# Publications

## Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets

ArXiv (2012)

NF Loureiro, AA Schekochihin, DA Uzdensky

A 2D linear theory of the instability of Sweet-Parker (SP) current sheets is developed in the framework of Reduced MHD. A local analysis is performed taking into account the dependence of a generic equilibrium profile on the outflow coordinate. The plasmoid instability [Loureiro et al, Phys. Plasmas {\bf 14}, 100703 (2007)] is recovered, i.e., current sheets are unstable to the formation of a large-wave-number chain of plasmoids ($k_{\rm max}\Lsheet \sim S^{3/8}$, where $k_{\rm max}$ is the wave-number of fastest growing mode, $S=\Lsheet V_A/\eta$ is the Lundquist number, $\Lsheet$ is the length of the sheet, $V_A$ is the Alfv\'en speed and $\eta$ is the plasma resistivity), which grows super-Alfv\'enically fast ($\gmax\tau_A\sim S^{1/4}$, where $\gmax$ is the maximum growth rate, and $\tau_A=\Lsheet/V_A$). For typical background profiles, the growth rate and the wave-number are found to {\it increase} in the outflow direction. This is due to the presence of another mode, the Kelvin-Helmholtz (KH) instability, which is triggered at the periphery of the layer, where the outflow velocity exceeds the Alfv\'en speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability, $\gmax \tau_A \sim k_{\rm max} \Lsheet\sim S^{1/2}$. The effect of viscosity ($\nu$) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers, $Pm=\nu/\eta$, it is found that $\gmax\sim S^{1/4}Pm^{-5/8}$ and $k_{\rm max} \Lsheet\sim S^{3/8}Pm^{-3/16}$, leading to the prediction that the critical Lundquist number for plasmoid instability in the $Pm\gg1$ regime is $\Scrit\sim 10^4Pm^{1/2}$. These results are verified via direct numerical simulation of the linearized equations, using a new, analytical 2D SP equilibrium solution.

## High Mach-number collisionless shock driven by a laser with an external magnetic field

EPJ Web of Conferences 59 (2013)

T Morita, Y Sakawa, Y Kuramitsu, T Ide, K Nishio, M Kuwada, H Ide, K Tsubouchi, H Yoneda, A Nishida, T Namiki, T Norimatsu, K Tomita, K Nakayama, K Inoue, K Uchino, M Nakatsutsumi, A Pelka, M Koenig, Q Dong, D Yuan, G Gregori, H Takabe

Collisionless shocks are produced in counter-streaming plasmas with an external magnetic field. The shocks are generated due to an electrostatic field generated in counter-streaming laser-irradiated plasmas, as reported previously in a series of experiments without an external magnetic field [T. Morita et al., Phys. Plasmas, 17, 122702 (2010), Kuramitsu et al., Phys. Rev. Lett., 106, 175002 (2011)] via laser-irradiation of a double-CH-foil target. A magnetic field is applied to the region between two foils by putting an electro-magnet (∼10 T) perpendicular to the direction of plasma expansion. The generated shocks show different characteristics later in time (t > 20ns). © Owned by the authors, published by EDP Sciences, 2013.

## Stream-orbit misalignment I: The dangers of orbit-fitting

ArXiv (2013)

JL Sanders, J Binney

Tidal streams don't, in general, delineate orbits. A stream-orbit misalignment is expected to lead to biases when using orbit-fitting to constrain models for the Galactic potential. In this first of two papers we discuss the expected magnitude of the misalignment and the resulting dangers of using orbit-fitting algorithms to constrain the potential. We summarize data for known streams which should prove useful for constraining the Galactic potential, and compute their actions in a realistic Galactic potential. We go on to discuss the formation of tidal streams in angle-action space, and explain why, in general, streams do not delineate orbits. The magnitude of the stream-orbit misalignment is quantified for a logarithmic potential and a multi-component Galactic potential. Specifically, we focus on the expected misalignment for the known streams. By introducing a two-parameter family of realistic Galactic potentials we demonstrate that assuming these streams delineate orbits can lead to order one errors in the halo flattening and halo-to-disc force ratio at the Sun. We present a discussion of the dependence of these results on the progenitor mass, and demonstrate that the misalignment is mass-independent for the range of masses of observed streams. Hence, orbit-fitting does not yield better constraints on the potential if one uses narrower, lower-mass streams.

