses. We find that such environments produce PeV blast waves, although the maximum energy depends on various parameters such as the injection rate and mass-loss rate of the winds. Multi-PeV energies can be reached if the progenitor mass-loss rates are of the order of 10−3 M ⊙ yr−1. It has been recently proposed that, prior to the explosion, hydrogen-rich massive stars can produce enhanced mass-loss rates. These enhanced rates would then favor the production of a PeV phase in early times after shock breakout.

Cosmic ray protons and electrons from supernova remnants

Context.The spectrum of cosmic ray protons and electrons released by supernova remnants throughout their evolution is poorly known because of the difficulty in accounting for particle escape and confinement downstream of a shock front, where both adiabatic and radiative losses are present. Since electrons lose energy mainly through synchrotron losses, it is natural to ask whether the spectrum released into the interstellar medium may be different from that of their hadronic counterpart. Independent studies of cosmic ray transport through the Galaxy require that the source spectrum of electrons and protons be very different. Therefore, the above question acquires a phenomenological relevance.Aims.Here we calculate the spectrum of cosmic ray protons released during the evolution of supernovae of different types, accounting for the escape from the upstream region and for adiabatic losses of particles advected downstream of the shock and liberated at later times. The same calculation is carried out for electrons, where in addition to adiabatic losses we take the radiative losses suffered behind the shock into account. These electrons are dominated by synchrotron losses in the magnetic field, which most likely is self-generated by cosmic rays accelerated at the shock.Methods.We use standard temporal evolution relations for supernova shocks expanding in different types of interstellar media together with an analytic description of particle acceleration and magnetic field amplification to determine the density and spectrum of cosmic ray particles. Their evolution in time is derived by numerically solving the equation describing advection with adiabatic and radiative losses for electrons and protons. The flux from particles continuously escaping the supernova remnants is also accounted for.Results.The magnetic field in the post-shock region is calculated by using an analytic treatment of the magnetic field amplification due to nonresonant and resonant streaming instability and their saturation. The resulting field is compared with the available set of observational results concerning the dependence of the magnetic field strength upon shock velocity. We find that when the field is the result of the growth of the cosmic-ray-driven nonresonant instability alone, the spectrum of electrons and protons released by a supernova remnant are indeed different; however, such a difference becomes appreciable only at energies ≳100−1000 GeV, while observations of the electron spectrum require such a difference to be present at energies as low as ∼10 GeV. An effect at such low energies requires substantial magnetic field amplification in the late stages of supernova remnant evolution (shock velocity ≪1000 km s−1); this may not be due to streaming instability but rather hydrodynamical processes. We comment on the feasibility of such conditions and speculate on the possibility that the difference in spectral shape between electrons and protons may reflect either some unknown acceleration effect or additional energy losses in cocoons around the sources.

On the growth of the thermally modified non-resonant streaming instability

ABSTRACT The cosmic rays non-resonant streaming instability is believed to be the source of substantial magnetic field amplification. In this work, we investigate the effects of the ambient plasma temperature on the instability and derive analytical expressions of its growth rate in the hot, demagnetized regime of interaction. To study its non-linear evolution, we perform hybrid-PIC simulations for a wide range of temperatures. We find that in the cold limit, about two-thirds of the cosmic rays drift kinetic energy is converted into magnetic energy. Increasing the temperature of the ambient plasma can substantially reduce the growth rate and the magnitude of the saturated magnetic field.

Three-dimensional simulations of non-resonant streaming instability and particle acceleration near non-relativistic astrophysical shocks

ABSTRACT We use particle-in-magnetohydrodynamics-cells to model particle acceleration and magnetic field amplification in a high-Mach, parallel shock in three dimensions and compare the result to 2D models. This allows us to determine whether 2D simulations can be relied upon to yield accurate results in terms of particle acceleration, magnetic field amplification, and the growth rate of instabilities. Our simulations show that the behaviour of the gas and the evolution of the instabilities are qualitatively similar for both the 2D and 3D models, with only minor quantitative differences that relate primarily to the growth speed of the instabilities. The main difference between 2D and 3D models can be found in the spectral energy distributions (SEDs) of the non-thermal particles. The 2D simulations prove to be more efficient, accelerating a larger fraction of the particles and achieving higher velocities. We conclude that, while 2D models are sufficient to investigate the instabilities in the gas, their results have to be treated with some caution when predicting the expected SED of a given shock.

