Stability of perpendicular magnetohydrodynamic shocks in materials with ideal and nonideal equations of state.

Magnetized target fusion approach to inertial confinement fusion involves the formation of strong shocks that travel along a magnetized plasma. Shocks, which play a dominant role in thermalizing the upstream kinetic energy generated in the implosion stage, are seldom free from perturbations, and they wrinkle in response to upstream or downstream disturbances. In Z-pinch experiments, significant plasma instability mitigation was observed with pre-embedded axial magnetic fields. To isolate effects, in this work we theoretically study the impact of perpendicular magnetic fields on the planar shock dynamics for different equations of state. For fast magnetosonic shocks in ideal gases, it was found that the magnetic field amplifies the intensity of the perturbations when γ>2 or it weakens them when γ<2. Weak shocks have been found to be stable regardless of the magnetic plasma intensity and gas compressibility; however, for sufficiently strong shocks the magnetic fields can promote a neutral stability/SAE at the shock if the adiabatic index is higher than 1+sqrt[2]. Results have been validated with numerical simulations performed with the FLASH code.

Perpendicular Subcritical Shock Structure in a Collisional Plasma Experiment.

We present a study of perpendicular subcritical shocks in a collisional laboratory plasma. Shocks are produced by placing obstacles into the supermagnetosonic outflow from an inverse wire array z pinch. We demonstrate the existence of subcritical shocks in this regime and find that secondary shocks form in the downstream. Detailed measurements of the subcritical shock structure confirm the absence of a hydrodynamic jump. We calculate the classical (Spitzer) resistive diffusion length and show that it is approximately equal to the shock width. We measure little heating across the shock (<10% of the ion kinetic energy) which is consistent with an absence of viscous dissipation.

Self-Generated Plasma Rotation in a Z-Pinch Implosion with Preembedded Axial Magnetic Field.

Using detailed spectroscopic measurements, highly resolved in both time and space, a self-generated plasma rotation is demonstrated using a cylindrical implosion with a preembedded axial magnetic field (B_{z0}). The rotation direction is found to depend on the direction of B_{z0} and its velocity is found comparable to the peak implosion velocity, considerably affecting the force and energy balance throughout the implosion. Moreover, the evolution of the rotation is consistent with magnetic flux surface isorotation, a novel observation in a Z pinch, which is a prototypical time dependent system.

Mitigation of magneto-Rayleigh-Taylor instability growth in a triple-nozzle, neutron-producing gas-puff Z pinch.

The gas-puff Z-pinch is a well-known source of x-rays and/or neutrons, but it is highly susceptible to the magneto-Rayleigh-Taylor instability (MRTI). Approaches to MRTI mitigation include density profile tailoring, in which nozzles are added or modified to alter the acceleration trajectory, and axial pre-magnetization, in which perturbations are smoothed out via magnetic field line tension. Here, we present two-dimensional magnetohydrodynamic simulations of loads driven by an 850 kA, 160 ns driver that suggest these mitigation strategies can be additive. The initial axial magnetic field, B_{z0}, to stabilize a 2.5-cm-radius Ne gas liner imploding onto an on-axis deuterium target can be reduced from 0.7 T to 0.3 T by adding a second liner with a radius of 1.25 cm. Because MRTI mitigation tends to increasingly lower yield with higher B_{z0}, the use of a lower field is advantageous. Here, we predict a reduction in yield penalty from >100× with the single liner to <10× with a double liner. A premagnetized, triple nozzle gas puff could therefore be an attractive source for intense neutrons or other fusion applications.

Multimode Hydrodynamic Instability Growth of Preimposed Isolated Defects in Ablatively Driven Foils.

The Nike KrF laser facility was used to study the evolution of isolated defects with characteristic sizes of <1 to 10s of µm in laser-accelerated plastic foils. The experimental platform permitted, for the first time, the systematic study of localized perturbation growth, which is inherently multimode, through ablative Richtmyer-Meshkov and Rayleigh-Taylor stages and into the strongly nonlinear regime. Initial target defects were relatively large amplitude, but spatially localized, and emulated tent, fill-tube, and other nonuniformities that are present in inertial confinement fusion capsules. Face-on x-ray radiography indicated initial growth of the perturbation in both depth and width, followed by its apparent closure due to oblique spike growth. Hollow jetlike profiles of laterally expanding, rising, Rayleigh-Taylor bubbles were observed on the rear surface of the target from each isolated defect. Radiation hydrodynamic simulations provided insight into the mechanism of the closure and other features of the bubble and spike evolution specific to isolated defects.

