Diffusive shock acceleration at laser-driven shocks: studying cosmic-ray accelerators in the laboratory

The non-thermal particle spectra responsible for the emission from many astrophysical systems are thought to originate from shocks via a first order Fermi process otherwise known as diffusive shock acceleration. The same mechanism is also widely believed to be responsible for the production of high energy cosmic rays. With the growing interest in collisionless shock physics in laser produced plasmas, the possibility of reproducing and detecting shock acceleration in controlled laboratory experiments should be considered. The various experimental constraints that must be satisfied are reviewed. It is demonstrated that several currently operating laser facilities may fulfil the necessary criteria to confirm the occurrence of diffusive shock acceleration of electrons at laser produced shocks. Successful reproduction of Fermi acceleration in the laboratory could open a range of possibilities, providing insight into the complex plasma processes that occur near astrophysical sources of cosmic rays.

STEADY-STATE SOLUTIONS IN NONLINEAR DIFFUSIVE SHOCK ACCELERATION

Stationary solutions to the equations of nonlinear 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 cutoff 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 the 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 nonresonant 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.

Shock acceleration in the solar corona

In this thesis acceleration of energetic particles at collisionless shock waves in space plasmas is studied using numerical simulations, with an emphasis on physical conditions applicable to the solar corona. The thesis consists of four research articles and an introductory part that summarises the main findings reached in the articles and discusses them with respect to theory of diffusive shock acceleration and observations. This thesis gives a brief review of observational properties of solar energetic particles and discusses a few open questions that are currently under active research. For example, in a few large gradual solar energetic particle events the heavy ion abundance ratios and average charge states show characteristics at high energies that are typically associated with flare-accelerated particles, i.e. impulsive events. The role of flare-accelerated particles in these and other gradual events has been discussed a lot in the scientific community, and it has been questioned if and how the observed features can be explained in terms of diffusive shock acceleration at shock waves driven by coronal mass ejections. The most extreme solar energetic particle events are the so-called ground level enhancements where particle receive so high energies that they can penetrate all the way through Earth's atmosphere and increase radiation levels at the surface. It is not known what conditions are required for acceleration into GeV/nuc energies, and the presence of both very fast coronal mass ejections and X-class solar flares makes it difficult to determine what is the role of these two accelerators in ground level enhancements. The theory of diffusive shock acceleration is reviewed and its predictions discussed with respect to the observed particle characteristics. We discuss how shock waves can be modeled and describe in detail the numerical model developed by the author. The main part of this thesis consists of the four scientific articles that are based on results of the numerical shock acceleration model developed by the author. The novel feature of this model is that it can handle complex magnetic geometries which are found, for example, near active regions in the solar corona. We show that, according to our simulations, diffusive shock acceleration can explain the observed variations in abundance ratios and average charge states, provided that suitable seed particles and magnetic geometry are available for the acceleration process in the solar corona. We also derive an injection threshold for diffusive shock acceleration that agrees with our simulation results very well, and which is valid under weakly turbulent conditions. Finally, we show that diffusive shock acceleration can produce GeV/nuc energies under suitable coronal conditions, which include the presence of energetic seed particles, a favourable magnetic geometry, and an enhanced level of ambient turbulence.

Cosmic-ray acceleration and escape from supernova remnants

Galactic cosmic-ray (CR) acceleration to the knee in the spectrum at a few PeV is only possible if the magnetic field ahead of a supernova remnant (SNR) shock is strongly amplified by CRs escaping the SNR. A model formulated in terms of the electric charge carried by escaping CRs predicts the maximum CR energy and the energy spectrum of CRs released into the surrounding medium. We find that historical SNRs such as Cas A, Tycho and Kepler may be expanding too slowly to accelerate CRs to the knee at the present time.

The transport of cosmic rays in self-excited magnetic turbulence

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.

A cosmic ray current-driven instability in partially ionised media

Context. We investigate the growth of hydromagnetic waves driven by streaming cosmic rays in the precursor environment of a supernova remnant shock.

Aims. 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.

Methods. 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.

Results. 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.

Conclusions. 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.

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.

Multi-Dimensional Simulations of the Expanding Supernova Remnant of SN 1987A

The expanding remnant from SN 1987A is an excellent laboratory for investigating the physics of supernovae explosions. There is still a large number of outstanding questions, such as the reason for the asymmetric radio morphology, the structure of the pre-supernova environment, and the efficiency of particle acceleration at the supernova shock. We explore these questions using three-dimensional simulations of the expanding remnant between days 820 and 10,000 after the supernova. We combine a hydrodynamical simulation with semi-analytic treatments of diffusive shock acceleration and magnetic field amplification to derive radio emission as part of an inverse problem. Simulations show that an asymmetric explosion, combined with magnetic field amplification at the expanding shock, is able to replicate the persistent one-sided radio morphology of the remnant. We use an asymmetric Truelove & McKee progenitor with an envelope mass of 10 M-circle dot and an energy of 1.5 x 10(44) J. A termination shock in the progenitor's stellar wind at a distance of 0 ''.43-0 ''.51 provides a good fit to the turn on of radio emission around day 1200. For the H II region, a minimum distance of 0 ''.63 +/- 0 ''.01 and maximum particle number density of (7.11 +/- 1.78) x 10(7) m(-3) produces a good fit to the evolving average radius and velocity of the expanding shocks from day 2000 to day 7000 after explosion. The model predicts a noticeable reduction, and possibly a temporary reversal, in the asymmetric radio morphology of the remnant after day 7000, when the forward shock left the eastern lobe of the equatorial ring.

