Cylindrical Wire Arrays Research Articles

Structure and dynamics of magneto-inertial, differentially rotating laboratory plasmas

We present a detailed characterization of the structure and evolution of differentially rotating plasmas driven on the MAGPIE pulsed-power generator (1.4 MA peak current, 240 ns rise time). The experiments were designed to simulate physics relevant to accretion discs and jets on laboratory scales. A cylindrical aluminium wire array Z pinch enclosed by return posts with an overall azimuthal off-set angle was driven to produce ablation plasma flows that propagate inwards in a slightly off-radial trajectory, injecting mass, angular momentum and confining ram pressure to a rotating plasma column on the axis. However, the plasma is free to expand axially, forming a collimated, differentially rotating axial jet that propagates at ${\approx }100\,{\rm km}\,{\rm s}^{-1}$ . The density profile of the jet corresponds to a dense shell surrounding a low-density core, which is consistent with the centrifugal barrier effect being sustained along the jet's propagation. We show analytically that, as the rotating plasma accretes mass, conservation of mass and momentum implies plasma radial growth scaling as $r \propto t^{1/3}$ . As the characteristic moment of inertia increases, the rotation velocity is predicted to decrease and settle on a characteristic value ${\approx }20\,{\rm km}\,{\rm s}^{-1}$ . We find that both predictions are in agreement with Thomson scattering and optical self-emission imaging measurements.

Multi frame radiography of supersonic water jets interacting with a foil target

Pulsed-power-driven underwater electrical explosion of cylindrical or conical wire arrays produces supersonic water jets that emerge from a bath, propagating through the air above it. Interaction of these jets with solid targets may represent a new platform for attaining materials at high pressure (>1010 Pa) conditions in a university-scale laboratory. However, measurements of the internal structure of such jets and how they interact with targets are difficult optically due to large densities and density contrasts involved. We utilized multi-frame x-ray radiographic imaging capabilities of the ID19 beamline at the European Synchrotron Radiation Facility to explore the water jet and its interaction with a 50 μm thick copper foil placed a few mm from the surface of water. The jet was generated with a ∼130 kA-amplitude current pulse of ∼450 ns rise time applied to a conical wire array. X-ray imaging revealed a droplet-type structure of the jet with an average density of <400 kg/m3 propagating with a velocity of ∼1400 m/s. Measurements of deformation and subsequent perforation of the target by the jet suggested pressures at the jet–target interface of ∼5 × 109 Pa. The results were compared to hydrodynamic simulations for better understanding of the jet parameters and their interaction with the foil target. These results can be used in future research to optimize the platform, and extend it to larger jet velocities in the case of higher driving currents supplied to the wire array.

Plasma flows during the ablation stage of an over-massed pulsed-power-driven exploding planar wire array

We characterize the plasma flows generated during the ablation stage of an over-massed exploding planar wire array, fielded on the COBRA pulsed-power facility (1 MA peak current, 250 ns rise time). The planar wire array is designed to provide a driving magnetic field (80–100 T) and current per wire distribution (about 60 kA), similar to that in a 10 MA cylindrical exploding wire array fielded on the Z machine. Over-massing the arrays enables continuous plasma ablation over the duration of the experiment without implosion. The requirement to over-mass on the Z machine necessitates wires with diameters of 75–100μm, which are thicker than wires usually fielded on wire array experiments. To test ablation with thicker wires, we perform a parametric study by varying the initial wire diameter between 33 and 100 μm. The largest wire diameter (100 μm) array exhibits early closure of the cathode-wire gap, while the gap remains open over the duration of the experiment for wire diameters between 33 and 75 μm. Laser plasma interferometry and time-gated extreme-ultraviolet (XUV) imaging are used to probe the plasma flows ablating from the wires. The plasma flows from the wires converge to generate a pinch, which appears as a fast-moving (V≈100kms−1) column of increased plasma density (n¯e≈2×1018cm−3) and strong XUV emission. Finally, we compare the results with three-dimensional resistive-magnetohydrodynamic (MHD) simulations performed using the code GORGON, the results of which reproduce the dynamics of the experiment reasonably well.

