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At least 397 records · Page 22

Nonstandard Analysis and Shock Wave Jump Conditions in a One-Dimensional Compressible Gas

Nonstandard analysis is a relatively new area of mathematics in which infinitesimal numbers can be defined and manipulated rigorously like real numbers. This report presents a fairly comprehensive tutorial on nonstandard analysis for physicists and engineers with many examples applicable to generalized functions. To demonstrate the power of the subject, the problem of shock wave jump conditions is studied for a one-dimensional compressible gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. To use conservations laws, smooth pre-distributions of the Dirac delta measure are applied whose supports are contained within the shock thickness. Furthermore, smooth pre-distributions of the Heaviside function are applied which vary from zero to one across the shock wave. It is shown that if the equations of motion are expressed in nonconservative form then the relationships between the jump functions for the flow parameters may be found unambiguously. The analysis yields the classical Rankine-Hugoniot jump conditions for an inviscid shock wave. Moreover, non-monotonic entropy jump conditions are obtained for both inviscid and viscous flows. The report shows that products of generalized functions may be defined consistently using nonstandard analysis; however, physically meaningful products of generalized functions must be determined from the physics of the problem and not the mathematical form of the governing equations.

Baty, Roy S.↗

Experimental Shock Transformation of Gypsum to Anhydrite: A New Low Pressure Regime Shock Indicator

The shock behavior of gypsum is important in understanding the Cretaceous/Paleogene event and other terrestrial impacts that contain evaporite sediments in their targets (e.g., Mars Exploration Rover Spirit detected sulfate at Gusev crater, [1]). Most interest focuses on issues of devolatilization to quantify the production of SO2 to better understand its role in generating a temporary atmosphere and its effects on climate and biota [2,3]. Kondo and Ahrens [4] measured induced radiation emitted from single crystal gypsum shocked to 30 and 40 GPa. They observed greybody emission spectra corresponding to temperatures in the range of 3,000 to 4,000 K that are a factor of 2 to 10 times greater than calculated pressure-density energy equation of state temperatures (Hugoniot) and are high enough to melt gypsum. Chen et al. [5] reported results of shock experiments on anhydrite, gypsum, and mixtures of these phases with silica. Their observations indicated little or no devolatilization of anhydrite shocked to 42 GPa and that the fraction of sulfur, by mass, that degassed is approx.10(exp -2) of theoretical prediction. In another report of shock experiments on calcite, anhydrite, and gypsum, Badjukov et al. [6] observed only intensive plastic deformation in anhydrite shock loaded at 63 GPa, and gypsum converted to anhydrite when shock loaded at 56 GPa but have not experimentally shocked gypsum in a step-wise manner to constrain possible incipient transformation effects. Schmitt and Hornemann [7] shock loaded anhydrite and quartz to a peak pressure of 60 GPa and report the platy anhydrite grains were completely pseudomorphed by small crystallized anhydrite grains. However, no evidence of interaction between the two phases could be observed and they suggested that recrystallization of anhydrite grains is the result of a solid-state transformation. They concluded that significant decomposition of anhydrite requires shock pressures higher than 60 GPa. Gupta et al. [8] reanalyzed the calcite and anhydrite shock wave experiments of Yang [9] using improved equations of state of porous materials and vaporized products. They determined the pressures for incipient and complete vaporization to be 32.5 and 122 GPa for anhydrite GPa which is a factor of 2 to 3 lower than reported earlier by Yang [9]. These studies are not in agreement regarding the onset of sulfate decomposition and documentation of shock effects in gypsum is incomplete.

Bell, Mary S.↗

Method and System for Weakening Shock Wave Strength at Leading Edge Surfaces of Vehicle in Supersonic Atmospheric Flight

A method and system are provided to weaken shock wave strength at leading edge surfaces of a vehicle in atmospheric flight. One or more flight-related attribute sensed along a vehicle's outer mold line are used to control the injection of a non-heated, non-plasma-producing gas into a local external flowfield of the vehicle from at least one leading-edge surface location along the vehicle's outer mold line. Pressure and/or mass flow rate of the gas so-injected is adjusted in order to cause a Rankine-Hugoniot Jump Condition along the vehicle's outer mold line to be violated.

