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The vertical plane transverse emittance of accelerated electron bunches at the AWAKE experiment at CERN has been determined, using three different methods of data analysis. This is a proof-of-principle measurement using the existing AWAKE electron spectrometer to validate the measurement technique. Large values of the geometric emittance, compared to that of the injection beam, are observed ($\sim \SI{0.5}{\milli\metre\milli\radian}$ compared with $\sim \SI{0.08}{\milli\metre\milli\radian}$), which is in line with expectations of emittance growth arising from plasma density ramps and large injection beam bunch size. Future iterations of AWAKE are anticipated to operate in conditions where emittance growth is better controlled, and the effects of the imaging systems of the existing and future spectrometer designs on the ability to measure the emittance are discussed. Good performance of the instrument down to geometric emittances of approximately $\SI{1e-4}{\milli\metre\milli\radian}$ is required, which may be possible with improved electron optics and imaging., Comment: 20 pages, 9 figures

We present ab initio global general-relativistic Particle-in-cell (GR-PIC) simulations of compact millisecond neutron star magnetospheres in the axisymmetric aligned rotator configuration. We investigate the role of GR and plasma supply on the polar cap particle acceleration efficiency - the precursor of coherent radio emission - employing a new module for the PIC code OSIRIS, designed to model plasma dynamics around compact objects with fully self-consistent GR effects. We provide a detailed description of the main sub-algorithms of the novel PIC algorithm, including a charge-conserving current deposit scheme for curvilinear coordinates. We demonstrate efficient particle acceleration in the polar caps of compact neutron stars with denser magnetospheres, numerically validating the spacelike current extension provided by force-free models. We show that GR relaxes the minimum required poloidal magnetospheric current for the transition of the polar cap to the accelerator regime, thus justifying the observation of weak pulsars beyond the expected death line. We denote that spin-down luminosity intermittency and radio pulse nullings for older pulsars might arise from the interplay between the polar and outer gaps. Also, narrower radio beams are expected for weaker low-obliquity pulsars., Comment: 23 pages, 8 figures, 2 tables, accepted to New Astronomy

This work describes a novel radiation algorithm designed to capture the three-dimensional, space-time resolved electromagnetic field structure emitted by large ensembles of charged particles. % in particle-in-cell (PIC) codes. The algorithm retains the full set of degrees of freedom that characterize electromagnetic waves by employing the Li\'enard-Wiechert fields to retrieve radiation emission. Emitted electric and magnetic fields are deposited in a virtual detector using a temporal interpolation scheme. This feature is essential to accurately predict field amplitudes and preserve the continuous character of radiation emission, even though particle dynamics is known only in a discrete set of temporal steps. Our algorithm retains and accurately captures, by design, full spatial and temporal coherence effects. We demonstrate that our numerical approach recovers well known theoretical radiated spectra in standard scenarios of radiation emission. We show that the algorithm is computationally efficient by computing the full spatiotemporal radiation features of High Harmonic Generation through a plasma mirror in a Particle-In-Cell (PIC) simulation.

Coherent light sources, such as free electron lasers, provide bright beams for biology, chemistry, physics, and advanced technological applications. Increasing the brightness of these sources requires progressively larger devices, with the largest being several km long (e.g., LCLS). Can we reverse this trend, and bring these sources to the many thousands of labs spanning universities, hospitals, and industry? Here we address this long-standing question by rethinking basic principles of radiation physics. At the core of our work is the introduction of quasi-particle-based light sources that rely on the collective and macroscopic motion of an ensemble of light-emitting charges to evolve and radiate in ways that would be unphysical when considering single charges. The underlying concept allows for temporal coherence and superradiance in fundamentally new configurations, providing radiation with clear experimental signatures and revolutionary properties. The underlying concept is illustrated with plasma accelerators but extends well beyond this case, such as to nonlinear optical configurations. The simplicity of the quasi-particle approach makes it suitable for experimental demonstrations at existing laser and accelerator facilities., Comment: 15 pages, 4 figures

A precise characterization of the incoming proton bunch parameters is required to accurately simulate the self-modulation process in the Advanced Wakefield Experiment (AWAKE). This paper presents an analysis of the parameters of the incoming proton bunches used in the later stages of the AWAKE Run 1 data-taking period. The transverse structure of the bunch is observed at multiple positions along the beamline using scintillating or optical transition radiation screens. The parameters of a model that describes the bunch transverse dimensions and divergence are fitted to represent the observed data using Bayesian inference. The analysis is tested on simulated data and then applied to the experimental data.