Rarefaction Flows and Mitigation of Imprint in Direct-Drive Implosions.

Using highly resolved 3D radiation-hydrodynamic simulations, we identify a novel mechanism by which the deleterious impact of laser imprinting is mitigated in direct-drive inertial confinement fusion. Unsupported shocks and associated rarefaction flows, commonly produced with short laser bursts, are found to reduce imprint modulations prior to target acceleration. Optimization through the choice of laser pulse with picket(s) and target dimensions may improve the stability of lower-adiabat designs, thus providing the necessary margin for ignition-relevant implosions.

Effects of a Preembedded Axial Magnetic Field on the Current Distribution in a Z-Pinch Implosion.

The fundamental physics of the magnetic field distribution in a plasma implosion with a preembedded magnetic field is investigated within a gas-puff Z pinch. Time and space resolved spectroscopy of the polarized Zeeman effect, applied for the first time, reveals the impact of a preembedded axial field on the evolution of the current distribution driven by a pulsed-power generator. The measurements show that the azimuthal magnetic field in the imploding plasma, even in the presence of a weak axial magnetic field, is substantially smaller than expected from the ratio of the driving current to the plasma radius. Much of the current flows at large radii through a slowly imploding, low-density plasma. Previously unpredicted observations in higher-power imploding-magnetized-plasma experiments, including recent, unexplained structures observed in the magnetized liner inertial fusion experiment, may be explained by the present discovery. The development of a force-free current configuration is suggested to explain this phenomenon.

Solution of the Noh problem with an arbitrary equation of state.

The classic self-similar solutions of the nonstationary compressible Euler equations obtained for a blast-wave propagation (Sedov, Taylor, and von Neumann), a shock-wave implosion (Guderley, Landau, and Stanyukovich), or an impulsive loading of a planar target (von Hoerner, Häfele, and Zel'dovich) have all been derived for a polytropic ideal gas. None of them can be generalized for a fluid with an arbitrary equation of state (EOS), such as the van der Waals EOS of a non-ideal-gas or a three-term EOS of a condensed material. We demonstrate here that the Noh accretion-shock problem is an exception. Its self-similar solutions exist in cylindrical and spherical geometry for fluids and materials with an arbitrary EOS. Such solutions for finite accretion-shock strength and nonuniform inflow velocity are constructed semianalytically with a model three-term equation of state that includes cold, thermal ion (lattice), and thermal electron contributions to the pressure and internal energy. Examples are presented for aluminum and copper. Other material- and EOS-specific semianalytic solutions of the Noh problem can be easily constructed using the same method for any material that in the pressure range of interest can be approximated as a dissipation-free fluid with an arbitrary equation of state.

Controlling Rayleigh-Taylor Instabilities in Magnetically Driven Solid Metal Shells by Means of a Dynamic Screw Pinch.

Magnetically driven implosions of solid metal shells are an effective vehicle to compress materials to extreme pressures and densities. Rayleigh-Taylor instabilities (RTI) are ubiquitous, yet typically undesired features in all such experiments where solid materials are rapidly accelerated to high velocities. In cylindrical shells ("liners"), the magnetic field driving the implosion can exacerbate the RTI. We suggest an approach to implode solid metal liners enabling a remarkable reduction in the growth of magnetized RTI (MRTI) by employing a magnetic drive with a tilted, dynamic polarization, forming a dynamic screw pinch. Our calculations, based on a self-consistent analytic framework, demonstrate that the cumulative growth of the most deleterious MRTI modes may be reduced by as much as 1 to 2 orders of magnitude. One key application of this technique is to generate increasingly stable, higher-performance implosions of solid metal liners to achieve fusion [M. R. Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)]. We weigh the potentially dramatic benefits of the solid liner dynamic screw pinch against the experimental tradeoffs required to achieve the desired drive field history and identify promising designs for future experimental and computational studies.

Compact hohlraum configuration with parallel planar-wire-array x-ray sources at the 1.7-MA Zebra generator.

A compact Z-pinch x-ray hohlraum design with parallel-driven x-ray sources is experimentally demonstrated in a configuration with a central target and tailored shine shields at a 1.7-MA Zebra generator. Driving in parallel two magnetically decoupled compact double-planar-wire Z pinches has demonstrated the generation of synchronized x-ray bursts that correlated well in time with x-ray emission from a central reemission target. Good agreement between simulated and measured hohlraum radiation temperature of the central target is shown. The advantages of compact hohlraum design applications for multi-MA facilities are discussed.

