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Laser energy is absorbed in the corona of the spherical target and then is transported by thermal conduction from the low density plasma to the high density region further in. As a result the maximum pressure occurs in this denser region – this is called the ablation surface. In the derivation of the Fokker–Planck equation it is assumed that each particle interacts simultaneously with a large number of other particles, and the dominant effect is stochastic small deflections resulting from collisions with a large number of distant particles. Large deflections from close encounters are relatively rare, and are ignored. The usual approach to the derivation of transport coefficients is a linearisation of the Fokker–Planck equation for plasma close to thermal equilibrium. It can easily be shown that the heat flux from the critical surface to the ablation surface is nonlinear. The first solution of the nonlinear heat flow problem was found by Bell.

A two-dimensional magneto-hydrodynamic simulation incorporating cold start conditions is used to explain the early phase of carbon fiber Z-pinch experiments. The rapid development of large scale, nonlinear m=0 perturbations in the plasma corona is reproduced. X-ray bright spot formation in the necks of the instability is followed by bright spot bifurcation and fast axial motion. Bright spot bifurcation is found to be due to axial components of the j×B force and occurs off-axis due to the presence of a residual core of unionized carbon. Artificial diagnostic images are generated from the simulations data to allow direct comparison with experimental x-ray imaging and laser probing diagnostics. The accurate reproduction of the experimental images provides confirmation that the experimentally observed features are a repercussion of the non-linear development of the m=0 instability in an ionizing medium.

Experiments where a laser-generated proton beam is used to probe the megagauss strength self-generated magnetic fields from a nanosecond laser interaction with an aluminum target are presented. At intensities of 1015 Wcm(-2) and under conditions of significant fast electron production and strong heat fluxes, the electron mean-free-path is long compared with the temperature gradient scale length and hence nonlocal transport is important for the dynamics of the magnetic field in the plasma. The hot electron flux transports self-generated magnetic fields away from the focal region through the Nernst effect [A. Nishiguchi et al., Phys. Rev. Lett. 53, 262 (1984)] at significantly higher velocities than the fluid velocity. Two-dimensional implicit Vlasov-Fokker-Planck modeling shows that the Nernst effect allows advection and self-generation transports magnetic fields at significantly faster than the ion fluid velocity, v(N)/C(s) approximate to 10.

Fast electron energy spectra have been measured for a range of intensities between 1018 and 1021 W cm-2 and for different target materials using electron spectrometers. Several experimental campaigns were conducted on petawatt laser facilities at the Rutherford Appleton Laboratory and Osaka University, where the pulse duration was varied from 0.5 to 5 ps relevant to upcoming fast ignition integral experiments. The incident angle was also changed from normal incidence to 40° in p -polarized. The results confirm a reduction from the ponderomotive potential energy on fast electrons at the higher intensities under the wide range of different irradiation conditions. © 2009 American Institute of Physics.

A laser generated proton beam was used to measure the megagauss strength self-generated magnetic fields from a nanosecond laser interaction with an aluminum target. At intensities of 10 15 W cm -2, the significant hot electron production and strong heat fluxes result in non-local transport becoming important to describe the magnetic field dynamics. Two-dimensional implicit Vlasov-Fokker-Planck modeling shows that fast advection of the magnetic field from the focal region occurs via the Nernst effect at significantly higher velocities than the sound speed, v N/c s ≈ 10. © 2011 IOP Publishing Ltd.

Experiments reporting magnetic-field generation by the ablative nonlinear Rayleigh–Taylor (RT) instability are reviewed. The experiments show how large-scale magnetic fields can, under certain circumstances, emerge and persist in strongly driven laboratory and astrophysical flows at drive pressures exceeding one million times atmospheric pressure.

The wire-array z-pinch has in a very short time achieved remarkable performance as a powerful (>200?TW), pulsed soft x-ray source of high efficiency (~15%) and of great relevance to inertial confinement fusion. The underlying physics involves the transformation of wire cores to a plasma corona, the occurrence of uncorrelated axial instabilities, inward flowing low magnetic Reynolds number jets, sometimes an accumulated stable and dynamically confined precursor column, an almost constant velocity implosion when gaps occur in the wire cores and finally at stagnation a fast-rising soft x-ray pulse of typically 5?ns FWHM. Nested arrays improve the performance and can operate in several modes. Three hohlraum designs have been tested; one of these, the dynamic hohlraum, has achieved a radiation temperature of ~230?eV and has compressed a capsule from 2 to ~0.8?mm diameter with a neutron yield of > 1010 thermal DD neutrons. Lower mass stainless steel wire arrays are used for K? radiation sources. Generally implosions lead to more energy radiated than the implosive kinetic energy, and this is hypothesized as being due to ion viscous heating, as fast-growing short wavelength nonlinear MHD instabilities are dissipated; record ion temperatures of 200?300?keV are predicted and have been measured for the stainless steel array on Z at Sandia.

