In this paper, a new type of artificial viscosity, based on the divergence of velocity gradient, is developed for the Lagrangian Lax-Wendroff cell-centered schemes. Similar approaches led previously to the development of tensor viscosity in methods with staggered grids. The velocity gradient can be split into the compressible, symmetric, and rotational components that each have a different effect on shock waves or rotational flows. We demonstrate the effects of using each component or their combinations on a set of typical hydrodynamics testing problems.The new artificial viscosity leads to far greater robustness and symmetry compared to the original HLL-type one for the Saltzman test. For treating radial shocks (Noh), the best results are achieved by combination of symmetric and rotational terms, while for the tests involving rotational flow (Taylor-Green vortex) or instability formation (Richtmyer-Meshkov), the compressible part of the velocity gradient is more suitable, as it does not suppress the vorticity of the flow.

An experimental platform for laser-driven ion (sub-MeV) acceleration and potential applications was commissioned at the HiLASE laser facility. The auxiliary beam of the Bivoj laser system operating at a GW level peak power (~10 J in 5–10 ns) and 1–10 Hz repetition rate enabled a stable production of high-current ion beams of multiple species (Al, Ti, Fe, Si, Cu, and Sn). The produced laser–plasma ion sources were fully characterized against the laser intensity on the target (1013–1015 W/cm2) by varying the laser energy, focal spot size, and pulse duration. The versatility and tuneability of such high-repetition-rate laser–plasma ion sources are of potential interest for user applications. Such a statistically accurate study was facilitated by the large amount of data acquired at the high repetition rate (1–10 Hz) provided by the Bivoj laser system.

This paper describes a cell-centered Lax-Wendroff type scheme with artificial dissipation for Lagrangian fluid dynamics on general unstructured 3D meshes. The method is an extension of a similar 2D approach to 3D. The dissipative terms are inspired by the finite volume HLL flux formulation and are used as artificial viscosity in the momentum equation and as artificial energy flux in the energy equation. Special treatment is formulated for contact discontinuities and mesh-aligned interfaces. The proposed second order method provides reasonable results for typical 3D hydrodynamic tests, such as Noh, Sedov, Kidder and spherical Sod problems.

In the context of ion acceleration driven by ultra-high contrast lasers using thin foils, there is a clear trend towards increasing ion energy when the target thickness is reduced. However when the target is too thin and the prepulse strength is not negligible, this trend is reversed due to degradation of the target mainly caused by prepulse-induced shocks, among other effects (thermal plasma expansion, early onset of transparency, etc). In this paper, we propose and motivate the use of multi-layered targets for the purpose of enhancing the target normal sheath acceleration mechanism by means of attenuating the shock waves inside the target. It is demonstrated through hydrodynamic simulations that multi-layered targets, composed of alternating layers of plastic and gold, can significantly delay the time of shock wave breakout, reducing the shock energy that breaks out of the target and shortening the plasma scale-length. This approach paves the way for enhanced laser-driven ion acceleration using thinner targets even for relatively low contrast lasers.

In this work, we investigate the application of the plasma shutters for heavy ion acceleration driven by a high-intensity laser pulse. We use particle-in-cell and hydrodynamic simulations. The laser pulse, transmitted through the opaque shutter, gains a steep-rising front and its peak intensity is locally increased at the cost of losing part of its energy. These effects have a direct influence on subsequent ion acceleration from the ultrathin target behind the shutter. In our 3D simulations of silicon nitride plasma shutter and a silver target, the maximal energy of high-Z ions increases significantly when the shutter is included for both linearly and circularly polarized laser pulses. Moreover, application of the plasma shutter for linearly polarized pulse results in focusing of ions toward the laser axis in the plane perpendicular to the laser polarization. The generated high energy ion beam has significantly lower divergence compared to the broad ion cloud, generated without the shutter. The effects of prepulses are also investigated assuming a double plasma shutter. The first shutter can withstand the assumed sub-ns prepulse (treatment of ns and ps prepulses by other techniques is assumed) and the pulse shaping occurs via interaction with the second shutter. On the basis of our theoretical findings, we formulated an approach toward designing a double plasma shutter for high-intensity and high-power laser pulses and built a prototype.

