Z-pinch Experiments Research Articles

Solar Opacity Calculations: Recent Theoretical Advances Prompted by Laser and Z-Pinch Experiments

Solar Opacity Calculations: Recent Theoretical Advances Prompted by Laser and Z-Pinch Experiments

Neutron-producing gas puff Z-pinch experiments on a fast, low-impedance, 0.5 MA linear transformer driver

A study on the neutron production from single and double gas puff Z-pinches on the CESZAR linear transformer driver with ∼0.45 MA current and 170 ns rise time is presented. Total neutron yield measurements made with a LaBr activation detector are compared for three configurations, using a double nozzle setup. When a single, hollow, deuterium gas shell was used, reliable implosions could only be attained at higher load mass than the optimal value to match implosion time with the driver rise time, with neutron yields of ∼106 per pulse. The use of a double gas puff configuration with a deuterium center jet allowed a reduction in the shell density and operation closer to machine-matched conditions, recording up to (4.1 ± 0.3) × 107 neutrons/pulse when either Kr or D2 was used in the shell. For a comparable mass and implosion time, using a higher atomic-number gas in the outer shell results in more unstable plasma surface and smaller plasma radius at the location of instability bubbles, which, however, do not seem to consistently correlate with a higher neutron yield. Comparing implosion dynamics with models and neutron yields with literature scaling suggests that the machine current is not well coupled to the plasma during the final stages of compression. Optimizing current and energy coupling to the pinched plasma is critical to improving performance, particularly in low-impedance drivers.

Self-driven ion deflectometry measurements using MeV fusion-driven protons and accelerated deuterons in the deuterated hybrid x-pinch on the MAIZE LTD generator

We report on the results of point-projection ion deflectometry measurements from a mid-size university z-pinch experiment. A 1 MA 8 kJ LTD generator at the University of Michigan (called MAIZE) drove a hybrid x-pinch (HXP) with a deuterated polyethylene fiber load to produce a point-like source of MeV ions for backlighting. In these experiments, 2.7 MeV protons were generated by DD beam-target fusion reactions. Due to the kinematics of beam-target fusion, the proton energies were down-shifted from the more standard 3.02 MeV proton energy that is released from the center-of-mass rest frame of a DD reaction. In addition to the 2.7 MeV protons, strongly anisotropic beams of 3 MeV accelerated deuterons were detected by ion diagnostics placed at a radial distance of 90 mm from the x-pinch. Numerical reconstruction of experimental data generated by deflected hydrogen ion trajectories evaluated the total current in the vacuum load region. Numerical ion-tracking simulations show that accelerated deuteron beams exited the ion source region at large angles with respect to the pinch current direction.

Electrode durability and sheared-flow-stabilized Z-pinch fusion energy

The sheared-flow-stabilized (SFS) Z-pinch concept is on a path to commercialization at Zap Energy. Recent experiments on the Fusion Z-pinch Experiment (FuZE) and newly commissioned FuZE-Q devices are advancing the state of the art in pinch current, stable plasma duration, and deuterium–deuterium fusion neutron production. The SFS Z-pinch configuration offers the promise of a compact fusion device owing to its simple geometry, unity beta, and absence of external magnetic field coils. In addition to a robust experimental program pushing plasma performance toward breakeven conditions, Zap Energy has parallel programs developing power handling systems suitable for future power plants. Technologies under development include high-repetition-rate pulsed power, high-duty-cycle electrodes, and liquid metal wall systems. The issue of electrode durability in future SFS Z-pinch power plants is elaborated on and compared with plasma material interaction regimes in other industrial processes and fusion energy systems.

Stability of perpendicular magnetohydrodynamic shocks in materials with ideal and nonideal equationsof state.

Magnetized target fusion approach to inertial confinement fusion involves the formation of strong shocks that travel along a magnetized plasma. Shocks, which play a dominant role in thermalizing the upstream kinetic energy generated in the implosion stage, are seldom free from perturbations, and they wrinkle in response to upstream or downstream disturbances. In Z-pinch experiments, significant plasma instability mitigation was observed with pre-embedded axial magnetic fields. To isolate effects, in this work we theoretically study the impact of perpendicular magnetic fields on the planar shock dynamics for different equationsof state. For fast magnetosonic shocks in ideal gases, it was found that the magnetic field amplifies the intensity of the perturbations when γ>2 or it weakens them when γ<2. Weak shocks have been found to be stable regardless of the magnetic plasma intensity and gas compressibility; however, for sufficiently strong shocks the magnetic fields can promote a neutral stability/SAE at the shock if the adiabatic index is higher than 1+sqrt[2]. Results have been validated with numerical simulations performed with the FLASH code.