Daso, Endwell O.↗

Acceleration Modes and Transitions in Pulsed Plasma Accelerators

Pulsed plasma accelerators typically operate by storing energy in a capacitor bank and then discharging this energy through a gas, ionizing and accelerating it through the Lorentz body force. Two plasma accelerator types employing this general scheme have typically been studied: the gas-fed pulsed plasma thruster and the quasi-steady magnetoplasmadynamic (MPD) accelerator. The gas-fed pulsed plasma accelerator is generally represented as a completely transient device discharging in approximately 1-10 microseconds. When the capacitor bank is discharged through the gas, a current sheet forms at the breech of the thruster and propagates forward under a j (current density) by B (magnetic field) body force, entraining propellant it encounters. This process is sometimes referred to as detonation-mode acceleration because the current sheet representation approximates that of a strong shock propagating through the gas. Acceleration of the initial current sheet ceases when either the current sheet reaches the end of the device and is ejected or when the current in the circuit reverses, striking a new current sheet at the breech and depriving the initial sheet of additional acceleration. In the quasi-steady MPD accelerator, the pulse is lengthened to approximately 1 millisecond or longer and maintained at an approximately constant level during discharge. The time over which the transient phenomena experienced during startup typically occur is short relative to the overall discharge time, which is now long enough for the plasma to assume a relatively steady-state configuration. The ionized gas flows through a stationary current channel in a manner that is sometimes referred to as the deflagration-mode of operation. The plasma experiences electromagnetic acceleration as it flows through the current channel towards the exit of the device. A device that had a short pulse length but appeared to operate in a plasma acceleration regime different from the gas-fed pulsed plasma accelerators was developed by Cheng, et al. The Coaxial High ENerGy (CHENG) thruster operated on the 10-microseconds timescales of pulsed plasma thrusters, but claimed high thrust density, high efficiency and low electrode erosion rates, which are more consistent with the deflagration mode of acceleration. Separate work on gas-fed pulsed plasma thrusters (PPTs) by Ziemer, et al. identified two separate regimes of performance. The regime at higher mass bits (termed Mode I in that work) possessed relatively constant thrust efficiency (ratio of jet kinetic energy to input electrical energy) as a function of mass bit. In the second regime at very low mass bits (termed Mode II), the efficiency increased with decreasing mass bit. Work by Poehlmann et al. and by Sitaraman and Raja sought to understand the performance of the CHENG thruster and the Mode I / Mode II performance in PPTs by modeling the acceleration using the Hugoniot Relation, with the detonation and deflagration modes representing two distinct sets of solutions to the relevant conservation laws. These works studied the proposal that, depending upon the values of the various controllable parameters, the accelerator would operate in either the detonation or deflagration mode. In the present work, we propose a variation on the explanation for the differences in performance between the various pulsed plasma accelerators. Instead of treating the accelerator as if it were only operating in one mode or the other during a pulse, we model the initial stage of the discharge in all cases as an accelerating current sheet (detonation mode). If the current sheet reaches the exit of the accelerator before the discharge is completed, the acceleration mode transitions to the deflagration mode type found in the quasi-steady MPD thrusters. This modeling method is used to demonstrate that standard gas-fed pulsed plasma accelerators, the CHENG thruster, and the quasi-steady MPD accelerator are variations of the same device, with the overall acceleration of the plasma depending upon the behavior of the plasma discharge during initial transient phase and the relative lengths of the detonation and deflagration modes of operation.

Polzin, Kurt A.↗

Bow Shock in Merging Cluster A520: The Edge of the Radio Halo and the Electron-Proton Equilibration Timescale