Diagnosing X-pinch and cylindrical wire array Z-pinch with an all-optical framing camera on the “QiangGuang-I” facility

An all-optical framing camera has been established on the 1-MA “QiangGuang-I” facility for investigating the imploding dynamics of the X-pinch and the cylindrical wire array Z-pinch. This camera measures the photons flux distribution by detecting the photon-induced refractive index changes in the InP semiconductor with a probe laser beam. The InP-based imaging sensor with a 100 nm thick Al film and a 10 μm thick gold transmission grating of 20 μm spatial period was fabricated based on the lithography method. Two sequential frames with 1.5 ns time resolution and 13 ns inter frame separation time can be recorded in one single shot. Framing images indicating the plasma generation and dissipation of the X-pinch and the cylindrical wire array Z-pinch have been obtained, showing that this framing camera is a promising technique for investigating the mechanisms of the Z-pinch and other high energy density physics.

Generalized computational ablation model of multi-wire cylindrical Z-pinches

The generalized computational ablation model of multi-wire Z-pinches is developed. Using derived equations, one can calculate at each moment of time both the mass ablation rate from single and nested cylindrical wire arrays as well as the matter ablation velocity. These two important variables provide the capability to numerically simulate high energy density Z-pinch experiments in a wide range of load parameters: the initial multi-wire array radius up to tens of centimeters, the inter-wire gap up to a few millimeters, the Z-pinch implosion time up to a few microseconds, and the current amplitude in a load up to tens of mega-amperes. The generalized ablation model makes it possible to reproduce the main characteristics of the Z-pinch implosion, such as the moment of starting and following movement trajectory of current-plasma sheath, timing of x-ray pulse generation, its duration, x-ray power, and total radiation energy, in radiative magneto-hydrodynamic calculations. The generalized computational ablation model of tungsten multi-wire Z-pinch was validated using results of experiments with explosive magneto-cumulative generators (Russia) and was applied further to various pulsed power generators such as Z-accelerator, PTS, MAGPIE, and Angara-5-1.

Supersonic jet generation by underwater sub-microsecond electrical explosions of wire arrays

Experiments in which supersonic water jets are generated by underwater sub-μs timescale electrical explosions of cylindrical and conical wire arrays are presented. These are compared with previous experiments [Maler et al., Phys. Plasmas 28, 063509 (2021)] in which the generation of supersonic water jets was demonstrated using a μs timescale generator. Although in the present experiments less energy is deposited into the wire arrays, the water jets acquire higher velocities compared to when the deposited energy is higher but the timescale is slower. That is, with a higher energy density deposition rate, faster radial wire expansion is induced resulting in a stronger converging shockwave and a faster waterflow behind its front. In addition, two dimensional hydrodynamic numerical simulations show that the formation of the water jet is the result of extremely high pressure at the axis of the shockwave implosion and the cumulative edge effect realized at the array output.

Linearly Polarized High-Purity Gaussian Beam Shaping and Coupling for 330 GHz/500 MHz DNP-NMR Application

Terahertz waves generated by vacuum electron devices have been successfully applied in dynamic nuclear polarization enhanced nuclear magnetic resonance (DNP-NMR) technology to significantly enhance the sensitivity of high-field NMR. To reduce the magnetic field interference, the high-power terahertz wave source and the NMR spectrometer need to be separated by a few meters apart. Corrugated horns and directional couplers are key components for shaping high linearly polarized terahertz Gaussian beam and accurately coupling electromagnetic power in the transmission system. In this paper, a corrugated TE11-HE11 mode converter and a three-port directional coupler realized by its inner cylindrical wire array are proposed for a 330 GHz/500 MHz DNP-NMR system. The output mode of the mode converter presents a characteristic of highly linear polarization, which is 98.8% at 330 GHz for subsequent low loss transmission. The designed three-port directional coupler can produce approximately −33 dB electromagnetic wave power on port 3 in the frequency range between 300–360 GHz stably, which can be used to measure the electromagnetic wave power of the transmission line in real-time. The designed mode converter and direction coupler can be installed and replaced easily in the corrugated waveguide transmission system.

