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We derive functional equations for distributions of six classical statistics (ascents, descents, left-to-right maxima, right-to-left maxima, left-to-right minima, and right-to-left minima) on separable and irreducible separable permutations. The equations are used to find a third degree equation for joint distribution of ascents and descents on separable permutations that generalizes the respective known result for the descent distribution. Moreover, our general functional equations allow us to derive explicitly (joint) distribution of any subset of maxima and minima statistics on irreducible, reducible and all separable permutations. In particular, there are two equivalence classes of distributions of a pair of maxima or minima statistics. Finally, we present three unimodality conjectures about distributions of statistics on separable permutations., Comment: To appear in Discrete Applied Mathematics

Interactions between magnetic fields advected by matter play a fundamental role in the Universe at all possible scales. A crucial role these interactions play is in making turbulent fields highly anisotropic, leading to observed ordered fields. These in turn, are important evolutionary factors for all the systems within and around. Despite scant evidence, due to the difficulty in measuring even near-Earth events, the magnetic field compression factor in these interactions, measured at very varied scales, is limited to a few. However, compressing matter in which a magnetic field is embedded, results in compression up to several thousands. Here we show, using laboratory experiments and matching three-dimensional hybrid simulations, that there is indeed a very effective saturation of the compression when two independent magnetic fields are advected by plasmas encounter. We found that the observed saturation is linked to a build-up of the magnetic pressure at the inflows encounter point, which decelerates them and thereby stops further compression. Moreover, the growth of an electric field, induced by the incoming flows and the magnetic field, acts in redirecting the inflows transversely, further hampering field compression.

The ability to synthesize realistic data in a parametrizable way is valuable for a number of reasons, including privacy, missing data imputation, and evaluating the performance of statistical and computational methods. When the underlying data generating process is complex, data synthesis requires approaches that balance realism and simplicity. In this paper, we address the problem of synthesizing sequential categorical data of the type that is increasingly available from mobile applications and sensors that record participant status continuously over the course of multiple days and weeks. We propose the paired Markov Chain (paired-MC) method, a flexible framework that produces sequences that closely mimic real data while providing a straightforward mechanism for modifying characteristics of the synthesized sequences. We demonstrate the paired-MC method on two datasets, one reflecting daily human activity patterns collected via a smartphone application, and one encoding the intensities of physical activity measured by wearable accelerometers. In both settings, sequences synthesized by paired-MC better capture key characteristics of the real data than alternative approaches.

A linear model of synergetic current drive (SCD) with lower-hybrid wave (LHW) and electron cyclotron wave (ECW) is proposed to efficiently calculate the quantitative SCD efficiency and reveal the conditions for the occurrence of SCD. In this model, the response function dominated by collisions in the presence of LHW is derived from the adjoint equations by using perturbation and Green-Function techniques, where the relativistic effect and the trapped effect are taken into account. The SCD efficiency is compared with the commonly used ECW current drive (ECCD) efficiency in the parameter space using our linear model. The results show two features of the synergy effect, One is that it is inclined to occurs at smaller $y = 2\omega_{c}/\omega$ with the fixed ECW parallel refractive index $n_{\parallel}$, and the other is that the threshold values of $y$, at which the synergy effect becomes sufficiently significant, shifts towards higher values with a decreasing $n_{\parallel}$. The quasilinear simulation on ECCD and SCD efficiency with a two-dimensional Fokker-Planck code are consistent with the results of the linear model in trends. Based on the linear SCD efficiency, criteria for the occurrence and the sufficient significance of the synergy effect are suggested, which indicate that the synergy effect is dependent on the power factor that quantifies the degree of the overlap of the two waves' quasilinear domains, the LHW power, and synergy electrons. The present work provides a method of quick matching and calculating of SCD with LHW and ECW, and may be important for the real-time application of the SCD in future reactors.

In this work, we present an analytical study on the surface plasmon polaritons in a two dimensional parity anomaly Chern insulator. The connections between the topology in the bulk implied by the BHZ model and the dispersion relations of the surface plasmons have been revealed. Anisotropy has been considered during the calculations of the dispersion relations which allows different permittivities perpendicular to the conductive plane. Two surface plasmon modes each contains two branches of dispersion relations have been found. The topologically non-trivial case gives quite different Hall conductivities compared with the trivial one, which leads to significant modifications of the dispersion curves or even the absence of particular branch of the surface plasmons. Our investigations pave a possible way for the detection of the parity anomaly in a two-dimensional Chern insulator via plasmonic responses.

