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The factors that influence the symmetry of an imploding detonation are investigated experimentally and theoretically. Detonations in sub-atmospheric acetylene-oxygen were initiated and made to converge in an apparatus that followed that of Lee and Lee (Phys Fluids 8:2148-2152, 1965). The width of the test section was controlled with a wave-shaping insert, which formed the test section against the viewing window, creating an effectively two-dimensional problem with a channel width comparable to the detonation cell size. The convergence of the detonation was observed via self-luminous open-shutter photography and high-speed videography. The resulting videos were analyzed to quantify the wave speed, degree of asymmetry, and direction and magnitude of the offset in the center of convergence. To determine the experimental parameters that influence the symmetry of the imploding wave, the wave-shaping insert was intentionally canted by 0.3{\deg}-0.6{\deg}, accentuating the asymmetry of the imploding detonation. The experiment was modeled using a Huygens construction wherein the detonation is treated as a collection of wavelets, each assumed to propagate locally at a velocity determined by the channel width. The results of the model reproduced the observed offsets in detonation convergence from the center of the apparatus, confirming that velocity deficits resulting from the narrow channel width control the observed asymmetry.

The effect of magnetic tension and diffusion on the perturbation growth of a liquid-metal liner subjected to the magneto-Rayleigh-Taylor (MRT) instability is investigated. An initially magnetic-field-free liquid-metal slab of finite thickness is surrounded by two lower-density regions. Within the lower region, a constant axial magnetic field of arbitrary magnitude is applied. The numerical examination of the MRT instability growth, initiated by a seeded perturbation parallel to the magnetic field at the liner's unstable interface, is performed for both perfectly conductive and resistive liners. To this end, a novel level set-based two-phase incompressible solver for ideal/resistive magnetohydrodynamic (MHD) flows within the finite-difference framework is introduced. Utilizing the implemented numerical toolkit, the impact of different Alfven numbers and magnetic Reynolds numbers on the MRT growth rate and feedthrough at the upper interface of the liner is studied. Accounting for the finite resistivity of the liner results in an increase in the MRT growth and feedthrough compared to the ideal MHD case. The results indicate that magnetic diffusion primarily affects the MRT growth rate for higher wavenumbers, while for smaller wavenumbers, the effect of finite resistivity is only observed over a longer duration of instability development. We further demonstrate that decreasing the Alfven number results in the faster emergence of the magnetic diffusion effect on the MRT growth rate. It is also observed that a greater electrical conductivity jump across the liner results in an increased perturbation growth. Lastly, the impact of surface tension on MRT instability growth for both ideal and resistive MHD cases is studied across different wavenumbers, specifically for Bond numbers related to fusion applications.

Development of a two-phase incompressible solver for magnetic flows in the magnetostatic case is presented. The proposed numerical toolkit couples the Navier-Stokes equations of hydrodynamics with Maxwell's equations of electromagnetism to model the behaviour of magnetic flows in the presence of a magnetic field. To this end, a rigorous implementation of a second-order two-phase solver for incompressible nonmagnetic flows is introduced first. This solver is implemented in the finite-difference framework, where a fifth-order conservative level set method is employed to capture the evolution of the interface, along with an incompressible solver based on the projection scheme to model the fluids. The solver demonstrates excellent performance even with high density ratios across the interface (Atwood number $\approx 1$), while effectively preserving the mass conservation property. Subsequently, the numerical discretization of Maxwell's equations under the magnetostatic assumption is described in detail, utilizing the vector potential formulation. The primary second-order solver for two-phase flows is extended to the case of magnetic flows, by incorporating the Lorentz force into the momentum equation, accounting for high magnetic permeability ratios across the interface. The implemented solver is then utilized for examining the deformation of ferrofluid droplets in both quiescent and shear flow regimes across various susceptibility values of the droplets. The results suggest that increasing the susceptibility value of the ferrofluid droplet can affect its deformation and rotation in low capillary regimes. In higher capillary flows, increasing the magnetic permeability jump across the interface can further lead to droplet breakup as well. The effect of this property is also investigated for the Rayleigh-Taylor instability growth in magnetic fluids.