Preliminary study for the laboratory experiment of cosmic-rays driven magnetic field amplification

To understand astrophysical magnetic-field amplification, we conducted a feasibility study for a laboratory experiment of a non-resonant streaming instability at the Photo Injector Test Facility at DESY, Zeuthen site (PITZ). This non-resonant streaming instability, also known as Bell’s instability, is generally regarded as a candidate for the amplification of interstellar magnetic field in the upstream region of supernova-remnant shocks, which is crucial for the efficiency of diffusive shock acceleration. In the beam-plasma system composed of a radio-frequency electron gun and a gas-discharge plasma cell, the goal of our experiment is to demonstrate the development of the non-resonant streaming instability and to find its saturation level in the laboratory environment. Since we find that the electron beam will be significantly decelerated on account of an electrostatic streaming instability, which will decrease the growth rate of desired non-resonant streaming instability, we discuss possible ways to suppress the electrostatic streaming instability by considering the characteristics of a field-emission-based quasi continuous-wave electron beam.

Core-collapse supernovae as cosmic ray sources.

Core-collapse supernovae produce fast shocks which pervade the dense circumstellar medium (CSM) of the stellar progenitor. Cosmic rays (CRs) if accelerated at these shocks can induce the growth of electromagnetic fluctuations in the foreshock medium. In this study, using a self-similar description of the shock evolution, we calculate the growth time-scales of CR-driven instabilities. We select a sample of nearby core-collapse radio supernova of type II and Ib/Ic. From radio data, we infer the parameters which enter in the calculation of the instability growth times. We find that extended IIb SNe shocks can trigger fast intra-day instabilities, strong magnetic field amplification, and CR acceleration. In particular, the non-resonant streaming instability can contribute to about 50 percent of the magnetic field intensity deduced from radio data. This results in the acceleration of CRs in the range 1-10 PeV within a few days after the shock breakout. In order to produce strong magnetic field amplification and CR acceleration, a fast shock pervading a dense CSM is necessary. In that aspect, IIn supernovæ are also good candidates. But a detailed modelling of the blast wave dynamics coupled with particle acceleration is mandatory for this class of object before providing any firm conclusions. Finally, we find that the trans-relativistic object SN 2009bb even if it produces more modest magnetic field amplification can accelerate CRs up to 2-3 PeV within 20 d after the outburst.

On magnetic field amplification and particle acceleration near non-relativistic collisionless shocks: Particles in MHD Cells simulations

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 non-relativistic super-Alfénic shocks with various magnetic field obliquity. We recover all the features from previous studies when the magnetic field is parallel to the normal to the shock. In contrast with previous particle-in-cell and hybrid simulations, we find that particle acceleration and magnetic field amplification also occur when the magnetic field is oblique to the normal to the shock but on larger timescales than in the parallel case. We show that in our oblique shock simulations the streaming of supra-thermal particles induces a corrugation of the shock front. Such oscillations of both the shock front and the magnetic field then locally helps the particles to enter the upstream region and to initiate a non-resonant streaming instability and finally to induce diffuse particle acceleration.

On magnetic field amplification and particle acceleration near non-relativistic astrophysical shocks: particles in MHD cells simulations

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 non-relativistic shocks with various Alfvenic Mach numbers and magnetic field obliquity. We recover all the features of both magnetic field amplification and particle acceleration from previous studies when the magnetic field is parallel to the normal to the shock. In contrast with previous particle-in-cell-hybrid simulations, we find that particle acceleration and magnetic field amplification also occur when the magnetic field is oblique to the normal to the shock but on larger timescales than in the parallel case. We show that in our simulations, the supra-thermal particles are experiencing acceleration thanks to a pre-heating process of the particle similar to a shock drift acceleration leading to the corrugation of the shock front. Such oscillations of the shock front and the magnetic field locally help the particles to enter the upstream region and to initiate a non-resonant streaming instability and finally to induce diffuse particle acceleration.