The nonlinear evolution of electromagnetic instabilities driven by the interpenetration of two $e^-\,e^+$ plasma clouds is explored using {\it ab initio} kinetic plasma simulations. We show that the plasma clouds slow down due to both oblique and Weibel generated electromagnetic fields, which deflect the particle trajectories, transferring bulk forward momentum into transverse momentum and thermal velocity spread. This process causes the flow velocity $v_{inst}$ to decrease approximately by a factor of $\sqrt{1/3}$ in a time interval $\Delta t_{\alpha B} \omega_p \sim c/(v_{fl}\sqrt{\alpha_B})$, where $\alpha_B$ is the magnetic equipartition parameter determined by the non-linear saturation of the instabilities, $v_{fl}$ is the initial flow speed, and $\omega_p$ is the plasma frequency. For the $\alpha_B$ measured in our simulations, $\Delta t_{\alpha B}$ is close to $10 \times$ the instability growth time. We show that as long as the plasma slab length $L > v_{fl} \Delta t_{\alpha B}$, the plasma flow is expected to slow down by a factor close to $1/\sqrt{3}$.

We present numerical simulations and experimental results of the self-modulation of a long proton bunch in a plasma with linear density gradients along the beam path. Simulation results agree with the experimental results reported in arXiv:2007.14894v2: with negative gradients, the charge of the modulated bunch is lower than with positive gradients. In addition, the bunch modulation frequency varies with gradient. Simulation results show that dephasing of the wakefields with respect to the relativistic protons along the plasma is the main cause for the loss of charge. The study of the modulation frequency reveals details about the evolution of the self-modulation process along the plasma. In particular for negative gradients, the modulation frequency across time-resolved images of the bunch indicates the position along the plasma where protons leave the wakefields. Simulations and experimental results are in excellent agreement., Comment: 13 pages, 11 figures

We use a relativistic ionization front to provide various initial transverse wakefield amplitudes for the self-modulation of a long proton bunch in plasma. We show experimentally that, with sufficient initial amplitude ($\ge(4.1\pm0.4)$ MV/m), the phase of the modulation along the bunch is reproducible from event to event, with 3 to 7% (of 2$\pi$) rms variations all along the bunch. The phase is not reproducible for lower initial amplitudes. We observe the transition between these two regimes. Phase reproducibility is essential for deterministic external injection of particles to be accelerated., Comment: Letter and Supplemental Material, 6 figures, 8 pages

The laser interaction with an electron-positron-ion mixed plasma is studied, from the perspective of the associated high-order harmonic generation. For an idealized mixed plasma which is assumed with a sharp plasma-vacuum interface and uniform density distribution, when it is irradiated by a weakly relativistic laser pulse, well-defined signals at harmonics of the plasma frequency in the harmonic spectrum are observed. These characteristic signals are attributed to the inverse two-plasmon decay of the counterpropagating monochromatic plasma waves which are excited by the energetic electrons and the positron beam accelerated by the laser. Particle-in-cell simulations show the signal at twice the plasma frequency can be observed for a pair density as low as $\sim 10^{-5}$ of the plasma density. In the self-consistent scenario of pair production by an ultraintense laser striking a solid target, particle-in-cell simulations, which account for quantum electrodynamic effects (photon emission and pair production), show that dense (greater than the relativistically-corrected critical density) and hot pair plasmas can be created. The harmonic spectrum shows weak low order harmonics, indicating a high laser absorption due to quantum electrodynamic effects. The characteristic signals at harmonics of the plasma frequency are absent, because broadband plasma waves are excited due to the high plasma inhomogeneity introduced by the interaction. However, the high frequency harmonics are enhanced due to the high-frequency modulations from the direct laser coupling with created pair plasmas., Comment: Accepted in Physical Review E (Phys. Rev. E)

Plasma wakefield dynamics over timescales up to 800 ps, approximately 100 plasma periods, are studied experimentally at the Advanced Wakefield Experiment (AWAKE). The development of the longitudinal wakefield amplitude driven by a self-modulated proton bunch is measured using the external injection of witness electrons that sample the fields. In simulation, resonant excitation of the wakefield causes plasma electron trajectory crossing, resulting in the development of a potential outside the plasma boundary as electrons are transversely ejected. Trends consistent with the presence of this potential are experimentally measured and their dependence on wakefield amplitude are studied via seed laser timing scans and electron injection delay scans., Comment: 11 pages, 8 figures

In 2017, AWAKE demonstrated the seeded self-modulation (SSM) of a 400 GeV proton beam from the Super Proton Synchrotron (SPS) at CERN. The angular distribution of the protons deflected due to SSM is a quantitative measure of the process, which agrees with simulations by the two-dimensional (axisymmetric) particle-in-cell code LCODE. Agreement is achieved for beam populations between $10^{11}$ and $3 \times 10^{11}$ particles, various plasma density gradients ($-20 \div 20\%$) and two plasma densities ($2\times 10^{14} \text{cm}^{-3}$ and $7 \times 10^{14} \text{cm}^{-3}$). The agreement is reached only in the case of a wide enough simulation box (at least five plasma wavelengths)., Comment: 8 pages, 9 figures, 1 table

We present a Monte Carlo collisional scheme that models single Compton scattering between leptons and photons in particle-in-cell codes. The numerical implementation of Compton scattering can deal with macro-particles of different weights and conserves momentum and energy in each collision. Our scheme is validated through two benchmarks for which exact analytical solutions exist: the inverse Compton spectra produced by an electron scattering with an isotropic photon gas and the photon-electron gas equilibrium described by the Kompaneets equation. It opens new opportunities for numerical investigation of plasma phenomena where a significant population of high energy photons is present in the system.

