J. G. Kirk

Max Planck Institute for Nuclear Physics · Theoretical Astrophysics

We study the acceleration of charged particles by ultra-relativistic shocks using test-particle Monte-Carlo simulations. Two field configurations are considered: (i) shocks with uniform upstream magnetic field in the plane of the shock, and (ii) shocks in which the upstream magnetic field has a cylindrical geometry. Particles are assumed to diffuse...

We study the acceleration of charged particles by ultra-relativistic shocks using test-particle Monte-Carlo simulations. Two field configurations are considered: (i) shocks with uniform upstream magnetic field in the plane of the shock, and (ii) shocks in which the upstream magnetic field has a cylindrical geometry. Particles are assumed to diffuse...

Using an eigenfunction expansion to solve the transport equation, complemented by Monte-Carlo simulations, we show that ultrarelativistic shocks can be effective particle accelerators even when they fail to produce large amplitude turbulence in the downstream plasma. This finding contradicts the widely held belief that a uniform downstream magnetic...

Using an eigenfunction expansion to solve the transport equation, complemented by Monte-Carlo simulations, we show that ultrarelativistic shocks can be effective particle accelerators even when they fail to produce large amplitude turbulence in the downstream plasma. This finding contradicts the widely held belief that a uniform downstream magnetic...

Motivated by the detection of very-high-energy (VHE) gamma rays deep in the afterglow emission of a gamma-ray burst (GRB), we revisit predictions of the maximum energy to which electrons can be accelerated at a relativistic blast wave. Acceleration at the weakly magnetized forward shock of a blast wave can be limited by either the rapid damping of...

Motivated by the detection of very high energy gamma-rays deep in the afterglow emission of a gamma-ray burst, we revisit predictions of the maximum energy to which electrons can be accelerated at a relativistic blast wave. Acceleration at the weakly-magnetized forward shock of a blast-wave can be limited either by the rapid damping of turbulence g...

Two-fluid (electron–positron) plasma modeling has shown that inductive acceleration can convert Poynting flux directly into bulk kinetic energy in the relativistic flows driven by rotating magnetized neutron stars and black holes. Here, we generalize this approach by adding an ion fluid. Solutions are presented in which all particles are accelerate...

We study electron and positron acceleration at the termination shock of a striped pulsar wind. Drift motion along the shock surface keeps either electrons or positrons -but not both, close to the equatorial plane of the pulsar, where they are accelerated by the first-order Fermi process. Their energy spectrum is a power law, and both the X-ray flux...

Two-fluid (electron-positron) plasma modelling has shown that inductive acceleration can convert Poynting flux directly into bulk kinetic energy in the relativistic flows driven by rotating magnetized neutron stars and black holes. Here, we generalize this approach by adding an ion fluid. Solutions are presented in which all particles are accelerat...

We calculate the shape of the large-scale anisotropy of TeV–PeV cosmic-rays (CR) in different models of the interstellar turbulence. In general, the large-scale CR anisotropy (CRA) is not a dipole, and its shape can be used as a new probe of the turbulence. The 400 TeV and 2 PeV data sets of IceTop can be fitted with Goldreich-Sridhar turbulence an...

We calculate the shape of the large-scale anisotropy of TeV-PeV cosmic-rays (CR) in different models of the interstellar turbulence. In general, the large-scale CR anisotropy (CRA) is not a dipole, and its shape can be used as a new probe of the turbulence. The 400 TeV and 2 PeV data sets of IceTop can be fitted with Goldreich-Sridhar turbulence an...

We study particle acceleration at the termination shock of a striped pulsar wind by integrating trajectories in a prescribed model of the magnetic field and flow pattern. Drift motion on the shock surface maintains either electrons or positrons on "Speiser" orbits in a ring-shaped region close to the equatorial plane of the pulsar, enabling them to...

The ~400 MeV flaring emission from the Crab Nebula is naturally explained as the result of an abrupt reduction in the mass-loading of the pulsar wind. Very few particles are then available to carry the current required to maintain wave activity, causing them to achieve high Lorentz factors. When they penetrate the Nebula, a tightly beamed, high lum...

We show that the mysterious, rapidly variable emission at ~400 MeV observed from the Crab Nebula by the AGILE and Fermi experiments could be the result of a sudden drop in the mass-loading of the pulsar wind. The current required to maintain wave activity in the wind is then carried by very few particles of high Lorentz factor. On impacting the Neb...

