arXiv subjects
Publications and source records attributed to J. G. Kirk.
In a strong magnetic field, ultra-relativistic electrons or positrons undergo spin flip transitions as they radiate, preferentially spin polarizing in one direction -- the Sokolov-Ternov effect. Here we show that this effect could occur very rapidly (in less than 10 fs) in high intensity ($I\gtrsim10^{23}$ W/cm$^{2}$) laser-matter interactions, resulting in a high degree of electron spin polarization (70%-90%).
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 are stable. In high-intensity optical pulses, where radiation reaction strongly modifies the trajectories, the production of collimated gamma-rays and the initiation of non-linear cascades of electron-positron pairs can be optimized by a suitable choice of the intensity ratio.
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 synchrotron emission: we show that a beam of $10^9$ 1 GeV electrons colliding with a 30 fs laser pulse of intensity $10^{22}~\text{Wcm}^{-2}$ will emit 6300 photons with energy greater than 700 MeV, $60\times$ the number predicted by classical theory.
In high-intensity (> 10^21W/cm^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.
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, including a classical radiation reaction term, we examine this effect in the hole-boring scenario. We find the collective effects of a pair plasma "cushion" substantially reduce the reflectivity, converting the absorbed flux into high-energy gamma-rays. There is also a modest increase in the laser intensity needed to achieve threshold for a non-linear pair cascade.
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 increased to 320PW (I = 10^25W/cm^2) 40% of the laser energy is converted to gamma-ray photons and 10% to electron-positron pairs. In both cases there is strong feedback between the QED emission processes and the plasma physics; the defining feature of the new `QED-plasma' regime reached in these interactions.
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. Additionally, 35% of the laser energy is converted to a burst of gamma-rays of intensity 10^22W/cm^2, potentially the most intense gamma-ray source available in the laboratory. This absorption results in a strong feedback between both pair and gamma-ray production and classical plasma physics in the new `QED-plasma' regime.
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 equations of MHD, but these break down in the outer parts, when the density of charge carriers drops below a critical value. This paper reviews the wave properties of the inner part (striped wind), and uses a relativistic two-fluid model (cold electrons and positrons) to re-examine the nonlinear electromagnetic modes that propagate in the outer parts. It is shown that in a radial wind, two solutions exist for circularly polarised electromagnetic modes. At large distances one of them turns into a freely expanding flow containing a vacuum wave, whereas the other decelerates, corresponding to a confined flow.
Based on an analysis of a specific electron trajectory in counter-propagating beams, Bell & Kirk (PRL 101, 200403 (2008)) 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 nonlinear 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 10^{24} Watts/sq cm per beam. The same result is found by modelling one of the beams as a wave reflected at the surface of an overdense solid.
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, this condition is conventionally implemented as an upper cut-off in energy space -- particles are then permitted to escape from any part of the system, once their energy exceeds this limit. However, because accelerated particles are responsible for substantial amplification of the ambient magnetic field in a region upstream of the shock front, we examine an alternative approach in which particles escape over a spatial boundary. We use a simple iterative scheme that constructs stationary numerical solutions to the coupled kinetic and hydrodynamic equations. For parameters appropriate for supernova remnants, we find stationary solutions with efficient acceleration when the escape boundary is placed at the point where growth and advection of strongly driven non-resonant waves are in balance. We also present the energy dependence of the distribution function close to the energy where it cuts off - a diagnostic that is in principle accessible to observation.
We investigate the so-called non-resonant 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 non-resonant mode in SN1006 and RX J1713.7-3946 are presented.
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 instability, in which the unstable waves are excited beyond the linear regime. In a snapshot of the resultant field, particle transport simulations are carried out. The use of a static snapshot of the field is reasonable given that the Larmor period for particles is typically very short relative to the instability growth time. The diffusion rate is found to be close to, or below, the Bohm limit for a range of energies. This provides the first explicit demonstration that self-excited turbulence reduces the diffusion coefficient and has important implications for cosmic ray transport and acceleration in supernova remnants.