Generation of supersonic jets from underwater electrical explosions of wire arrays

Underwater electrical explosion experiments of cylindrical or conical wire arrays accompanied by the generation of fast (up to ∼4500 m/s) water jets are presented. In these experiments, a pulse generator with a stored energy of up to ∼5.7 kJ, current amplitude of up to ∼340 kA, and rise time of ∼0.85 μs was used to electrically explode copper and aluminum wire arrays underwater. Streak and fast framing shadow imaging was used to extract the space–time resolved velocity of the ejected jet from the array while it propagates in air. The jet generation occurs due to high pressure and density of water formed in the vicinity of the array axis by the imploding shockwave. It was shown that the velocity of the jet ejected from the array depends on the array geometry and the thickness of the water layer above the array. The results suggest that ≥50% of the energy deposited into the array is transferred to the kinetic energy of this jet and the axial waterflow.

Study of Interaction of Plasma Flows with Magnetic Field During Implosion of Cone-Cylindrical Nested Arrays

The results of the studies of the compression of the plasma of cone-cylindrical nested arrays of mixed composition at current flow through them of up to 3 MA at the Angara-5-1 facility are presented. The outer array of the nested array is a conical array of thin nylon fibers or tungsten wires, while the inner one is a cylindrical tungsten wire array. The implosion of current in this type of nested arrays is a unique opportunity for simulating the interaction of magnetized plasma flows with a strong magnetic field. In the space between the inner and outer arrays, the super-Alfven plasma flow from the outer array collides with the magnetic field of the discharge current through the inner array. As a result of this interaction in the space between arrays, different plasma flow modes are implemented: pre-Alfven (Vr VА), and a mode with the formation of the transition region—a shock wave (SW) between arrays, depending on the ratio of the plasma formation rates of arrays of nested array and on the ratio of their radii. The SW region formation in the space between arrays occurs near the inner array, where the kinetic pressure of the plasma flow from the outer array is balanced by the magnetic pressure of the discharge current of the inner array. New experimental data was obtained on the features of the SW region formation near the surface of the inner array and the nature of its change during the interaction. The use of an external conical array enabled us to obtain the SW position depending on the ratio of radii of the outer and inner arrays in one shot. It is shown that the interaction of plasma flows of the outer conical array with the magnetic field of the inner cylindrical array leads to a significant decrease in the zipper-effect at the final stage of plasma compression of the inner array and the pinch formation. The obtained experimental results are compared with the results of simulating the plasma motion between the arrays using the three-dimensional radiation-magnetohydrodynamic code MARPLE3D.

Study of the Time Dependence of the Plasma Formation Intensity at the Current Implosion of Cylindrical Wire and Fiber Arrays from Different Substances