The theory of diffusive acceleration at shock fronts, which applies only if the fluid speed is nonrelativistic , yields a simple formula for the power-law index s of accelerated particles: s = 3 r /( r – 1), where r is the compression ratio of the shock front. Although the acceleration process depends on there being effective pitch-angle scattering...

We study the role of local interstellar turbulence in shaping the large-scale anisotropy in the arrival directions of TeV-PeV cosmic-rays (CRs) on the sky. Assuming pitch-angle diffusion of CRs in a magnetic flux tube containing the Earth, we compute the CR anisotropy for Goldreich-Sridhar turbulence, and for isotropic fast modes. The narrow defici...

Electrons in plasmas produced by next-generation ultraintense lasers (I>5×1022W/cm2) can be spin polarized to a high degree (10%–70%) by the laser pulses on a femtosecond time scale. This is due to electrons undergoing spin-flip transitions as they radiate γ-ray photons, preferentially spin polarizing in one direction. Spin polarization can modify...

We investigate the effects on electron acceleration of an electromagnetically modified termination shock (TS) in pulsar wind nebulae (PWNe). The physics of the magnetized pulsar wind is simulated in a two-fluid code with a magnetic shear wave which converts in superluminal waves when the plasma density is below a certain threshold. This condition c...

We study the acceleration of electrons and positrons at an electromagnetically modified, ultra-relativistic shock in the context of pulsar wind nebulae (PWNe). We simulate the outflow produced by an obliquely rotating pulsar in proximity of its termination shock with a two-fluid code which uses a magnetic shear wave to mimic the properties of the w...

We calculate the large-scale cosmic-ray (CR) anisotropies predicted for a range of Goldreich-Sridhar (GS) and isotropic models of interstellar turbulence, and compare them with IceTop data. In general, the predicted CR anisotropy is not a pure dipole; the cold spots reported at 400 TeV and 2 PeV are consistent with a GS model that contains a smooth...

The dynamics of electrons in counter-propagating, circularly polarized laser beams are shown to exhibit attractors whose ability to trap particles depends on the ratio of the beam intensities and a single parameter describing radiation reaction. Analytical expressions are found for the underlying limit cycles and the parameter range in which they a...

Abstract. ELI-NP facility will enable for the first time the use of two 10 PW laser beams for quantum electrodynamics (QED) experiments. The first beam will accelerate electrons to relativistic energies. The second beam will subject relativistic electrons to the strong electromagnetic field generating QED processes: intense gamma ray radiation...

Perpendicular shocks are shown to be rapid particle accelerators that perform optimally when the ratio $u_{\rm s}$ of the shock speed to the particle speed roughly equals the ratio $1/\eta$ of the scattering rate to the gyro frequency. We use analytical methods and Monte-Carlo simulations to solve the kinetic equation that governs the anisotropy ge...

Strong waves can mediate a shock transition between a pulsar wind and its surroundings, playing the role of an extended precursor, in which the energy is effectively transferred from fields to non-thermal particles. The damping of such precursors results in an essentially unmagnetized shock near the equator. In this context, we discuss the stabilit...

It is possible using current high intensity laser facilities to reach the quantum radiation reaction regime for energetic electrons. An experiment using a wakefield accelerator to drive GeV electrons into a counterpropagating laser pulse would demonstrate the increase in the yield of high energy photons caused by the stochastic nature of quantum sy...

SNR 1987A is the expanding remnant from the brightest supernova since the invention of the telescope. The remnant has been monitored extensively in the radio at variety of wavelengths and provides a wealth of data on which to base a simulation. Questions to be answered include estimating the efficiency of particle acceleration at shock fronts, dete...

In high-intensity (> 10^21W/cm^2) laser-matter interactions gamma-ray photon emission by the electrons can strongly aff?ect the electron's dynamics and copious numbers of electron-positron pairs can be produced by the emitted photons. We show how these processes can be included in simulations by coupling a Monte-Carlo algorithm describing the emiss...

