14 Search Results

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 wasmore » found that the magnetic field amplifies the intensity of the perturbations when $$\gamma$$ > 2 or it weakens them when $$\gamma$$ < 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 + $$\sqrt{2}$$. Finally, results have been validated with numerical simulations performed with the FLASH code.« less

A zero-dimore » mensional magnetic implosion model with a coupled equivalent circuit for the description of an imploding nested wire array or gas puff is presented. Circuit model results have been compared with data from imploding stainless steel wire arrays, and good agreement has been found. The total energy coupled to the load, $E_{j\times B}$, has been applied to a simple semi-analytic K-shell yield model, and excellent agreement with previously reported K-shell yields across all wire array and gas puff platforms is seen. Trade space studies in implosion radius and mass have found that most platforms operate near the predicted maximum yield. In some cases, the K-shell yield may be increased by increasing the mass or radius of the imploding array or gas puff.« less

Despite the extensive literature accumulated since the pioneering works of D'yakov and Kontorovich in the 1950s, the stability of steady shocks is still an open question when realistic boundary conditions are accounted. The consideration of a supporting mechanism, which is indeed a necessary condition for shock steadiness, modifies the perturbation shock dynamics in the unstable range. The Noh problem is a suitable example to form steady expanding shocks. This configuration is of great interest to the high-energy-density-physics community because of its direct application to inertial confinement fusion and astrophysics, for which the stagnation of a supersonically converging material via anmore » accretion shock front is ubiquitous. Here in this work, we extend the generalized Noh problem, both base-flow solution and linear stability analysis, to conditions where endothermic or exothermic transformations undergo across the shock. Within the spontaneous acoustic emission conditions found for a van der Waals gas, we find that cylindrical and spherical expanding shocks become literally unstable for sufficiently high mode numbers. Counterintuitively, the effect of exothermicity or endothermicity across the shock is found to be stabilizing or destabilizing, respectively.« less

We describe a simple practical numerical method for simulating plasma driven within a vacuum chamber by a pulsed power generator. Typically, in this type of simulation, the vacuum region adjacent to the plasma is approximated as a highly resistive, light fluid; this involves computationally expensive solvers describing the diffusion of the magnetic field through this fluid. Instead, we provide a recipe for coupling pulsed power generators to the magnetohydrodynamics (MHD) domain by approximating the perfectly insulating vacuum as a light, perfectly conducting, inviscid MHD fluid and discuss the applicability of this counter-intuitive technique. This much more affordable ideal MHD representationmore » is particularly useful in situations where a plasma exhibits interesting three-dimensional phenomena, either due to the design of the experiment or due to developing instabilities. We verified that this coupling recipe works by modeling an exactly solvable flux compression generator as well as a self-similar Noh-like solution and demonstrated convergence to the theoretical solution. We also showed examples of simulating complex three-dimensional pulsed power devices with this technique. We release our code implementation to the public (see https://github.com/beresnyak/verif_coupling).« less

We present a theoretical stability analysis for an expanding accretion shock that does not involve a rarefaction wave behind it. The dispersion equation that determines the eigenvalues of the problem and the explicit formulae for the corresponding eigenfunction profiles are presented for an arbitrary equation of state and finite-strength shocks. For spherically and cylindrically expanding steady shock waves, we demonstrate the possibility of instability in a literal sense, a power-law growth of shock-front perturbations with time, in the range of $$h_c< h<1+2 {\mathcal {M}}_2$$ , where $$h$$ is the D'yakov-Kontorovich parameter, $$h_c$$ is its critical value corresponding to the onsetmore » of the instability and $${\mathcal {M}}_2$$ is the downstream Mach number. Shock divergence is a stabilizing factor and, therefore, instability is found for high angular mode numbers. As the parameter $$h$$ increases from $$h_c$$ to $$1+2 {\mathcal {M}}_2$$ , the instability power index grows from zero to infinity. This result contrasts with the classic theory applicable to planar isolated shocks, which predicts spontaneous acoustic emission associated with constant-amplitude oscillations of the perturbed shock in the range $$h_c< h<1+2 {\mathcal {M}}_2$ . Examples are given for three different equations of state: ideal gas, van der Waals gas and three-terms constitutive equation for simple metals.« less