Implementation of extreme ultraviolet spectroscopy on a sheared-flow-stabilized Z pinch

A diagnostic for extreme ultraviolet spectroscopy was fielded on the sheared-flow-stabilized (SFS) fusion Z-pinch experiment (FuZE-Q) for the first time. The spectrometer collected time-gated plasma emission spectra in the 5–40 nm wavelength (30–250 eV) range for impurity identification, radiative power studies, and for plasma temperature and density measurements. The unique implementation of the diagnostic included fast (10 ns risetime) pulsed high voltage electronics and a multi-stage differential pumping system that allowed the vacuum-coupled spectrometer to collect three independently timed spectra per FuZE-Q shot while also protecting sensitive internal components. Analysis of line emission identifies oxygen (N-, C-, B-, Be-, Li-, and He-like O), peaking in intensity shortly after maximum current (&amp;gt;500 kA). This work provides a foundation for future high energy spectroscopy experiments on SFS Z-pinch devices.

Engineering Paradigms for Sheared-Flow-Stabilized Z-Pinch Fusion Energy

The sheared-flow-stabilized Z-pinch concept is on a path to commercialization at Zap Energy. Recent experiments on the Fusion Z-pinch Experiment (FuZE) device corroborate expected plasma stability and thermonuclear fusion reaction rates. Experimental campaigns are underway to increase the pinch current, the stable plasma duration, and the DD fusion neutron production. The next-generation device FuZE-Q is currently undergoing commissioning and will begin operation at current levels where scientific breakeven-equivalent conditions are expected in the near future. The Z-pinch configuration offers the promise of a compact fusion device owing to its simple geometry, unity beta, and absence of external magnetic field coils. In addition to a robust experimental program pushing plasma performance toward breakeven conditions, Zap Energy has parallel programs developing power handling systems suitable for future power plants. Technologies under development include high-average-power repetitive pulsed power, high-duty-cycle cathodes, and liquid-metal wall systems. High-level features of the conceptual power plant core design are elaborated and compared with other approaches to fusion energy.

Experimental study of the mechanism of prepulse current on Z-pinch plasma using Faraday rotation diagnosis.

The prepulse current is an effective way to optimize the load structure and improve the implosion quality of the Z-pinch plasma. Investigating the strong coupling between the preconditioned plasma and pulsed magnetic field is essential for the design and improvement of prepulse current. In this study, the mechanism of the prepulse current on the Z-pinch plasma was revealed by determining the two-dimensional magnetic field distribution of preconditioned and nonpreconditioned single-wire Z-pinch plasma with a high-sensitivity Faraday rotation diagnosis. When the wire was nonpreconditioned, the current path was consistent with the plasma boundary. When the wire was preconditioned, the distributions of current and mass density presented good imploding axial uniformity, and the imploding speed of the current shell was higher than that of the mass shell. In addition, the mechanism of the prepulse current suppressing the magneto-Rayleigh-Taylor instability was revealed, which formed a sharp density profile of the imploding plasma and slowed the shock wave driven by the magnetic pressure. This discovery is essential and instructive for the design of preconditioned wire-array Z-pinch experiments.

Development of a High-Energy X-ray Backlighting System for Z-pinch Experiments

A backlighting system is developed for Z-pinch experiments that is composed of a pulsed X-ray generator (the backlighter), a scintillator, an optical module, and an intensified charge-coupled device (ICCD). By optimizing the geometrical layout, choosing the appropriate scintillator, and optimizing the parameters of the optical module, the system is successfully designed. The key properties of the system are theoretically calculated based on parameters of the X-rays and the scintillator. Calculation results of sensitivity show that the amount of scintillator fluorescence falls in the linear dynamic range of the ICCD. Spatial resolution is calculated to be 241 µm, which is mainly determined by the geometrical layout and the size of the X-ray focal spot. Temporal resolution is calculated to be 2.3 ns, which is mainly determined by the decay time of the scintillator. Calculation results indicate that the properties of the system meet the requirements of the Z-pinch capsule diagnostics. The system has been fabricated. Performance of the system is tested through static W wire experiments in the laboratory. Experimental results show that 250-µm W wire is clearly seen in the image when X-ray fluence is high, while 100-µm W wire cannot be seen.