A novel setup allows the Weibel instability and its interplay with the Biermann battery to be probed in laser-driven collisionless plasmas. Ab initio particle-in-cell (PIC) simulations of the interaction of short ($ \le ps$) intense $(a_0 \ge 1)$ laser-pulses with overdense plasma targets show observable Weibel generated magnetic fields. This field strength surpasses that of the Biermann battery, usually dominant in experiments, as long as the gradient scale length is much larger than the local electron inertial length; this is achievable by carefully setting the appropriate gradients in the front of the target e.g. by tuning the delay between the main laser pulse and the pre-pulse.

We show that the Weibel or currente filamentation instability can lead to the emission of circularly polarized radiation. Using particle-in-cell (PIC) simulations and a radiation post-processing numerical algorithm, we demonstrate that the level of circular polarization increases with the initial plasma magnetization, saturating at ~13% when the magnetization, given by the ratio of magnetic energy density to the electron kinetic energy density, is larger than 0.05. Furthermore, we show that this effect requires an ion-electron mass ratio greater than unity. These findings, which could also be tested in currently available laboratory conditions, show that the recent observation of circular polarization in gamma ray burst afterglows could be attributed to the presence of magnetized current filaments driven by the Weibel or the current filamentation instability., Comment: 8 pages, 5 figures submitted to Astrophysical Journal Letters

We give direct experimental evidence for the observation of the full transverse self-modulation of a relativistic proton bunch propagating through a dense plasma. The bunch exits the plasma with a density modulation resulting from radial wakefield effects with a period reciprocal to the plasma frequency. We show that the modulation is seeded by using an intense laser pulse co-propagating with the proton bunch which creates a relativistic ionization front within the bunch. We show by varying the plasma density over one order of magnitude that the modulation period scales with the expected dependence on the plasma density., Comment: 4 figures, AWAKE collaboration paper, Submitted to PRL

High energy particle accelerators have been crucial in providing a deeper understanding of fundamental particles and the forces that govern their interactions. In order to increase the energy or reduce the size of the accelerator, new acceleration schemes need to be developed. Plasma wakefield acceleration, in which the electrons in a plasma are excited, leading to strong electric fields, is one such promising novel acceleration technique. Pioneering experiments have shown that an intense laser pulse or electron bunch traversing a plasma, drives electric fields of 10s GV/m and above. These values are well beyond those achieved in conventional RF accelerators which are limited to ~0.1 GV/m. A limitation of laser pulses and electron bunches is their low stored energy, which motivates the use of multiple stages to reach very high energies. The use of proton bunches is compelling, as they have the potential to drive wakefields and accelerate electrons to high energy in a single accelerating stage. The long proton bunches currently available can be used, as they undergo self-modulation, a particle-plasma interaction which longitudinally splits the bunch into a series of high density microbunches, which then act resonantly to create large wakefields. The AWAKE experiment at CERN uses intense bunches of protons, each of energy 400 GeV, with a total bunch energy of 19 kJ, to drive a wakefield in a 10 m long plasma. Bunches of electrons are injected into the wakefield formed by the proton microbunches. This paper presents measurements of electrons accelerated up to 2 GeV at AWAKE. This constitutes the first demonstration of proton-driven plasma wakefield acceleration. The potential for this scheme to produce very high energy electron bunches in a single accelerating stage means that the results shown here are a significant step towards the development of future high energy particle accelerators., Comment: 7 pages, 4 figures. Updated acknowledgements and one reference

Strong magnetic fields in magnetospheres of neutron stars (especially magnetars) and other astrophysical objects may release their energy in violent, intense episodes of magnetic reconnection. While reconnection has been studied extensively, the extreme field strength near neutron stars introduces new effects: synchrotron cooling and electron-positron pair production. Using massively parallel particle-in-cell simulations that self-consistently incorporate these new quantum-electrodynamic effects, we investigate relativistic magnetic reconnection in the strong-field regime. We show that reconnection in this regime can efficiently convert magnetic energy to X-ray and gamma-ray radiation and thus power bright high-energy astrophysical flares. Rapid radiative cooling causes strong plasma and magnetic field compression in compact plasmoids. In the most extreme cases, the field can approach the critical quantum limit, leading to copious pair production.

The collision of ultrashort high-density $e^-$ or $e^-$ and $e^+$ beams at 10s of GeV, to be available at the FACET II and in laser wakefield accelerator experiments, can produce highly collimated $\gamma$ rays (few GeVs) with peak brilliance of $10^{27}~\mathrm{ph/s~mm^2 mrad^2 0.1\% BW}$ and up to $10^5$ nonlinear Breit-Wheeler pairs. We provide analytical estimates of the photon source properties and of the yield of secondary pairs, finding excellent agreement with full-scale 3D self-consistent particle-in-cell simulations that include quantum electrodynamics effects. Our results show that beam-beam collisions can be exploited as secondary sources of $\gamma$ rays and provide an alternative to beam-laser setups to probe quantum electrodynamics effects at the Schwinger limit.