The meeting of astrophysical plasmas and their magnetic fields creates many reconnection sites. We experimentally compare the reconnection rate of laser-driven magnetic reconnection when it takes place at a single site and multiple sites. For a single site, where the ram pressure dominates the magnetic pressure, the measured reconnection rate exceeds the well-established rate of 0.1. However, in the case of multiple close-by sites, we observed a reduction of the reconnection rate. Hybrid-PIC simulations support this observation and suggest that the distortion of the Hall field as well as the concomitant obstruction of one of the outflows are detrimental to the magnetic reconnection rate.

Deciphering the conditions under which neutron captures occur in the Universe to synthesize heavy elements is an endeavour pursued since the 1950s, but that has proven elusive up to now due to the experimental difficulty of generating the extreme neutron fluxes required. It has been evoked that laser-driven (pulsed) neutron sources could produce neutron beams with characteristics suitable to achieve nucleosynthesis in the laboratory. In this scheme, the laser first generates an ultra-high-current, high-energy proton beam, which is subsequently converted into a dense neutron beam. Here we model, in a self-consistent manner, the transport of laser-accelerated protons through the neutron converter, the subsequent neutron generation and propagation, and finally the neutron capture reactions in a gold ($^{197}$Au) chosen as an illustrative example. Using the parameters of present-day available lasers, as well as of those foreseeable in the near future, we find that the final yield of the isotopes containing two more neutrons than the seed nuclei is negligible. Our investigation highlights that the areal density of the laser-driven neutron source is a critical quantity and that it would have to be increased by several orders of magnitude over the current state of the art in order to offer realistic prospects for laser-based generation of neutron-rich isotopes., Comment: 10 pages, 5 figures

A bijection between $(31245,32145,31254,32154)$-avoiding permutations and $(31425,32415,31524,32514)$-avoiding permutations is constructed, which preserves five classical set-valued statistics. Combining with two codings of permutations due respectively to Baril--Vajnovszki and Martinez--Savage proves an enumerative conjecture posed by Gao and Kitaev. Moreover, the generating function for the common counting sequence is proved to be algebraic., Comment: Final remarks are added: 28 pages, 6 figures

The propagation and energy coupling of intense laser beams in plasmas are critical issues in laser-driven inertial confinement fusion. Applying magnetic fields to such a setup has been evoked to enhance fuel confinement and heating, and mitigate laser energy losses. Here we report on experimental measurements demonstrating improved transmission and increased smoothing of a high-power laser beam propagating in an underdense magnetized plasma. We also measure enhanced backscattering, which our simulations show is due to hot electrons confinement, thus leading to reduced target preheating.

Laguerre histories (restricted or not) are certain weighted Motzkin paths with two types of level steps. They are, on one hand, in natural bijection with the set of permutations, and on the other hand, yield combinatorial interpretations for the moments of Laguerre polynomials via Flajolet's combinatorial theory of continued fractions. In this paper, we first introduce a reflection-like involution on restricted Laguerre histories. Then, we demonstrate its power by composing this involution with three bijections due to Fran\ccon-Viennot, Foata-Zeilberger, and Yan-Zhou-Lin, respectively. A host of equidistribution results involving various (multiset-valued) permutation statistics follow from these applications. As byproducts, seven apparently new Mahonian statistics present themselves; new interpretations of known Mahonian statistics are discovered as well. Finally, in our effort to show the interconnections between these Mahonian statistics, we are naturally led to a new link between the variant Yan-Zhou-Lin bijection and the Kreweras complement., Comment: 7 figures and 3 tables

Colliding collisionless shocks appear in a great variety of astrophysical phenomena and are thought to be possible sources of particle acceleration in the Universe. We have previously investigated particle acceleration induced by single super-critical shocks (whose magnetosonic Mach number is higher than the critical value of 2.7) (Yao et al. 2021, 2022), as well as the collision of two sub-critical shocks (Fazzini et al. 2022). Here, we propose to make measurements of accelerated particles from interpenetrating super-critical shocks to observe the ''phase-locking effect'' (Fazzini et al. 2022) from such an event. This effect is predicted to significantly boost the energy spectrum of the energized ions compared to a single supercritical collisionless shock. We thus anticipate that the results obtained in the proposed experiment could have a significant impact on our understanding of one type of primary source (acceleration of thermal ions as opposed to secondary acceleration mechanisms of already energetic ions) of ion energization of particles in the Universe.