## Pair plasma cushions in the hole-boring scenario

Plasma Physics and Controlled Fusion 55 (2013)

JG Kirk, AR Bell, CP Ridgers

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. © 2013 IOP Publishing Ltd.

## Effect of collisions on amplification of laser beams by Brillouin scattering in plasmas

Physics of Plasmas 20 (2013)

KA Humphrey, DC Speirs, R Bingham, RMGM Trines, P Norreys, F Fiuza, RA Cairns, LO Silva

We report on particle in cell simulations of energy transfer between a laser pump beam and a counter-propagating seed beam using the Brillouin scattering process in uniform plasma including collisions. The results presented show that the ion acoustic waves excited through naturally occurring Brillouin scattering of the pump field are preferentially damped without affecting the driven Brillouin scattering process resulting from the beating of the pump and seed fields together. We find that collisions, including the effects of Landau damping, allow for a more efficient transfer of energy between the laser beams, and a significant reduction in the amount of seed pre-pulse produced. © 2013 AIP Publishing LLC.

## EIDOSCOPE: Particle acceleration at plasma boundaries

Experimental Astronomy 33 (2012) 491-527

A Vaivads, G Andersson, SD Bale, CM Cully, J de Keyser, M Fujimoto, S Grahn, S Haaland, H Ji, YV Khotyaintsev, A Lazarian, B Lavraud, IR Mann, R Nakamura, TKM Nakamura, Y Narita, A Retinò, F Sahraoui, A Schekochihin, SJ Schwartz, I Shinohara, L Sorriso-Valvo

We describe the mission concept of how ESA can make a major contribution to the Japanese Canadian multi-spacecraft mission SCOPE by adding one cost-effective spacecraft EIDO (Electron and Ion Dynamics Observatory), which has a comprehensive and optimized plasma payload to address the physics of particle acceleration. The combined mission EIDOSCOPE will distinguish amongst and quantify the governing processes of particle acceleration at several important plasma boundaries and their associated boundary layers: collisionless shocks, plasma jet fronts, thin current sheets and turbulent boundary layers. Particle acceleration and associated cross-scale coupling is one of the key outstanding topics to be addressed in the Plasma Universe. The very important science questions that only the combined EIDOSCOPE mission will be able to tackle are: 1) Quantitatively, what are the processes and efficiencies with which both electrons and ions are selectively injected and subsequently accelerated by collisionless shocks? 2) How does small-scale electron and ion acceleration at jet fronts due to kinetic processes couple simultaneously to large scale acceleration due to fluid (MHD) mechanisms? 3) How does multi-scale coupling govern acceleration mechanisms at electron, ion and fluid scales in thin current sheets? 4) How do particle acceleration processes inside turbulent boundary layers depend on turbulence properties at ion/electron scales? EIDO particle instruments are capable of resolving full 3D particle distribution functions in both thermal and suprathermal regimes and at high enough temporal resolution to resolve the relevant scales even in very dynamic plasma processes. The EIDO spin axis is designed to be sun-pointing, allowing EIDO to carry out the most sensitive electric field measurements ever accomplished in the outer magnetosphere. Combined with a nearby SCOPE Far Daughter satellite, EIDO will form a second pair (in addition to SCOPE Mother-Near Daughter) of closely separated satellites that provides the unique capability to measure the 3D electric field with high accuracy and sensitivity. All EIDO instrumentation are state-of-the-art technology with heritage from many recent missions. The EIDOSCOPE orbit will be close to equatorial with apogee 25-30 RE and perigee 8-10 RE. In the course of one year the orbit will cross all the major plasma boundaries in the outer magnetosphere; bow shock, magnetopause and magnetotail current sheets, jet fronts and turbulent boundary layers. EIDO offers excellent cost/benefits for ESA, as for only a fraction of an M-class mission cost ESA can become an integral part of a major multi-agency L-class level mission that addresses outstanding science questions for the benefit of the European science community. © 2011 Springer Science+Business Media B.V.

## Measuring electron-positron annihilation radiation from laser plasma interactions

Review of Scientific Instruments 83 (2012)

H Chen, R Tommasini, J Seely, CI Szabo, U Feldman, N Pereira, G Gregori, K Falk, J Mithen, CD Murphy

We investigated various diagnostic techniques to measure the 511 keV annihilation radiations. These include step-wedge filters, transmission crystal spectroscopy, single-hit CCD detectors, and streaked scintillating detection. While none of the diagnostics recorded conclusive results, the step-wedge filter that is sensitive to the energy range between 100 keV and 700 keV shows a signal around 500 keV that is clearly departing from a pure Bremsstrahlung spectrum and that we ascribe to annihilation radiation. © 2012 American Institute of Physics.