Turbulence-induced magnetic fields in shock precursors

Galactic cosmic rays are believed to be mostly accelerated at supernova shocks. However, the interstellar magnetic field is too weak to efficiently accelerate galactic cosmic rays up to the highest energies, i.e. $10^{15}$ eV. A stronger magnetic field in the pre-shock region could provide the efficiency required. Bell's cosmic-ray nonresonant streaming instability has been claimed to be responsible for the amplification of precursor magnetic fields. However, an alternative mechanism has been proposed in which the cosmic-ray pressure gradient forms the shock precursor and drives turbulence, amplifying the magnetic field via the small-scale dynamo. A key ingredient for the mechanism to operate are the inhomogeneities present in the interstellar medium (ISM). These inhomogeneities are the consequence of turbulence. In this work we explore the magnetic field amplification in different ISM conditions through 3D MHD numerical simulations.

Role of the mean electric field in diffusive shock acceleration

Diffusive shock acceleration in the mean electric field produced during the development of Bell’s nonresonant streaming instability is considered. It is shown that the electric field lowers the efficiency of acceleration, for particles producing the instability (protons and nuclei) and raising the efficiency of acceleration for particles with the opposite electric charge (electrons). This effect is important for shock waves propagating with speeds above 10000 km s−1 in the interstellar medium or for slower shock waves propagating in a medium with weak magnetic field.

Non-resonant magnetohydrodynamics streaming instability near magnetized relativistic shocks

We present in this paper both a linear study and numerical relativistic magnetohydrodynamic (MHD) simulations of the non-resonant streaming instability occurring in the precursor of relativistic shocks. In the shock front rest frame, we perform a linear analysis of this instability in a likely configuration for ultra-relativistic shock precursors. This considers magneto-acoustic waves having a wave vector perpendicular to the shock front and the large-scale magnetic field. Our linear analysis is achieved without any assumption on the shock velocity and is thus valid for all velocity regimes. In order to check our calculation, we also perform relativistic MHD simulations describing the propagation of the aforementioned magneto-acoustic waves through the shock precursor. The numerical calculations confirm our linear analysis, which predicts that the growth rate of the instability is maximal for ultra-relativistic shocks and exhibits a wavenumber dependence ∝ kx1/2. Our numerical simulations also depict the saturation regime of the instability where we show that the magnetic amplification is moderate but nevertheless significant (δB/B ≤ 10). This latter fact may explain the presence of strong turbulence in the vicinity of relativistic magnetized shocks. Our numerical approach also introduces a convenient means to handle isothermal (ultra-)relativistic MHD conditions.

ENVIRONMENTAL LIMITS ON THE NONRESONANT COSMIC-RAY CURRENT-DRIVEN INSTABILITY

We investigate the so-called nonresonant cosmic-ray streaming instability, first discussed by Bell (2004). The extent to which thermal damping and ion-neutral collisions reduce the growth of this instability is calculated. Limits on the growth of the nonresonant mode in SN1006 and RX J1713.7-3946 are presented.

Diffusive Shock Acceleration with Magnetic Amplification by Nonresonant Streaming Instability in Supernova Remnants

We investigate the diffusive shock acceleration in the presence of the nonresonant streaming instability introduced by Bell. The numerical MHD simulations of the magnetic field amplification combined with the analytical treatment of cosmic-ray acceleration permit us to calculate the maximum energy of particles accelerated by high-velocity supernova shocks. The estimates for the Cas A, Kepler, SN 1006, and Tycho historical supernova remnants are given. We also found that the amplified magnetic field is preferentially oriented perpendicular to the shock front downstream of the fast shock. This explains the origin of the radial magnetic fields observed in young supernova remnants.

Modeling Bell’s Nonresonant Cosmic‐Ray Instability

We have studied the nonresonant streaming instability of charged energetic particles moving through a background plasma, discovered by Bell. We confirm his numerical results regarding a significant magnetic field amplification in the system. A detailed physical picture of the instability development and of the magnetic field evolution is given.