Dense Z-pinch Research Articles

Assessment of relevant pinch magnitudes of plasma focus devices based on non-uniform internal distributions of density and temperature

A novel model of the dense z-pinch of a plasma focus (PF) discharge is presented, assuming Gaussian radial distributions of density and temperature inside the pinch. The model is used to assess the temperature, size and lifetime of the focus conflating with available experimental data gathered from discharges in Deuterium performed in the PF PACO with three cathode configurations. The resulting estimations were mean pinch temperatures between 1 and 12 keV, and pinch durations between 10 and 120 ns, each magnitude decreasing and increasing with the filling pressure, respectively. Moreover, the relation found between the mean pinch radius and temperature, and , is consistent with an adiabatic compression given by mm keV3/4. The estimated width of the Gaussian profile is in agreement with spectroscopic images obtained in another small device.

Hall Magnetohydrodynamics Simulations of Hall-Physics-Driven Effects in Low-Density Plasmas Surrounding Dense Z-Pinch Liners

Hall Magnetohydrodynamics Simulations of Hall-Physics-Driven Effects in Low-Density Plasmas Surrounding Dense Z-Pinch Liners

Whence Z-pinches? A personal view

The first Dense Z-Pinch (DZP) conference, in 1984, marked an attempt to use then-modern pulsed power with a Z-pinch to work toward thermonuclear fusion energy. This 11th DZP conference in China is a good time to look back, to comment on progress since, and to project forward. What follows is a personal perspective: scattered comments from a sympathetic outsider and one-time participant. In these 35 years, Z-pinch theory has evolved from little more than cartoons to fully 3D MHD computer simulations, measurements have gone from mostly time- and spatially integrated diagnostics to monochromatic imaging, highly resolved x-ray spectroscopy, and active laser probing. Large pulsed power generators now drive x-ray-producing Z-pinches that are powerful enough for many applications; thermonuclear fusion may work single-shot in the future.

Spatial distribution of ion emission in gas-puff z-pinches and dense plasma foci

Mega-ampere dense plasma foci and deuterium gas-puff z-pinches can accelerate deuterons to multi-MeV energies. Diagnostic measurements of the properties of these ions provide information about ion acceleration in z-pinch plasmas. In particular, the results from ion pinhole cameras seem to be useful for the discussion of ion acceleration mechanisms. Recently, we have used various configurations of ion pinhole cameras in deuterium gas-puff experiments on the GIT-12 generator at the Institute of High Current Electronics in Tomsk and on the HAWK generator at the US Naval Research Laboratory in Washington. The stack of radiochromic films and CR-39 solid-state nuclear track detectors recorded deuterons with energies up to 30 MeV. From our ion diagnostics, we obtained the spatial distribution of the ion source and the ion-beam divergence during the ion emission. This ion-beam divergence was found to decrease with increasing deuteron energy. At 20 MeV, the divergence of each of the individual micro-beams that composed the ion source was on the order of 10 mrad. The deflection of each micro-beam due to the azimuthal magnetic and/or radial electric fields resulted in radial stripes observed by the beam-profile detectors. By analyzing the ion pinhole images, we found that the deuterons were emitted both from a central spot and from a ring-shaped region with a rather large diameter, on the order of 1 cm. The origin and particular diameter of this ring is attributed to the geometry of the electrodes and to the distribution of the current density before the disruption.

Investigation of wire-array Z-pinches by laser probing diagnostics

Laser diagnostics provides powerful tools for the investigation of dense Z-pinches. In this paper, wire-array Z-pinches are investigated at the 1 MA Zebra generator using laser diagnostics at different wavelengths coupled with x-ray diagnostics. Plasma dynamics during the ablation, implosion, and stagnation stages are observed by multiframe diagnostics. Cascading and nonprecursor implosions are studied in wire arrays. Ultraviolet diagnostics allows deep penetration into the Z-pinch plasma at stagnation. End-on probing reveals the complicated structure of the precursor. Strong magnetohydrodynamic instabilities are found in a dense pinch hidden in the trailing plasma. Small-scale instabilities are seen in the Z-pinch plasma with micrometer resolution. Probing of the pinch from four directions shows asymmetrical trailing plasma in some configurations of wire arrays. Faraday rotation diagnostics reveals the magnetic fields and the current distribution in the plasma of the precursor and Z-pinch. Redistribution of current in the trailing plasma is seen during kink and sausage instabilities in the stagnation stage. The formation of micropinches and hot spots in the Z-pinch is analyzed with coupled laser and x-ray diagnostics. Different laser diagnostics allow the study of Z-pinch plasmas in all stages, including fast dynamics and instabilities.