## Analysing surveys of our Galaxy - I. Basic astrometric data

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 419 (2012) 2251-2263

PJ McMillan, J Binney

## Inelastic x-ray scattering from shocked liquid deuterium

Physical Review Letters 109 (2012)

SP Regan, K Falk, G Gregori, PB Radha, SX Hu, TR Boehly, BJB Crowley, SH Glenzer, OL Landen, DO Gericke, T Döppner, DD Meyerhofer, CD Murphy, TC Sangster, J Vorberger

The Fermi-degenerate plasma conditions created in liquid deuterium by a laser-ablation - driven shock wave were probed with noncollective, spectrally resolved, inelastic x-ray Thomson scattering employing Cl Lyα line emission at 2.96 keV. These first x-ray Thomson scattering measurements of the microscopic properties of shocked deuterium show an inferred spatially averaged electron temperature of 8±5 eV, an electron density of 2.2(±0.5)×1023 cm-3, and an ionization of 0.8 (-0.25, +0.15). Two-dimensional hydrodynamic simulations using equation-of-state models suited for the extreme parameters occurring in inertial confinement fusion research and planetary interiors are consistent with the experimental results. © 2012 American Physical Society.

## The non-thermal emission of extended radio galaxy lobes with curved electron spectra

ArXiv (2011)

P Duffy, KM Blundell

The existing theoretical framework for the energies stored in the synchrotron-emitting lobes of radio galaxies and quasars doesn't properly account for the curved spectral shape that many of them exhibit. We characterise these spectra using parameters that are straightforwardly observable in the era of high-resolution, low-frequency radio astronomy: the spectral curvature and the turnover in the frequency spectrum. This characterisation gives the Lorentz factor at the turnover in the energy distribution (we point out that this is distinctly different from the Lorentz factor corresponding to the turnover frequency in a way that depends on the amount of curvature in the spectrum) and readily gives the equipartition magnetic field strength and the total energy of the radiating plasma obviating the need for any assumed values of the cutoff frequencies to calculate these important physical quantities. This framework readily yields the form of the X-ray emission due to inverse-Compton (IC) scattering of Cosmic Microwave Background (CMB) photons by the electrons in the plasma having Lorentz factors of $\sim$1000. We also present the contribution to CMB anisotropies due to relativistic plasmas such as giant radio galaxy lobes, expressed in terms of the extent to which the lobes have their magnetic field and particle energies are in equipartition with one another.

## Lyman-alpha emission properties of simulated galaxies: interstellar medium structure and inclination effects

ArXiv (2012)

A Verhamme, Y Dubois, J Blaizot, T Garel, R Bacon, J Devriendt, B Guiderdoni, A Slyz

[abridged] Aims. The aim of this paper is to assess the impact of the interstellar medium (ISM) physics on Lyman-alpha (Lya) radiation transfer and to quantify how galaxy orientation with respect to the line of sight alters observational signatures. Methods. We compare the results of Lya radiation transfer calculations through the ISM of a couple of idealized galaxy simulations with different ISM models. Results. First, the small-scale structuration of the ISM plays a determinant role in shaping a galaxys Lya properties.The artificially warm, and hence smooth, ISM of G1 yields an escape fraction of 50 percent at the Lya line center, and produces symmetrical double-peak profiles. On the contrary, in G2, most young stars are embedded in thick star-forming clouds, and the result is a 10 times lower escape fraction. G2 also displays a stronger outflowing velocity field, which favors the escape of red-shifted photons, resulting in an asymmetric Lya line. Second, the Lya properties of G2 strongly depend on the inclination at which it is observed: From edge-on to face-on, the line goes from a double-peak profile with an equivalent width of -5 Angstrom to a 15 times more luminous red-shifted asymmetric line with EW 90 Angstrom. Conclusions. Lya radiation transfer calculations can only lead to realistic properties in simulations where galaxies are resolved into giant molecular clouds, putting these calculations out of reach of current large scale cosmological simulations. Finally, we find inclination effects to be much stronger for Lya photons than for continuum radiation. This could potentially introduce severe biases in the selection function of narrow-band Lya emitter surveys, which could indeed miss a significant fraction of the high-z galaxy population.