A characteristic feature of the implosion of multiwire arrays on powerful high-current electrophysical facilities (ZR, Angara-5-1, Julong-1 (PTS), MAGPIE, etc.) is the process of extended wire ablation. It is based on the fact that the substance of the wires is not converted into plasma instantly, but is supplied into the discharge relatively slowly at the rate $$\dot {m}(t)$$ in about 70–80% of the rise time of the facility current. It is believed that the plasma is formed on the surface of the cores of the exploded wires due to the energy coming from the hot plasma corona surrounding the core of the wire in the form of the heat flux and emission. In this paper, we propose a new approach to determining the quantity $$\dot {m}(t)$$ as the main quantitative characteristic of the process of the extended wire ablation in wire (or fiber) arrays. A method is presented, using which it is possible to determine experimentally the time dependence of the quantity $$\dot {m}(t)$$ both at the initial stage of the plasma formation and at its final stage, when $$\dot {m}(t)$$ → 0. In fact, by measuring the current Ip with a magnetic probe located inside the wire array near the surface of the wires, it is possible to find the current flowing in the plasma formation region Is as the difference between the total current through the liner and the current Ip. The time dependence Is(t) thus defined is nonmonotonic, and the quantity $$\dot {m}(t)\sim I_{s}^{2}\left( t \right)$$ correspondingly decreases at the final stage of the implosion of the wire array. The intensity of the plasma formation of arrays made form wires and fibers of different substances (Al, Cu, Mo, W, Bi, and kapron) was determined in experiments at the Angara-5-1 facility, the decay rate of this quantity at the stage of the plasma formation termination and its effect on the pulse and emission parameters were analyzed. The obtained results are compared with the data of the numerical MHD simulation.

Shockwave generation by electrical explosion of cylindrical wire arrays in hydrogen peroxide/water solutions

We report the results of experiments investigating the implosion of a shock generated by the electrical explosion of a cylindrical aluminum wire array immersed in a >80% hydrogen peroxide/water solution. This solution was chosen as an additional energy source to the supplied electrical energy to generate the imploding flow with higher velocity. The experiments were conducted using a generator with the stored energy of ∼4.8 kJ, delivering to the array a ≤280 kA current rising during ∼1 μs. The backlighted images of the imploding shocks were recorded using a streak camera. Using different diameter wires, the explosion of arrays, characterized by critically damped and under-damped discharges, was studied. The experiments revealed that an array explosion in a 92% H2O2/H2O solution results in the second strong shock generated after the peak of the deposited electrical power, a solid indication of H2O2 detonation. This second shock converges ∼40% faster than the first strong shock generated by the wire explosion. One-dimensional hydrodynamic simulations of the shock convergence in H2O2/H2O solutions support this proposition.

Enhancement of Shock Wave Generated by Underwater Electrical Wire-Array Explosion at a Fixed Energy and Mass of Wire-Array

An energy-efficient method for further enhancing the shock wave generated by underwater electrical wire-array explosion at a fixed energy was developed. Based on the configuration of a cylindrical wire-array, the method was to replace one wire of 0.2-mm diameter with N thinner wires, while the total mass of these N wires was kept equal to the mass of that 0.2-mm wire. As the number of wires increased, the maximum wave pressure at the axis of the wire-array increased from 28 MPa for 1 wire of 0.2-mm diameter to about 90 MPa for 16 wires of 0.05-mm diameter. The shock wave generated by one single wire was proportional to 1/(N) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> rather than 1/N, which should be the reason for the enhancement. The interaction of shock waves from each single wire was discussed. It might be roughly divided into two kinds, “non-overlapping” and “overlapping.” The “non-overlapping” occurred only in the wire-array with not more than four wires. While propagating toward the axis of the wirearray, the shock waves from the wires did not overlap even when they were close to the axis. The shock wave at the axis is simply the summation of the shock waves from all wires. In contrast, the “overlapping” occurred in the wire-array with not less than seven wires. The shock waves from the wires overlapped even when they were far from the axis. Due to the converging effect of shock waves, the shock wave at the axis is considerably lower than the summation of shock waves from all wires, especially when the number of wires is larger.

Pulsed power driven cylindrical wire array explosions in different media

Cylindrical copper wire array explosions were carried out in de-ionized water, sodium polytungstate solution, nitromethane, and polyester in order to obtain high energy density conditions in the vicinity of implosion using the generated converging shock waves. The use of different materials in which the array is immersed can contribute to this goal with higher density resulting in higher shock velocities and possible combustion. The generated shock waves were captured by a framing and a streak camera, and shock velocities were calculated and compared. The pressure behind the shock front was calculated using the known hydrodynamic relations (for water, polytungstate, and polyester) and compared to two-dimensional hydrodynamic simulations coupled with the equations of state (for water and polyester). It was shown that despite lower shock wave velocity in polytungstate solution than in water, the pressures generated are similar in both materials. In polyester, both shock velocities and generated pressures are 2–4 times higher than in water. It was also shown that it is possible to carry out these explosions in a solid which has several advantages compared to liquids, such as not relying on waterproof systems and easier transportation.