Measurements of the production of the weakly decaying charmed hadrons: D 0 , D + , D + s and + c in both Z 0 ! c c and Z 0 ! b b events are reported. By summing the partial contributions from each of these states we measure the partial width for Z 0 decays into a c c pair as: c c had = 0 : 167 0:011(stat) 0:011(sys) 0:005(br) where the errors are s...

A search for charginos and neutralinos, predicted by supersymmetric theories, has been performed using a data sample of 10.3 pb^-1 at centre-of-mass energies of sqrt(s) = 170 and 172 GeV with the OPAL detector at LEP. No evidence for these particles has been found. The results are combined with those from previous OPAL chargino and neutralino searc...

We have searched for unstable neutral and charged heavy leptons, N and L^+/-, and for excited states of neutral and charged leptons, nu*, e*, mu* and tau*, in e^+e^- collisions at centre-of-mass energies of 170 and 172 GeV using the OPAL detector at LEP. No evidence for their existence was found. From the analysis of charged-current decays of pair-...

We analyse the damping by radiation reaction and by Compton drag of strong, superluminal electromagnetic waves in the context of pulsar winds. The associated radiation signature is found by estimating the efficiency and the characteristic radiation frequencies. Applying these estimates to the gamma-ray binary containing PSR B1259-63, we show that t...

Pulses from a 10 PW laser are predicted to produce large numbers of gamma-rays and electron-positron pairs on hitting a solid target. However, a pair plasma, if it accumulates in front of the target, may partially shield it from the pulse. Using stationary, one-dimensional solutions of the two-fluid (electron-positron) and Maxwell equations, includ...

Electron-positron plasmas are a prominent feature of the high energy Universe. In the relativistic winds from pulsars and black holes it is thought that non-linear quantum electrodynamics (QED) processes cause electromagnetic energy to cascade into an e-e+ plasma. We show that next-generation 10PW lasers, available in the next few years, will gener...

In simulations of a 12.5PW laser (focused intensity I = 4x10^23W/cm^2) striking a solid aluminium target 10% of the laser energy is converted to gamma-rays. A dense electron-positron plasma is generated with a maximum density of 10^26/m^3; seven orders of magnitude denser than pure e-e+ plasmas generated with 1PW lasers. When the laser power is inc...

Nonlinear electromagnetic waves with superluminal phase velocity can propagate in the winds around isolated pulsars, and around some pulsars in binary systems. Using a short-wavelength approximation, we find and analyze an integrable system of equations that govern their evolution in spherical geometry. A confined mode is identified that stagnates...

The dynamics of a standing shock front in a Poynting-flux dominated relativistic flow is investigated by using a one-dimensional, relativistic, two-fluid simulation. An upstream flow containing a circularly polarized, sinusoidal magnetic shear wave is considered, mimicking a wave driven by an obliquely rotating pulsar. It is demonstrated that this...

Pulsar winds, containing charged particles, waves and a net (phase-averaged) magnetic field, are thought to fuel the high-energy emission from several gamma-ray binaries. They terminate where the ram pressure matches that of the surroundings - which, in binaries, is provided by the wind of the companion. Before termination, pulsed emission can be p...

A novel absorption mechanism for linearly polarized lasers propagating in relativistically underdense solids in the ultrarelativistic (a∼100) regime is presented. The mechanism is based on strong synchrotron emission from electrons reinjected into the laser by the space charge field they generate at the front of the laser pulse. This laser absorpti...

Unpulsed, high-energy emission from pulsar binaries can be attributed to the interaction of a pulsar wind with that of a companion star. At the shock between the outflows, particles carried away from the pulsar magnetosphere are accelerated and radiate both in synchrotron and inverse Compton processes. This emission constitutes a significant fracti...

The termination shock of a pulsar wind is located roughly where the ram pressure matches that of the surrounding medium. Downstream of the shock, MHD models of the diffuse nebular emission suggest the plasma is weakly magnetized. However, the transition from a Poynting-dominated MHD wind to a particle-dominated flow is not well understood. We discu...

In simulations of a 10 PW laser striking a solid, we demonstrate the possibility of producing a pure electron-positron plasma by the same processes as those thought to operate in high-energy astrophysical environments. A maximum positron density of 10(26) m(-3) can be achieved, 7 orders of magnitude greater than achieved in previous experiments. Ad...