The scaling laws for laser wakefield acceleration in the nonlinear, self-guided regime [Lu et al. Phys. Rev. Spec. Top. Accel. Beams 10, 061301 (2007)] are examined in detail using the quasi-3D version of the particle-in-cell code OSIRIS. We find that the scaling laws continue to work well as the plasma density is reduced while the normalized laser amplitude is kept fixed. For fixed laser energy, the energy gain of an isolated bunch of electrons can be improved with some loss in the bunch charge by shortening the normalized pulse length until self-guiding no longer occurs, and through the use of asymmetric longitudinal profiles with rapid rise times. For example, without any external guiding a 15 J,.8\mu m laser with a pulse length of 46 fs (39 fs) is found to generate a quasi-mono-energetic bunch of 355pC (227pC) with a max energy of 3.25 (4.04) GeV with an acceleration distance of 2.43 cm (3.08cm). Furthermore, a bunch with 39.4pC and a maximum energy 4.6 GeV is produced for an asymmetric laser with a rapid rise time. Studies for 30 J and 100 J lasers are also presented.

Dirac neutrino masses require two distinct neutral Weyl spinors per generation, with a special arrangement of masses and interactions with charged leptons. Once this arrangement is perturbed, lepton number is no longer conserved and neutrinos become Majorana particles. If these lepton number violating perturbations are small compared to the Dirac mass terms, neutrinos are quasi-Dirac particles. Alternatively, this scenario can be characterized by the existence of pairs of neutrinos with almost degenerate masses, and a lepton mixing matrix which has 12 angles and 12 phases. In this work we discuss the phenomenology of quasi-Dirac neutrino oscillations and derive limits on the relevant parameter space from various experiments. In one parameter perturbations of the Dirac limit, very stringent bounds can be derived on the mass splittings between the almost degenerate pairs of neutrinos. However, we also demonstrate that with suitable changes to the lepton mixing matrix, limits on such mass splittings are much weaker, or even completely absent. Finally, we consider the possibility that the mass splittings are too small to be measured and discuss bounds on the new, non-standard lepton mixing angles from current experiments for this case.

Current Filamentation Instability (CFI) is capable of generating strong magnetic fields relevant to explain radiation processes in astrophysical objects and lead to the onset of particle acceleration in collisionless shocks. Probing such extreme scenarios in the laboratory is still an open challenge. In this work, we investigate the possibility of using neutral $e^{-}$ $e^{+}$ beams to explore the CFI with realistic parameters, by performing 2D particle-in-cell simulations. We show that CFI can occur unless the rate at which the beam expands due to finite beam emittance is larger than the CFI growth rate and as long as the role of competing electrostatic two-stream instability (TSI) is negligible. We also show that the longitudinal energy spread, typical of plasma based accelerated electron-positron fireball beams, plays a minor role in the growth of CFI in these scenarios.

The head-on collision between electrostatic shocks is studied via multi-dimensional Particle-In-Cell simulations. It is found that the shock velocities drop significantly and a strong magnetic field is generated after the interaction. This transverse magnetic field is due to the Weibel instability caused by pressure anisotropies due to longitudinal electron heating while the shocks approach each other. Finally, it is shown that this phenomenon can be explored in the laboratory with current laser facilities within a significant parameter range.

A numerical study on ion acceleration in electrostatic shock waves is presented, with the aim of determining the best plasma configuration to achieve quasi-monoenergetic ion beams in laser-driven systems. It was recently shown that tailored near-critical density plasmas characterized by a long-scale decreasing rear density profile lead to beams with low energy spread [F. Fi\'uza et al., Physical Review Letters 109, 215001 (2012)]. In this work, a detailed parameter scan investigating different plasma scale lengths is carried out. As result, the optimal plasma spatial scale length that allows for minimizing the energy spread while ensuring a significant reflection of ions by the shock is identified. Furthermore, a new configuration where the required profile has been obtained by coupling micro layers of different densities is proposed. Results show that this new engineered approach is a valid alternative, guaranteeing a low energy spread with a higher level of controllability., Comment: 10 pages, 6 figures

AWAKE is a proton-driven plasma wakefield acceleration experiment. % We show that the experimental setup briefly described here is ready for systematic study of the seeded self-modulation of the 400\,GeV proton bunch in the 10\,m-long rubidium plasma with density adjustable from 1 to 10$\times10^{14}$\,cm$^{-3}$. % We show that the short laser pulse used for ionization of the rubidium vapor propagates all the way along the column, suggesting full ionization of the vapor. % We show that ionization occurs along the proton bunch, at the laser time and that the plasma that follows affects the proton bunch. %, Comment: Presented as an invited talk at the EPS=Plasma Physics Conference 2017

Current models predict the hose instability to crucially limit the applicability of plasma-wakefield accelerators. By developing an analytical model which incorporates the evolution of the hose instability over long propagation distances, this work demonstrates that the inherent drive-beam energy loss, along with an initial beam energy spread detune the betatron oscillations of beam electrons, and thereby mitigate the instability. It is also shown that tapered plasma profiles can strongly reduce initial hosing seeds. Hence, we demonstrate that the propagation of a drive beam can be stabilized over long propagation distances, paving the way for the acceleration of high-quality electron beams in plasma-wakefield accelerators. We find excellent agreement between our models and particle-in-cell simulations.