## Dynamics of secular evolution

ArXiv (2012)

J Binney

The text of lectures to the 2011 Tenerife Winter School. The School's theme was "Secular Evolution of Galaxies" and my task was to present the underlying stellar-dynamical theory. Other lecturers were speaking on the role of bars and chemical evolution, so these topics are avoided here. We start with an account of the connections between isolating integrals, quasiperiodicity and angle-action variables - these variables played a unifying role throughout the lectures. This leads on to the phenomenon of resonant trapping and how this can lead to chaos in cuspy potentials and phase-space mixing in slowly evolving potentials. Surfaces of section and frequency analysis are introduced as diagnostics of phase-space structure. Real galactic potentials include a fluctuating part that drives the system towards unattainable thermal equilibrium. Two-body encounters are only one source of fluctuations, and all fluctuations will drive similar evolution. We derive the orbit-averaged Fokker-Planck equation and relations that hold between the second-order diffusion coefficients and both the power spectrum of the fluctuations and the first-order diffusion coefficients. From the observed heating of the solar neighbourhood we show that the second-order diffusion coefficients must scale as J^{1/2}. We show that periodic spiral structure shifts angular momentum outwards, heating at the Lindblad resonances and mixing at corotation. The equation that would yield the normal modes of a stellar disc is first derived and then used to discuss the propagation of tightly-wound spiral waves. The winding up of such waves is explains why cool stellar discs are responsive systems that amplify ambient noise. An explanation is offered of why the Lin-Shu-Kalnajs dispersion relation and even global normal-mode calculations provide a very incomplete understanding of the dynamics of stellar discs.

## Constraining stellar assembly and active galactic nucleus feedback at the peak epoch of star formation

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 425 (2012) L96-L100

T Kimm, S Kaviraj, JEG Devriendt, SH Cohen, RA Windhorst, Y Dubois, A Slyz, NP Hathi, RRE Jr, RW O'Connell, MA Dopita, J Silk

## Feeding compact bulges and supermassive black holes with low angular momentum cosmic gas at high redshift

Monthly Notices of the Royal Astronomical Society 423 (2012) 3616-3630

Y Dubois, C Pichon, M Haehnelt, T Kimm, A Slyz, J Devriendt, D Pogosyan

We use cosmological hydrodynamical simulations to show that a significant fraction of the gas in high redshift rare massive haloes falls nearly radially to their very centre on extremely short time-scales. This process results in the formation of very compact bulges with specific angular momentum a factor of 5-30 smaller than the average angular momentum of the baryons in the whole halo. Such low angular momentum originates from both segregation and effective cancellation when the gas flows to the centre of the halo along well-defined cold filamentary streams. These filaments penetrate deep inside the halo and connect to the bulge from multiple rapidly changing directions. Structures falling in along the filaments (satellite galaxies) or formed by gravitational instabilities triggered by the inflow (star clusters) further reduce the angular momentum of the gas in the bulge. Finally, the fraction of gas radially falling to the centre appears to increase with the mass of the halo; we argue that this is most likely due to an enhanced cancellation of angular momentum in rarer haloes which are fed by more isotropically distributed cold streams. Such an increasingly efficient funnelling of low angular momentum gas to the centre of very massive haloes at high redshift may account for the rapid pace at which the most massive supermassive black holes grow to reach observed masses around 10 9M ⊙ at an epoch when the Universe is barely 1 Gyr old. © 2012 The Authors Monthly Notices of the Royal Astronomical Society © 2012 RAS.

## Measurements of radiative shock properties using X-ray Thomson scattering

IEEE International Conference on Plasma Science (2009)

A Visco, RP Drake, MJ Grosskopf, SH Glenzer, DH Froula, G Gregori

## Design considerations for unmagnetized collisionless-shock measurements in homologous flows

Astrophysical Journal 749 (2012)

RP Drake, G Gregori

The subject of this paper is the design of practical laser experiments that can produce collisionless shocks mediated by the Weibel instability. Such shocks may be important in a wide range of astrophysical systems. Three issues are considered. The first issue is the implications of the fact that such experiments will produce expanding flows that are approximately homologous. As a result, both the velocity and the density of the interpenetrating plasma streams will be time dependent. The second issue is the implications of the linear theory of the Weibel instability. For the experiments, the instability is in a regime where standard simplifications do not apply. It appears feasible but non-trivial to obtain adequate growth. The third issue is collisionality. The need to keep resistive magnetic-field dissipation small enough implies that the plasmas should not be allowed to cool substantially. © 2012. The American Astronomical Society. All rights reserved.

