Perfectly conducting incompressible fluid model of a wire array implosion

An incompressible perfectly conducting magnetohydrodynamic model is applied to describe a multiwire array implosion on the (r,θ)(r,θ) plane using the theory of analytic functions. The plasma columns emerging from the electrical explosion of individual wires move and change the shape of their cross section in the magnetic field produced by the currents flowing on the surfaces of the columns and closing through a cylindrical return current can. Geometry of both the “global” and “private” magnetic fields and self-consistent distributions of the electric currents on the conducting surfaces are determined for any wire array configuration including nested wire arrays, wires close to the return current can, etc. The coupled equations of motion and magnetostatics for an essentially two-dimensional problem are reduced to one-dimensional parametric governing equations, written for the boundary of the fluid contours. The implosion dynamics is shown to be driven by a competition between the implosion pressure, making the array converge to the axis as a set of individual plasma columns, and the tidal pressure that makes the wires merge, forming an annular conducting shell. Their relative roles are determined by the gap-to-diameter ratio πRc(t)/NRw(t).πRc(t)/NRw(t). If this ratio is large at early time, then the array implodes as a set of individual plasma columns. Otherwise, when the ratio is about π or less, the tidal forces prevail, and the plasma columns tend to form a shell-like configuration before they start converging to the axis of the array. The model does not allow the precursor plasma streams to be ejected from the wires to the axis, indicating that this process is governed by the finite plasma conductivity and could only be described with a proper conductivity model. © 2002 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70839/2/PHPAEN-9-4-1366-1.pd

The stability of expanding reactive shocks in a van der Waals fluid

Despite the extensive literature accumulated since the pioneering works of Dyakov 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 an accretion shock front is ubiquitous. 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 [J. W. Bates and D. C. Montgomery, The Dyakov-Kontorovich instability of shock waves in real gases, Phys. Rev. Lett. 84, 1180 (2000)], 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.A.C.R. and C.H. work has been supported with project No. PID2019-108592RB-C41 Ministry of Science and Innovation (MCINN). C.H. work has been also supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M (H2SFE-CM-UC3M). A.L.V. work has been supported by the National Nuclear Security Administration of the U.S. Department of Energy

On the stability of piston-driven planar shocks

We present a theoretical and numerical stability analysis for a piston-driven planar shock against two-dimensional perturbations. The results agree with the well-established theory for isolated planar shocks: in the range of hc < h < 1 + 2M2, where h is the Dyakov-Kontorovich (DK) parameter related to the slope of the Rankine-Hugoniot curve, hc is its critical value corresponding to the onset of the spontaneous acoustic emission (SAE) and M2 is the downstream Mach number, non-decaying oscillations of shock-front ripples occur. The effect of the piston is manifested in the presence of additional frequencies occurring by the reflection of the sonic waves on the piston surface that can reach the shock. An unstable behaviour of the shock perturbation is found to be possible when there is an external excitation source affecting the shock, whose frequency coincides with the self-induced oscillation frequency in the SAE regime, thereby being limited to the range hc < h < 1 + 2M2. An unstable evolution of the shock is also observed for planar shocks restricted to one-dimensional perturbations within the range 1 < h < 1 + 2M2. Both numerical integration of the Euler equations via the method of characteristics and theoretical analysis via Laplace transform are employed to cross-validate the results.The work of A.C.R and C.H. has been supported with project TED2021-129446B-C41 (MICINN/FEDER, UE). The work of C.H. has also received support from the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M (H2SAFE-CM-UC3M). The work of A.L.V. has been supported by the National Nuclear Security Administration of the US Department of Energy

Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion

Stable and unstable supersonic stagnation of an axisymmetric rotating magnetized plasma

The Naval Research Laboratory "Mag Noh problem", described in this paper, is a self-similar magnetized implosion flow, which contains a fast MHD outward propagating shock of constant velocity. We generalize the classic Noh (1983) problem to include azimuthal and axial magnetic fields as well as rotation. Our family of ideal MHD solutions is five-parametric, each solution having its own self-similarity index, gas gamma, magnetization, the ratio of axial to the azimuthal field, and rotation. While the classic Noh problem must have a supersonic implosion velocity to create a shock, our solutions have an interesting three-parametric special case with zero initial velocity in which magnetic tension, instead of implosion flow, creates the shock at $t=0+$. Our self-similar solutions are indeed realized when we solve the initial value MHD problem with finite volume MHD code Athena. We numerically investigated the stability of these solutions and found both stable and unstable regions in parameter space. Stable solutions can be used to test the accuracy of numerical codes. Unstable solutions have also been widely used to test how codes reproduce linear growth, transition to turbulence, and the practically important effects of mixing. Now we offer a family of unstable solutions featuring all three elements relevant to magnetically driven implosions: convergent flow, magnetic field, and a shock wave.Comment: 24 pages, 9 figures, submitted to JF

Stability of expanding accretion shocks for an arbitrary equation of state

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 hc < h < 1 + 2M2, where h is the D’yakov-Kontorovich parameter, hc is its critical value corresponding to the onset of the instability and M2 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 hc to 1 + 2M2, 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 hc < h < 1 + 2M2. Examples are given for three different equations of state: ideal gas, van der Waals gas and three-terms constitutive equation for simple metals.C.H. work is produced with the support of a 2019 Leonardo Grant for Researchers and Cultural Creators, BBVA Foundation and project PID2019-108592RB-C41 (MICINN/FEDER, UE). A.L.V. work was supported by the National Nuclear Security Administration of the U.S. Department of Energy. D.M-R work was supported by project PID2019-108592RA-C43 (MICINN/FEDER, UE)