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 off at low energy. We approximate a low-energy cut-off with monoenergetic electrons. We compute the synchrotron self-Compton (SSC) spectrum of such distribution, and using the IDV source S5~0716+714 as an example, we compare it to the observed SED of S5~0716+714. The hard radio spectrum is well-fitted by this model, and the optical data can be accommodated by a power-law extension to the electron spectrum. We therefore examine the scenario of an injection of electrons that is a double power law in energy with a hard low-energy component that does not contribute to the synchrotron opacity. We show that the double power-law injection model is in good agreement with the observed SED of S5~0716+714. For intrinsic variability, we find that a Doppler factor of D\geq30 can explain the observed SED provided that low-frequency (<32 GHz) emission originates from a larger region than the higher-frequency emission. To fit the entire spectrum, D\geq65 is needed. We find the constraint imposed by induced Compton scattering at high T_B is insignificant in our model. We confirm that electron distribution with a low-energy cut-off can explain the high T_B in compact radio sources. We show that synchrotron spectrum from such distributions naturally accounts for the observed hard radio continuum with a softer optical component, without the need for an inhomogeneous source.
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 the boundary conditions (spectral Galerkin method). To test this algorithm in the homogeneous case, we derive an analytical expression for the growth rate of the Weibel instability for a relativistic Maxwellian distribution and compare it with the numerical results. In the inhomogeneous case, we present solutions of the dispersion relation for the relativistic tearing mode, making no assumption about the thickness of the current sheet, and check the numerical method against the analytical expression.
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 magnetic field. We quantify the extent to which temperature and ionisation fractions modify this picture. Using a kinetic description of the plasma we derive the dispersion relation for a collisionless thermal plasma with a streaming cosmic ray current. Fluid equations are then used to discuss the effects of neutral-ion collisions. We calculate the extent to which the environment into which the cosmic rays propagate influences the growth of the magnetic field, and determines the range of possible growth rates. If the cosmic ray acceleration is efficient, we find that very large neutral fractions are required to stabilise the growth of the non-resonant mode. For typical supernova parameters in our galaxy, thermal effects do not significantly alter the growth rates. For weakly driven modes, ion-neutral damping can dominate over the instability at more modest ionisation fractions. In the case of a supernova shock interacting with a molecular clouds, such as in RX J1713.7-3946, with high density and low ionisation, the modes can be rapidly damped.
(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 energy density than the magnetic field and are sufficiently energetic that inverse Compton scattering is not limited to the Thomson regime. We present a simple, time-dependent, semi-analytical solution of the electron kinetic equation that treats both continuous and impulsive injection, cooling via synchrotron and inverse Compton radiation, (taking into account Klein-Nishina effects) and energy dependent particle escape. The kinetic equation for an arbitrary, time-dependent source function is solved by the method of Laplace transformations. Using an approximate expression for the energy loss rate that takes into account synchrotron and inverse Compton losses including Klein-Nishina effects for scattering off an isotropic photon field with either a power-law or black-body distribution, we find explicit expressions for the cooling time and escape probability of individual electrons. This enables the full, time-dependent solution to be reduced to a single quadrature. From the electron distribution, we then construct the time-dependent, multi-wavelength emission spectrum. We compare our solutions with several limiting cases and discuss the general appearance and temporal behaviour of spectral features (i.e., cooling breaks, bumps etc.). As a specific example, we model the broad-band energy spectrum of the open stellar association Westerlund-2 at different times of its evolution, and compare it with observations.
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 that pulsed emission may be produced. The possible pulse shapes and polarisation properties are described. Particle acceleration at the termination shock of the wind is discussed, and it is argued that two distinct mechanisms must be operating, with the first-order Fermi mechanism producing the high-energy electrons (above 1 TeV) and either magnetic annihilation or resonant absorption of ion cyclotron waves responsible for the 100 MeV to 1 TeV electrons. Finally, MHD models of the morphology of the nebula are discussed and compared with observation.
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 stability to runaway production of soft photons and paris, and find conditions for it to automatically quench by reaching a steady state with an optical depth to photon-photon annihilation larger than unity. We discuss applications to broad-band gamma-ray emitters, in particular supermassive black holes. Automatic quenching limits the gamma-ray luminosity of these objects and predicts substantial pair loading of the jets of less active sources.