We studied the prominent bow shock in the merging galaxy cluster A520 using a deep Chandra X-ray observation and archival VLA radio data. This shock is a useful diagnostic tool, owing to its clear geometry and relatively high Mach number. At the "nose" of the shock, we measure a Mach number of M=2.4(sup 0.4, sub -0.2). The shock becomes oblique away from the merger axis, with the Mach number falling to approx. 1.6 around 30 deg from the nose. The electron temperature immediately behind the shock nose is consistent with that from the Rankine-Hugoniot adiabat, and is higher (at a 95% confidence) than expected for adiabatic compression of electrons followed by Coulomb electron-proton equilibration, indicating the presence of equilibration mechanisms faster than Coulomb collisions. This is similar to an earlier finding for the Bullet cluster. We also combined four archival VLA data sets to obtain a better image of the cluster's giant radio halo at 1.4 GHz. An abrupt edge of the radio halo traces the shock front, and no emission is detected in the pre-shock region. If the radio edge were due only to adiabatic compression of relativistic electrons in pre-shock plasma, we would expect a pre-shock radio emission detectable in this radio data set; however, an interferometric artifact dominates the uncertainty, so we cannot rule this model out. Other interesting features of the radio halo include a peak at the remnant of the cool core, suggesting that the core used to have a radio minihalo, and a peak marking a possible region of high turbulence.

Wang, Qian H. S.↗

Detonation to Deflagration-Mode Transitions in Pulsed Plasma Accelerators

PULSED plasma accelerators typically operate by storing energy in a capacitor bank and then discharging this energy through a gas. The current in such discharges will ionize the gas and produce a strong magnetic field, which interacts with the flowing current to accelerate the plasma through the Lorentz body force. For the present work, two plasma accelerator types employing this general scheme are of interest: the gas-fed pulsed plasma thruster (PPT) 1 and the quasi-steady magnetoplasmadynamic (MPD) accelerator. 2 The gas-fed pulsed plasma accelerator is generally understood as a completely transient device discharging in ∼1-10 μs. When the capacitor bank is discharged through the gas, a current sheet forms at the breech of the thruster and propagates forward under a j × B body force, entraining and accelerating propellant it encounters. This process is sometimes referred to in literature as 'snowplowing' the propellant or accelerating the gas in a detonation-mode because the current sheet representation approximates that of a strong detonation shockwave propagating through the gas. For these devices, acceleration of the initial current sheet ceases when either the current sheet reaches the end of the device and is ejected or when the current in the circuit reverses, striking a new 'crowbar' discharge at the breech and depriving the initial sheet of additional acceleration. In general, PPTs typically claim thrust efficiencies (ratio of jet kinetic energy to input electrical energy) registering in the teens or lower. 3 In the quasi-steady MPD accelerator, the pulse is lengthened to ∼1 ms or longer and maintained at an approximately constant level during discharge through the use of a pulse-forming network (PFN) of capacitors. After an initial transient discharge, which is typically short relative to the overall discharge period, the plasma assumes a relatively steady-state configuration, known as 'quasi-steady' MPD operation. 2 In this state, ionized gas flows through a stationary current channel in a manner that is sometimes referred to as deflagration-mode operation owing to the similarities to deflagration waves in gases. The plasma experiences electromagnetic acceleration as the plasma flows through the current channel towards the exit of the device. Quasi-steady MPD thrusters claim efficiencies up to 50% for certain propellants.4 There has been significant and sustained research over several decades on both gas-fed PPTs and quasi-steady MPD thrusters, however there have been pulsed thrusters that do not appear to exactly fit either classification, instead possessing a mixture of operational qualities characteristic of both thruster variants. The Coaxial High ENerGy (CHENG) thruster by Cheng, et al.5 operated on the short 10 μs timescales characteristic of PPTs, but claimed the high thrust densities, high efficiencies, and low electrode erosion rates that are more consistent with the MPD/deflagration mode of plasma acceleration. Gas-fed PPT research by Ziemer, et al. 3, 6 identified two separate regimes of performance in those thrusters. The regime at higher mass bits (termed Mode I in that work) possessed relatively constant thrust efficiency as a function of mass bit, while the second regime at very low mass bits (termed Mode II) exhibited an increase in efficiency with decreasing mass bit. Work by Poehlmann et al.7 and by Sitaraman and Raja8 sought to understand the performance of the CHENG thruster and the Mode I/Mode II performance in PPTs by modeling the acceleration using the Hugoniot Relation, with the detonation and deflagration modes of plasma acceleration representing two distinct sets of solutions to the relevant conservation laws. In these works, it was proposed that the values of the various controllable parameters determined whether the accelerator would operate in detonation or deflagration mode. Our hypothesized view of the acceleration process in the CHENG thruster and in PPTs experiencing a transition from Mode I to Mode II is inspired by observations of the transition from the PPT mode of operation to the quasi-steady MPD mode. Specifically, the quasi-steady MPD was discovered by driving a PPT to extended pulse lengths. Above a certain pulse length threshold the transient plasma current sheet transitions into a stable plasma acceleration mode that 'replicates in every observable detail steady flow self-field magnetoplasmadynamic acceleration.' 9 In the present work, instead of treating the accelerator as if it were only operating in a single mode during a pulse, we consider the initial stage of the discharge in all cases as a current sheet forming at the breach of the accelerator and moving towards the exit as a detonation wave. If the current sheet reaches the exit of the accelerator before the discharge is completed, the view of the acceleration mode transitions to the deflagration mode-type found in quasi-steady MPD thrusters. In previous work10 we presented a modeling framework that first captured the time-evolution of the current sheet (detonation) mode of the thruster and then transitioned into the quasi-steady MPD (deflagration) mode of plasma acceleration. In the present work, variations of the controllable parameters - specifically the pulsed circuit properties, the amount of mass injected into the thruster, and the relative timing between the initial gas injection and the initiation of the plasma current sheet - will be used to explore the thruster performance. A range of parameters are explored to demonstrate that standard gas-fed pulsed plasma accelerators, the CHENG thruster, and the quasi-steady MPD accelerator are variations of the same device, with the overall acceleration of the plasma depending upon the behavior of the plasma discharge during initial transient phase and the relative lengths of the detonation and deflagration modes of operation.