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.

Thermonuclear neutron emission from a sheared-flow stabilized Z-pinch

The fusion Z-pinch experiment (FuZE) is a sheared-flow stabilized Z-pinch designed to study the effects of flow stabilization on deuterium plasmas with densities and temperatures high enough to drive nuclear fusion reactions. Results from FuZE show high pinch currents and neutron emission durations thousands of times longer than instability growth times. While these results are consistent with thermonuclear neutron emission, energetically resolved neutron measurements are a stronger constraint on the origin of the fusion production. This stems from the strong anisotropy in energy created in beam-target fusion, compared to the relatively isotropic emission in thermonuclear fusion. In dense Z-pinch plasmas, a potential and undesirable cause of beam-target fusion reactions is the presence of fast-growing, “sausage” instabilities. This work introduces a new method for characterizing beam instabilities by recording individual neutron interactions in plastic scintillator detectors positioned at two different angles around the device chamber. Histograms of the pulse-integral spectra from the two locations are compared using detailed Monte Carlo simulations. These models infer the deuteron beam energy based on differences in the measured neutron spectra at the two angles, thereby discriminating beam-target from thermonuclear production. An analysis of neutron emission profiles from FuZE precludes the presence of deuteron beams with energies greater than 4.65 keV with a statistical uncertainty of 4.15 keV and a systematic uncertainty of 0.53 keV. This analysis demonstrates that axial, beam-target fusion reactions are not the dominant source of neutron emission from FuZE. These data are promising for scaling FuZE up to fusion reactor conditions.

Measurement of magnetic field distribution produced by high-current pulse using Zeeman splitting of Na emission distributed by laser ablation.

Measurement of the magnetic field distribution in Z-pinch experiments remains an ongoing challenge. We present a method of measuring the radial distribution of the magnetic field around a copper rod using Zeeman splitting of sodium (Na) emission lines, in which an Na layer is formed by the laser ablation of NaCl crystals on a load surface. The load consists of a copper rod of 2mm diameter and is pre-covered on its surface by the NaCl crystals. An 8ns pulsed laser with an energy of 1J and wavelength of 532nm is focused on the crystals. The Na plasma is produced and expands from the surface of the copper rod into a vacuum. After applying a pulsed current with a peak value of 375 kA to the load, the Na 3s-3p doublet displays significant Zeeman splitting patterns. The self-luminosity of the Na plasma is recorded by a spectrometer coupled with an intensified charge-coupled device camera from an end-on view to eliminate the effects of different observing angles and Doppler shifts. We determine the magnetic field by fitting the measured spectra with the calculated results of the Voigt profile. The measurable range of radial position is 5-7mm, and the corresponding magnetic field is 5-15T. The averaged error of curve fitting is less than 12%.

Load dynamics of double planar foil liners and double planar wire arrays on the UM MAIZE LTD generator

In previous studies using the University of Nevada, Reno's (UNR's) high-impedance Zebra Marx generator (1.9 Ω, 1.7 MA, 100 ns), Double Planar Wire Arrays (DPWAs) proved to be excellent radiators, and Double Planar Foil Liners (DPFLs) proved useful for future inertial confinement fusion applications. This article presents the results of joint UNR/UM (University of Michigan) experiments with aluminum (Al) DPWAs, Al DPFLs, and tungsten (W) DPWAs using UM's Michigan Accelerator for Inductive Z-Pinch Experiments (MAIZE) generator, a low-impedance Linear Transformer Driver (LTD) (0.1 Ω, 0.5–1 MA, and 100–250 ns). The main goals of this study were twofold: the first was a pioneering effort to test whether a relatively heavy Al DPFL could successfully be imploded on a low-impedance university-scale LTD like the MAIZE generator, and, if so, to analyze the results and make comparisons to the optimized, lighter DPWA configurations that have been previously studied. The DPWAs consisted of two planes of micrometer-scale diameter Al or W wires, while the DPFLs consisted of two planes of micrometer-scale thickness Al foils. Diagnostics include filtered Si-diodes, an absolutely calibrated filtered PCD, x-ray pinhole cameras, spectrometers, and gated optical self-emission imaging. The implosion dynamics and radiative properties of Al DPWAs and DPFLs and W DPWAs on the MAIZE LTD are discussed and compared. Time-dependent load inductance calculations derived from measurements of the load current and a MAIZE circuit model provide a relative measurement of pinch strength. In experiments on MAIZE, W planar wire arrays exhibited a higher peak load inductance throughout the pinch than Al DPWAs and DPFLs, while x-ray pulses from Al DPFLs had the longest emission duration.