Magneto-hydrodynamics is one of the foremost models in plasma physics with applications in inertial confinement fusion, astrophysics and elsewhere. Advanced numerical methods are needed to get an insight into the complex physical phenomena. The classical Lagrangian methods are typically limited to the low orders of convergence and suffer from violation of the divergence-free condition for magnetic field or conservation of the invariants. This paper is the first part of a new series about high-order non-ideal magneto-hydrodynamics, where a multi-dimensional conservative Lagrangian method based on curvilinear finite elements is presented. The condition on zero divergence of magnetic field and conservation of mass, momentum, magnetic flux and the total energy are satisfied exactly. The curvilinear elements prevent entangling of the computational mesh and its imprinting into the solution. A high-order conservative time integration is applied, where an arbitrary order of convergence is attained for problems of ideal magneto-hydrodynamics. The resistive magnetic field diffusion is solved by an implicit scheme. Description of the method is given and multiple test problems demonstrating properties of the scheme are performed. The construction of the method and possible future directions of development are discussed.

In this work we investigated the use of a plasma shutter in the form of a thin foil for laser-driven ion acceleration enhancement. It is shown with the help of 3D particle-in-cell simulations that the laser pulse intensity can be increased and its profile steepened after burning through the plasma shutter. The enhanced intensity profile has a positive effect on the subsequent ion acceleration from the main foil, significantly increasing the maximal ion energy. The pre-expansion of the plasma shutter caused by prepulses is investigated using 2D hydrodynamic simulations. A scheme using a double plasma shutter configuration (the first one filtering out the prepulses and the second one shaping the main pulse) is proposed.

Detailed description of the transport processes in plasma is crucial for many disciplines. When the mean-free-path of the electrons is comparable or exceeds a characteristic length scale of the plasma profile, non-local behaviorcan be observed. Predictions of the diffusion theory are not valid and non-local electric and magnetic fields are generated. Kinetic modelingof these phenomena on time scales several orders of magnitude longer than the electron-electron collision time has proven to be cumbersome due to prohibitive requirements on the time step and violation of the conservation laws in the classical explicit Vlasov-Fokker-Planck methods. Therefore, a multi-dimensional conservative implicit Vlasov-Fokker-Planck-Maxwell method is proposed, where the distribution function is approximated by a truncated Cartesian tensor expansion. The electric and magnetic fields are modeledself-consistently, describing the generation process and emergence of non-locality in detail. Mixed finite elements are employed in space and the velocity dimension is discretized by staggered finite differences. Conservation properties are proved theoretically and the overall features are benchmarked on a series of physically representative problems. The second order convergence in velocity and the spatial order proportional to the polynomial order of the finite elements is shown. Further possible extensions of the method are discussed. (C) 2021 Elsevier Inc. All rights reserved.

The magneto-hydrodynamic model is widely used for description of magnetized fluids in plasma dynamics, microfluidics, astrophysics and many other applications. In terms of modelling, the Lagrangian formulation is favourable for the rapid expansion during laser­target interaction for example. This is the case for inertial fusion and laboratory astrophysics applications, which are our primary interest. However, the proposed numerical method remains general and can be applied elsewhere. The conservation properties and divergence-free magnetic field are crucial aspects, which are not satisfied by the traditional numerical schemes. Here, the Lagrangian hydrodynamics using curvilinear finite elements is extended to the resistive magneto-hydrodynamics. An energy-conserving numerical scheme is formulated maintaining divergence-free magnetic field. The mixed finite element formulation provides theoretically arbitrary order of the spatial convergence and application on unstructured Lagrangian grids in multiple dimensions. An example of a physically relevant numerical simulation is presented.

