Session JM1: Mini-conference on Shock Acceleration in Space and Astrophysical Plasmas II

Shock acceleration and magnetic field amplification.

Recent developments, both theoretical and observational, indicate that high energy particles accelerated by a shock interact with the background plasma to amplify the magnetic field by an order of magnitude or more above its value far upstream. This new feature of shock acceleration resolves the long-standing difficulty that the galactic cosmic ray spectrum continues as an unbroken power law up to 10$^{15}$eV. It has been used to explain the narrow x-ray features seen at the outer shocks of supernova remnants. Magnetic field amplification is strongest for high velocity shocks propagating into relatively dense plasmas. This turns attention towards very young supernova remnants, gamma-ray bursts, jets and accretion systems. We consider scenarios for cosmic ray acceleration above 10$^{15}$eV within the galaxy and the possibility that cosmic rays might be important for the dynamics of relativistic jets.   

The Importance of Large-Scale Irregular Magnetic Fields in Particle Acceleration by Astrophysical Shocks.

Magnetic fields in space have an irregular, or turbulent, component that gives rise to spatial meandering and braiding of the lines of magnetic force. This large-scale structure has several important consequences that are relevant to our understanding of particle acceleration at astrophysical shocks, such as those associated with supernovae, the termination of the solar wind, and near the Sun. We will discuss recent numerical simulations which illustrate the basic physics. Particular attention is placed on the importance of the angle between the mean magnetic field and the shock normal. For the case of a parallel shock, acceleration of particles to very high energies (e.g. the knee in the cosmic-ray spectrum, or $>$GeV energy solar cosmic rays) requires very special conditions to explain the observations. These include a strong increase in the magnetic field, perhaps due to excitation from the streaming cosmic rays. In this talk, we show that no such special circumstances are required when one considers acceleration at nearly perpendicular shocks. We will also discuss the physics of the well-known injection problem, and suggest that, in actuality, there is no such problem.   

Global Signatures of Ion Acceleration near the Quasi-Parallel Bow Shock

The Earth's bow shock is one of the most interested and studied collisionless shocks in space. It is believed that the scattering of field-aligned ion beams between upstream and downstream waves of the quasi-parallel shock leads to the acceleration of solar wind ions, via Fermi mechanism, and the diffuse ion distribution. In this study, we investigate the self-consistent ion energization and global ion signatures around the quasi-parallel bow shock using 3-D global hybrid simulations. First, transverse ion beam whistler waves and compressional waves are constantly present in the foreshock. The wave spectra show different characteristics at various distances from the bow shock. Second, the bow shock and foreshock ions possess a diffuse ion distribution with a non-thermal spectral break at energy $\sim 15$-$30KeV$ for cases with $M_A =5$-9, and the differential ion flux evolves with the field-aligned distance to the shock by an e-folding distance of 3-$9\ R_E$ at various energy channels. Third, the diffuse ion distribution with energetic ions up to $\sim 10^2 KeV$ is also present in the broad region of the downstream magnetosheath. Finally, for the case in which the IMF geometry leads to a high-latitude magnetic reconnection, the coupling between the bow shock and the magnetospheric cusp in the particle signatures is examined. The bow shock is found to be a major source of the cusp energetic ions. In general, simulation results are in good agreement with satellite observations.   

Electron acceleration in relativistic GRB shocks

The shock model of gamma-ray bursts (GRBs) contains two equipartition parameters: the magnetic energy density and the kinetic energy density of the electrons relatve to the total energy density of the shock, $\epsilon_B$ and $\epsilon_e$, respectively. These are free parameters within the model. Whereas the Weibel shock theory and numerical simulations fix $\epsilon_B$ at the level of $\sim$few$\times(10^{-3}...10^{-4}) $, no understanding of $\epsilon_e$ exists so far. Here we demonstrate that it inevitably follows from the Weibel shock theory that $\epsilon_e\simeq\sqrt{\epsilon_B}$. The GRB afteglow data fully agree with this theoretical prediction. Our result explains why the electrons are close to equipartition in GRBs. The $\epsilon_e-\epsilon_B$ relation can be used to reduce the number of free parameters in afterglow models.   