Dynamics and energy coupling of gas puff Z-pinches on a fast linear transformer driver

Gas puff Z-pinch experiments with annular Ar and Ne gas shells have been conducted on the Compact Experimental System for Z-pinch and Ablation Research (CESZAR) linear transformer driver (LTD) with 500 kA current and 160 ns rise time. Here, we present results from the first systematic gas puff Z-pinch experiments using a fast (≤200 ns) LTD as a driver, in which we show that 7% of the stored energy in the capacitors is coupled to plasma kinetic energy as estimated via self-emission and laser schlieren images. 0D and 1D simulations—which do not allow instability growth and thus reach greater maximum average velocities—using initial conditions inferred from experimental implosion trajectories predict coupling in excess of 10% of the stored energy. The Ar and Ne implosions were comparably massed and thus achieved similar maximum kinetic energies, though the Ne pinches were more stable and the x-ray pulses were longer and produced higher yield: 2–5 ns and 0.21–0.52 J (0.15–0.37 J/cm) of Ar K-shell and 12–25 ns and 2.2–3.9 J (1.6–2.6 J/cm) of Ne K-shell, respectively. The difference in stability is most likely attributed to variations in initial conditions such as density distribution and gas breakdown initiation.

Seeding the explosion of a high-current-density conductor in a controlled manner through the addition of micron-scale surface defects

Inhomogeneities in a current-carrying conductor promote non-uniform heating and expansion through the complex feedback between current density, electrical resistivity, Ohmic heating, temperature, and hydrodynamics. Three-dimensional-magnetohydrodynamic (3D-MHD) simulations suggest that μm-scale resistive inclusions or voids seed local overheating and through hydrodynamic explosion generate continuously growing craters which become several times larger than the initial perturbation. The ejected mass is the genesis of an electrothermally driven plasma filament which develops at lower current than plasmas on uniform surfaces adjacent to the defect. This result suggests that 1D or even 2D treatments are largely inadequate for detailed prediction of plasma formation. To test computational predictions, z-pinch experiments driven to 1 MA studied ultra-high-purity aluminum rods which were then machined to include pairs of quasi-hemispherical voids or “engineered defects (ED)” on the current-carrying surface. ED are the dominant current-density perturbation and reproducibly drive local overheating which can be compared with 3D-MHD simulation. Data from high-resolution-gated imagers of visible surface emissions confirm many simulation predictions, including the surface topography of local overheating, and the propensity for neighboring ED to prematurely source plasmas which then connect to form a plasma filament. Results also provide conditional support of theory which suggests heating similarity; that is, heating is independent of ED size for geometrically scaled ED.

Gyrokinetic and extended-MHD simulations of a flow shear stabilized Z-pinch experiment

Axisymmetric (m = 0) gyrokinetic and extended-MHD simulations of a sheared-flow Z-pinch plasma are performed with the high-order finite volume code COGENT. The present gyrokinetic model solves the long-wavelength limit of the gyrokinetic equation for both ion and electron species coupled to the electrostatic gyro-Poisson equation for the electrostatic potential. The extended-MHD model is electromagnetic and includes the effects of the gyro-viscous pressure tensor, diamagnetic electron and ion heat fluxes, and generalized Ohm's law. A prominent feature of this work is that the radial profiles for the plasma density and temperature are taken from the fusion Z-pinch experiment (FuZE), and the magnetic field profile is obtained as a solution of the MHD force balance equation. Such an approach allows to address realistic plasma parameters and provide insights into the current and planned experiments. In particular, it is demonstrated that the radial profiles play an important role in stabilization, as the embedded guiding center (E×B) drift has a strong radial shear, which can contribute to the Z-pinch stabilization even in the absence of the fluid flow shear. The results of simulations for the FuZE plasma parameters show a decrease in the linear growth rate with an increase in the flow shear; however, full stabilization in the linear regime is not observed even for large (comparable to the Alfvén velocity) radial variations of the axial flow. Nonlinear stability properties of the FuZE plasmas are also studied, and it is found that profile broadening can have a pronounced stabilizing effect in the nonlinear regime.