Polzin, Kurt A.↗

Beyond Basic Drag in Interplanetary CME Modeling: Effects of Solar Wind Pileup and High-Speed Streams

Coronal mass ejections (CMEs) cause severe space weather effects throughout our solar system. As a fast CME propagates through interplanetary space, it accumulates solar wind materials at its front. This pileup of materials, or CME-driven sheath, can be important in determining the geoeffectiveness of a CME. We take an existing arrival time model that includes expansion and deformation of the CME flux rope (ANTEATR; Kay & Gopalswamy, 2018, https://doi.org/10.1029/2018JA025780; Kay & Nieves-Chinchilla, 2021a, https://doi.org/10.1029/2020JA028911) and add a pileup procedure (PUP) as a physics-based approach to modeling the CME-driven sheath. ANTEATR-PUP solves the Rankine-Hugoniot equations for an oblique shock to determine the shock speed and sheath density, magnetic field, and temperature. The extra sheath mass affects the background drag calculation. Additionally, ANTEATR can now use any 1D profile for the background solar wind as opposed to the simple empirical models it previously relied upon. We present initial results from ANTEATR-PUP and compare with previous ANTEATR findings. Using results from an MHD simulation, we explore the effects of interactions with a static high-speed stream (HSS) on the CME's and sheath's interplanetary evolution. The drag forces essentially disappear while a CME remains within the HSS, but reappear stronger once the CME exits. The HSS-CME interaction produces the largest changes in the CME and sheath properties at 1 au when it occurs either close to the Sun near the inner simulation boundary at 0.1 au or right before the CME reaches 1 au. We estimate that these changes could significantly affect the geoeffectiveness.

C Kay↗

Non-contact velocity measurement instruments and systems, and related methods

Methods for calibration of non-contact velocity measurements and systems for implementing the same are described. Generally, the method comprises inducing a shock wave into a sample at a stress intensity that varies across the sample's elastic limit, which corresponds to the elastic-plastic state transition of the sample. That transition state may be at the sample's Hugoniot elastic limit. The velocity of the sample is measured using a non-contact velocity measurement instrument such as a velocimeter. The measurement may be compared to a predicted velocity or a velocity measurement made by another system to determine calibration parameters.