Nonthermal Acceleration in Relativistic Collisionless Shocks

Modeling of nonthermal emission from relativistic outflows in astrophysics commonly leads to the conclusion that relativistic collisionless shocks accelerate nonthermal particles. Yet, such acceleration has not been detected so far in self-consistent particle-in-cell simulations of collisionless shocks, raising questions about both the underlying mechanism and the applicability of such simulations. We present here the first evidence of nonthermal acceleration in unmagnetized relativistic shocks in pair plasma found in a long-term large-scale particle-in-cell simulation. Accelerated particles appear as a distinct power-law tail on top of the thermal downstream distribution. The particles are accelerated in the self-generated magnetic turbulence of the Weibel instability that mediates unmagnetized shocks. By tracing particle orbits we find that particles gain most energy when they bounce between the upstream and downstream regions surrounding the shock transition, implying Fermi-I type of acceleration. By contrast, magnetized pair shocks (mediated by coherent magnetic reflections of particles rather than Weibel instability) do not show nonthermal acceleration in the relativistic limit due to insufficient downstream turbulence. These simulations place constraints on the magnetization of astrophysical pair plasmas that can produce nonthermal radiation. Extensions to electron-ion plasmas will also be discussed.   

Particle Acceleration and Radiation in Relativistic Collisionless Shocks

We summarize PIC simulation results of particle acceleration and radiation mechanisms in both strongly magnetized and unmagnetized relativistic collisionless shocks, using advanced 2-and-3D PIC codes including radiation and radiation damping. We demonstrate the critical roles played by macroscopic electromagnetic fields in both acceleration and radiation processes, by varying the amplitude and direction of the comoving magnetic field in both upstream and downstream plasmas. We also study the effects of varying the Lorentz factor, density contrast, plasma temperature and electron:ion mass ratio. In the weak-field (Alfven speed $<<$ c) limit, particles are accelerated diffusively by Weibel-instability-generated magnetic turbulence, nonlinear plasma oscillations and longitudinal electric fields caused by charge separation. In the ultrastrong field (electron Alfven speed $>>$ c) limit, electrons are accelerated mainly by the ponderomotive (\textbf{jxB}) force while ions are accelerated by charge separation electric fields. In the latter case we find the formation of well-defined power-law but highly anisotropic momentum spectra. The radiation mechanisms are also distinct in the different regimes. We will present the results of radiation power output, spectra and polarization.   

A new mechanism for relativistic particle acceleration via wave-particle interaction

Often in laboratory, space and astrophysical plasma, high energy populations are observed. Two puzzling factors still defy our understanding. First, such populations of high energy particles produce power law distributions that are not only ubiquitous but also persistent in time. Such persistence is in direct contradiction to the H theorem that states the ineluctable transition of physical systems towards thermodynamic equilibrium, and ergo Maxwellian distributions. Second, such high energy populations are efficiently produced, much more efficiently than processes that we know can produce. A classic example of such a situation is cosmic rays where power alws extend up to tremendolus energy ranges. In the present work, we identify a new mechanism for particle acceleration via wave-particle interaction. The mechanism is peculiar to special relativity and has no classical equivalent. That explains why it is not observed in most simulation studies of plasma processes, based on classical physics. The mechanism is likely to be active in systems undergoing streaming instabilities and in particular shocked systems. The new mechanism can produce energy increases vastly superior to previously known mechanisms (such as Fermi acceleration) and can hold the promise of explaining at least some of the observed power laws.   

Ubiquitous Suprathermal Power Law Tails with Spectral Index -5

There is a great commonality in the spectra of low-energy (less than about a few MeV/nucleon) particles and suprathermal tails of the solar wind and pickup ions. When expressed as distribution functions in velocity space, all these spectra are power laws with a specific and common spectral index of –5. This is the case for all particle species examined so far and in all regions of the heliosphere explored up to now. Voyager 1 has been observing such spectra throughout the heliosheath it traversed and found -5 spectra in the low-energy particles accelerated at termination shock. These –5 spectra prevail during the most quiet times in the solar wind, far away from shocks, as well as in the regions downstream of shocks. The –5 spectra share some remarkable features. For example, it can be shown that such a spectral index is to be expected if the tails are formed by stochastic acceleration due to compressional turbulence in the solar wind (in which the particles are accelerated by and do an equal amount of work on the turbulence) and a cascade in energy, analogous to turbulent (Kolmogorov) cascades. Here we concentrate on observation evidence for the common spectral shapes.   

A Common Spectral Shape for Particles Accelerated in Turbulence and at Shocks

One of the more significant observations in heliospheric physics in recent years has been the ubiquitous suprathermal tails, which appear to have the same spectral index of -5, when expressed as a distribution function. Moreover, this same spectral shape occurs for particles accelerated at the termination shock of the solar wind. A theory is presented for why this unique spectral shape occurs and the implications of this result are discussed for particle acceleration in turbulence and at shocks. It is argued that the particles are stochastically accelerated in compressional turbulence, and that an equilibrium is established when the particles receive energy from and do an equal amount of work on the turbulence. The suprathermal tails are formed by a process analogous to turbulent cascades.