Realizing the full potential of ultrahigh-intensity lasers for particle and radiation generation will require multi-beam arrangements due to technology limitations. Here, we investigate how to optimize their coupling with solid targets. Experimentally, we show that overlapping two intense lasers in a mirror-like configuration onto a solid with a large preplasma can greatly improve the generation of hot electrons at the target front and ion acceleration at the target backside. The underlying mechanisms are analyzed through multidimensional particle-in-cell simulations, revealing that the self-induced magnetic fields driven by the two laser beams at the target front are susceptible to reconnection, which is one possible mechanism to boost electron energization. In addition, the resistive magnetic field generated during the transport of the hot electrons in the target bulk tends to improve their collimation. Our simulations also indicate that such effects can be further enhanced by overlapping more than two laser beams.

The double Weyl semimetal (DWSM) is a newly proposed topological material that hosts Weyl points with chiral charge n=2. The disorder effect in DWSM is investigated by adopting the tight-binding Hamiltonian. Using the transfer matrix method and the noncommutative Kubo formula, we numerically calculate the localization length and the Hall conductivity in the presence of the on-site nonmagnetic disorder or orbital (spin-flip) disorders, and give the corresponding global phase diagrams. For the on-site nonmagnetic disorder, the system undergoes the DWSM-3D quantum anomalous hall (3D QAH) and normal insulator (NI)-DWSM phase transitions, and evolves into the diffusive metal (DM) phase before being localized by strong disorders, which is consistent with the Weyl semimetal. For \sigma_x orbital disorder, we find that increasing disorder can generate a pair of Weyl nodes at the boundary of the Brillouin zone and induce a 3D QAH-DWSM phase transition. Then we investigate the combined effect of orbital disorders for both disordered 3D QAH phase and DWSM phase. The disorder-induced transitions can be well understood in terms of an effective medium theory based on self-consistent Born approximation., Comment: 8 pages, 9 figures

Contemporary ultraintense, short-pulse laser systems provide extremely compact setups for the production of high-flux neutron beams, such as those required for nondestructive probing of dense matter, research on neutron-induced damage in fusion devices or laboratory astrophysics studies. Here, by coupling particle-in-cell and Monte Carlo numerical simulations, we examine possible strategies to optimise neutron sources from ion-induced nuclear reactions using 1-PW, 20-fs-class laser systems. To improve the ion acceleration, the laser-irradiated targets are chosen to be ultrathin solid foils, either standing alone or preceded by a plasma layer of near-critical density to enhance the laser focusing. We compare the performance of these single- and double-layer targets, and determine their optimum parameters in terms of energy and angular spectra of the accelerated ions. These are then sent into a converter to generate neutrons via nuclear reactions on beryllium and lead nuclei. Overall, we identify configurations that result in neutron yields as high as $\sim 10^{10}\,\rm n\,sr^{-1}$ in $\sim 1$-cm-thick converters or instantaneous neutron fluxes above $10^{23}\,\rm n\,cm^{-2}\,s^{-1}$ at the backside of $\lesssim 100$-$\mu$m-thick converters. Considering a realistic repetition rate of one laser shot per minute, the corresponding time-averaged neutron yields are predicted to reach values ($\gtrsim 10^7\,\rm n \,sr^{-1}\,s^{-1}$) well above the current experimental record, and this even with a mere thin foil as a primary target. A further increase in the time-averaged yield up to above $10^8\,\rm sr^{-1}\,s^{-1}$ is foreseen using double-layer targets., Comment: 16 pages, 8 figures, 2 tables