We investigate the formation of collisionless magnetized shocks triggered by the interaction between magnetized plasma flows and miniature-sized (order of plasma kinetic-scales) magnetic obstacles resorting to massively parallel, full particle-in-cell simulations, including the electron kinetics. The critical obstacle size to generate a compressed plasma region ahead of these objects is determined by independently varying the magnitude of the dipolar magnetic moment and the plasma magnetization. We find that the effective size of the obstacle depends on the relative orientation between the dipolar and plasma internal magnetic fields, and we show that this may be critical to form a shock in small-scale structures. We study the microphysics of the magnetopause in different magnetic field configurations in 2D and compare the results with full 3D simulations. Finally, we evaluate the parameter range where such miniature magnetized shocks can be explored in laboratory experiments.

Raman and Brillouin amplification are two schemes for amplifying and compressing short laser pulses in plasma. Analytical models have already been derived for both schemes, but the full consequences of these models are little known or used. Here, we present new criteria that govern the evolution of the attractor solution for the seed pulse in Raman and Brillouin amplification, and show how the initial laser pulses need to be shaped to control the properties of the final amplified seed and improve the amplification efficiency., Comment: 14 pages, 4 figures, submitted to Physical Review Letters in July 2016

We calculate small correction terms to gravitational potential near $p$-branes embedded in a constant NS $B$ field background in the context of M-theory or string theory. The normalizable wave functions of gravity fluctuations around the brane describe only massive modes. We compute such wave functions analytically. We estimate the correction to gravitational potential for small and long distances, and show that there is an intermediate range of distances in which we can identify $4D$ gravity on the brane below a crossover scale given in terms of components of the $B$ field. The $4D$ gravity is metastable and for distances much larger than the crossover scale the $5D$ gravity is recovered., Comment: 7 pages, 2 figures, Latex

We identify and explore a high orbital angular momentum (OAM) harmonics generation and amplification mechanism that manipulates the OAM independently of any other laser property, by preserving the initial laser wavelength, through stimulated Raman backscattering in a plasma. The high OAM harmonics spectra can extend at least up to the limiting value imposed by the paraxial approximation. We show with theory and particle-in-cell simulations that the orders of the OAM harmonics can be tuned according to a selection rule that depends on the initial OAM of the interacting waves. We illustrate the high OAM harmonics generation in a plasma using several examples including the generation of prime OAM harmonics. The process can also be realised in any nonlinear optical Kerr media supporting three-wave interactions., Comment: 12 pages, 4 figures (accepted for publication in Physical Review Letters)

Plasma accelerators can sustain very high acceleration gradients. They are promising candidates for future generations of particle accelerators for several scientific, medical and technological applications. Current plasma based acceleration experiments operate in the relativistic regime, where the plasma response is strongly non-linear. We outline some of the key properties of wakefield excitation in these regimes. We outline a multidimensional theory for the excitation of plasma wakefields in connection with current experiments. We then use these results and provide design guidelines for the choice of laser and plasma parameters ensuring a stable laser wakefield accelerator that maximizes the quality of the accelerated electrons. We also mention some of the future challenges associated with this technology., Comment: presented at the CERN Accelerator School- CAS 2019: Plasma Wake Acceleration, Sesimbra, Portugal, 11-22 March 2019; Replaced Section 6 with respect to initial submission with an update on recent developments

Twisted Laguerre-Gaussian lasers, with orbital angular momentum and characterised by doughnut shaped intensity profiles, provide a transformative set of tools and research directions in a growing range of fields and applications, from super-resolution microcopy and ultra-fast optical communications to quantum computing and astrophysics. The impact of twisted light is widening as recent numerical calculations provided solutions to long-standing challenges in plasma-based acceleration by allowing for high gradient positron acceleration. The production of ultrahigh intensity twisted laser pulses could then also have a broad influence on relativistic laser-matter interactions. Here we show theoretically and with ab-initio three-dimensional particle-in-cell simulations, that stimulated Raman backscattering can generate and amplify twisted lasers to Petawatt intensities in plasmas. This work may open new research directions in non-linear optics and high energy density science, compact plasma based accelerators and light sources., Comment: 18 pages, 4 figures, 1 table