Equilibrium and Steady State of Dense Z-Pinches Superposing a Small Amount of Axial Flux

The pressure equilibrium and steady state of z-pinches trapping a small amount of axial magnetic flux are studied. The Bennett relation and the Pease–Braginskii-current are modified, taking into account the superposed axial field. The line energy density decreases in the modified Bennett relation, but the decrease is only of the order ε2, where ε = (the axial field strength at the axis)/(the azimuthal field strength at the plasma periphery) ≪ 1. On the other hand, the current in the steady state can increase without being limited by the Pease–Braginskii-current. Hence, the radiation collapse is prevented. The decrease of line energy density in the modified Bennett relation is almost canceled in the steady state.

Neutron spectra from beam-target reactions in dense Z-pinches

The energy spectrum of neutrons emitted by a range of deuterium and deuterium-tritium Z-pinch devices is investigated computationally using a hybrid kinetic-MHD model. 3D MHD simulations are used to model the implosion, stagnation, and break-up of dense plasma focus devices at currents of 70 kA, 500 kA, and 2 MA and also a 15 MA gas puff. Instabilities in the MHD simulations generate large electric and magnetic fields, which accelerate ions during the stagnation and break-up phases. A kinetic model is used to calculate the trajectories of these ions and the neutron spectra produced due to the interaction of these ions with the background plasma. It is found that these beam-target neutron spectra are sensitive to the electric and magnetic fields at stagnation resulting in significant differences in the spectra emitted by each device. Most notably, magnetization of the accelerated ions causes the beam-target spectra to be isotropic for the gas puff simulations. It is also shown that beam-target spectra can have a peak intensity located at a lower energy than the peak intensity of a thermonuclear spectrum. A number of other differences in the shapes of beam-target and thermonuclear spectra are also observed for each device. Finally, significant differences between the shapes of beam-target DD and DT neutron spectra, due to differences in the reaction cross-sections, are illustrated.

UV Laser-Probing Diagnostics for the Dense Z Pinch

Laser diagnostics at 266 nm were developed for the investigation of dense Z-pinch plasma at the 1 MA Zebra generator. A three-channel diagnostic can be configured as shadowgraphy and interferometry with two temporal frames or as a Faraday rotation polarimeter. Absorption and refraction of ultraviolet (UV) radiation in dense plasma is significantly smaller compared with regular diagnostics at the wavelength of 532 nm. Therefore, UV diagnostics allow direct investigation of the fine structure of the dense Z-pinch, development of instabilities, and a distribution of magnetic fields in Z-pinch plasma. Micropinches and instabilities with characteristic scales of 15-200 μm were observed in 1 MA wire-array Z pinches. Development of instabilities in wire-array Z pinches is in agreement with the magnetohydrodynamic simulations. Interferometry at the wavelength of 266 nm allows measurement of plasma density in the range (1-2)×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> in the ablating wires, imploding plasma, stagnating pinch, and trailing material. A fast plasma motion was observed at the stagnation stage with two-frame shadowgraphy. Plasma motion at stagnation and prolonged implosion of trailing mass can provide the additional kinetic energy in the Z pinch and can be a source of enhanced X-ray radiation. A Faraday rotation diagnostic reveals a distribution of magnetic fields in the pinch and trailing material. The magnetic field strength and current were reconstructed from the rotation angles and phase shifts in plasma using the Abel transform. Current in the pinch can switch from the high-inductance neck and redistribute to the trailing material when resistance of peripheral plasma drops owing to heating by X-ray radiation. Further development of UV diagnostics to short wavelengths can help to apply well-established optical methods to Z-pinch plasma in multiMA pulsed power facilities.

