Physics

Boron carbide (B 4 C) is of both fundamental scientific and practical interest in inertial confinement fusion (ICF) and high energy density physics experiments. We report the results of a comprehensive computational study of the equation of state (EOS) of B 4 C in the liquid, warm dense matter, and plasma phases. Our calculations are cross-validated by comparisons with Hugoniot measurements up to 61 megabar from planar shock experiments performed at the National Ignition Facility (NIF). Our computational methods include path integral Monte Carlo, activity expansion, as well as all-electron Green's function Korringa-Kohn-Rostoker and molecular dynamics that are both based on density functional theory. We calculate the pressure-internal energy EOS of B 4 C over a broad range of temperatures ( ∼ 6 × 10 3 --5 × 10 8 K) and densities (0.025--50 g/cm 3 ). We assess that the largest discrepancies between theoretical predictions are ≲ 5% near the compression maximum at 1--2 × 10 6 K. This is the warm-dense state in which the K shell significantly ionizes and has posed grand challenges to theory and experiment. By comparing with different EOS models, we find a Purgatorio model (LEOS 2122) that agrees with our calculations. The maximum discrepancies in pressure between our first-principles predictions and LEOS 2122 are ∼ 18% and occur at temperatures between 6 × 10 3 --2 × 10 5 K, which we believe originate from differences in the ion thermal term and the cold curve that are modeled in LEOS 2122 in comparison with our first-principles calculations. In addition, we have developed three new equation of state models and applied them to 1D hydrodynamic simulations of a polar direct-drive NIF implosion, demonstrating that these new models are now available for future ICF design studies.

We present a sawtooth model that explains observations where the central safety factor, q 0 , stays well below one, which is irreconcilable with current models that predict a reset to q 0 =1 after the crash. We identify the structure of the field around the magnetic axis with elements of the Lie group SL(2,R) and find a transition to an alternating-hyperbolic geometry when q 0 =2/3 . This transition is driven by an ideal MHD instability and leads to a chaotic magnetic field near the axis.

One of the paradigm-shifting phenomena triggered in laser-plasma interactions at relativistic intensities is the so-called relativistic transparency. As the electrons become heated by the laser to relativistic energies, the plasma becomes transparent to the laser light even though the plasma density is sufficiently high to reflect the laser pulse in the non-relativistic case. This paper highlights the impact that relativistic transparency can have on laser-matter interactions by focusing on a collective phenomenon that is associated with the onset of relativistic transparency: plasma birefringence in thermally anisotropic relativistic plasmas. The optical properties of such a system become dependent on the polarization of light, and this can serve as the basis for plasma-based optical devices or novel diagnostic capabilities.

Interaction of coherent structures known as blobs in the scrape-off layer of magnetic confinement fusion devices is investigated. Isolated and interacting seeded blobs as well as full plasma turbulence are studied with a two dimensional fluid code. The features of the blobs (size, amplitude, position) are determined with a blob tracking algorithm, which identifies them as coherent structures above a chosen density threshold and compared to a conventional center of mass approach. The agreement of these two methods is shown to be affected by the parameters of the blob tracking algorithm. The benchmarked approach is then extended to a population of interacting plasma blobs with statistically distributed amplitudes, sizes and initial positions for different levels of intermittency. As expected, for decreasing intermittency, we observe an increasing number of blobs deviating from size-velocity scaling laws of perfectly isolated blobs. This is found to be caused by the interaction of blobs with the electrostatic potential of one another, leading to higher average blob velocities. The degree of variation from the picture of perfectly isolated blobs is quantified as a function of the average waiting time of the seeded blobs.

Relativistic electrons generated by the interaction of petawatt-class short laser pulses with solid targets can be used to generate bright X-rays via bremsstrahlung. The efficiency of laser energy transfer into these electrons depends on multiple parameters including the focused intensity and pre-plasma level. This paper reports experimental results from the interaction of a high intensity petawatt-class glass laser pulses with solid targets at a maximum intensity of 10 19 W/cm 2 . In-situ measurements of specularly reflected light are used to provide an upper bound of laser absorption and to characterize focused laser intensity, the pre-plasma level and the generation mechanism of second harmonic light. The measured spectrum of electrons and bremsstrahlung radiation provide information about the efficiency of laser energy transfer.