Soft x-ray imaging system used for Z-pinch experiments

基于塑料闪烁体转换和光学条纹相机的方法建立了一套用于Z箍缩实验中的软X射线条纹图像诊断系统, 解决了以往实验中使用的X射线条纹相机易被电磁环境干扰以及相机电极部件易被实验产生的高速粒子损伤的问题. 诊断系统的光谱响应范围主要集中在0.2—10 keV, 系统的空间分辨率经过理论评估小于120 μm, 通过标定闪烁体对X射线的时间响应特性给出了系统的时间分辨率约为1 ns. 诊断系统拍摄到了铝丝阵内爆等离子体的一维空间和时间分辨的X射线条纹图像, 给出了等离子体的内爆一致性和辐射均匀性等特征信息.

Diagnosis and Analysis of Load Current Divergence in Z-Pinch Experiments

During the later stage of stagnation in Z-pinch experiments, a current divergence phenomenon often occurs that downstream current (load current measured in a vacuum) declines slowly to zero, while upstream current (current measured outside vacuum) normally decays with quasi-sinusoidal oscillation. To investigate the formation mechanism of this current divergence, the possible abnormal discharge channels in vacuum are captured by optical imaging in this article. Both time integral image and time-resolved image show that current divergence is accompanied by the surface flashover on the vacuum insulator. The time-resolved images also verified that the time when downstream current starts slow decline corresponds to the time when surface flashover occurs. Surface flashover changes the circuit topology and forms the freewheeling branch of the load inductance L. An equivalent circuit is also established to analyze the current divergence. The discharge channel with low resistance R results in large time constant (L/R) and makes the downstream current drop slowly, while the external impedance can make the upstream current keep the waveform of oscillation attenuation even under the condition of internal flashover. Moreover, the influence caused by current divergence is discussed in the aspect of load voltage and the energy dissipation on generator. According to the simulation results, with an appropriate resistance, an additional branch can help protect the upstream components.

Axial magnetic flux amplification in Hall-magnetohydrodynamic simulations of externally magnetized z-pinches

It is shown that externally magnetized gas-puff z-pinches under compression can exhibit robust axial flux amplification under suitable axial boundary conditions. This effect relies upon the Hall term in the generalized Ohm's law to generate azimuthal currents in the presence of a driving axial electric field. Under dynamic compression, the total current tends to flow in a mostly force-free boundary layer, separating the predominately azimuthal field outside the layer and the predominately axial field inside the layer. The effect only appears to occur if the axial boundaries allow for outflow or absorption of electromagnetic energy. The effect is mitigated by imposing either periodic or conducting axial boundary conditions. A semi-analytic equilibrium analysis agrees with steady-state solutions of the time-dependent electron-magnetohydrodynamic equations and provides an estimate of the scaling of the boundary layer as well as suggesting a scenario for the formation of the boundary layer. When operative, the effect can significantly impede plasma compression due to the increase in axial flux that diffuses into the pre-compressed plasma or through the presence of conductors that inhibit movement of the generated axial flux. Several facilities have noted unusual implosion behavior in z-pinch experiments with applied axial fields that does not appear to be explainable within the standard magnetohydrodynamic model. It is suggested that these experiments can be explained by the axial flux amplification and concentration effect.

Plasma exhaust in a sheared-flow-stabilized Z pinch

The fusion Z-pinch experiment device produces a 0.3 cm radius by 50 cm-long Z pinch between the end of the inner electrode of a coaxial plasma gun and an end wall 50 cm away. The plasma column is stabilized for thousands of instability growth times by an embedded radially sheared axial plasma flow. To investigate the effect of end wall design on Z-pinch plasma behavior, the solid end wall with a central exhaust port is replaced with a spoked end wall with a solid hub. While the Z-pinch plasma behavior was largely unaffected, the plasma exhausted from the Z-pinch provides an experimental platform to study magnetic confinement and detachment. Current and density signals are compared between two cases: a low energy and a high energy case. Plasma is found to be frozen-in flux in the Z-pinch assembly region. The exhaust of plasma from the flux conserving region is found to be dependent on the ratio of plasma ram and thermal pressures to the local magnetic pressure, calculated from an equilibrium model at the end wall. Plasma exhaust is observed to increase with the spoked end wall only for the high energy conditions as its ratio of ram and thermal pressures to the magnetic pressure increases.