Synchrotron based X-ray radiography of convergent shock waves driven by underwater electrical explosion of a cylindrical wire array

We present X-ray radiography images showing the propagation of shock waves generated by electrical explosion of a cylindrical arrangement of wires in water driven by pulsed power. In previous experiments [S. N. Bland et al., Phys. Plasmas 24, 082702 (2017)], the merger of shock waves from adjacent wires has produced a highly symmetrical, cylindrical shock wave converging on the axis, where it is expected to produce a high density, strongly coupled plasma ideal for warm dense matter research. However, diagnostic limitations have meant that much of the dynamics of the system has been inferred from the position of the front of the cylindrical shock and timing/spectra of light emitted from the axis. Here, we present a synchrotron-based radiography of such experiments—providing direct quantitative measurements on the formation of the convergent shock wave, the increased density of water on the axis caused by its arrival, and its “bounce” after arrival on the axis. The obtained images are compared with two-dimensional hydrodynamic simulations, which reproduce the observed dynamics with a satisfactory agreement in density values.

Study of interaction between plasma flows and the magnetic field at the implosion of nested wire arrays

At the Angara-5-1 facility investigation was carried out which studied the interaction of plasma flows and the magnetic field. They are created by the current implosion of cylindrical nested wire arrays, the inner and outer array of which are composed from thin wires or dielectric fibers. It has been shown experimentally that at the plasma formation stage it is possible to realize various modes of interaction between plasma flows and the magnetic field of the discharge current inside the nested array. A mechanism is proposed for the interaction of plasma flows of the outer array with the magnetic field and the current-carrying plasma of the inner array. The stability of the plasma compression of the inner array at the final stage of its compression depends on the nature of this interaction. Obtained experimental data on the dynamics of interaction of plasma flows with the magnetic field in the gap between arrays are compared with the results of 2D-simulation of the implosion of nested arrays according to the RMHD MARPLE code. It is experimentally and theoretically confirmed that when a nested array is imploded with certain parameters around the inner array, a plasma quasi-closed shell is formed in the azimuthal direction.

Convergence of shock waves between conical and parabolic boundaries

Convergence of shock waves, generated by underwater electrical explosions of cylindrical wire arrays, between either parabolic or conical bounding walls is investigated. A high-current pulse with a peak of ∼550 kA and rise time of ∼300 ns was applied for the wire array explosion. Strong self-emission from an optical fiber placed at the origin of the implosion was used for estimating the time of flight of the shock wave. 2D hydrodynamic simulations coupled with the equations of state of water and copper showed that the pressure obtained in the vicinity of the implosion is ∼7 times higher in the case of parabolic walls. However, comparison with a spherical wire array explosion showed that the pressure in the implosion vicinity in that case is higher than the pressure in the current experiment with parabolic bounding walls because of strong shock wave reflections from the walls. It is shown that this drawback of the bounding walls can be significantly minimized by optimization of the wire array geometry.

Experimental investigations of ablation stream interaction dynamics in tungsten wire arrays: Interpenetration, magnetic field advection, and ion deflection