A review of recent experiments on the MAGPIE generator (1 MA, 250 ns) aimed at studying the implosion dynamics of wire array Z-pinches is presented. The first phase of implosion is dominated by the gradual ablation of stationary wire cores and gradual redistribution of the array mass by the precursor plasma flow. It is found that the rate of wire ablation depends on the magnitude of the global (collective) magnetic field of the array, and increases with the field. The existence of the modulation of the ablation rate along the wires leads to the presence of a 'trailing' mass left behind by the imploding current sheath. The trailing mass provides an alternative path for the current, reducing the force available for compression of the pinch at stagnation. The observed dependence of the ablation rate on inter-wire separation suggests an explanation for the existence of the optimal wire number maximizing the x-ray power. Axially resolved spectroscopy shows the presence of the x-ray 'bright' spots (< 150 µm) emitting intense continuum radiation.

We present new data from High Energy Density (HED) laboratory experiments designed to explore the interaction of a heavy hypersonic radiative jet with a cross wind. The jets are generated with the MAGPIE pulsed power machine where converging conical plasma flows are produced from a cylindrically symmetric array of inclined wires. Radiative hypersonic jets emerge from the convergence point. The cross wind is generated by ablation of a plastic foil via soft-X-rays from the plasma convergence region. Our experiments show that the jets are deflected by the action of the cross wind with the angle of deflection dependent on the proximity of the foil. Shocks within the jet beam are apparent in the data. Analysis of the data shows that the interaction of the jet and cross wind is collisional and therefore in the hydro-dynamic regime. MHD plasma code simulations of the experiments are able to recover the deflection behaviour seen in the experiments. We consider the astrophysical relevance of these experiments applying published models of jet deflection developed for AGN and YSOs. Fitting the observed jet deflections to quadratic trajectories predicted by these models allows us to recover a set of plasma parameters consistent with the data. We also present results of 3-D numerical simulations of jet deflection using a new astrophysical Adaptive Mesh Refinement code. These simulations show highly structured shocks occurring within the beam similar to what was observed in the experiments, Submitted to ApJ. For a version with figures go to http://web.pas.rochester.edu/~afrank/labastro/CW/Jet-Wind-Frank.pdf

We report on experiments on the MAGPIE generator (1 MA, 250 ns) to study the physics of plasma formation in wire array Z-pinches. It is shown that the gradual redistribution of the array mass by the precursor plasma flow from wire cores plays a very important role in implosion dynamics. It is found that the rate of wire ablation depends on the magnitude of the global (collective) magnetic field of the array and increases with the field. Due to this dependence, the azimuthal variations of the global magnetic field affect the implosion dynamics. The existence of the modulation of the ablation rate along the wires leads to the presence of a 'trailing' mass left behind by the imploding current sheath. The trailing mass provides an alternative path for the current, reducing the force available for compression of the pinch at stagnation. The observed dependence of the ablation rate on inter-wire separation suggests an explanation for the existence of the optimal wire number maximizing the x-ray power.

Progress in understanding the physics of dynamic-hohlraums is reviewed for a system capable of generating 13 TW of axial radiation for high temperature (>200 eV) radiation-flow experiments and ICF capsule implosions.

During the early stages of a wire array Z-pinch implosion, low density plasma streams toward the axis by virtue of the Lorentz force. This streaming precursor plasma may initially be highly collisionless with respect to ion–ion collisions and therefore cannot be modeled using standard fluid theory. The hybrid method in this paper models both collisional and collisionless behavior with ions exchanging energy and momentum with other ions via a Monte Carlo algorithm equivalent to a small-angle kinetic solution and with an electron fluid via a frictional force. It is shown that the axial stagnation of the plasma flow occurs once the density becomes sufficiently high to initiate a nonlinear rise in electron–ion energy exchange, resulting in the thermal equilibration between radiatively cooling electrons and hot, thermalized ions. This then gives rise to a dense, long-lived precursor column on axis, as observed experimentally. The column is held in place by the kinetic pressure of the streaming precursor plasma, which is balanced by the thermal pressure of the plasma in the column at the column’s edge.