Colliding collisionless shocks appear in a great variety of astrophysical phenomena and are thought to be possible sources of particle acceleration in the Universe. To investigate the detailed dynamics of this phenomenon, we have performed a dedicated laboratory experiment. We have generated two counter-streaming subcritical collisionless magnetized shocks by irradiating two teflon (CF$_2$) targets with 100 J, 1 ns laser beams on the LULI2000 laser facility. The interaction region between the plasma flows was pre-filled with a low density background hydrogen plasma and initialized with an externally applied homogeneous magnetic field perpendicular to the shocks. We report here on measurements of the plasma density and temperature during the formation of the supercritical shocks, their transition to subcritical, and final interpenetration. We have also modeled the macroscopic evolution of the system via hydrodynamic simulations and the microphysics at play during the interaction via Particle-In-Cell simulations. The main goal was to understand what was the effect of the second shock on particle energization. We found that in the presence of two shocks the ambient ions reach energies around 1.5 times of the ones obtained with single shocks. Both the presence of the downstream zone of the second shock and of the downstream zone common for the two shocks play a role in the different energization: the characteristics of the perpendicular electric fields in the two areas allow, indeed, certain particles to keep being accelerated or to avoid being decelerated.

Magnetic reconnection is a ubiquitous astrophysical process that rapidly converts magnetic energy into some combination of plasma flow energy, thermal energy, and non-thermal energetic particles, including energetic electrons. Various reconnection acceleration mechanisms in different low-$\beta$ (plasma-to-magnetic pressure ratio) and collisionless environments have been proposed theoretically and studied numerically, including first- and second-order Fermi acceleration, betatron acceleration, parallel electric field acceleration along magnetic fields, and direct acceleration by the reconnection electric field. However, none of them have been heretofore confirmed experimentally, as the direct observation of non-thermal particle acceleration in laboratory experiments has been difficult due to short Debye lengths for \textit{in-situ} measurements and short mean free paths for \textit{ex-situ} measurements. Here we report the direct measurement of accelerated non-thermal electrons from low-$\beta$ magnetically driven reconnection in experiments using a laser-powered capacitor coil platform. We use kiloJoule lasers to drive parallel currents to reconnect MegaGauss-level magnetic fields in a quasi-axisymmetric geometry. The angular dependence of the measured electron energy spectrum and the resulting accelerated energies, supported by particle-in-cell simulations, indicate that the mechanism of direct electric field acceleration by the out-of-plane reconnection electric field is at work. Scaled energies using this mechanism show direct relevance to astrophysical observations. Our results therefore validate one of the proposed acceleration mechanisms by reconnection, and establish a new approach to study reconnection particle acceleration with laboratory experiments in relevant regimes., Comment: 13 pages, 6 figures

Single-crystal europium iron garnet (EuIG) thin films epitaxially strain-grown on gadolinium gallium garnet (GGG)(100) substrates using off-axis sputtering have strain-induced perpendicular magnetic anisotropy (PMA). By varying the sputtering conditions, we have tuned the europium/iron (Eu/Fe) composition ratios in the films to tailor the film strains. The films exhibited an extremely smooth, particle-free surface with roughness as low as 0.1 nm as observed using atomic force microscopy. High-resolution x-ray diffraction analysis and reciprocal space maps showed in-plane epitaxial film growth, very smooth film/substrate interface, excellent film crystallinity with a small full width at half maximum of 0.012$^{\circ}$ in the rocking curve scans, and an in-plane compressive strain without relaxation. In addition, spherical aberration-corrected scanning transmission electron microscopy showed an atomically abrupt interface between the EuIG film and GGG. The measured squarish out-of-plane magnetization-field hysteresis loops by vibrating sample magnetometry in conjunction with the measurements from angle-dependent x-ray magnetic dichroism demonstrated the PMA in the films. We have tailored the magnetic properties of the EuIG thin films, including saturation magnetization ranging from 71.91 to 124.51 emu/c.c. (increase with the (Eu/Fe) ratios), coercive field from 27 to 157.64 Oe, and the strength of PMA field ($H_\bot$) increasing from 4.21 to 18.87 kOe with the in-plane compressive strain from -0.774 to -1.044%. We have also investigated spin transport in Pt/EuIG bi-layer structure and evaluated the real part of spin mixing conductance to be $3.48\times10^{14} {\Omega}^{-1}m^{-2}$. We demonstrated the current-induced magnetization switching with a low critical switching current density of $3.5\times10^6 A/cm^2$, showing excellent potential for low-dissipation spintronic devices., Comment: 29 pages, 9 figures, 1 table