On current computer architectures, GMRES' performance can be limited by its communication cost to generate orthonormal basis vectors of the Krylov subspace. To address this performance bottleneck, its $s$-step variant orthogonalizes a block of $s$ basis vectors at a time, potentially reducing the communication cost by a factor of $s$. Unfortunately, for a large step size $s$, the solver can generate extremely ill-conditioned basis vectors, and to maintain stability in practice, a conservatively small step size is used, which limits the performance of the $s$-step solver. To enhance the performance using a small step size, in this paper, we introduce a two-stage block orthogonalization scheme. Similar to the original scheme, the first stage of the proposed method operates on a block of $s$ basis vectors at a time, but its objective is to maintain the well-conditioning of the generated basis vectors with a lower cost. The orthogonalization of the basis vectors is delayed until the second stage when enough basis vectors are generated to obtain higher performance. Our analysis shows the stability of the proposed two-stage scheme. The performance is improved because while the same amount of computation as the original scheme is required, most of the communication is done at the second stage of the proposed scheme, reducing the overall communication requirements. Our performance results with up to 192 NVIDIA V100 GPUs on the Summit supercomputer demonstrate that when solving a 2D Laplace problem, the two-stage approach can reduce the orthogonalization time and the total time-to-solution by the respective factors of up to $2.6\times$ and $1.6\times$ over the original $s$-step GMRES, which had already obtained the respective speedups of $2.1\times$ and $1.8\times$ over the standard GMRES. Similar speedups were obtained for 3D problems and for matrices from the SuiteSparse Matrix Collection., Comment: Accepted for publication in IPDPS'24

CholeskyQR2 and shifted CholeskyQR3 are two state-of-the-art algorithms for computing tall-and-skinny QR factorizations since they attain high performance on current computer architectures. However, to guarantee stability, for some applications, CholeskyQR2 faces a prohibitive restriction on the condition number of the underlying matrix to factorize. Shifted CholeskyQR3 is stable but has $50\%$ more computational and communication costs than CholeskyQR2. In this paper, a randomized QR algorithm called Randomized Householder-Cholesky (\texttt{rand\_cholQR}) is proposed and analyzed. Using one or two random sketch matrices, it is proved that with high probability, its orthogonality error is bounded by a constant of the order of unit roundoff for any numerically full-rank matrix, and hence it is as stable as shifted CholeskyQR3. An evaluation of the performance of \texttt{rand\_cholQR} on a NVIDIA A100 GPU demonstrates that for tall-and-skinny matrices, \texttt{rand\_cholQR} with multiple sketch matrices is nearly as fast as, or in some cases faster than, CholeskyQR2. Hence, compared to CholeskyQR2, \texttt{rand\_cholQR} is more stable with almost no extra computational or memory cost, and therefore a superior algorithm both in theory and practice., Comment: 43 pages

A technique by which a spacecraft can interact with flows of ionized gas in space (the solar wind or interstellar medium) to be accelerated to velocities greater than the wind velocity is explored. Inspired by the dynamic soaring maneuvers performed by sea birds and gliders in which differences in wind speed are exploited to gain velocity, in the proposed technique a lift-generating spacecraft circles between regions of the heliosphere that have different wind speeds, gaining energy without the use of propellant and only modest onboard power requirements. The spacecraft motion can be modeled as a series of elastic collisions between regions of the medium moving at different speeds. Models of the trajectory are developed to predict the potential velocity gains and the maximum velocity that may be achieved in terms of the lift-to-drag ratio of the vehicle. A lift-generating mechanism is proposed in which power is extracted from the flow over the vehicle in the flight direction and then used to accelerate the surrounding medium in the transverse direction, generating lift. Large values of lift-to-drag ratio are shown to be possible in the case where a small transverse velocity is imparted over a large area of interaction. The requirement for large interaction area in the extremely low density of the heliosphere precludes the use of physical wings, but the use of plasma waves generated by compact, directional antennas to impart momentum on the surrounding medium is feasible, with R-waves, X-waves, Alfven, and magnetosonic waves appearing as promising candidates. A mission is defined in which dynamic soaring is performed on the termination shock of the heliosphere, speeds of 2% of c to be reached within 2.5 years of launch without the expenditure of propellant. The technique may comprise the first stage for a multistage mission to achieve true interstellar flight to other solar systems., Comment: Minor correction to notation in Eq. (2). This correction does not affect the results or findings

The structural stability of a lightsail under the laser flux necessary for interstellar flight is studied analytically and numerically. A sinusoidal perturbation is introduced into a two-dimensional thin-film sail to determine if the sail remains stable or if the perturbations grow in amplitude. A reflective material that gives specular reflection of the laser illumination is assumed in determining the resulting loading on the sail, although other reflection models can be incorporated as well. The quasi-static solution of the critical point between shape stability and instability is found by equating the bending moments induced on the sail due to radiation pressure with the restoring moments caused by the strength of the sail and the tension applied at the edges of the sail, permitting analytical expressions for the elastic modulus and boundary tension magnitude to be found as a function of sail properties and the amplitude and wave number of the initial perturbation. These expressions are also derived from a formal variational energy approach. A numerical model of the sail dynamics is developed by discretizing the sail into finite elements. By introducing torsional and rectilinear springs between the elements into the numerical model, a hierarchy of models is produced that can incorporate the effects of bending and applied tension. The numerical models permit the transient dynamics of a perturbed sail to be compared to the analytic results of the quasi-static analysis. The analytic expressions can correctly predict the stability boundary found in the numerical simulations. The stiffness required to make a sail stable against uncontrolled perturbation growth is shown to be unfeasible for known materials. A modest tensioning of the sail (e.g., via an inflatable structure or spinning of the sail) can maintain a stable sail shape under all wavelengths and amplitudes of perturbations.