47 OTHER INSTRUMENTATION↗

Dynamic Properties of FeCrMnNi, a High Entropy Alloy

High entropy alloys (HEAs) represent a new class of materials that potentially possess an ideal combination of high strength and ductility and may be candidate materials that can withstand high amounts of damage before failure, especially under extreme conditions. To this end, a series of shock/spall loading experiments were conducted on an Fe/Cr/Mn/Ni HEA to assess not only its equation of state (EOS) but also its resistance to damage and failure. A single-stage light gas gun was used to conduct a series of flyer plate symmetric impact experiments coupled with recovery of the samples for post-mortem microstructural analysis to obtain fundamental understanding regarding the damage morphology. Our results show that the measured EOS for this alloy was in reasonable agreement with an estimated Hugoniot value. Additionally, the spall strength of these alloys was found to vary between 1.4 and 1.9 GPa within the same plate but was comparable to other iron-based conventional alloys. DOE/NV/03624--1059

36 MATERIALS SCIENCE↗

Dynamic properties of FeCrMnNi, a High Entropy Alloy

The goal of this paper was to assess the dynamic properties of a new class of materials, High entropy alloys (HEAs). Specifically, gas gun experiments coupled with recovery were performed on a specific HEA, FeCrMnNi, to measure its equation of state (EOS) and its spall strength, which is a measure of the stress required to nucleate voids under shock loading conditions. While there has been a plethora of work performed to assess the mechanical properties of these HEAs under uniaxial stress conditions as a function of strain rate, investigation of its properties in dynamic extremes remains rare. The current work fills this gap in knowledge for this novel class of materials. Our results show that the measured EOS for this material at one velocity was in reasonable agreement with an estimated Hugoniot. Furthermore, while the spall strength for this material was found to be ~1.9 GPa, with some variation based on sample location, the main failure mode wasbrittle. This brittle failure leading to formation of cracks in the material is different than the ductile failure observed in pure iron and its alloys. DOE/NV/03624--1298

36 MATERIALS SCIENCE↗

Experimental Pathways for Detecting Double Superionicity in Planetary Ices

The ice giant planets Uranus and Neptune are assumed to contain large amounts of planetary ices such as water, methane, and ammonia. The properties of mixtures of such ices at the extreme pressures and temperatures of planetary interiors are not yet well understood. Ab initio computer simulations have predicted that a number of ices exhibit a hydrogen superionic state and a doubly superionic state. Since the latter state has not yet been generated with experiments, we outline here two possible pathways for reaching and detecting such a state with dynamic compression experiments. Here, we suggest X-ray diffraction as the principal tool for detecting when the material becomes doubly superionic and the sublattice of one of the heavy nuclei melts. That would require a temperature of ~3500 K and pressures greater than ~200 GPa for H 3 NO 4 , which we use as an example material here. Such conditions can be reached with experiments that employ an initial shock that is followed by a ramp compression wave. Alternatively, one may use triple-shock compression because a single shock does not yield sufficiently high densities.

Neptune↗

An analytical expression for temperature in a thermodynamically consistent model with a Mie-Gruneisen equation for pressure

The objective of this paper is to develop an analytical expression for temperature in a thermodynamically consistent model with a Mie-Gruneisen equation for pressure. This expression for the temperature is obtained for both constant and variable specific heat models and can be used in common models for the material yield strength that include thermal softening due to increase in temperature. Additionally, the material parameters in the model can easily be calibrated to match known experimental data and the model has been used to determine the value of the shock pressure at the onset of melting during shock loading.

42 ENGINEERING↗

Thermal interfaces in dynamic compression experiments

Temperature is a difficult thermodynamic variable to measure in dynamic compression experiments. Optical pyrometry is a general-purpose technique for measuring temperature from a radiant surface, but that surface is often the interface between distinct materials with temperatures that vary spatially along the loading direction. This leads to a fundamental problem: how does the measured interface temperature relate to this temperature profile along the compression axis? Numerical analysis of loading history and thermal diffusion at these interfaces shows that seemingly subtle changes in experiment geometry can lead to very different temperature profiles. We compare these results to laboratory temperature measurements of shock-compressed tin.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Drive-pressure optimization in ramp-wave compression experiments through differential evolution