Experiments on a two parallel wire Z-pinch are reported. The pinch was driven by a 160 kA peak current, 65 ns 10–90% rise time pulsed power source. Aluminium (15 µm) and tungsten (7.5 µm) wires with varying separations (0.3, 0.6 and 1.5 mm) were used. In addition to the plasma at each wire and its associated corona, a plasma column centred between the wires is formed, well before implosion of the wires. The expansion of the coronal plasma around each wire is asymmetric. Both the wire plasmas and the central plasma develop instabilities—characteristic m = 0 in the wire plasmas and predominantly m = 1 in the central plasma; the m = 0 perturbations in the wires are spatially correlated; the m = 1 perturbations in the central plasma are in the plane containing the wires. The development of instability in the central plasma implies a transfer of some current from the wires to the central plasma.

This paper considers the early behavior of the current-carrying coronal plasma formed around the relatively colder liquid-vapor core of a wire. This has applications to both a wire array before global effects dominate and a single wire. An analytic, theoretical model is developed where the Joule heating in the coronal plasma is thermally conducted to the cold core. The balance of both energy and pressure are assumed, and it is further assumed that the Hall parameter is much less than one throughout the domain. This last assumption will be violated near the outside radius of the corona where runaway conditions and lower hybrid turbulence can also occur. The nonlinear second-order differential equation for the normalized temperature variation with a normalized radius has only one free dimensionless parameter, which is the ratio of the applied axial electric field to the mean radial temperature gradient (in electronvolts/m). The inverse of this ratio scales essentially as $${{T^2 } \mathord{\left/ {\vphantom {{T^2 } {\sqrt n }}} \right. \kern-\nulldelimiterspace} {\sqrt n }}$$ , thus showing that both a low Hall parameter and a low magnetic Reynolds' number can occur when the mean free path is less than the collisionless skin depth, a criterion for the onset of current or heat-flow driven electrothermal instabilities.

Radiation from the interior of a dynamic hohlraum within a wire-array Z pinch is used to generate high-power x-ray pulses in both the up and down axial directions through radiation exit holes (REHs) in the anode and cathode, respectively. Despite a concerted effort to ensure a symmetrical up-down configuration, the measured peak top radiated power remained about twice that of the bottom (with similar total radiated energies from each REH), as compared to current simulations that predict equal powers. This large asymmetry suggests the need for improved physics models and simulation capabilities.

Nested wire array Z-pinch experiments carried out on the MAGPIE generator (1.4 MA, 240 ns) [I. H. Mitchell et al., Rev. Sci. Instrum. 67, 1553 (1996)] are described. In the experiments, a high inductance connection to the inner array was used to suppress the current flowing through it. This allowed the current division expected in experiments on larger generators to be emulated, where the number of wires in the outer array acts to shield the inner array. Initially the suppression of current resulted in the wires of the inner array remaining as small discrete bodies, while the wires of the outer array ablated, prefilling the array with plasma in an identical way to a single array experiment. During implosion the outer array accelerated towards the inner array, snowploughing up the prefilled plasma, producing a rise in x-ray emission. When the outer array traveled past the inner array, a fast inductive transfer of current occurred between them, and the inner array then accelerated towards the axis where it stagnated to produce the main x-ray pulse. The risetime of the main x-ray pulse was significantly shorter than in single array experiments. The dependence of the shape of the x-ray pulse on the configuration of the outer and inner arrays was explored.

Jet research has long relied upon a combination of analytical, observational and numerical studies to elucidate the complex phenomena involved. One element missing from these studies (which other physical sciences utilize) is the controlled experimental investigation of such systems. With the advent of high-power lasers and fast Z-pinch machines it is now possible to experimentally study similar systems in a laboratory setting. Such investigations can contribute in two useful ways. They can be used for comparison with numerical simulations as a means to validate simulation codes. More importantly, however, such investigations can also be used to complement other jet research, leading to fundamentally new knowledge. In the first part of this article, we analyze the evolution of magnetized wide-angle winds in a collapsing environment. We track the ambient and wind mass separately and describe a physical mechanism by which an ionized central wind can entrain the ambient gas giving rise to internal shells of molecular material on short time scales. The formation of internal shells in molecular outflows has been found to be an important ingredient in describing the observations of convex spurs in P-V diagrams (Hubble wedges in M-V diagrams). In the second part, we present astrophysically relevant experiments in which supersonic jets are created using a conical wire array Z-pinch. The conically convergent flow generates a standing shock around the axis which collimates the flow into a Mach ∼ 30 jet. The jet formation process is closely related to the work of Canto et al. (1988) for hydrodynamic jet collimation. The influence of radiative cooling on collimation and stability is studied by varying the wire material (A1, Fe, and W).