In simulations of a 10PW laser striking a solid we demonstrate the possibility of producing a pure electron-positron plasma by the same processes as those thought to operate in high-energy astrophysical environments. A maximum positron density of 10^26/m^3 is achieved, seven orders of magnitude greater than achieved in previous experiments. Additio...

Pulsar winds are the ideal environment for the study of non-linear electromagnetic waves. It is generally thought that a pulsar launches a striped wind, a magnetohydrodynamic entropy wave, where plasma sheets carried along with the flow separate regions of alternating magnetic field. But when the density drops below a critical value, or equivalentl...

To date, seven gamma-ray pulsars are known, showing pulsed emission up to tens of GeV and associated light-curves with a double-pulse structure. We study this pulsed high-energy emission in the framework of the striped wind model. By numerical integration of the time-dependent emissivity in the current sheets, we compute the phase-dependent spectra...

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.

Recent work on the properties of superluminal waves in pulsar winds is summarized. It is speculated that these waves play an important role in the termination shock that divides the wind from the surrounding nebula.

The energy lost by a rotation-powered pulsar is carried by a relativistic flow containing a mixture of electromagnetic fields and particles. In the inner regions, this is thought to be a magnetically dominated, cold, electron-positron wind that is well described by the MHD equations. However, beyond a critical radius r cr, the same particle, energy...

High-energy emission from blazars is thought to arise in a relativistic jet launched by a supermassive black hole. The rapid variability of the emission suggests that structure of length scale smaller than the gravitational radius of the central black hole is imprinted on the jet as it is launched, and modulates the radiation released after it has...

High energy emission from blazars is thought to arise in a relativistic jet launched by a supermassive black hole. The emission site must be far from the hole and the jet relativistic, in order to avoid absorption of the photons. In extreme cases, rapid variability of the emission suggests that structures of length-scale smaller than the gravitatio...

Gamma-ray and electron-positron pair production will figure prominently in laser-plasma experiments with next generation lasers. Using a Monte Carlo approach we show that straggling effects arising from the finite recoil an electron experiences when it emits a high energy photon, increase the number of pairs produced on further interaction with the...

Particle-in-cell (PIC) simulations of relativistic shocks are in principle capable of predicting the spectra of photons that are radiated incoherently by the accelerated particles. The most direct method evaluates the spectrum using the fields given by the Lienard-Wiechart potentials. However, for relativistic particles this procedure is computatio...

The radio, optical, X-ray and gamma-ray nebulae that surround many pulsars are thought to arise from synchrotron and inverse Compton emission. The energy powering this emission, as well as the magnetic fields and relativistic particles, are supplied by a "wind" driven by the central object. The inner parts of the wind can be described using the equ...

Linear acceleration emission occurs when a charged particle is accelerated parallel to its velocity. We evaluate the spectral and angular distribution of this radiation for several special cases, including constant acceleration (hyperbolic motion) of finite duration. Based on these results, we find the following general properties of the emission f...

Particle-in-cell simulations of relativistic, weakly magnetized collisionless shocks show that particles can gain energy by repeatedly crossing the shock front. This requires scattering off self-generated small length-scale magnetic fluctuations. The radiative signature of this first-order Fermi acceleration mechanism is important for models of bot...

The first-order Fermi process at relativistic shocks requires the generation of strong turbulence in the vicinity of the shock front. Recent particle in cell simulations have demonstrated that this mechanism can be studied self-consistently at weakly magnetised shocks. The radiative signature of this first-order Fermi acceleration mechanism is impo...

Based on an analysis of a specific electron trajectory in counter-propagating beams, Bell and Kirk (2008 Phys. Rev. Lett. 101 200403) recently suggested that laboratory lasers may shortly be able to produce significant numbers of electron–positron pairs. We confirm their results using an improved treatment of non-linear Compton scattering in the la...

In supernova remnants, the nonlinear amplification of magnetic fields upstream of collisionless shocks is essential for the acceleration of cosmic rays to the energy of the "knee" at 1015.5 eV. A nonresonant instability driven by the cosmic ray current is thought to be responsible for this effect. We perform two-dimensional, particle-in-cell simula...

The theory of pulsar winds and the nebulae they energize is currently celebrating its golden jubilee. Ten years before the discovery of pulsars it was already apparent that the magnetic field and relativistic particles that produce the radiation of the Crab Nebula must have their origin in a central stellar object [104]. Today, about 50 similarly p...