The Advanced Proton Driven Plasma Wakefield Acceleration Experiment (AWAKE) aims at studying plasma wakefield generation and electron acceleration driven by proton bunches. It is a proof-of-principle R&D experiment at CERN and the world's first proton driven plasma wakefield acceleration experiment. The AWAKE experiment will be installed in the former CNGS facility and uses the 400 GeV/c proton beam bunches from the SPS. The first experiments will focus on the self-modulation instability of the long (rms ~12 cm) proton bunch in the plasma. These experiments are planned for the end of 2016. Later, in 2017/2018, low energy (~15 MeV) electrons will be externally injected to sample the wakefields and be accelerated beyond 1 GeV. The main goals of the experiment will be summarized. A summary of the AWAKE design and construction status will be presented., Comment: 7 pages, 7 figures, 2 tables

An investigation of magnetic fields generated in an expanding bubble of plasma with misaligned temperature and density gradients (driving the Biermann battery mechanism) is performed. With gradient scales $L$, large-scale magnetic fields are generated by the Biermann battery mechanism with plasma $\beta \sim 1$, as long as $L$ is comparable to the ion inertial length $d_i$. For larger system sizes, $L/d_e > 100$ (where $d_e$ is the electron inertial length), the Weibel instability generates magnetic fields of similar magnitude but with wavenumber $k d_e \sim 0.2$. In both cases, the growth and saturation of these fields have a weak dependence on mass ratio $m_i/m_e$, indicating electron mediated physics. A scan in system size is performed at $m_i/m_e = 2000$, showing agreement with previous results with $m_i/m_e = 25$. In addition, the instability found at large system sizes is quantitatively demonstrated to be the Weibel instability. Furthermore, magnetic and electric energy spectra at scales below the electron Larmor radius are found to exhibit power law behavior with spectral indices $-16/3$ and $-7/3$, respectively.

This report describes the conceptual steps in reaching the design of the AWAKE experiment currently under construction at CERN. We start with an introduction to plasma wakefield acceleration and the motivation for using proton drivers. We then describe the self-modulation instability --- a key to an early realization of the concept. This is then followed by the historical development of the experimental design, where the critical issues that arose and their solutions are described. We conclude with the design of the experiment as it is being realized at CERN and some words on the future outlook. A summary of the AWAKE design and construction status as presented in this conference is given in [1]., Comment: 15 pages, 24 figures, 1 table, 111 references, 121 author from 36 organizations

The classification of lepton mixing matrices from finite residual symmetries is reviewed, with emphasis on the role of vanishing sums of roots of unity for the solution of this problem., Comment: 6 pages, no figures, talk presented at XXXIX International Conference of Theoretical Physics "Matter to the Deepest," Ustron, Poland, September 13-18, 2015

Collisionless shocks occur in various fields of physics. In the context of space and astrophysics they have been investigated for many decades. However, a thorough understanding of shock formation and particle acceleration is still missing. Collisionless shocks can be distinguished into electromagnetic and electrostatic shocks. Electromagnetic shocks are of importance mainly in astrophysical environments and they are mediated by the Weibel or filamentation instability. In such shocks, charged particles gain energy by diffusive shock acceleration. Electrostatic shocks are characterized by a strong electrostatic field, which leads to electron trapping. Ions are accelerated by reflection from the electrostatic potential. Shock formation and particle acceleration will be discussed in theory and simulations.

An emissivity formula is derived using the generalised Fermi-Weizacker-Williams method of virtual photons which accounts for the recoil the charged particle experiences as it emits radiation. It is found that through this derivation the formula obtained by Sokolov et al using QED perturbation theory is recovered. The corrected emissivity formula is applied to nonlinear Thomson scattering scenarios in the transition from the classical to the quantum regime, for small values of the nonlinear quantum parameter \chi. Good agreement is found between this method and a QED probabilistic approach for scenarios where both are valid. In addition, signatures of the quantum corrections are identified and explored., Comment: 11 pages, 4 figures, submitted for publication

The microphysics of relativistic collisionless sheared flows is investigated in a configuration consisting of a globally neutral, relativistic $e^-e^+$ beam streaming through a hollow plasma/dielectric channel. We show through multidimensional PIC simulations that this scenario excites the Mushroom instability (MI), a transverse shear instability on the electron-scale, when there is no overlap (no contact) between the $e^-e^+$ beam and the walls of the hollow plasma channel. The onset of the MI leads to the conversion of the beam's kinetic energy into magnetic (and electric) field energy, effectively slowing down a globally neutral body in the absence of contact. The collisionless shear physics explored in this configuration may operate in astrophysical environments, particularly in highly relativistic and supersonic settings where macroscopic shear processes are stable.