Launching large (> 1 g) well-characterized projectiles to velocities beyond 10 km/s is of interest for a number of scientific fields but is beyond the reach of current hypervelocity launcher technology. This paper reports the development of an explosively driven light-gas gun that has demonstrated the ability to launch 8 mm diameter, 0.36 g magnesium projectiles to 10.4 km/s. The implosion-driven launcher (IDL) uses the linear implosion of a pressurized tube to shock-compress helium gas to a pressure of \SI{5}{\giga\pascal}, which then expands to propel a projectile to hypervelocity. The launch cycle of the IDL is explored with the use of down-bore velocimetry experiments and a quasi-one-dimensional internal ballistics solver. A detailed overview of the design of the 8 mm launcher is presented, with an emphasis on the unique considerations which arise from the explosively driven propellant compression and the resulting extreme pressures and temperatures. The high average driving pressure results in a launcher that is compact, with a total length typically less than a meter. The possibility to scale the design to larger projectile sizes (25 mm diameter) is demonstrated. Finally, concepts for a modified launch cycle which may allow the IDL to reach significantly greater projectile velocities are explored conceptually and with preliminary experiments.

A propulsion concept in which a spacecraft interacts with high-velocity pellets and the interstellar medium is proposed. The pellets are slower than the spacecraft and are accelerated backwards as they are overtaken, imparting a forward acceleration on the spacecraft. This maneuver is possible due to the interaction with a fixed medium (interstellar medium, ISM); as the spacecraft travels through the medium, it is able to extract power from the relative wind. This concept relies upon the relative velocities (shear) between the pellet stream and the fixed medium in order to concentrate the energy of the pellets into the spacecraft and is thus termed wind-pellet shear sailing. The equations governing the mass ratio of pellets to the spacecraft and its dependence on the final spacecraft velocity are derived; the critical role of the efficiency of the power extraction and transfer process is identified. Natural sources of energy are considered as a means to accelerate the pellets to velocities of 1000 to 6000 km/s. Techniques for onboard generation of power via electromagnetic interaction with the ISM are reviewed, with a repetitively stroked plasma magnet being identified as a promising approach. The necessity of the spacecraft to detect and track the pellets as they are overtaken dictates the desired properties of the pellets. Pellet pushers (accelerators) on board the spacecraft are also preliminarily explored in their engineering considerations, with electric field accelerators of charged nanometric particles, Lorentz-force accelerated ionized pellets, or expansion of vaporized pellets via a nozzle being highlighted as potential approaches. A preliminary mission profile is defined in which a 500-kg scientific payload is delivered to orbit about alpha-Centauri within 30 years, using wind-pellet shear sailing as the intermediate stage to bring the spacecraft from 2% to 5.5% of c.

The application of directed energy to spacecraft mission design is explored using rapid transit to Mars as the design objective. An Earth-based laser array of unprecedented size (10~m diameter) and power (100~MW) is assumed to be enabled by ongoing developments in photonic laser technology. A phased-array laser of this size and incorporating atmospheric compensation would be able to deliver laser power to spacecraft in cislunar space, where the incident laser is focused into a hydrogen heating chamber via an inflatable reflector. The hydrogen propellant is then exhausted through a nozzle to realize specific impulses of 3000 s. The architecture is shown to be immediately reusable via a burn-back maneuver to return the propulsion unit while still within range of the Earth-based laser. The ability to tolerate much greater laser fluxes enables realizing the combination of high thrust and high specific impulse, making this approach favorable in comparison to laser-electric propulsion and occupying a parameter space similar to gas-core nuclear thermal rockets (without the requisite reactor). The heating chamber and its associated regenerative cooling and propellant handling systems are crucial elements of the design that receive special attention in this study. The astrodynamics and the extreme aerocapture maneuver required at Mars arrival after a 45-day transit are also analyzed in detail. The application of laser-thermal propulsion as an enabling technology for other rapid transit missions in the solar system and beyond is discussed.