The theory of pulsar winds and the nebulae they energize is currently celebrating its golden jubilee. Ten years before the discovery of pulsars it was already apparent that the magnetic field and relativistic particles that produce the radiation of the Crab Nebula must have their origin in a central stellar object [104]. Today, about 50 similarly p...

Stationary solutions to the equations of non‐linear diffusive shock acceleration play a fundamental role in the theory of cosmic‐ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to escape from the system. Because the scattering mean‐free‐path is thought to be an increasing function of energy...

Stationary solutions to the equations of non-linear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to escape from the system. Because the scattering mean-free-path is thought to be an increasing function of energy...

We discuss the results of modeling the TeV γ-ray spectra of two active galactic nuclei, Mrk 501 and Mrk 421, that have almost the same redshifts: z = 0.031 and 0.034, respectively. The effect of intergalactic γ-ray absorption is treated as an uncertainty in the measurement of the intrinsic spectrum. Although the objects differ, we obtain satisfacto...

Prolific electron-positron pair production is possible at laser intensities approaching 10;{24} W cm;{-2} at a wavelength of 1 mum. An analysis of electron trajectories and interactions at the nodes (B=0) of two counterpropagating, circularly polarized laser beams shows that a cascade of gamma rays and pairs develops. The geometry is generalized qu...

We examine the problem of particle acceleration at a relativistic shocks assuming pitch-angle scattering and using a Hartree-Fock method to approximate the associated eigenfunctions. This leads to a simple transcendental equation determining the power-law index, $s$, given the up and downstream velocities. We compare our results with accurate numer...

Using recent polarimetric observations of the Crab Nebula in the hard X-ray band by INTEGRAL, we show that the absence of vacuum birefringence effects constrains O(E/M) Lorentz violation in QED to the level |\xi| < 9x10^{-10} at three sigma CL, tightening by more than three orders of magnitude previous constraints. We show that planned X-ray polari...

We re-examine the maximum brightness temperature that a synchrotron source can sustain by adapting standard synchrotron theory to an electron distribution that exhibits a deficit at low energy. The absence of low energy electrons reduces the absorption of synchrotron photons, allowing the source to reach a higher brightness temperature without the...

The process of diffusive shock acceleration relies on the efficacy with which hydromagnetic waves can scatter charged particles in the precursor of a shock. The growth of self-generated waves is driven by both resonant and non-resonant processes. We perform high-resolution magnetohydrodynamic simulations of the non-resonant cosmic ray driven instab...

Recent observations of the polarization of the optical pulses from the Crab pulsar motivated detailed comparative studies of the emission predicted by the polar cap, the outer gap and the two‐pole caustics models. In this work, we study the polarization properties of the synchrotron emission emanating from the striped wind model. We use an explici...

This Conference is the fifth of a series of Workshops on High Energy Gamma- ray Experiments, following the Conferences held in Perugia 2003, Bari 2004, Cividale del Friuli 2005, Elba Island 2006. This year the focus was on the use of gamma-ray to study the Dark Matter component of the Universe, the origin and propagation of Cosmic Rays, Extra Large...

First order Fermi acceleration at the outer shocks of supernova remnants can be a very efficient process. The pressure of the cosmic rays may have a significant effect on the fluid properties of the upstream plasma, creating an extended shock precursor. It has been suggested by Bell (2004) that cosmic rays in the precursor will also have a strong i...

The process of first order Fermi acceleration in supernova remnant shocks has long been the favoured mechanism for producing cosmic rays in our galaxy. One of the major difficulties with this picture however is that it must be pushed to its limits to even approach the so-called knee of the cosmic-ray spectrum, below which most particles are believe...

Rapid inverse Compton cooling sets in when the brightness temperature (T_B) of a self-absorbed synchrotron source with power-law electrons reaches ~10^{12} K. However, T_B inferred from observations of intra-day variable sources (IDV) are well above the "Compton catastrophe" limit. This can be understood if the underlying electron distribution cuts...

We present an algorithm for solving the linear dispersion relation in an inhomogeneous, magnetised, relativistic plasma. The method is a generalisation of a previously reported algorithm that was limited to the homogeneous case. The extension involves projecting the spatial dependence of the perturbations onto a set of basis functions that satisfy...