In this paper we show a plausible mechanism that could lead to the formation of the Dark Lanes in Lunar Swirls, and the electromagnetic shielding of the lunar surface that results in the preservation of the white colour of the lunar regolith. We present the results of a fully self-consistent 2 and 3 dimensional particle-in-cell simulations of mini-magnetospheres that form above the lunar surface and show that they are consistent with the formation of `lunar swirls' such as the archetypal formation Reiner Gamma. The simulations show how the microphysics of the deflection/shielding of plasma operates from a kinetic-scale cavity, and show that this interaction leads to a footprint with sharp features that could be the mechanism behind the generation of `dark lanes'. The physics of mini-magnetospheres is described and shown to be controlled by space-charge fields arising due to the magnetized electrons and unmagnetized ions. A comparison between model and observation is shown for a number of key plasma parameters., Comment: 14 pages, 10 figures

Electron-scale surface waves are shown to be unstable in the transverse plane of a shear flow in an initially unmagnetized plasma, unlike in the (magneto)hydrodynamics case. It is found that these unstable modes have a higher growth rate than the closely related electron-scale Kelvin-Helmholtz instability in relativistic shears. Multidimensional particle-in-cell simulations verify the analytic results and further reveal the emergence of mushroom-like electron density structures in the nonlinear phase of the instability, similar to those observed in the Rayleigh Taylor instability despite the great disparity in scales and different underlying physics. Macroscopic ($\gg c/\omega_{pe}$) fields are shown to be generated by these microscopic shear instabilities, which are relevant for particle acceleration, radiation emission and to seed MHD processes at long time-scales.

The spatial-temporal evolution of the purely transverse current filamentation instability is analyzed by deriving a single partial differential equation for the instability and obtaining the analytical solutions for the spatially and temporally growing current filament mode. When the beam front always encounters fresh plasma, our analysis shows that the instability grows spatially from the beam front to the back up to a certain critical beam length; then the instability acquires a purely temporal growth. This critical beam length increases linearly with time and in the non-relativistic regime it is proportional to the beam velocity. In the relativistic regime the critical length is inversely proportional to the cube of the beam Lorentz factor $\gamma_{0b}$. Thus, in the ultra-relativistic regime the instability immediately acquires a purely temporal growth all over the beam. The analytical results are in good agreement with multidimensional particle-in-cell simulations performed with OSIRIS. Relevance of current study to recent and future experiments on fireball beams is also addressed.

We explore the role of the background plasma ion motion in self-modulated plasma wakefield accelerators. We employ J. Dawson's plasma sheet model to derive expressions for the transverse plasma electric field and ponderomotive force in the narrow bunch limit. We use these results to determine the on-set of the ion dynamics, and demonstrate that the ion motion could occur in self-modulated plasma wakefield accelerators. Simulations show the motion of the plasma ions can lead to the early suppression of the self-modulation instability and of the accelerating fields. The background plasma ion motion can nevertheless be fully mitigated by using plasmas with heavier plasmas., Comment: 23 pages, 6 figures

A new magnetic field generation mechanism in electrostatic shocks is found, which can produce fields with magnetic energy density as high as 0.01 of the kinetic energy density of the flows on time scales $ \tilde \, 10^4 \, {\omega}_{pe}^{-1}$. Electron trapping during the shock formation process creates a strong temperature anisotropy in the distribution function, giving rise to the pure Weibel instability. The generated magnetic field is well-confined to the downstream region of the electrostatic shock. The shock formation process is not modified and the features of the shock front responsible for ion acceleration, which are currently probed in laser-plasma laboratory experiments, are maintained. However, such a strong magnetic field determines the particle trajectories downstream and has the potential to modify the signatures of the collisionless shock.

It is shown that co-linear injection of electrons or positrons into the wakefield of the self-modulating particle beam is possible and ensures high energy gain. The witness beam must co-propagate with the tail part of the driver, since the plasma wave phase velocity there can exceed the light velocity, which is necessary for efficient acceleration. If the witness beam is many wakefield periods long, then the trapped charge is limited by beam loading effects. The initial trapping is better for positrons, but at the acceleration stage a considerable fraction of positrons is lost from the wave. For efficient trapping of electrons, the plasma boundary must be sharp, with the density transition region shorter than several centimeters. Positrons are not susceptible to the initial plasma density gradient., Comment: 9 pages, 9 figures, 1 table, 44 references

We preform hybrid simulations of super Alfvenic quasi-parallel shock, driven by a Coronal Mass Ejection (CME), propagating in the Outer Coronal or Solar Wind at distances of between 3 to 6 solar radii. The hybrid treatment of the problem enable the study of the shock propagation on the ion time scale, preserving ion kinetics and allowing for a self consistent treatment of the shock propagation and particle acceleration. The CME plasma drags the embedded magnetic field lines stretching from the sun, and propagates out into interplanetary space at a greater velocity than the in-situ solar wind, driving the shock, and producing very energetic particles. Our results show electromagnetic Alfven waves are generated at the shock front. The waves propagate upstream of the shock and are produced by the counter streaming ions of the solar wind plasma being reflected at the shock. A significant fraction of the particles are accelerated in two distinct phases: first, particles drift from the shock and are accelerated in the upstream region and, second, particles arriving at the shock get trapped, and are accelerated at the shock front. A fraction of the particles diffused back to the shock, which is consistent with the Fermi acceleration mechanism., Comment: Accepted for publication in Astrophysical Journal 18th June 2014