This paper expands upon recent experimental results [Campbell et al., Phys. Rev. Lett. 125, 035001 (2020)], where thin-foil liner implosions were driven by a dynamic screw pinch (DSP) and found to have magneto-Rayleigh–Taylor instability (MRTI) amplitudes up to three times smaller than in implosions driven by a standard z-pinch (SZP). Here, the expanded discussion presented herein includes: (1) a detailed comparison of the MRTI growth measured in the experiment with that calculated from theory; (2) measurements of axial magnetic field injection into the liner interior prior to the implosion, as well as the subsequent compression of this field during themore » implosion; (3) an in-depth description of how the helical geometry of the DSP can result in earlier implosion and stagnation times relative to the SZP; and (4) particle-in-cell simulations showing different electron drift behavior in the anode–cathode gap of the DSP relative to the SZP, and how this difference may be related to the different current waveforms recorded during the experiments.« less

High energy gain in inertial fusion schemes requires the propagation of a thermonuclear burn wave from hot to cold fuel. We consider the problem of burn propagation when a magnetic field is orthogonal to the burn wave. Using an extended-MHD model with a magnetized α energy transport equation, we find that the magnetic field can reduce the rate of burn propagation by suppressing electron thermal conduction and α particle flux. Magnetic field transport during burn propagation is subject to competing effects: the field can be advected from cold to hot regions by ablation of cold fuel, while the Nernst andmore » α particle flux effects transport the field from hot to cold fuel. These effects, combined with the temperature increase due to burn, can cause the electron Hall parameter to grow rapidly at the burn front. This results in the formation of a self-insulating layer between hot and cold fuel, which reduces electron thermal conductivity and α transport, increases the temperature gradient, and reduces the rate of burn propagation.« less

Not provided.

Absolute Hugoniot measurements for empty plastic foams at ~10% of solid polystyrene density and supporting rad-hydro simulation results are reported. Planar foam slabs, ~400 μm thick and ~500 μm wide, some of which were covered with a 10 μm solid plastic ablator, were directly driven by 4 ns long Nike krypton-fluoride 248 nm wavelength laser pulses that produced strong shock waves in the foam. The shock and mass velocities in our experiments were up to 104 km/s and 84 km/s, respectively, and the shock pressures up to ~9 Mbar. The motion of the shock and ablation fronts was recorded usingmore » side-on monochromatic x-ray imaging radiography. Here, the steadiness of the observed shock and ablation fronts within ~1% has been verified. The Hugoniot data inferred from our velocity measurements agree with the predictions of the SESAME and CALEOS equation-of-state models near the highest pressure ~9 Mbar and density compression ratio ~5. In the lower pressure range 2–5 Mbar, a lower shock density compression is observed than that predicted by the models. Possible causes for this discrepancy are discussed.« less

Bell-Plesset (BP) effects account for the influence of global convergence or divergence of the fluid flow on the evolution of the interfacial perturbations embedded in the flow. The development of the Rayleigh-Taylor instability in radiation-driven spherical capsules and magnetically-driven cylindrical liners necessarily includes a significant contribution from BP effects due to the time dependence of the radius, velocity, and acceleration of the unstable surfaces or interfaces. An analytical model is presented that, for an ideal incompressible fluid and small perturbation amplitudes, exactly evaluates the BP effects in finite-thickness shells through acceleration and deceleration phases. The time-dependent dispersion equations determining themore » “instantaneous growth rate” are derived. It is demonstrated that by integrating this approximate growth rate over time, one can accurately evaluate the number of perturbation e-foldings during the inward acceleration phase of the implosion. As a result, in the limit of small shell thickness, exact thin-shell perturbationequations and approximate thin-shell dispersion equations are obtained, generalizing the earlier results [E. G. Harris, Phys. Fluids 5, 1057 (1962); E. Ott, Phys. Rev. Lett. 29, 1429 (1972); A. B. Bud'ko et al., Phys. Fluids B 2, 1159 (1990)].« less