In this article we present a 1D single-material conservative remapping method that relies on high accurate reconstructions: polynomial (P-4, P-1 with slope limiter) and non-linear hyperbolic tangent (THINC) representations. Such remapping procedure is intended to be used pairwise with a cell-centered Lagrangian scheme along with a rezone strategy to build a so-called indirect Arbitrary-Lagrangian-Eulerian scheme. Most of practically used Lagrangian schemes are second-order accurate. The goal of this work is to handle with accuracy contact using THINC reconstructions. At the same time, the smooth part of the solution is dealt with quartic polynomials, resulting locally in fifth order accurate remapping method. To ensure robustness, TVD-like reconstructions (P-1 with slope limiter) are employed otherwise. A simple feature tracking algorithm is designed to assign a reconstruction type per cell (P-4, P-1(lim) or THINC). This tracking algorithm is based on the nature of the contact waves which are traveling at the fluid velocity, while the shocks are compressive and detectable by following a change of cell volumes. Numerical results assess the behavior of such a remapping method on pure remapping problems of a scalar quantity and in the context of the full hydrodynamics equations. The associated indirect cell-centered ALE numerical scheme is run and produces numerical results that are presented to assess the extreme accuracy gained by such a remapping procedure employing a mix of reconstruction types. (C) 2020 Elsevier Ltd. All rights reserved.

We present a multi-material cell model (closure model) for demanding arbitrary Lagrangian-Eulerian (ALE) simulations of fluids and solids. It is based on the interface-aware sub-scale dynamics (IASSD) approach which utilizes the exact material interface geometry within the computational cell to calculate internal material interactions. Our formulation of the closure model also aims to improve the accuracy in low-speed impact events. Voids are used to represent ambient vacuum and internal free boundaries of the distinct materials. Void regions can close and open at contact surfaces, allowing a transition from contact physics to free motion in vacuum. The coupling of void closure and opening with a new formulation of the IASSD model for solids is tested on several one- and two-dimensional numerical examples, ranging from gas expansion in vacuum to planar and round object impacts at various speeds. (C) 2020 Published by Elsevier Ltd.

The nuclear reaction known as proton-boron fusion has been triggered by a subnanosecond laser system focused onto a thick boron nitride target at modest laser intensity (∼10^{16}W/cm^{2}), resulting in a record yield of generated α particles. The estimated value of α particles emitted per laser pulse is around 10^{11}, thus orders of magnitude higher than any other experimental result previously reported. The accelerated α-particle stream shows unique features in terms of kinetic energy (up to 10 MeV), pulse duration (∼10 ns), and peak current (∼2 A) at 1 m from the source, promising potential applications of such neutronless nuclear fusion reactions. We have used a beam-driven fusion scheme to explain the total number of α particles generated in the nuclear reaction. In this model, protons accelerated inside the plasma, moving forward into the bulk of the target, can interact with ^{11}B atoms, thus efficiently triggering fusion reactions. An overview of literature results obtained with different laser parameters, experimental setups, and target compositions is reported and discussed.

The second and final year of the Erasmus Plus programme ’Innovative Education and Training in high power laser plasmas’, otherwise known as PowerLaPs, is described. The PowerLaPs programme employs an innovative paradigm in that it is a multi-centre programme, where teaching takes place in five separate institutes with a range of different aims and styles of delivery. The ’in-class’ time is limited to 4 weeks a year, and the programme spans 2 years. PowerLaPs aims to train students from across Europe in theoretical, applied and laboratory skills relevant to the pursuit of research in laser plasma interaction physics and inertial confinement fusion. Lectures are intermingled with laboratory sessions and continuous assessment activities. The programme, which is led by workers from the Hellenic Mediterranean University and supported by co-workers from the Queen’s University Belfast, the University of Bordeaux, the Czech Technical University in Prague, Ecole Polytechnique, the University of Ioannina, the University of Salamanca and the University of York, has just finished its second and final year. Six Learning Teaching Training activities have been held at the Queen’s University Belfast, the University of Bordeaux, the Czech Technical University, the University of Salamanca and the Institute of Plasma Physics and Lasers of the Hellenic Mediterranean University. The last of these institutes hosted two 2-week-long Intensive Programmes, while the activities at the other four universities were each 5 days in length. In addition, a ’Multiplier Event’ was held at the University of Ioannina, which will be briefly described. In this second year,the work has concentrated on training in both experimental diagnostics and simulation techniques appropriate to the study of plasma physics, high power laser matter interactions and high energy density physics. The nature of the programme will be described in detail, and some metrics relating to the activities carried out will be presented. In particular, this paper will focus on the overall assessment of the programme.