Raman and Brillouin amplification of laser pulses in plasma have been shown to produce picosecond pulses of petawatt power. In previous studies, filamentation of the probe pulse has been identified as the biggest threat to the amplification process, especially for Brillouin amplification, which employs the highest plasma densities. Therefore it has been proposed to perform Brillouin scattering at densities below $n_{cr}/4$ to reduce the influence of filamentation. However, parastic Raman scattering can become a problem at such densities, contrary to densities above $n_{cr}/4$, where it is suppressed. In this paper, we investigate the influence of parasitic Raman scattering on Brillouin amplification at densities below $n_{cr}/4$. We expose the specific problems posed by both Raman backward and forward scattering, and how both types of scattering can be mitigated, leading to an increased performance of the Brillouin amplification process., Comment: 13 pages, 3 figures, 1 table. arXiv admin note: text overlap with arXiv:1311.2034

In this paper, we determine the electron beam quality requirements to obtain exponential radiation amplification in the ion-channel laser, where a relativistic electron beam wiggles in a focusing ion-channel that can be created in a wakefield accelerator. The beam energy and wiggler parameter spreads should be limited. Those spread limits are functions of the Pierce parameter, which is calculated here without neglecting the radiation diffraction. Two dimensional and three dimensional simulations of the self-consistent ion-channel laser confirm our theoretical predictions.

Strong shear flow regions found in astrophysical jets are shown to be important dissipation regions, where the shear flow kinetic energy is converted into electric and magnetic field energy via shear instabilities. The emergence of these self-consistent fields make shear flows significant sites for radiation emission and particle acceleration. We focus on electron-scale instabilities, namely the collisionless, unmagnetized Kelvin-Helmholtz instability (KHI) and a large-scale dc magnetic field generation mechanism on the electron scales. We show that these processes are important candidates to generate magnetic fields in the presence of strong velocity shears, which may naturally originate in energetic matter outburst of active galactic nuclei and gamma-ray bursters. We show that the KHI is robust to density jumps between shearing flows, thus operating in various scenarios with different density contrasts. Multidimensional particle-in-cell (PIC) simulations of the KHI, performed with OSIRIS, reveal the emergence of a strong and large-scale dc magnetic field component, which is not captured by the standard linear fluid theory. This dc component arises from kinetic effects associated with the thermal expansion of electrons of one flow into the other across the shear layer, whilst ions remain unperturbed due to their inertia. The electron expansion forms dc current sheets, which induce a dc magnetic field. Our results indicate that most of the electromagnetic energy developed in the KHI is stored in the dc component, reaching values of equipartition on the order of $10^{-3}$ in the electron time-scale, and persists longer than the proton time-scale. Particle scattering/acceleration in the self generated fields of these shear flow instabilities is also analyzed.

For many plasma physics problems, three-dimensional and kinetic effects are very important. However, such simulations are very computationally intensive. Fortunately, there is a class of problems for which there is nearly azimuthal symmetry and the dominant three-dimensional physics is captured by the inclusion of only a few azimuthal harmonics. Recently, it was proposed [A. Lifschitz et al., J. Comp. Phys. 228 (5) (2009) 1803-1814] to model one such problem, laser wakefield acceleration, by expanding the fields and currents in azimuthal harmonics and truncating the expansion after only the first harmonic. The complex amplitudes of the fundamental and first harmonic for the fields were solved on an r-z grid and a procedure for calculating the complex current amplitudes for each particle based on its motion in Cartesian geometry was presented using a Marder's correction to maintain the validity of Gauss's law. In this paper, we describe an implementation of this algorithm into OSIRIS using a rigorous charge conserving current deposition method to maintain the validity of Gauss's law. We show that this algorithm is a hybrid method which uses a particles-in-cell description in r-z and a gridless description in $\phi$. We include the ability to keep an arbitrary number of harmonics and higher order particle shapes. Examples, for laser wakefield acceleration, plasma wakefield acceleration, and beam loading are also presented and directions for future work are discussed.

New acceleration technology is mandatory for the future elucidation of fundamental particles and their interactions. A promising approach is to exploit the properties of plasmas. Past research has focused on creating large-amplitude plasma waves by injecting an intense laser pulse or an electron bunch into the plasma. However, the maximum energy gain of electrons accelerated in a single plasma stage is limited by the energy of the driver. Proton bunches are the most promising drivers of wakefields to accelerate electrons to the TeV energy scale in a single stage. An experimental program at CERN -- the AWAKE experiment -- has been launched to study in detail the important physical processes and to demonstrate the power of proton-driven plasma wakefield acceleration. Here we review the physical principles and some experimental considerations for a future proton-driven plasma wakefield accelerator., Comment: 12 pages, 5 figures, submitted to Plasma Phys. Control. Fusion special edition for LPAW 2013. Small updates after comments from Journal referees