Z-pinch Load Research Articles

Impact of the radial density profile on the Z-pinch stability at a microsecond rise time of the driving current

This paper considers the instabilities of imploding aluminum metal-puff Z-pinches with an outer plasma shell. An experiment was performed on the GIT-12 generator (3.2–3.6 MA, ∼1 μs implosion times, and ∼15 cm initial Z-pinch radius). It was shown that the density profile of the Z-pinch material had the dominant effect on the growth and suppression of instabilities. Two Z-pinch load configurations were used. The first configuration provided a tailored density profile (TDP) [A. L. Velikovich et al., Phys. Rev. Lett. 77, 853 (1996)], which ensured the suppression of the magneto-Rayleigh–Taylor (MRT) instability in the Z-pinch. For the second configuration, the density profile was changed in such a way that a density notch from 10 to 0.5 μg/cm3 occurred at a radius of about 3 cm from the Z-pinch axis. The notch in the density profile and the nonmonotonic increase in density resulted in a completely unstable compression of the Z-pinch. This gave rise to large-scale instabilities, which were detected by optical diagnostics. The instabilities grew and were not suppressed even in the stagnation phase, despite a sharp increase in the density of the Z-pinch material near the axis. The results were interpreted using the model proposed by Curzon et al. [Proc. R. Soc. London A 257, 386 (1960)]. The total instability amplitude is the sum of the amplitudes of MRT and magneto-hydrodynamic (MHD) instabilities. The growth of the total instability in the density notch region is due to the development of MRT instability. Thus, if the density profile has a notch, the Z-pinch compression in the stagnation phase occurs under strong perturbations at the magnetic field/plasma interface. This results in a dramatic growth of MHD instabilities. Hence, a stable implosion of a Z-pinch with TDP is possible only if the density increases monotonically toward the axis.

Exploring the parameter space of MagLIF implosions using similarity scaling. III. Rise-time scaling

Magnetized liner inertial fusion (MagLIF) is a z-pinch magneto-inertial-fusion concept studied at the Z Pulsed Power Facility of Sandia National Laboratories. Two important metrics characterizing current delivery to a z-pinch load are the peak current and the current-rise time, which is roughly the time interval to reach the peak current. It is known that, when driving a z-pinch load with a longer current-rise time, the performance of the z-pinch decreases. However, a theory to understand and quantify this effect is still lacking. In this paper, we utilize a framework based on similarity scaling to analytically investigate the variations in the performance of MagLIF loads when varying the current-rise time, or equivalently, the implosion timescale. To maintain similarity between the implosions, we provide scaling prescriptions of experimental input parameters defining a MagLIF load and derive the expected scaling laws for stagnation conditions and for various performance metrics. We compare predictions of the theory to 2D numerical simulations using the radiation, magneto-hydrodynamic code hydra. For several metrics, we find acceptable agreement between the theory and simulations. Our results show that the voltage φload near the MagLIF load follows a weak scaling law φload∝tφ−0.12 with respect to the characteristic timescale tφ of the voltage source, instead of the ideal φload∝tφ−1 scaling. This occurs because the imploding height of the MagLIF load must increase to preserve end losses. As a consequence of the longer imploding liners, the required total laser preheat energy and delivered electric energy increase. Overall, this study helps understand the trade-offs of the MagLIF design space when considering future pulsed-power generators with shorter and longer current-rise times.

Model of a 5-MA Linear-Transformer-Driver Accelerator: Comparison of MITL Performance for Bremsstrahlung Electron Beam Diodes and Z-Pinch Loads

A transmission line circuit model was conducted to compare the performances of the two-level 2.5 Ω magnetically insulated transmission lines (MITLs) system of a 5-MA linear-transformer-driver (LTD) accelerator for two kinds of typical loads, including bremsstrahlung electron beam diodes and Z-pinch loads. Both the electron current loss in the pulse front during the magnetic insulation setup process and the electron flow distribution in the magnetic insulation steady state were analyzed. When the accelerator drives an electron beam diode load with impedance of 1.20 Ω (a single level), the duration of the magnetic insulation setup is about 12 ns, the current loss is about 130 kA in a single MITL level, the maximum electron flow current is about 50 kA in the end of MITL, and its amplitude decreases gradually after the steady magnetic insulation is established. When the accelerator drives a Z-pinch load with length of 1.5 cm, radius of 1.2 cm, and mass of 0.3 mg/cm, the duration of the magnetic insulation setup is almost zero, the maximum electron flow current in the end of MITL can reach about 55 kA (a single level), and the waveform of the electron flow resembles a saddle shape, which reaches the peak at the pinch stagnation time.