Models of the laser propagation and absorption are a crucial part of the laser–plasma interaction models. Hydrodynamic codes are afflicted by usage of the simplified, not self-consistent, models of the geometrical optics, limiting their physical accuracy. A robust and efficient method is presented for computing the stationary wave solution, not restricted to this field of application exclusively. The method combines the semi-analytic and high-order differential approaches to benefit from both. Flexibility of the discretization is maintained, including the discontinuous methods. Performance of the model is evaluated for the problem of a transition layer by comparison with the analytic solution. Reliable results on coarse computational meshes and high convergence rates on fine meshes are obtained. The relevance to the current fusion research and non-local energy transport is pointed out.

Hydrodynamic simulations of laser-produced plasmas represent a useful tool allowing them to investigate processes during laser-plasma interaction, which are often impossible to observe directly during the experiments. They allow not only interpretation of experimental results, but are also often used for designing the experimental setup or detailed analysis of particular processes during the experiment. In this paper, we describe the application of the Arbitrary Lagrangian-Eulerian (ALE) numerical methods, benefiting from the computational mesh moving with the fluid in a Lagrangian manner, while enforcing its geometric quality by a regular mesh smoothing mechanism. The basic ALE algorithm is enhanced by additional physical models (realistic EOS, laser absorption mechanism, heat conductivity model, cylindrical geometry, two-temperature model, phase transition model, magnetic field model, . . . ), allowing to perform realistic simulations of laser/target interactions. The performance of the code is demonstrated on selected realistic numerical tests.

The pre-plasma effects have been extensively studied experimentally and numerically and techniques for suppressing the pre-pulse are known widely. However, the increasing availability of the (multi-)PW-class laser systems enables to perform experiments with ultra-high laser intensities. The simulations of the pre-plasma formation and the effect on the main laser pulse must be reconsidered, since the systems are always limited in the contrast available and the created pre-plasma affects the interaction considerably. Our recent investigation of the topic revealed that the non-local transport of energy going beyond the paradigm of the diffusive approximation plays an important role in the process. An over-critical plateau is formed, where the main pulse is absorbed partially before reaching the solid target. Moreover, strong filamentation of the laser field occurs in the plasma. This effect is studied further by the means of the hydrodynamic simulations of the pre-plasma followed by the kinetic simulations of the interaction of the main pulse.

The experimental study of the plasma projectile acceleration in the laser-induced cavity pressure acceleration (LICPA) scheme is reported. In the experiment performed at the kilojoule PALS laser facility, the parameters of the projectile were measured using interferometry, a streak camera and ion diagnostics, and the measurements were supported by two-dimensional hydrodynamic simulations. It is shown that in the LICPA accelerator with a 200-J laser driver, a 4-mu g gold plasma projectile is accelerated to the velocity of 140 km/s with the energetic acceleration efficiency of 15-19% which is significantly higher than those achieved with the commonly used ablative acceleration and the highest among the ones measured so far for any projectiles accelerated to the velocities >= 100 km/s. This achievement opens the possibility of creation and investigation of high-energy-density matter states with the use of moderate-energy lasers and may also have an impact on the development of the impact ignition approach to inertial confinement fusion.

Reliable simulations of laser–target interaction on the macroscopic scale are burdened by the fact that the energy transport is very often non-local. This means that the mean-free-path of the transported species is larger than the local gradient scale lengths and transport can be no longer considered diffusive. Kinetic simulations are not a feasible option due to tremendous computational demands, limited validity of the collisional operators and inaccurate treatment of thermal radiation. This is the point where hydrodynamic codes with non-local radiation and electron heat transport based on first principles emerge. The simulation code PETE (Plasma Euler and Transport Equations) combines both of them with a laser absorption method based on the Helmholtz equation and a radiation diffusion scheme presented in this article. In the case of modelling ablation processes it can be observed that both, thermal and radiative, transport processes are strongly non-local for laser intensities of 1013 W/cm2 and above. In this paper simulations for various laser intensities and different ablator materials are presented, where the non-local and diffusive treatments of radiation transport are compared. Significant discrepancies are observed, supporting importance of non-local transport for inertial confinement fusion related studies as well as for pre-pulse generated plasma in ultra-high intensity laser–target interaction.