The systematic study of inversion sequences avoiding triples of relations was initiated by Martinez and Savage. For a triple $(\rho_1,\rho_2,\rho_3)\in\{<,>,\leq,\geq,=,\neq,-\}^3$, they introduced $\I_n(\rho_1,\rho_2,\rho_3)$ as the set of inversion sequences $e=e_1e_2\cdots e_n$ of length $n$ such that there are no indices $1\leq i)$ and $\I_n(>,\neq,\geq)$ that preserves the distinct entries and further posed a symmetry conjecture of ascents on these two classes of restricted inversion sequences. Concerning Lin's symmetry conjecture, an algebraic proof using the kernel method was recently provided by Andrews and Chern, but a bijective proof still remains mysterious. The goal of this article is to establish bijectively both Lin's symmetry conjecture and the $\gamma$-positivity of the ascent polynomial on $\I_n(>,\neq,>)$. The latter result implies that the distribution of ascents on $\I_n(>,\neq,>)$ is symmetric and unimodal., Comment: 23 pages, 2 figures

We build a Cu-MoTe2-Cu device model and use first-principles density functional theory to study the transport properties of single-layer Td-MoTe2. We obtained the effect of strain on the energy band structure, transport properties, and photocurrent. The strain-induced photocurrent shows an anisotropy that reflects the modulation of the energy bands, including the Weyl point, by strain. The photocurrent can be suppressed to almost zero when the strain is applied along the vacuum direction. In contrast, the photocurrent can be significantly increased when the strain is applied along the transport direction. The transport properties and magnitude of the photocurrent in the MoTe2-based device can be effectively modulated by adjusting the strength and direction of the strain., Comment: 6 pages, 6 figures

We study the effect of the strain on the band structure and the valley-dependent transport property of graphene heterojunctions. It is found that valley-dependent separation of electrons can be achieved by utilizing the strain and on-site energies. In the presence of the strain, the values of the transmission can be effectively adjusted by changing the strengths of the strain, while the transport angle basically keeps unchanged. When an extra on-site energy is simultaneously applied to the central scattering region, not only are the electrons of valleys K and K' separated into two distinct transmission lobes in opposite transverse directions, but the transport angles of two valleys can be significantly changed. Therefore, one can realize an effective modulation of valley-dependent transport by changing the strength and stretch angle of the strain and on-site energies, which can be exploited for graphene-based valleytronics devices., Comment: 7 pages, 10 figures

In this work, we propose a ferromagnetic Bi$_2$Se$_3$ as a candidate to hold the coexistence of Weyl- and nodal-line semimetal phases, which breaks the time reversal symmetry. We demonstrate that the type-I Weyl semimetal phase, type-I-, type-II- and their hybrid nodal-line semimetal phases can arise by tuning the Zeeman exchange field strength and the Fermi velocity. Their topological responses under U(1) gauge field are also discussed. Our results raise a new way for realizing Weyl and nodal-line semimetals and will be helpful in understanding the topological transport phenomena in three-dimensional material systems.

We present the results of the first commissioning phase of the ``short focal length'' area (SFA) of the Apollon laser facility (located in Saclay, France), which was performed with the first available laser beam (F2), scaled to a nominal power of one petawatt. Under the conditions that were tested, this beam delivered on target pulses of 10 J average energy and 24 fs duration. Several diagnostics were fielded to assess the performance of the facility. The on-target focal spot, its spatial stability, the temporal intensity profile prior to the main pulse, as well as the resulting density gradient formed at the irradiated side of solid targets, have been thoroughly characterized, with the goal of helping users design future experiments. Emissions of energetic electrons, ions, and electromagnetic radiation were recorded, showing good laser-to-target coupling efficiency and an overall performance comparable with that of similar international facilities. This will be followed in 2022 by a further commissioning stage at the multi-petawatt level.