Impact of power flow on Z-pinch loads

Magnetically insulated transmission lines (MITLs) are used to deliver tens of MA to a Z-pinch load. The MITLs suffer current losses due to contaminant plasma located in the anode–cathode gap which is swept toward the load along the power flow. The swept up contaminant plasma can deposit mass and energy onto the load resulting in deformations or the seeding of macroscopic instabilities. This paper discusses 2D fully kinetic simulations of the contaminant plasma evolution which predict the current losses and the flux of mass and energy onto the load. The effects of a dynamic, i.e., imploding, load are shown to increase both the current loss and the mass and energy flux. The MITL used is a conical, radially converging design which is a feature common to MA-scale Z-pinch accelerators.

Wire, hybrid, and laser-cut X-pinches as Talbot–Lau backlighters for electron density diagnostics

Talbot–Lau x-ray deflectometry (TXD) enables refraction-based imaging for high-energy-density physics experiments, and thus, it has been studied and developed with the goal of diagnosing plasmas relevant to inertial confinement and magnetic liner inertial fusion. X-pinches, known for reliably generating fast (∼1 ns), small (∼1 µm) x-ray sources, were driven on the compact current driver generator for ablation structure and implosion studies (∼200 kA, 150 ns) as a potential backlighter source for TXD. Considering that different X-pinch configurations have characteristic advantages and drawbacks as x-ray generating loads, three distinct copper X-pinch configurations were studied: the wire X-pinch, the hybrid X-pinch, and the laser-cut X-pinch. The Cu K-shell emission from each configuration was characterized and analyzed regarding the specific backlighter requirements for an 8 keV TXD system: spatial and temporal resolution, number of sources, time of emission, spectrum, and reproducibility. Recommendations for future experimental improvements and applications are presented. The electron density of static objects was retrieved from Moiré images obtained through TXD. This allowed to calculate the mass density of static samples within 4% of the expected value for laser-cut X-pinches, which were found to be the optimal X-pinch configuration for TXD due to their high reproducibility, small source size (⩽5 µm), short duration (∼1 ns), and up to 106 W peak power near 8 keV photon energy. Plasma loads were imaged through TXD for the first-time using laser-cut X-pinch backlighting. Experimental images were compared with simulations from the x-ray wave-front propagation code, demonstrating that TXD can be a powerful x-ray refraction-based diagnostic for dense Z-pinch loads. Future plans for Talbot–Lau interferometry diagnostics in the pulsed-power environment are described.

Effect of tailored density profiles on the stability of imploding Z-pinches at microsecond rise time megaampere currents

To study the effect of the radial density profile of the material of a metal-plasma Z-pinch load on the development of magneto-Rayleigh–Taylor (MRT) instabilities, experiments have been performed at the Institute of High Current Electronics with the GIT-12 generator which produces microsecond rise time megaampere currents. The Z-pinch load was an aluminum plasma jet (PJ) with an outer plasma shell. This configuration leads to the formation of a uniform current sheath in a Z-pinch load upon application of a high-voltage pulse. It was successfully used in experiments with hybrid deuterium gas-puffs (Klir et al 2020 New J. Phys. 22 103036). The initial density profiles of the Z-pinch loads were estimated from the pinch current and voltage waveforms using the zero-dimensional ‘snowplow’ model, and they were verified by simulating the expansion of the PJ formed by a vacuum arc using a two-dimensional quasi-neutral hybrid model (Shmelev et al 2020 Phys. Plasmas 27 092708). Two Z-pinch load configurations were used in the experiments. The first configuration provided tailored load density profiles, which could be described as ρ(r) ≈ 1/r^s for s > 2. In this case, MRT instabilities were suppressed and thus a K-shell radiation yield of 11 kJ cm−1 and a peak power of 0.67 TW cm−1 could be attained at a current of about 3 MA. For the second configuration, the radial density profiles were intentionally changed using a reflector. This led to the appearance of a notch in the density profiles at radii of 1–3 cm from the pinch axis and to magnetohydrodynamic instabilities at the final implosion stage. As a result, the K-shell radiation yield more than halved and the power decreased to 0.15 TW cm−1 at a current of about 3.5 MA.