Steady-state modeling of current loss in a post-hole convolute driven by high power magnetically insulated transmission lines

Quasiequilibrium power flow in two radial magnetically insulated transmission lines (MITLs) coupled to a vacuum post-hole convolute is studied at $50\text{ }\text{ }\mathrm{TW}--200\text{ }\text{ }\mathrm{TW}$ using three-dimensional particle-in-cell simulations. The key physical dimensions in the model are based on the ZR accelerator [D. H. McDaniel, et al., Proceedings of 5th International Conference on Dense Z-Pinches, edited by J. Davis (AIP, New York, 2002), p. 23]. The voltages assumed for this study result in electron emission from all cathode surfaces. Electrons emitted from the MITL cathodes upstream of the convolute cause a portion of the MITL current to be carried by an electron sheath. Under the simplifying assumptions made by the simulations, it is found that the transition from the two MITLs to the convolute results in the loss of most of the sheath current to anode structures. The loss is quantified as a function of radius and correlated with Poynting vector stream lines which would be followed by individual electrons. For a fixed MITL-convolute geometry, the current loss, defined to be the difference between the total (i.e. anode) current in the system upstream of the convolute and the current delivered to the load, increases with both operating voltage and load impedance. It is also found that in the absence of ion emission, the convolute is efficient when the load impedance is much less than the impedance of the two parallel MITLs. The effects of space-charge-limited (SCL) ion emission from anode surfaces are considered for several specific cases. Ion emission from anode surfaces in the convolute is found to increase the current loss by a factor of 2--3. When SCL ion emission is allowed from anode surfaces in the MITLs upstream of the convolute, substantially higher current losses are obtained. Note that the results reported here are valid given the spatial resolution used for the simulations.

Search for Drive Parameter of Neutron-Optimized Z-Pinches and Dense Plasma Foci

Dense plasma foci and deuterium gas puff Z-pinches are studied as sources of fusion neutrons. To design a neutron-optimized plasma focus, the drive parameter I0/(a(ρ0)1/2) has been discussed in the last 15 years. Here, I0, a, and ρ0 represent the peak discharge current, the inner electrode radius, and the initial gas density, respectively. In this paper, similarities between a dense plasma focus and a gas puff Z-pinch are shown. The drive parameter of dense plasma foci seems to be closely related to the I/(m)1/2 parameter of Z-pinches, where I and m stand for the current during stagnation and linear mass, respectively. On the 3-MA Z-pinch generator, it was found that the optimal I/(m)1/2 parameter reached the value of about 230 kA · (cm/μg)1/2. This optimal value can be explained by a tradeoff between the energy of fast deuterons and the number of fast and target deuterons. Obtained experimental results show that the optimal drive parameter cannot be fully explained without the consideration of ion acceleration mechanisms to fusion energies.

High-Resolution UV Laser Diagnostics on the 1-MA Zebra Generator

Laser diagnostics at the wavelength of 266 nm with a spatial resolution of 5-8 μm were developed for the investigation of dense <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -pinches at the 1-MA generator. The absorption and refraction in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -pinch plasma are significantly smaller at the ultraviolet (UV) wavelength of 266 nm compared to the optical range. This allows for observation of the fine internal structure of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -pinches at the stagnation phase. A UV laser beam penetrates through the trailing plasma around <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -pinches and shows strong instabilities of the dense pinch inside this plasma column. Kink instability, necks, and areas of disruption are seen in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z</i> -pinches at the peak of the X-ray pulse and later in time. UV two-frame side-on and end-on shadowgraphy show plasma dynamics in the pinch at stagnation.

Laser-produced plasma versus laser-assisted discharge plasma: physics and technology of extreme ultraviolet lithography light sources

Powerful extreme ultraviolet (EUV) sources at 13.5 nm are a prerequisite for the economical operation of lithography scanners for semi-conductor manufacturing. These sources have been under development for more than 10 years. At the beginning, many source concepts were considered. Compact technologies like dense plasma focus or capillary Z-pinch discharges reached very rapidly fundamental limits as far as power scalability and lifetime were concerned. Other complex technologies-like synchrotrons-eventually dropped out of the race as well, exceeding by far the footprint and cost targets. Over time, the technology solidified toward the two source concepts: on one hand, the discharge produced plasmas (DPP), which eventually led to the development of the current laser-assisted discharge plasma (LDP); on the other hand, the laser-produced plasmas (LPP). All these technologies generate hot and dense plasmas of similar properties, which emit EUV radiations efficiently as a black body radiator or Planck emitter, in a pulsed manner. The plasma generation method, however, is quite different. DPP uses a pulsed high-voltage current discharge to generate plasma heating a gaseous or vaporized material up to temperatures close to 200,000°C. As for LPP, microscopic droplets of molten tin are fired through a vacuum chamber, individually tracked, vaporized by a pre-pulse laser, and eventually irradiated by a pulsed high-power infrared CO2 laser at 50 to 100 kHz, creating a high-temperature tin plasma, which radiates EUV light. In the case of LDP the plasma is generated between two rotating discs. Partially immersed in baths filled with liquid tin, the discs are wetted and covered with a thin layer of liquid tin. A pulsed laser beam focused on one of the discs evaporates a small amount of tin and generates a tin cloud between the two discs. Next a capacitor bank, which is connected to the discs via the liquid tin, discharges and converts the tin cloud into a plasma heated up to 200,000°C as well.