Wire ablation dynamics model and its application to imploding wire arrays of different geometries.

The paper presents an extended description of the amplified wire ablation dynamics model (WADM), which accounts in a single simulation for the processes of wire ablation and implosion of a wire array load of arbitrary geometry and wire material composition. To investigate the role of wire ablation effects, the implosions of cylindrical and planar wire array loads at the university based generators Cobra (Cornell University) and Zebra (University of Nevada, Reno) have been analyzed. The analysis of the experimental data shows that the wire mass ablation rate can be described as a function of the current through the wire and some coefficient defined by the wire material properties. The aluminum wires were found to ablate with the highest rate, while the copper ablation is the slowest one. The lower wire ablation rate results in a higher inward velocity of the ablated plasma, a higher rate of the energy coupling with the ablated plasma, and a more significant delay of implosion for a heavy load due to the ablation effects, which manifest the most in a cylindrical array configuration and almost vanish in a single-planar array configuration. The WADM is an efficient tool suited for wire array load design and optimization in wide parameter ranges, including the loads with specific properties needed for the inertial confinement fusion research and laboratory astrophysics experiments. The data output from the WADM simulation can be used to simplify the radiation magnetohydrodynamics modeling of the wire array plasma.

Observation of strong oscillations of areal mass in an unsupported shock wave.

An experimental study of hydrodynamic perturbation evolution in a strong unsupported shock wave, which is immediately followed by an expansion wave, is reported. A planar solid plastic target rippled on the front side is irradiated with a 350-450 ps long laser pulse. The perturbation evolution in the target is observed using face-on monochromatic x-ray radiography during and for up to 4 ns after the laser pulse. The theoretically predicted large oscillations of the areal mass in the target are observed for the first time. Multiple phase reversals of the areal mass modulation are detected.

Analytical linear theory for the interaction of a planar shock wave with a two- or three-dimensional random isotropic acoustic wave field.

We present an analytical model that describes the linear interaction of a planar shock wave with an isotropic random sonic field. First, we study the interaction with a single-mode acoustic field. We present the exact evolution for the pressure, velocity, vorticity, and density field generated behind the shock wave, and we also calculate exact and closed analytical expressions for the asymptotic behavior of these modes. Applying superposition, we use the results obtained from the single-mode analysis in order to compute the interaction with 2D/3D isotropic random acoustic fields. We present analytical expressions for the average turbulent kinetic energy generated behind the shock, as well as the averaged vorticity and the density perturbations as a function of the shock strength M(1) and the gas compressibility γ. We also study the acoustic energy flux emitted by the shock front. Exact asymptotic analytical scaling laws are given for all the 3D averages downstream. A detailed comparison with previous works is shown.

Effect of shock-generated turbulence on the Hugoniot jump conditions.

Interaction of a shock wave with preshock random density nonuniformities is known to generate turbulence in the postshock flow. The turbulent motion, in turn, modifies the shock jump conditions. As first detected in the simulations by Hazak et al. [Phys. Plasmas 5, 4357 (1998)], shock compression of a deuterium-filled foam is less than that predicted for a uniform medium of the same average density. Exact analytical small-amplitude theory of this shock undercompression effect is reported, and explicit formulas for the turbulent corrections to the strong-shock Hugoniot jump conditions are presented.

Influence of induced axial magnetic field on plasma dynamics and radiative characteristics of Z pinches.

The influence of an induced axial magnetic field on plasma dynamics and radiative characteristics of Z pinches is investigated. An axial magnetic field was induced in a novel Z-pinch load: a double planar wire array with skewed wires (DPWAsk), which represents a planar wire array in an open magnetic configuration. The induced axial magnetic field suppressed magneto-Rayleigh-Taylor (MRT) instabilities (with m = 0 and m = 1 instability modes) in the Z-pinch plasma. The influence of the initial axial magnetic field on the structure of the plasma column at stagnation was manifested through the formation of a more uniform plasma column compared to a standard double planar wire array (DPWA) load [V. L. Kantsyrev et al., Phys. Plasmas 15, 030704 (2008)]. The DPWAsk load is characterized by suppression of MRT instabilities and by the formation of the sub-keV radiation pulse that occurs before the main x-ray peak. Gradients in plasma parameters along the cathode-anode gap were observed and analyzed for DPWAsk loads made from low atomic number Z (Al) and mid-Z (brass) wires.