Analytic Model and Optimization of Transmission-Line Impedance Transformers for Tens of MA-Class Pulsed Power Accelerator

The monolithic radial transmission line (MRTL) is a key component in tens of MA-class pulsed power accelerators, which connects the multiparallel modules of the prime pulsed power sources to the central vacuum insulator stack and magnetically insulated transmission line (stack-MITL system). The choice of electrical parameters of MRTL is essential for the entire accelerator design, which would bring great influences on the peak output current and the power couple efficiency. In Phys. Rev. Special Topics-Accel. Beam s, 2015, 18(10): 110401, some semianalytical formulae have been proposed to optimize the MRTL impedance that maximizes the peak current or peak power on the stack-MITL system. However, the formulae are only valid under several assumptions that are thought to be unpractical. In this article, an analytic model of the accelerator is developed to optimize the electrical parameters of MRTL. Analytical expressions of the output voltage and current at the terminal of MRTL are deduced. By simplifying the analytic model, mathematical expressions of the optimal MRTL output impedance that maximizes the peak current or peak power delivered from the prime power sources to the stack-MITL system are obtained. The factors that contribute to the optimal impedance are analyzed comprehensively with short-circuit load and Z-pinch load. Conclusions are beneficial to design the pulsed power accelerator in the future.

An initial study on liner-like Z-pinch loads with a novel configuration on Qiangguang-I facility

An initial study on liner-like Z-pinch loads with a novel configuration on Qiangguang-I facility

Implosion dynamics of triple-nozzle gas-puff z pinches on COBRA

Experiments on the 1-MA, 220-ns COBRA generator at Cornell University [J. B. Greenly et al., Rev. Sci. Instrum. 79, 073501 (2008)] were conducted to provide detailed measurements of structured cylindrical gas-puff z pinches. In the experiments, a 7 cm diameter triple-nozzle gas valve assembly with concentric outer and inner annular nozzles and a central gas jet initialize the z-pinch load with various working gases, radial density profiles, and externally applied axial magnetic fields. Planar laser-induced fluorescence provides a measure of the initial neutral gas density of the load, while three-frame laser shearing interferometry and multi-frame extreme ultraviolet (XUV) cameras reveal the formation and propagation of a magneto-Rayleigh–Taylor (MRT) unstable shock layer. Implosion trajectories are compared to simple, experimentally informed models and found to be in good agreement. Differences in the structure of the accelerating plasma sheath and evolution of the MRT instability are observed for different gas species and axial magnetic field strengths, correlating with differences in pinch uniformity and x-ray emission. The average instability growth is compared to linear MRT theory predictions using the instantaneous acceleration of the best-fit implosion models and characteristic instability wavelength, with the effective Atwood number and seed perturbation size as fit parameters. For high density argon center jets, ionization prior to the arrival of the imploding plasma sheath suggests a heating mechanism consistent with photoionization by XUV self-emission.

Investigating the influence of the wire-arrays’ electrical parameters on the load current of the z-pinch drivers

Wire arrays are the typical loads which have been widely used in z-pinch research studies. When a large pulsed power accelerator is designed, the electrical parameters of the z-pinch loads including the inductance and the resistance (or the equivalent resistance) must be considered. In this paper, the inductance and the resistance of the single planar wire arrays were introduced from the experiments carried out on a Qiangguang accelerator (1.5 MA, 100 ns). The lumped-element circuit model of the wire array was established using the PSPICE software, and the model was verified by comparing the simulation results with the experimental results. The influence of the electrical parameters on the accelerator’s driving current is investigated. It shows that the inductance affects the rising edge and the peak value of the current, while the resistance mainly affects the current waveform after the stagnation of the wire array pinch load. The inductance model based on the zero-dimensional equation is compared with the inductance model based on the experimental data, and the result shows that the two different inductance models give almost the same pinch current. It can be concluded that the zero-dimensional model is valid in circuit simulation to investigate the peak current of the designed z-pinch accelerator.

Simulation method of quadruple-level circuit model for stack and vacuum section of Julong-I facility

The quadruple-level circuit model for stack and vacuum section of Julong-I facility was established. To avoid complicated two-dimensional circuit simulation, the prediction-correction method was used to deal with the distribution of currents at the entrance of the quadruple-level insulation stack. The accuracy and efficiency were both ensured by this method. By applying this model to the FCM-PTS code coupled with the snow-plow model for the Z-pinch load, the current for each level of the outer magnetic insulation transmission line was obtained, while the coincidence of load currents between simulation and experiment was also improved.

GLIDER-A pulsed-current generator for laboratory astrophysics x-ray absorption experiments.

