John G. Kirk

Particle acceleration by ultrarelativistic shocks: theory and simulations

We consider the acceleration of charged particles near ultrarelativistic shocks, with Lorentz factor . We present simulations of the acceleration process and compare these with results from semi-analytical calculations. We show that the spectrum that results from acceleration near ultrarelativistic shocks is a power law, , with a nearly universal value for the slope of this power law. We confirm that the ultrarelativistic equivalent of the Fermi acceleration at a shock differs from its non-relativistic counterpart by the occurrence of large anisotropies in the distribution of the accelerated particles near the shock. In the rest frame of the upstream fluid, particles can only outrun the shock when their direction of motion lies within a small loss cone of opening angle around the shock normal. We also show that all physically plausible deflection or scattering mechanisms can change the upstream flight direction of relativistic particles originating from downstream by only a small amount: . This limits the energy change per shock crossing cycle to , except for the first cycle where particles originate upstream. In that case the upstream energy is boosted by a factor for those particles that are scattered back across the shock into the upstream region.

Reconnection in a striped pulsar wind

It is generally thought that most of the spin-down power of a pulsar is carried away in an MHD wind dominated by Poynting flux. In the case of an oblique rotator, a significant part of this energy can be considered to be in a low-frequency wave, consisting of stripes of a toroidal magnetic field of alternating polarity propagating in a region around the equatorial plane. Magnetic reconnection in such a structure has been proposed as a mechanism for transforming the Poynting flux into particle energy in the pulsar wind. We have reexamined this process and conclude that the wind accelerates significantly in the course of reconnection. This dilates the timescale over which the reconnection process operates so that the wind requires a much larger distance than was previously thought in order to convert the Poynting flux to particle flux. In the case of the Crab pulsar, the wind is still Poynting-dominated at the radius at which a standing shock is inferred from observation. An estimate of the radius of the termination shock for other pulsars implies that all except the millisecond pulsars have Poynting flux-dominated winds all the way out to the shock front.

Particle Acceleration at Ultrarelativistic Shocks: An Eigenfunction Method

We extend the eigenfunction method of computing the power-law spectrum of particles accelerated at a relativistic shock front to apply to shocks of arbitrarily high Lorentz factor. In agreement with the findings of Monte Carlo simulations, we find that the index of the power-law distribution of accelerated particles, which undergo isotropic diffusion in angle at an ultrarelativistic, unmagnetized shock, is s = 4.23 ± 0.01 (where s = -d ln f/d ln p with f the Lorentz invariant phase-space density and p the momentum). This corresponds to a synchrotron index for uncooled electrons of α = 0.62 (taking cooling into account α = 1.12), where α = -d ln Fνα/d ln α, Fν is the radiation flux, and ν is the frequency. We also present an approximate analytic expression for the angular distribution of accelerated particles, which displays the effect of particle trapping by the shock: compared with the nonrelativistic case the angular distribution is weighted more toward the plane of the shock and away from its normal. We investigate the sensitivity of our results to the transport properties of the particles and the presence of a magnetic field. Shocks in which the parameter σ (the ratio of Poynting to kinetic energy flux) upstream is not small are less compressive and lead to larger values of s.

Possibility of Prolific Pair Production with High-Power Lasers

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 qualitatively to linear polarization and laser beams incident on a solid target.

Shock-drift particle acceleration in superluminal shocks - A model for hot spots in extragalactic radio sources

Shock-drift acceleration at relativistic shock fronts is investigated using a fully relativistic treatment of both the microphysics of the shock-drift acceleration and the macrophysics of the shock front. By explicitly tracing particle trajectories across shocks, it is shown how the adiabatic invariance of a particles magnetic moment breaks down as the upstream shock speed becomes relativistic, and is recovered at subrelativistic velocities. These calculations enable the mean increase in energy of a particle which encounters the shock with a given pitch angle to be calculated. The results are used to construct the downstream electron distribution function in terms of the incident distribution function and the bulk properties of the shock. The synchrotron emissivity of the transmitted distribution is calculated, and it is demonstrated that amplification factors are easily obtained which are more than adequate to explain the observed constrasts in surface brightness between jets and hot spots. 72 refs.

External Compton emission from relativistic jets in Galactic black hole candidates and ultraluminous X-ray sources

Galactic binary systems that contain a black hole candidate show evidence of radio jets in their hard X-ray states. Unavoidably, photons from the companion star and/or the accretion disk are Compton-scattered by relativistic electrons in the jet, producing beamed X-rays and possibly gamma-rays. The importance of this process depends on the jet power and the Doppler boosting factor. For plausible values of these parameters, we show that the jet emission can contribute significantly to the hard state X-ray luminosity. Two sources - XTE J1118+480 and Cygnus X-1 - are modelled as representatives of black holes with low and high luminosity companion stars respectively. In XTE J1118+480, weak reflection features indicate that the jet emission is comparable to coronal emission. In Cygnus X-1, strong reflection features indicate coronal emission in the X-ray band, but the jet emission may emerge in the gamma-ray band. The absence of reflection features in the spectra of the ultraluminous compact X-ray sources in nearby galaxies suggests that they are dominated by jet emission. We show that a viable model for these sources is a stellar mass black hole with a high luminosity companion and a favourably oriented jet.

Modeling the TeV Gamma-Ray Spectra of Two Low-Redshift Active Galactic Nuclei: Markarian 501 and Markarian 421

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 satisfactory fits for both of them in a synchrotron self-Compton scenario. Compared to previous models, our fits are characterized by higher values of the Doppler factor (δ ≥ 50) and an electron injection spectrum extending to higher energies (γmax ≥ 1.5 × 105). In the case of Mrk 421, the observed difference in spectral slope in X-rays and TeV γ-rays between the high and low states can be explained as a variation of a single parameter—the maximum energy γmaxmc2 at which electrons are injected.

Pair production in counter-propagating laser beams

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 laser beams. Implementing an algorithm that integrates classical electron trajectories, we then examine a wide range of laser pulse shapes and polarizations. We find that counter-propagating, linearly polarized beams, with either aligned or crossed orientation, are likely to initiate a pair avalanche at intensities of approximately 1024 W cm−2 per beam. The same result is found by modelling one of the beams as a wave reflected at the surface of an overdense solid.

Modelling gamma-ray photon emission and pair production in high-intensity laser-matter interactions

In high-intensity (>10^2^1 Wcm^-^2) laser-matter interactions gamma-ray photon emission by the electrons can strongly affect 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 emission to a particle-in-cell code. The Monte Carlo algorithm includes quantum corrections to the photon emission, which we show must be included if the pair production rate is to be correctly determined. The accuracy, convergence and energy conservation properties of the Monte Carlo algorithm are analysed in simple test problems.

Monte Carlo calculations of pair production in high-intensity laser–plasma interactions

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 laser fields.