The generation and amplification of intergalactic magnetic fields in analogue laboratory experiments with high power lasers

The advent of high-power laser facilities has, in the past two decades, opened a new field of research where astrophysical environments can be scaled down to laboratory dimensions, while preserving the essential physics. This is due to the invariance of the equations of magneto-hydrodynamics to a class of similarity transformations. Here we review the relevant scaling relations and their application in laboratory astrophysics experiments with a focus on the generation and amplification of magnetic fields in cosmic environment. The standard model for the origin of magnetic fields is a multi stage process whereby a vanishing magnetic seed is first generated by a rotational electric field and is then amplified by turbulent dynamo action to the characteristic values observed in astronomical bodies. We thus discuss the relevant seed generation mechanisms in cosmic environment including resistive mechanism, collision-less and fluid instabilities, as well as novel laboratory experiments using high power laser systems aimed at investigating the amplification of magnetic energy by magneto-hydrodynamic (MHD) turbulence. Future directions, including efforts to model in the laboratory the process of diffusive shock acceleration are also discussed, with an emphasis on the potential of laboratory experiments to further our understanding of plasma physics on cosmic scales.

CENTAURUS A: THE EXTRAGALACTIC SOURCE OF COSMIC RAYS WITH ENERGIES ABOVE THE KNEE

The origin of cosmic rays at all energies is still uncertain. In this paper, we present and explore an astrophysical scenario to produce cosmic rays with energy ranging from below 10(15) to 3 x 10(20) eV. We show here that just our Galaxy and the radio galaxy Cen A, each with their own galactic cosmic-ray particles but with those from the radio galaxy pushed up in energy by a relativistic shock in the jet emanating from the active black hole, are sufficient to describe the most recent data in the PeV to near ZeV energy range. Data are available over this entire energy range from the KASCADE, KASCADE-Grande, and Pierre Auger Observatory experiments. The energy spectrum calculated here correctly reproduces the measured spectrum beyond the knee and, contrary to widely held expectations, no other extragalactic source population is required to explain the data even at energies far below the general cutoff expected at 6 x 10(19) eV, the Greisen-Zatsepin-Kuz'min turnoff due to interaction with the cosmological microwave background. We present several predictions for the source population, the cosmic-ray composition, and the propagation to Earth which can be tested in the near future.

Steady state ion acceleration by a circularly polarized laser pulse

The steady state ion acceleration at the front of a cold solid target by a circularly polarized flat-top laser pulse is studied with one-dimensional particle-in-cell (PIC) simulation. A model that ions are reflected by a steady laser-driven piston is used by comparing with the electrostatic shock acceleration. A stable profile with a double-flat-top structure in phase space forms after ions enter the undisturbed region of the target with a constant velocity. (C) 2007 Elsevier B.V. All rights reserved.

Advanced strategies for ion acceleration using high-power lasers

A short overview of laser-plasma acceleration of ions is presented. The focus is on some recent experimental results and the related theoretical work on advanced regimes. These latter include in particular target normal sheath acceleration using ultrashort low-energy pulses and structured targets, radiation pressure acceleration in both thick and ultrathin targets and collisionless shock acceleration in moderate density plasmas. For each approach, open issues and the need and potential for further developments are briefly discussed. © 2013 IOP Publishing Ltd.

Effect of plasma temperature on electrostatic shock generation and ion acceleration by laser

The effect of plasma temperature on electrostatic shock generated by a circularly polarized laser pulse in overdense plasma is studied by particle-in-cell simulation. Ion reflection and transmission in the collisionless electrostatic shock (CES) are investigated analytically. As the initial ion temperature is varied, a distinct transition from the laser-driven piston scenario with all ions being reflected to the CES scenario with partial ion reflection is found. The results show that at low but finite temperatures the ions are much more accelerated than if they were cold.

Shock creation and particle acceleration driven by plasma expansion into a rarefied medium

The expansion of a dense plasma through a more rarefied ionized medium is a phenomenon of interest in various physics environments ranging from astrophysics to high energy density laser-matter laboratory experiments. Here this situation is modeled via a one-dimensional particle-in-cell simulation; a jump in the plasma density of a factor of 100 is introduced in the middle of an otherwise equally dense electron-proton plasma with an uniform proton and electron temperature of 10 eV and 1 keV, respectively. The diffusion of the dense plasma, through the rarefied one, triggers the onset of different nonlinear phenomena such as a strong ion-acoustic shock wave and a rarefaction wave. Secondary structures are detected, some of which are driven by a drift instability of the rarefaction wave. Efficient proton acceleration occurs ahead of the shock, bringing the maximum proton velocity up to 60 times the initial ion thermal speed. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3469762]

Ion acceleration from the shock front induced by hole boring in ultraintense laser-plasma interactions

Ion-acceleration processes have been studied in ultraintense laser plasma interactions for normal incidence irradiation of solid deuterated targets via neutron spectroscopy. The experimental neutron spectra strongly suggest that the ions are preferentially accelerated radially, rather than into the bulk of the material from three-dimensional Monte Carlo fitting of the neutron spectra. Although the laser system has a 10(-7) contrast ratio, a two-dimensional magnetic hydrodynamics simulation shows that the laser pedestal generates a 10 mum scale length in the coronal plasma with a 3 mum scale-length plasma near the critical density. Two-dimensional particle-in-cell simulations, incorporating this realistic density profile, indicate that the acceleration of the ions is caused by a collisionless shock formation. This has implications for modeling energy transport in solid is caused by a collisionless shock formation. This has implications for modeling energy transport in solid density plasmas as well as cone-focused fast ignition using the next generation PW lasers currently under construction.