In the field of pulse-power, there has always been an interest on small and medium size pulsed-current generators (≤2 MA) which are affordable and of low maintenance. We developed the GLIDER, a compact and modular generator, that drives a gas-puff z-pinch load as a soft x-ray source (0.1-1 keV) for laboratory astrophysics absorption experiments. It comprises 48 bricks, tightly packed in a 1.7 m × 3.5 m × 0.8 m transformer oil container. Its compactness and reliability was enabled owing to unique multilayered oil-soaked insulators, and more than 100 post-hole convolutes. Its stripline includes interchangeable tiles for ease of construction and maintenance. Six triggering units enable current pulse shaping. The GLIDER was tested up to ±60 kV (34 kJ) and produced 2 MA in 450 ns rise time on a 5 nH load. We present grating spectra of K-shell absorption of neutral O and N proving the experimental concept and demonstrating column density and ionization measurements.

Generation of K-Shell Radiation of Noble Gases in the Microsecond Implosion Regime

Studies of K-shell plasma radiation sources were performed on the GIT-12 generator (4.7 MA, 1.7 μs). In the experiments, a new type of load configuration was used to form the Z-pinch plasma – a gas puff with an outer plasma shell. Noble gases neon and argon were used as working gases. The gas puff consisted of two cascades: a hollow cylindrical shell outside and a solid jet inside. The outer plasma shell was created with the help of plasma guns located on a diameter of 350 mm. A distinctive feature of these studies is that the experiments with the plasma radiation source were carried out in the microsecond implosion regime usually leading to a significant decrease in the efficiency of generation of K-shell x-rays. The use of the Z-pinch load of a new type significantly improved the efficiency of the microsecond plasma radiation source. As a result of optimization of the initial gas-puff parameters, a neon K-shell radiation yield of 14.7 kJ/cm at a peak implosion current of 3.5 MA was achieved. In experiments with argon gas puffs, the radiation yield reached 1.9 kJ/cm at a peak implosion current of 3.1 MA.

Full-Circuit Simulation of Next Generation China Z-Pinch Driver CZ30

To help design the next generation China Z-pinch driver CZ30, which is a 30 MA driver driven by linear transformer driver (LTD) modules, a new full-circuit simulation code called FCM-CZ30 was established. The code was used to perform simulation of CZ30 coupled with Z-pinch load. The results obtained from FCM-CZ30 are in a good agreement with those obtained from a commercial code called PSpice, which shows that the FCM-CZ30 is a reliable code. The inductance of the LTD system has a significant influence on the rise time of the load current, which is totally different from that in conventional Z-pinch drivers with multistage switches to compress the rise time of the pulse. For a wire-array load with an initial radius of 3.0 cm and a mass per unit length of 15 mg/cm, the peak value and the rise time (10%–90%) of the load current are 33.7 MA and 102.2 ns, respectively.

Field-Circuit Coupling Simulation of Petawatt-Class Z-Pinch Accelerator

Most of the previous studies of petawatt-class Z-pinch accelerator are performing the circuit simulation based on a full-circuit model. This model may cause nonignorable error because it is under the assumption of TEM modes transmission along the monolithic radial transmission lines (MRTLs). In this paper, a method for field-circuit coupling simulation of petawatt-class Z-pinch accelerator was developed, which considered the non-TEM modes in the MRTLs. A 3-D electromagnetic simulation (EMS) of the MRTLs was conducted, and MRTLs’ equivalent circuit was created based on the scattering transfer parameters drawn from the EMS. By inserting the MRTLs’ equivalent circuit into the pulsed generators and Z-pinch load, a field-circuit coupling model of the whole petawatt-class Z-pinch accelerator was obtained. This method was used in the simulation of Z800 accelerator, a petawatt-class Z-pinch accelerator, and the load was a wire array for Z-pinch. Compared to the previous circuit model, the load current obtained with the field-circuit coupling model was lower, and thus, the load-implosion time was longer. Then, we compared the load current of accelerators using exponential, hyperbolic, and linear MRTLs, respectively, and recommended the linear one. The relation between energy transmission efficiency and load parameters was also investigated.