The purpose of this paper is to bridge kinetic plasma descriptions and low frequency single fluid models. More specifically, the asymptotics leading to Magneto-Hydro-Dynamic (MHD) regimes starting from the Vlasov-Maxwell system are investigated. The analogy with the derivation, from the Vlasov-Poisson system, of a fluid representation for the ions coupled to the Boltzmann relation for electrons is also outlined. The aim is to identify asymptotic parameters explaining the transitions from one microscopic description to a macroscopic low frequency model. These investigations provide ground work for the derivation of multi-scale numerical methods, model coupling or physics based preconditioning.

While the front of a fluid shock is a few mean-free-paths thick, the front of a collisionless shock can be orders of magnitude thinner. By bridging between a collisional and a collisionless formalism, we assess the transition between these two regimes. We consider non-relativistic, un-magnetized, planar shocks in electron/ion plasmas. In addition, our treatment of the collisionless regime is restricted to high Mach number electrostatic shocks. We find that the transition can be parameterized by the upstream plasma parameter ? which measures the coupling of the upstream medium. For ???.12 , the upstream is collisional, i.e. strongly coupled, and the strong shock front is about M 1 λ mfp,1 thick, where λ mfp,1 and M 1 are the upstream mean-free-path and Mach number respectively. A transition occurs for ???.12 beyond which the front is ??M 1 λ mfp,1 ln?/? thick for ???.12 . Considering ? can reach billions in astrophysical settings, this allows to understand how the front of a collisionless shock can be orders of magnitude smaller than the mean-free-path, and how physics transitions continuously between these 2 extremes.

By exploiting the nonlinear amplification of the power deposition of RF waves, current condensation promises new pathways to the stabilisation of magnetic islands. We present a numerical analysis of current condensation, coupling a geometrical optics treatment of wave propagation and damping to a thermal diffusion equation solver in the island. Taking into account the island geometry and relativistic damping, previous analytical theory can be made more precise and specific scenarios can be realistically predicted. With this more precise description, bifurcations and associated hysteresis effects could be obtained in an ITER-like scenario at realistic parameter values. Moreover, it is shown that dynamically varying the RF wave launching angles can lead to hysteresis and help to avoid the nonlinear shadowing effect.

A problem arising in several engineering areas is to design magnets outside a volume that produce a desired magnetic field inside it. One instance of this problem is stellarator design, where it has recently been shown that permanent magnets can provide the required shaping of the magnetic field. Here we demonstrate a robust and efficient algorithm REGCOIL_PM to calculate the spatial distribution of these permanent magnets. The procedure involves a small number of fixed-point iterations, with a linear least-squares problem solved at each step. The method exploits the Biot-Savart Law's exact linearity in magnetization density and approximate linearity in magnet size, for magnets far from the target region. No constraint is placed on the direction of magnetization, so Halbach solutions are found naturally, and the magnitude of the magnetization can be made uniformly equal to a target value.

When applied to compute the density jump of a shock, the standard magnetohydrodynamic (MHD) formalism assumes, 1) that all the upstream material passes downstream, together with the momentum and energy it carries, and 2) that pressures are isotropic. In a collisionless shock, shock accelerated particles going back and forth around the front can invalid the first assumption. In addition, an external magnetic field can sustain stable pressure anisotropies, invaliding the second assumption. It is therefore unclear whether the density jump of a collisionless shock fulfils the MHD jump or not. Here we try to clarify this issue. A literature review is conducted on 68 articles dealing with Particle-In-Cell simulations of collisionless shocks. We analyze the factors triggering departure from the MHD density jump and quantify their influence on Δ RH , the relative departure from the Rankine-Hugoniot jump. For small departures we propose Δ RH =+O( 10 −1−3.7κ ) t κ −σO(1) where t is the timescale of the simulation, σ the magnetization parameter and κ a constant of order unity. The first term stems from the energy leakage into accelerated particle. The second term stems from the downstream anisotropy triggered by the field (assuming an isotropic upstream). This relation allows to assess to which extent a collisionless shock fulfils the RH density jump. In the strong field limit and for parallel shocks, the departure caused by the field saturates at a finite, negative, value. For perpendicular shocks, the departure goes to zero at small and high σ 's so that we find here a departure window. The results obtained have to be checked against full 3D simulations.