Publisher’s Note: “Relaxation model for extended magnetohydrodynamics: Comparison to magnetohydrodynamics for dense Z-pinches” [Phys. Plasmas 18, 012703 (2011)

Publisher’s Note: “Relaxation model for extended magnetohydrodynamics: Comparison to magnetohydrodynamics for dense Z-pinches” [Phys. Plasmas 18, 012703 (2011)

Relaxation model for extended magnetohydrodynamics: Comparison to magnetohydrodynamics for dense Z-pinches

It is shown that the two-fluid model under a generalized Ohm’s law formulation and the resistive magnetohydrodynamics (MHD) can both be described as relaxation systems. In the relaxation model, the under-resolved stiff source terms constrain the dynamics of a set of hyperbolic equations to give the correct asymptotic solution. When applied to the collisional two-fluid model, the relaxation of fast time scales associated with displacement current and finite electron mass allows for a natural transition from a system where Ohm’s law determines the current density to a system where Ohm’s law determines the electric field. This result is used to derive novel algorithms, which allow for multiscale simulation of low and high frequency extended-MHD physics. This relaxation formulation offers an efficient way to implicitly advance the Hall term and naturally simulate a plasma-vacuum interface without invoking phenomenological models. The relaxation model is implemented as an extended-MHD code, which is used to analyze pulsed power loads such as wire arrays and ablating foils. Two-dimensional simulations of pulsed power loads are compared for extended-MHD and MHD. For these simulations, it is also shown that the relaxation model properly recovers the resistive-MHD limit.

Generation of Ultrafast Jets Through the Implosion of a Nested Conical Wire Array

It is shown that in contrast to the electric pulse power driven implosion of a single conical wire array, the implosion of a nested conical wire array with opposite alternate opening angles can lead to the generation of fast jets, with velocities of the order 108 cm/s. This technique can be applied for the supersonic shear flow stabilization of a dense z-pinch, but possibly also for the fast ignition of a pre-compressed dense deuterium–tritium target.

Multicolor Soft X-Ray Imaging of $Z$-Pinch Radiation Sources on the Z-Machine Pulsed-Power Driver

Time-resolved X-ray pinhole imaging is employed for diagnosing fast Z-pinch implosions on the Z accelerator. Reflection from a multilayer mirror produces monochromatic 277-eV images of the Z-pinch plasma in the final stages of implosion and stagnation. Simultaneous imaging with a filtered pinhole camera or using a second mirror can yield multicolor X-ray images which contain spectral as well as spatial information, allowing for the study of radiation physics in dense Z-pinches.

Dynamics of conical wire array Z-pinch implosions

A modification of the wire array Z pinch, the conical wire array, has applications to the understanding of wire array implosions and potentially to pulse shaping relevant to inertial confinement fusion. Results are presented from imploding conical wire array experiments performed on university scale 1 MA generators—the MAGPIE generator (1 MA, 240 ns) at Imperial College London [I. H. Mitchell et al., Rev. Sci Instrum. 67, 1533 (1996)] and the Nevada Terawatt Facility’s Zebra generator (1 MA, 100 ns) at the University of Nevada, Reno [B. Bauer et al., in Dense Z-Pinches, edited by N. Pereira, J. Davis, and P. Pulsifer (AIP, New York, 1997), Vol. 409, p. 153]. This paper will discuss the implosion dynamics of conical wire arrays. Data indicate that mass ablation from the wires in this complex system can be reproduced with a rocket model with fixed ablation velocity. Modulations in the ablated plasma are present, the wavelength of which is invariant to a threefold variation in magnetic field strength. The axial variation in the array leads to a zippered precursor column formation. An initial implosion of a magnetic bubble near the cathode is followed by the implosion zippering upwards. Spectroscopic data demonstrating a variation of plasma parameters (e.g., electron temperature) along the Z-pinch axis is discussed, and experimental data are compared to magnetohydrodynamic simulations.