Ramp-wave dynamic-compression experiments are used to examine quasi-isentropic loading paths in materials. The gradual and continuous increase in pressure created by ramp waves make these types of experiments ideal for studying nonequilibrium material behavior, such as solidification kinetics. In ramp-wave compression experiments, the input drive pressure to the experimental setup may be exerted through one of a number of different mechanisms (e.g., magnetic fields, gas-gun-driven impactors, or high-energy lasers) and is generally required for simulating such experiments. Yet, regardless of the specific mechanism, this drive pressure cannot be measured directly (measurements are generally taken at a location near the back of the experimental setup through a transparent window), leading to an inverse problem where one must determine the drive pressure at the front of the experimental setup (i.e., the input) that corresponds to the particle velocity (the output) measured near the back of the experimental setup. Furthermore, we solve this inverse problem using a heuristic optimization algorithm, known as differential evolution, coupled with a multiphysics, hydrodynamics code that simulates the compression of the experimental setup. By running many rounds of forward simulations of the experimental setup, our optimization process iteratively searches for a drive pressure that is optimized to closely reproduce the experimentally measured particle velocity near the back of the experimental setup. While our optimization methodology requires a significant number of hydrodynamics simulations to be conducted, many of these can be performed in parallel, which greatly reduces the time cost of our methodology. One novel aspect of our method for determining the drive pressure is that it does not require physical modeling of the drive mechanism and can thus be broadly applied to many types of ramp-compression experiments, regardless of the drive mechanism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A theoretical approach for transient shock strengthening in high-energy-density laser compression experiments

In high-energy-density shock compression experiments, the desired state of compression is typically achieved by passing shock waves through a sequence of different materials. Here, a theoretical approach for transiently strengthening such shocks passing through interfaces of experimentally relevant impedance ratios is examined. A semi-analytical method based on characteristics analysis is used to solve the problem of a shock passing from one material to another through an intermediate region of non-uniform impedance; by appropriately designing this region, a greater shock strength can be achieved in the second material for a finite duration than in the absence of this region. When a shock passes into a material of higher impedance, the shock strengthening increases to a maximum before decreasing to an asymptotic value as the strength of the incident shock is increased. For shocks passing into materials of decreasing impedance, the shock strengthening increases monotonically as the strength of the incident shock is increased when the impedance ratio is above a critical threshold. Incorporating multiple intermediate materials can further increase the strength of the transmitted shock, with an exponential discretization of intermediate material impedances being the most effective distribution for strengthening strong shocks. The results suggest that up to 25% and 9% increases in pressure behind the leading shock can be achieved for materials of increasing and decreasing impedance, respectively. The technique is applied to the design of laser-driven dynamic compression experiments, and the results of the analysis are verified via comparison to simulations performed with the HYADES hydrodynamics code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Near-optimal combination of high performance and insensitivity in a shock compressed high explosive single crystal

Achieving the desired combination of superior detonation performance and insensitivity to shock initiation has been a long-standing goal in high explosive (HE) science and technology. Having previously established the shock insensitivity of 1,1-diamino-2,2-dinitroethene (also known as DADNE or FOX-7) single crystals to 20 GPa (extended to 25 GPa in this work), the FOX-7 detonation response was determined through wave profile measurements in ~250 μm thick single crystals shock compressed to 64 GPa. Quite unexpectedly, FOX-7 demonstrated the classic Chapman–Jouguet (C–J) detonation response—reaction completion in the detonation front (<0.7 ns) at pressures of 44 GPa and higher—not observed in other insensitive high explosives. Here, the experimentally determined C–J pressure (35 GPa), detonation wave velocities and the detonation products equation of state—together with shock insensitivity to 25 GPa—demonstrate that FOX-7 single crystals display a near-optimal combination of high performance and shock insensitivity, not observed in another HE crystal.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Phase transitions in Zr at sub-nanosecond time scales

Here solid-solid phase transitions are investigated in Zr thin films using shock compression induced by a short laser pulse (<1 ns). Shock wave profiles are measured at free surfaces for films of different thicknesses (a few micrometers) using chirped-pulse line velocimetry with 10 ps time resolution. Experiments are performed at pressures up to ~50 GPa, which is sufficient to reach the ω and β phases under equilibrium conditions. The shock wave structures are analyzed using a general Lagrangian analysis method, which allows for the calculation of stress–strain paths and assessments of phase transition behavior. In agreement with recent short laser pulse experiments using ultra-fast x-ray diffraction, we do not find any clear evidence of the α–ω transition, though this would be expected from the phase diagram. Instead, we infer a direct transformation to a metastable β-phase at lower shock pressures (<20 GPa) and equilibrium β at higher pressures. Through the velocimetry analysis, we find α–β transformation onset times of less than ~100 ps and completion times of less than ~200 ps.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