Due to their high cost of acquisition and operation, there are still a limited number of high-yield, high-flux neutron source facilities worldwide. In this context, laser-driven neutron sources offer a promising, cheaper alternative to those based on large-scale accelerators, with, in addition, the potential of generating compact neutron beams of high brightness and ultra-short duration. In particular, the predicted capability of next-generation petawatt (PW)-class lasers to accelerate protons beyond the 100 MeV range should unlock efficient neutron generation through spallation reactions. In this paper, this scenario is investigated numerically through particle-in-cell and Monte Carlo simulations, modeling, respectively, the laser acceleration of protons from thin-foil targets and their subsequent conversion into neutrons in secondary heavy-ion targets. Laser parameters relevant to the 1 PW LMJ-PETAL and 1-10 PW Apollon systems are considered. Under such conditions, neutron fluxes exceeding $10^{23}\,\rm n\,cm^{-2}\,s^{-1}$ are predicted, opening up attractive fundamental and applicative prospects., Comment: 16 pages, 13 figures

Collisionless shocks are ubiquitous in the Universe and are held responsible for the production of non-thermal particles and high-energy radiation. In the absence of particle collisions in the system, theoretical works show that the interaction of an expanding plasma with a pre-existing electromagnetic structure (as in our case) is able to induce energy dissipation and allow for shock formation. Shock formation can alternatively take place when two plasmas interact, through microscopic instabilities inducing electromagnetic fields which are able in turn to mediate energy dissipation and shock formation. Using our platform where we couple a fast-expanding plasma induced by high-power lasers (JLF/Titan at LLNL and LULI2000) with high-strength magnetic fields, we have investigated the generation of magnetized collisionless shock and the associated particle energization. We have characterized the shock to be collisionless and super-critical. We report here on measurements of the plasma density, temperature, the electromagnetic field structures, and particle energization in the experiments, under various conditions of ambient plasma and B-field. We have also modeled the formation of the shocks using macroscopic hydrodynamic simulations and the associated particle acceleration using kinetic particle-in-cell simulations. As a companion paper of \citet{yao2020laboratory}, here we show additional results of the experiments and simulations, providing more information to reproduce them and demonstrating the robustness of our interpreted proton energization mechanism to be shock surfing acceleration.

Aims. EXor-type objects are protostars that display powerful UV-optical outbursts caused by intermittent and powerful events of magnetospheric accretion. These objects are not yet well investigated and are quite difficult to characterize. Several parameters, such as plasma stream velocities, characteristic densities, and temperatures, can be retrieved from present observations. As of yet, however, there is no information about the magnetic field values and the exact underlying accretion scenario is also under discussion. Methods. We use laboratory plasmas, created by a high power laser impacting a solid target or by a plasma gun injector, and make these plasmas propagate perpendicularly to a strong external magnetic field. The propagating plasmas are found to be well scaled to the presently inferred parameters of EXor-type accretion event, thus allowing us to study the behaviour of such episodic accretion processes in scaled conditions. Results. We propose a scenario of additional matter accretion in the equatorial plane, which claims to explain the increased accretion rates of the EXor objects, supported by the experimental demonstration of effective plasma propagation across the magnetic field. In particular, our laboratory investigation allows us to determine that the field strength in the accretion stream of EXor objects, in a position intermediate between the truncation radius and the stellar surface, should be of the order of 100 gauss. This, in turn, suggests a field strength of a few kilogausses on the stellar surface, which is similar to values inferred from observations of classical T Tauri stars.

Permutation statistics $\wnm$ and $\rlm$ are both arising from permutation tableaux. $\wnm$ was introduced by Chen and Zhou, which was proved equally distributed with the number of unrestricted rows of a permutation tableau. While $\rlm$ is showed by Nadeau equally distributed with the number of $1$'s in the first row of a permutation tableau. In this paper, we investigate the joint distribution of $\wnm$ and $\rlm$. Statistic $(\rlm,\wnm,\rlmin,\des,(\underline{321}))$ is shown equally distributed with $(\rlm,\rlmin,\wnm,\des,(\underline{321}))$ on $S_n$. Then the generating function of $(\rlm,\wnm)$ follows. An involution is constructed to explain the symmetric property of the generating function. Also, we study the triple statistic $(\wnm,\rlm,\asc)$, which is shown to be equally distributed with $(\rlmax-1,\rlmin,\asc)$ as studied by Josuat-Verg$\grave{e}$s. The main method we adopt throughout the paper is constructing bijections based on a block decomposition of permutations., Comment: 19pages,1 figure