We set constraints on O(E/M) Lorentz Violation in QED in an effective field theory framework. A major consequence of such assumptions is the modification of the dispersion relations for electrons/positrons and photons, which in turn can affect the electromagnetic output of astrophysical objects. We compare the information provided by multiwavelengt...

(abridged) Models of many astrophysical gamma-ray sources assume they contain a homogeneous distribution of electrons that are injected as a power-law in energy and evolve by interacting with radiation fields, magnetic fields and particles in the source and by escaping. This problem is particularly complicated if the radiation fields have higher en...

We investigate the growth of hydromagnetic waves driven by streaming cosmic rays in the precursor environment of a supernova remnant shock. It is known that transverse waves propagating parallel to the mean magnetic field are unstable to anisotropies in the cosmic ray distribution, and may provide a mechanism to substantially amplify the ambient ma...

We review current theoretical ideas on pulsar winds and their surrounding nebulae. Relativistic MHD models of the wind of the aligned rotator, and of the striped wind, together with models of magnetic dissipation are discussed. It is shown that the observational signature of this dissipation is likely to be point-like, rather than extended, and tha...

Recent observations of the polarisation of the optical pulses from the Crab pulsar motivated detailed comparative studies of the emission predicted by the polar cap, the outer gap and the two-pole caustics models. In this work, we study the polarisation properties of the synchrotron emission emanating from the striped wind model. We use an explicit...

We investigate a magnetized plasma in which injected high energy gamma-rays annihilate on a soft photon field, that is provided by the synchrotron radiation of the created pairs. For a very wide range of magnetic fields, this process involves gamma-rays between 0.3 GeV and 30 TeV. We derive a simple dynamical system for this process, analyze its st...

We describe an algorithm that computes the linear dispersion relation of waves and instabilities in relativistic plasmas within a Vlasov-Maxwell description. The method used is fully relativistic and involves explicit integration of particle orbits along the unperturbed equilibrium trajectories. We check the algorithm against the dispersion curves...

We re-examined the brightness temperature (T B) prob-lem posed by rapidly varying blazars, known as intra-day variables (IDV's), such as S5 0716 + 714, which often display T B > 10 12 K, far exceed the limit imposed by inverse Compton cooling. Several of such IDV's have also shown a high degree of circular polarisation (CP) of the order of ∼ 1%, mu...

We set constraints on O(E/M) Lorentz Violation in QED in an effective field theory framework. One major consequence of such assumptions is the modification of the dispersion relations for electrons/positrons and photons, which in turn can affect the electromagnetic output of astrophysical objects. We consider the information provided by multiwavele...

The occurrence of the inverse Compton catastrophe when the synchrotron brightness temperature exceeds a threshold value, usually estimated to be 10^{12} K, appears to be in contradiction with observation because: (i) the threshold is substantially exceeded by several intra-day variable radio sources, but the inverse Compton emission is not observed...

Recently, Bell has reanalysed the problem of wave excitation by cosmic rays propagating in the pre-cursor region of a supernova remnant shock front. He pointed out a strong, non-resonant, current-driven instability that had been overlooked in the kinetic treatments, and suggested that it is responsible for substantial amplification of the ambient m...

In the kinetic theory of plasmas, particles are described by distribution functions whose evolution is determined by kinetic equations. The spectrum of fluctuations in the plasma includes distributions of weakly damped waves. The kinetic equation for the particles may be averaged over these fluctuations to find averaged kinetic equations, sometimes...

Many fundamental processes in the universe are determined by the magnetic field. The object in which we can study such processes in greatest detail is the Sun, and so it will be natural in this course of lectures to focus on the Sun. In the first lecture I aim to introduce you to it and then in the second to set up the basic theory for magnetic fie...

Results of a theoretical investigation indicate that the energetic electrons seen in hot spots could be produced by first-order Fermi acceleration at shock fronts. Results are presented for two types of pitch-angle scattering derived for different values of the spectrum of Alfven wave turbulence in the quasi-linear theory of plasma physics. The met...

I will review the status of theory of the first order Fermi accelerationmechanism at relativistic shocks. Recent Monte-Carlo simulations thatchallenge the results of the simple kinematicapproach will be discussed. These raise deeper questions concerning thenature of the transport process in the magnetic fields generated by shockfronts.