## Measurement of radiative shock properties by X-ray Thomson scattering

Physical Review Letters 108 (2012)

AJ Visco, RP Drake, SH Glenzer, T Döppner, G Gregori, DH Froula, MJ Grosskopf

X-ray Thomson scattering has enabled us to measure the temperature of a shocked layer, produced in the laboratory, that is relevant to shocks emerging from supernovas. High energy lasers are used to create a shock in argon gas which is probed by x-ray scattering. The scattered, inelastic Compton feature allows inference of the electron temperature. It is measured to be 34 eV in the radiative precursor and ∼60eV near the shock. Comparison of energy fluxes implied by the data demonstrates that the shock wave is strongly radiative. © 2012 American Physical Society.

## Employing laser-accelerated proton beams to diagnose high intensity laser-plasma interactions

AIP Conference Proceedings 1462 (2012) 149-154

G Sarri, CA Cecchetti, K Quinn, PA Norreys, R Trines, O Willi, J Fuchs, P McKenna, M Quinn, F Pegoraro, SV Bulanov, M Borghesi

A review of the proton radiography technique will be presented. This technique employs laser-accelerated laminar bunches of protons to diagnose the temporal and spatial characteristic of the electric and magnetic fields generated during high-intensity laser-plasma interactions. The remarkable temporal and spatial resolution that this technique can achieve (of the order of a picosecond and a few microns respectively) candidates this technique as the preferrable one, if compared to other techniques, to probe high intensity laser-matterinteractions. © 2012 American Institute of Physics.

## Generation of scaled protogalactic seed magnetic fields in laser-produced shock waves

Nature 481 (2012) 480-483

G Gregori, A Ravasio, CD Murphy, K Schaar, A Baird, AR Bell, A Benuzzi-Mounaix, R Bingham, C Constantin, RP Drake, M Edwards, ET Everson, CD Gregory, Y Kuramitsu, W Lau, J Mithen, C Niemann, H-S Park, BA Remington, B Reville, APL Robinson, DD Ryutov, Y Sakawa, S Yang, NC Woolsey, M Koenig, F Miniati

The standard model for the origin of galactic magnetic fields is through the amplification of seed fields via dynamo or turbulent processes to the level consistent with present observations. Although other mechanisms may also operate, currents from misaligned pressure and temperature gradients (the Biermann battery process) inevitably accompany the formation of galaxies in the absence of a primordial field. Driven by geometrical asymmetries in shocks associated with the collapse of protogalactic structures, the Biermann battery is believed to generate tiny seed fields to a level of about 10 -21 gauss (refs 7, 8). With the advent of high-power laser systems in the past two decades, a new area of research has opened in which, using simple scaling relations, astrophysical environments can effectively be reproduced in the laboratory. Here we report the results of an experiment that produced seed magnetic fields by the Biermann battery effect. We show that these results can be scaled to the intergalactic medium, where turbulence, acting on timescales of around 700 million years, can amplify the seed fields sufficiently to affect galaxy evolution. © 2012 Macmillan Publishers Limited. All rights reserved.

## Self-organized electromagnetic field structures in laser-produced counter-streaming plasmas

Nature Physics 8 (2012) 809-812

NL Kugland, DD Ryutov, P-Y Chang, RP Drake, G Fiksel, DH Froula, SH Glenzer, G Gregori, M Grosskopf, M Koenig, Y Kuramitsu, C Kuranz, MC Levy, E Liang, J Meinecke, F Miniati, T Morita, A Pelka, C Plechaty, R Presura, A Ravasio, BA Remington, B Reville, JS Ross, Y Sakawa, A Spitkovsky, H Takabe, H-S Park

Self-organization occurs in plasmas when energy progressively transfers from smaller to larger scales in an inverse cascade. Global structures that emerge from turbulent plasmas can be found in the laboratory and in astrophysical settings; for example, the cosmic magnetic field, collisionless shocks in supernova remnants and the internal structures of newly formed stars known as Herbig-Haro objects. Here we show that large, stable electromagnetic field structures can also arise within counter-streaming supersonic plasmas in the laboratory. These surprising structures, formed by a yet unexplained mechanism, are predominantly oriented transverse to the primary flow direction, extend for much larger distances than the intrinsic plasma spatial scales and persist for much longer than the plasma kinetic timescales. Our results challenge existing models of counter-streaming plasmas and can be used to better understand large-scale and long-time plasma self-organization. © 2012 Macmillan Publishers Limited. All rights reserved.