Charged particles can be accelerated to high energies by collisionless shock waves in astrophysical environments, such as supernova remnants. By interacting with the magnetized ambient medium, these shocks can transfer energy to particles. Despite increasing efforts in the characterization of these shocks from satellite measurements at the Earth's bow shock and powerful numerical simulations, the underlying acceleration mechanism or a combination thereof is still widely debated. Here, we show that astrophysically relevant super-critical quasi-perpendicular magnetized collisionless shocks can be produced and characterized in the laboratory. We observe characteristics of super-criticality in the shock profile as well as the energization of protons picked up from the ambient gas to hundreds of keV. Kinetic simulations modelling the laboratory experiment identified shock surfing as the proton acceleration mechanism. Our observations not only provide the direct evidence of early stage ion energization by collisionless shocks, but they also highlight the role this particular mechanism plays in energizing ambient ions to feed further stages of acceleration. Furthermore, our results open the door to future laboratory experiments investigating the possible transition to other mechanisms, when increasing the magnetic field strength, or the effect induced shock front ripples could have on acceleration processes.

We analyze, using experiments and 3D MHD numerical simulations, the dynamics and radiative properties of a plasma ablated by a laser (1 ns, 10$^{12}$-10$^{13}$ W/cm$^2$) from a solid target, as it expands into a homogeneous, strong magnetic field (up to 30 T) transverse to its main expansion axis. We find that as soon as 2 ns after the start of the expansion, the plasma becomes constrained by the magnetic field. As the magnetic field strength is increased, more plasma is confined close to the target and is heated by magnetic compression. We also observe a dense slab that rapidly expands into vacuum after ~ 8 ns; however, this slab contains only ~ 2 % of the total plasma. As a result of the higher density and increased heating of the confined plasma, there is a net enhancement of the total x-ray emissivity induced by the magnetization., Comment: 15 pages, 4 figures, Supplementary Information, submitted to PRL

We study the reduced energy spectrum $\{E_{i}^{(n)}\}$, which is constructed by picking one level from every $n$ levels of the original spectrum $\{E_{i}\}$, in a Gaussian ensemble of random matrix with Dyson index $\beta\in \left( 0,\infty \right) $. It's shown $\{E_{i}^{(n)}\}$ bears the same form of probability distribution as $\{E_{i}\}$ with a rescaled parameter $\gamma =\frac{n(n+1)}{2}\beta +n-1$. Notably, the $n$-th order level spacing and non-overlapping gap ratio in $\{E_{i}\}$ become the lowest-order ones in $\{E_{i}^{(n)}\}$, hence their distributions will rescale in an identical way. Numerical evidences are provided by simulating random spin chain as well as modelling random matrices. Our results establish the higher-order spacing distributions in random matrix ensembles beyond GOE,GUE,GSE, and reveals a hierarchy of structures hidden in the energy spectrum., Comment: 8 pages, 4 figures

Investigating in the laboratory the process of matter accretion onto forming stars through scaled experiments is important in order to better understand star and planetary systems formation and evolution. Such experiments can indeed complement observations by providing access to the processes with spatial and temporal resolution. A first step has been made in [G. Revet et al., Science Advances 3, e1700982 (2017), arXiv:1708.02528]. in allowing such investigations. It revealed the existence of a two components stream: a hot shell surrounding a cooler inner stream. The shell was formed by matter laterally ejected upon impact and refocused by the local magnetic field. That laboratory investigation was limited tonormal incidence impacts. However, in young stellar objects, complex structure of magnetic fields causes variability of the incidentangles of the accretion columns. This led us to undertake an investigation, using laboratory plasmas, of the consequence of having a slanted accretion impacting a young star. Here we use high power laser interactions and strong magnetic field generation in the laboratory, complemented by numerical simulations, to study the asymmetry induced upon accretion structures when columns of matter impact the surface of young stars with an oblique angle. Compared to the scenario where matter accretes normal to the star surface, we observe strongly asymmetric plasma structure, strong lateral ejecta of matter, poor confinement of the accreted material and reduced heating compared to the normal incidence case. Thus, slanted accretion is a configuration that seems to be capable of inducing perturbations of the chromosphere and hence possibly influence the level of activity of the corona.