Experiments have been carried out to investigate the collisional dynamics of ablation streams produced by cylindrical wire array z-pinches. A combination of laser interferometric imaging, Thomson scattering, and Faraday rotation imaging has been used to make a range of measurements of the temporal evolution of various plasma and flow parameters. This paper presents a summary of previously published data, drawing together a range of different measurements in order to give an overview of the key results. The paper focuses mainly on the results of experiments with tungsten wire arrays. Early interferometric imaging measurements are reviewed, then more recent Thomson scattering measurements are discussed; these measurements provided the first direct evidence of ablation stream interpenetration in a wire array experiment. Combining the data from these experiments gives a view of the temporal evolution of the tungsten stream collisional dynamics. In the final part of the paper, we present new experimental measurements made using an imaging Faraday rotation diagnostic. These experiments investigated the structure of magnetic fields near the array axis directly; the presence of a magnetic field has previously been inferred based on Thomson scattering measurements of ion deflection near the array axis. Although the Thomson and Faraday measurements are not in full quantitative agreement, the Faraday data do qualitatively supports the conjecture that the observed deflections are induced by a static toroidal magnetic field, which has been advected to the array axis by the ablation streams. It is likely that detailed modeling will be needed in order to fully understand the dynamics observed in the experiment.

Plasma outflows from wire-based z-pinch experiments driven at currents of hundreds of kiloamperes.

Preliminary results on the latest experiments regarding plasma outflows from different wire-based z-pinch configurations performed in the Llampudken generator (∼350kA in ∼350ns) are presented. These outflows are produced from three different experiments: cylindrical, conical and nested conical arrays. Our experiments show that it is indeed possible to produce plasma outflows from moderate size pulsed power drivers with currents of some hundreds of kiloamperes. Each one of the configurations studied here can produce a dense plasma outflow characterized by its own set of dimensionless parameters; such as Reynolds number, magnetic Reynolds number, amongst others. A dense magnetized, magneto-hydrodynamically unstable plasma outflow is produced using a modified cylindrical wire array, whereas strongly collimated jets are produced from the conical configurations. Moreover, it is possible to mimic the episodic emission of plasma outflow in a collimated jet by producing temporally separated implosions from the nested conical configuration. Finally, the characteristic and dynamics of each outflow are presented and discussed.

Underwater Electrical Explosion of Wires and Wire Arrays and Generation of Converging Shock Waves

A brief review of the results obtained in recent research of underwater electrical explosions of wires and wire arrays using microsecond-, submicrosecond-, and nanosecond-timescale high-current generators is presented. In a microsecond-timescale wire explosion, good agreement was attained between the results of experiments and the results of magnetohydrodynamic calculations coupled with equations of state (EOS) and modern conductivity models. Conversely, in a nanosecond-timescale wire explosion, the wire resistance and the EOS were modified in order to fit experimental data. In experiments with cylindrical and spherical wire arrays, generation of a converging shock wave (SW) was demonstrated allowing formation of an extreme state of water in the vicinity of either the axis or the origin of the SW’s implosion. In addition, it is shown that SW convergence in superspherical geometry allows one to achieve larger values of pressure, density, and temperature of water in the vicinity of the axis of convergence than in the case of a spherical implosion. The results of experiments and numerical analysis showed that a cylindrical SW keeps its symmetry along the main path of its convergence. In addition, it is shown that underwater electrical explosion of an X-pinch wire configuration and a cone wire array allows one to generate fast jets of metal and water, respectively, without using chemical explosions.

Study of ablation and implosion stages in wire arrays using coupled ultraviolet and X-ray probing diagnostics

Star and cylindrical wire arrays were studied using laser probing and X-ray radiography at the 1-MA Zebra pulse power generator at the University of Nevada, Reno. The Leopard laser provided backlighting, producing a laser plasma from a Si target which emitted an X-ray probing pulse at the wavelength of 6.65 Å. A spherically bent quartz crystal imaged the backlit wires onto X-ray film. Laser probing diagnostics at the wavelength of 266 nm included a 3-channel polarimeter for Faraday rotation diagnostic and two-frame laser interferometry with two shearing interferometers to study the evolution of the plasma electron density at the ablation and implosion stages. Dynamics of the plasma density profile in Al wire arrays at the ablation stage were directly studied with interferometry, and expansion of wire cores was measured with X-ray radiography. The magnetic field in the imploding plasma was measured with the Faraday rotation diagnostic, and current was reconstructed.