One- and two-dimensional modeling of argon K-shell emission from gas-puff Z-pinch plasmas

In this paper, a theoretical model is described and demonstrated that serves as a useful tool for understanding K-shell radiating Z-pinch plasma behavior. Such understanding requires a self-consistent solution to the complete nonlocal thermodynamic equilibrium kinetics and radiation transport in order to realistically model opacity effects and the high-temperature state of the plasma. For this purpose, we have incorporated into the MACH2 two-dimensional magnetohydrodynamic (MHD) code [R. E. Peterkin et al., J. Comput. Phys. 140, 148 (1998)] an equation of state, called the tabular collisional radiative equilibrium (TCRE) model [J. W. Thornhill et al., Phys. Plasmas 8, 3480 (2001)], that provides reasonable approximations to the plasma’s opacity state. MACH2 with TCRE is applied toward analyzing the multidimensional implosion behavior that occurred in Decade Quad (DQ) [D. Price et al., Proceedings of the 12th IEEE Pulsed Power Conference, Monterey, CA, edited by C. Stallings and H. Kirbie (IEEE, New York, 1999), p. 489] argon gas puff experiments that employed a 12cm diameter nozzle with and without a central gas jet on axis. Typical peak drive currents and implosion times in these experiments were ∼6MA and ∼230ns. By using Planar Laser Induced Fluorescence measured initial density profiles as input to the calculations, the effect these profiles have on the ability of the pinch to efficiently produce K-shell emission can be analyzed with this combined radiation-MHD model. The calculated results are in agreement with the experimental result that the DQ central-jet configuration is superior to the no-central-jet experiment in terms of producing more K-shell emission. These theoretical results support the contention that the improved operation of the central-jet nozzle is due to the better suppression of instabilities and the higher-density K-shell radiating conditions that the central-jet configuration promotes. When we applied the model toward projecting argon K-shell yield behavior for Sandia National Laboratories’ ZR machine (∼25MA peak drive currents, ∼100ns implosion times) [D. McDaniel et al., Proceedings of the 5th International Conference on Dense Z-Pinches, Albuquerque, NM, 2002, edited by J. Davis, C. Deeney, and N. R. Pereira (American Institute of Physics, New York, 2002), Vol. 651, p. 23] for experiments that utilize the 12cm diameter central-jet nozzle configuration, it predicts over 1MJ of K-shell emission is attainable.

Deuterated fibre Z-pinch on the S-300 generator

Dense Z-pinch experiments were carried out on the S-300 generator (3.5 MA, 100 ns, 0.15 Ω) at the Kurchatov Institute in Moscow. The experiments were performed at a peak current of 2 MA with a rise time of about 100 ns. The Z-pinch was formed from a deuterated polyethylene fibre of 100 μm diameter and 1 cm length. The optical emission began early in the discharge and the coronal plasma expanded with a radial velocity of about 2×106 cm s−1. The optical and XUV emission continued for several hundreds of nanoseconds. The peak power of sub-keV radiation reached 30 GW near the maximum current. The total emitted energy exceeded 5 kJ. The neutron yield from the D-D reaction reached 2×107 per shot. The mean energy of neutrons obtained from time-of-flight analysis in the axial (downstream) direction was near 2.45 MeV.

Spectroscopic modeling of radiation from Cu and Mo X-pinches produced on the UNR 1 MA Zebra generator

X-pinches are a source for studying radiative properties of plasmas of very small sizes, high densities and temperatures applicable to high-energy density plasmas such as dense Z-pinches. Recently, spatially resolved and spatially integrated X-ray spectral data have been accumulated during Mo and Cu X-pinch experiments on the Zebra generator. During these experiments configurations, other then the 2-wire X-pinches, such as 4-wire X-pinches and asymmetric X-pinches have been spectroscopically studied and computationally analyzed. We present here modeling of the K-shell and L-shell radiation from Cu X-pinches with two and four wires and the comparison with experimental spectra. L-shell radiation from symmetric and asymmetric Mo X-pinches with two wires and X-pinches with four wires have also been analyzed and compared. Dependence of the plasma spatial structure, temperature, and density on wire materials and load configurations are discussed.