The shaping of astrophysical outflows into bright, dense and collimated jets due to magnetic pressure is here investigated using laboratory experiments. We notably look at the impact on jet collimation of a misalignment between the outflow, as it stems from the source, and the magnetic field. For small misalignments, a magnetic nozzle forms and redirects the outflow in a collimated jet. For growing misalignments, this nozzle becomes increasingly asymmetric, disrupting jet formation. Our results thus suggest outflow/magnetic field misalignment to be a plausible key process regulating jet collimation in a variety of objects from our Sun's outflows to extragalatic jets. Furthermore, they provide a possible interpretation for the observed structuring of astrophysical jets. Jet modulation could be interpreted as the signature of changes over time in the outflow/ambient field angle, and the change in the direction of the jet could be the signature of changes in the direction of the ambient field.

The notion of a 12-representable graph was introduced by Jones et al.. This notion generalizes the notions of the much studied permutation graphs and co-interval graphs. It is known that any 12-representable graph is a comparability graph, and also that a tree is 12-representable if and only if it is a double caterpillar. Moreover, Jones et al.\ initiated the study of 12-representability of induced subgraphs of a grid graph, and asked whether it is possible to characterize such graphs. This question in is meant to be about induced subgraphs of a grid graph that consist of squares, which we call square grid graphs. However, an induced subgraph in a grid graph does not have to contain entire squares, and we call such graphs line grid graphs. In this paper we answer the question of Jones et al.\ by providing a complete characterization of $12$-representable square grid graphs in terms of forbidden induced subgraphs. Moreover, we conjecture such a characterization for the line grid graphs and give a number of results towards solving this challenging conjecture. Our results are a major step in the direction of characterization of all 12-representable graphs since beyond our characterization, we also discuss relations between graph labelings and 12-representability, one of the key open questions in the area., Comment: To appear in Discussiones Mathematicae Graph Theory

Magnetized laser-produced plasmas are central to many novel laboratory astrophysics and inertial confinement fusion studies, as well as in industrial applications. Here we provide the first complete description of the three-dimensional dynamics of a laser-driven plasma plume expanding in a 20 T transverse magnetic field. The plasma is collimated by the magnetic field into a slender, rapidly elongating slab, whose plasma-vacuum interface is unstable to the growth of the "classical", fluid-like magnetized Rayleigh-Taylor instability., Comment: Accepted for publication in Physical Review Letters

Magnetic reconnection occurs when two plasmas having co-planar but anti-parallel magnetic fields meet. At the contact point, the field is locally annihilated and the magnetic energy can be released into the surrounding plasma. Theory and numerical modelling still face many challenges in handling this complex process, the predictability of which remains elusive. Here we test, through a laboratory experiment conducted in a controlled geometry, the effect of changing the field topology from two-dimensional to three-dimensional. This is done by imposing an out-of-plane (guide) magnetic field of adjustable strength. A strong slowing down or even halting of symmetric reconnection is observed, even for a weak guide-field. Concomitantly, we observe a delayed heating of the plasma in the reconnection region and modified particle acceleration, with super-Alfvenic outflows ejected along the reconnection layer. These observations highlight the importance of taking into account three-dimensional effects in the many reconnection events taking place in natural and laboratory environments., Comment: 5 figures

We show efficient laser driven proton acceleration up to 14MeV from a 50 $\mu$m thick cryogenic hydrogen ribbon. Pulses of the short pulse laser ELFIE at LULI with a pulse length of $\approx$ 350 fs at an energy of 8 J per pulse are directed onto the target. The results are compared to proton spectra from metal and plastic foils with different thicknesses and show a similar good performance both in maximum energy as well as in proton number. Thus, this target type is a promising candidate for experiments with high repetition rate laser systems., Comment: 9 pages