Analytical linear theory for the interaction of a planar shock wave with a two- or three-dimensional random isotropic density field.

We present an analytical linear model describing the interaction of a planar shock wave with an isotropic random pattern of density nonuniformities. This kind of interaction is important in inertial confinement fusion where shocks travel into weakly inhomogeneous cryogenic deuterium-wicked foams, and also in astrophysics, where shocks interact with interstellar density clumps. The model presented here is based on the exact theory of space and time evolution of the perturbed quantities generated by a corrugated shock wave traveling into a small-amplitude single-mode density field. Corresponding averages in both two and three dimensions are obtained as closed analytical expressions for the turbulent kinetic energy, acoustic energy flux, density amplification, and vorticity generation downstream. They are given as explicit functions of the two parameters (adiabatic exponent γ and shock strength M(1)) that govern the dynamics of the problem. In addition, these explicit formulas are simplified in the important asymptotic limits of weak and strong shocks and highly compressible fluids.

Basic hydrodynamics of Richtmyer-Meshkov-type growth and oscillations in the inertial confinement fusion-relevant conditions.

In inertial confinement fusion (ICF), the possibility of ignition or high energy gain is largely determined by our ability to control the Rayleigh-Taylor (RT) instability growth in the target. The exponentially amplified RT perturbation eigenmodes are formed from all sources of the target and radiation non-uniformity in a process called seeding. This process involves a variety of physical mechanisms that are somewhat similar to the classical Richtmyer-Meshkov (RM) instability (in particular, most of them are active in the absence of acceleration), but differ from it in many ways. In the last decade, radiographic diagnostic techniques have been developed that made direct observations of the RM-type effects in the ICF-relevant conditions possible. New experiments stimulated the advancement of the theory of the RM-type processes. The progress in the experimental and theoretical studies of such phenomena as ablative RM instability, re-shock of the RM-unstable interface, feedout and perturbation development associated with impulsive loading is reviewed.

Stability of a shock-decelerated ablation front.

Experimental study of a shock-decelerated ablation front is reported. A planar solid plastic target is accelerated by a laser across a vacuum gap and collides with a lower-density plastic foam layer. While the target is accelerated, a fast Rayleigh-Taylor (RT) growth of the seeded single-mode perturbation at the ablation front is observed. After the collision, the velocity of the ablation front is seen to remain constant. The reshock quenches the RT growth but does not trigger any Richtmyer-Meshkov growth at the ablation front, which is shown to be consistent with both theory and simulations.

Analytical linear theory for the interaction of a planar shock wave with an isotropic turbulent vorticity field.

An exact analytical model for the interaction between an isolated shock wave and an isotropic turbulent vorticity field is presented. The interaction with a single-mode two-dimensional (2D) divergence-free vorticity field is analyzed in detail, giving the time and space evolutions of the perturbed quantities downstream. The results are generalized to study the interaction of a planar shock wave with an isotropic three-dimensional (3D) or 2D preshock vorticity field. This field is decomposed into Fourier modes, and each mode is assumed to interact independently with the shock front. Averages of the downstream quantities are made by integrating over the angles that define the orientation of the upstream velocity field. The ratio of downstream/upstream kinetic energies is in good agreement with existing numerical and experimental results for both 3D and 2D preshock vorticity fields. The generation of sound and the sonic energy flux radiated downstream from the shock front is also discussed in detail, as well as the amplification of transverse vorticity across the shock front. The anisotropy is calculated for the far downstream fields of both velocity and vorticity. All the quantities characteristic of the shock-turbulence interaction are reduced to closed-form exact analytical expressions. They are presented as explicit functions of the two parameters that govern the dynamics of the interaction: the adiabatic exponent gamma and the shock Mach number M1 . These formulas are further reduced to simpler exact asymptotic expressions in the limits of weak and strong shock waves (M_{1}-11, M_{1}1) and high shock compressibility of the gas (gamma-->1) .

Experimental evidence of impact ignition: 100-fold increase of neutron yield by impactor collision.

We performed integrated experiments on impact ignition, in which a portion of a deuterated polystyrene (CD) shell was accelerated to about 600 km/s and was collided with precompressed CD fuel. The kinetic energy of the impactor was efficiently converted into thermal energy generating a temperature of about 1.6 keV. We achieved a two-order-of-magnitude increase in the neutron yield by optimizing the timing of the impact collision, demonstrating the high potential of impact ignition for fusion energy production.