On the design of magnetically insulated transmission lines for z-pinch loads

Many papers have been published on the theory of magnetic insulation and the use of Zflow analysis of magnetically insulated transmission lines (MITLs). We describe herein a novel design process using the circuit code SCREAMER for a real-world MITL for z-pinch loads based on the Zflow model of magnetic insulation. In particular, we design a 15-TW, 10-MA, 100-ns double-disk transmission line using only circuit modeling tools and Zflow analysis of the MITL. Critical issues such as current loss to the anode during the setup of magnetic insulation and the transition from a non-emitting vacuum power feed to an MITL play a large role in the MITL design. This very rapid design process allows us for the first time to explore innovative MITL designs such as variable-impedance MITLs that provide a significantly lower total inductance and improved energy delivery to the load. The tedious process of modeling the final MITL design with highly resolved 2D and 3D electromagnetic particle-in-cell codes occurs as a validation step, not as part of the design process.

Validation of MHD Code FLUX-rz Using Scintillation Measurements of Thermal Radiation in Nested Wire Array <inline-formula> <tex-math notation="LaTeX">$Z$ </tex-math> </inline-formula>-Pinch

This paper demonstrates the improved simulation of a Z-pinch experiment with 2-D magnetohydrodynamic code FLUX-rz developed in RFNC-VNIIEF. A Z-pinch load was nested wire array powered by a helical magnetocumulative generator with the current pulse $I_{\max } \approx 4.2$ MA and effective rise time $\tau \approx 400$ ns. Validation of X-ray spectral measurements carried out with scintillation detector filters pointed out a necessity to take into consideration both the scintillator “dead” layer and oxide films on the aluminum filter surface.

Study of Triple Ar Gas Puff Z-Pinches on 0.9-MA, 200-ns COBRA

Ar gas puff z-pinch experiments were conducted on the 0.9-MA, 200-ns COBRA generator at Cornell University. In the experiments, a triple-nozzle gas valve was used to produce the z-pinch load with concentric outer and inner gas puffs and a central gas jet. We used a planer laser-induced fluorescence to measure the initial gas profile of the load, two four-frame 4-ns gated extreme ultraviolet cameras to image the imploding plasma, and filtered photoconducting diamond detectors to measure the X-ray output. We have observed the shock heating and/or photoionization of the dense center jet by the imploding plasma. With an outer-to-inner plenum pressure ratio of 1:3, deacceleration of the imploding plasma occurred when the outer plasma shell imploded on the inner shell resulting in a stable implosion. By varying the plenum pressure for the center jet, the X-ray emission was optimized. An Ar K-shell X-ray (3–4 keV) yield of 77 ± 17 J was produced at a current level of 0.87 ± 0.2 MA and an implosion time of 200 ns.

Atomization and merging of two Al and W wires driven by a 1 kA, 10 ns current pulse

Possibility of preconditioning of wires in wire array Z-pinch loads by an auxiliary low-level current pulse was investigated in experiments with two aluminum or two polyimide-coated tungsten wires. It was found that the application of a 1 kA, 10 ns current pulse could convert all the length of the Al wires (1 cm long, 15 μm diameter) and ∼70% of length of the W wires (1 cm long, 15 μm diameter, 2 μm polyimide coating) into a gaseous state via ohmic heating. The expansion and merging of the wires, positioned at separations of 1–3 mm, were investigated with two-wavelength (532 nm and 1064 nm) laser interferometry. The gasified wire expanded freely in a vacuum and its density distribution at different times could be well described using an analytic model for the expansion of the gas into vacuum. Under an energy deposition around its atomization enthalpy of the wire material, the aluminum vapor column had an expansion velocity of 5–7 km/s, larger than the value of ∼4 km/s from tungsten wires. The dynamic atomic polarizabilities of tungsten for 532 nm and 1064 nm were also estimated.

Investigation of Switch Designs for the Dynamic Load Current Multiplier Scheme on the SPHYNX Microsecond Linear Transformer Driver

SPHINX is a microsecond linear transformer driver LTD, used essentially for implosion of Z-pinch loads in direct drive mode. It can deliver a 6-MA current pulse within 800 ns into a Z-pinch load. The dynamic load current multiplier concept enables the current pulse to be modified by increasing its amplitude while reducing its rise time before being delivered to the load. This compact system is made up of concentric electrodes (autotransformer), a dynamic flux extruder (cylindrical wire array), a vacuum convolute (eight postholes), and a vacuum closing switch, which is the key component of the system. Several different schemes are investigated for designing a vacuum switch suitable for operating the dynamic load current multiplier on the SPHINX generator for various applications, including isentropic compression experiments and Z-pinch radiation effects studies. In particular, the design of a compact vacuum surface switch and a multichannel vacuum switch, located upstream of the load are studied. Electrostatic simulations supporting the switch designs are presented along with test bed experiments. Initial results from shots on the SPHINX driver are also presented.