Due to their particular properties, the beams of the multi-MeV protons generated during the interaction of ultraintense (I>10(19) W/cm(2)) short pulses with thin solid targets are most suited for use as a particle probe in laser-plasma experiments. The recently developed proton imaging technique employs the beams in a point-projection imaging scheme as a diagnostic tool for the detection of electric fields in laser-plasma interaction experiments. In recent investigations carried out at the Rutherford Appleton Laboratory (RAL, UK), a wide range of laser-plasma interaction conditions of relevance for inertial confinement fusion (ICF)/fast ignition has been explored. Among the results obtained will be discussed: the electric field distribution in laser-produced long-scale plasmas of ICF interest; the measurement of highly transient electric fields related to the generation and dynamics of hot electron currents following ultra-intense laser irradiation of targets; the observation in underdense plasmas, after the propagation of ultra-intense laser pulses, of structures identified as the remnants of solitons produced in the wake of the pulse.

Experiments on the implosion dynamics of single and nested nickel wire arrays driven by the MAGPIE generator with a 1-MA, 240-ns current pulse are reported. Like aluminum and tungsten wire discharges, the plasma formed from individual wires has a core-corona structure. In a single nickel array, a wire core size of 75 /spl mu/m before the implosion was measured by X-ray radiography. The precursor plasma is formed on axis and is m=1 unstable. The implosion of the array occurs later than predicted by the 0-D model, indicating that a fraction of current flows through the precursor plasma. This is in contrast with copper arrays (copper has the similar radiation properties as nickel, Z/sub nickel/=28, Z/sub copper/=29) where the precursor plasma is uniform and implosion time is as predicted by 0-D model. Experiments with nickel nested arrays show that the expansion of the wires in the outer and the inner array is similar and a precursor plasma is formed on the axis earlier than in single arrays. It appears from the experimental data that a significantly larger fraction of the current is flowing through the inner array.

A simplified algebraic model is set up to describe the principal features of the physics of wire array behavior in the early phases. Each wire is assumed to have evolved into a liquid-vapor core surrounded by a coronal plasma which carries most of the current. This plasma is unstable to m=0 instabilities, this instability being MHD or possibly electrothermal driven by inward radial heat flow on each wire. The joule heating occurs mainly in the necks of the sausage mode; flux limited heat flow transfers the energy to the core which erodes and ablates as a plasma at the sound speed. Free expansion at this velocity occurs into the lobes of the m=0 structure, and by rocket action the J_/spl times/B_ inward global force deflects the flow into inward precursor-jets. It is shown that the magnetic Reynolds' number is less than one, and for a rapidly rising current results in negligible current or magnetic field in the precursor, as found usually in experiments. In addition, it is found that in the necks the Hall parameter is much less than one, consistent with the field-free model of flux limited heat flow.

A phenomenological model of wire array Z-pinch implosions, based on the analysis of experimental data obtained on the mega-ampere generator for plasma implosion experiments (MAGPIE) generator [I. H. Mitchell et al., Rev. Sci. Instrum. 67, 1533 (1996)], is described. The data show that during the first ∼80% of the implosion the wire cores remain stationary in their initial positions, while the coronal plasma is continuously jetting from the wire cores to the array axis. This phase ends by the formation of gaps in the wire cores, which occurs due to the nonuniformity of the ablation rate along the wires. The final phase of the implosion starting at this time occurs as a rapid snowplow-like implosion of the radially distributed precursor plasma, previously injected in the interior of the array. The density distribution of the precursor plasma, being peaked on the array axis, could be a key factor providing stability of the wire array implosions operating in the regime of discrete wires. The modified “initial” conditions for simulations of wire array Z-pinch implosions with one-dimension (1D) and two-dimensions (2D) in the r–z plane, radiation-magnetohydrodynamic (MHD) codes, and a possible scaling to a larger drive current are discussed.

Both dynamic and equilibrium z pinches are mostly described, whether in theory or in simulation, by conventional magnetohydrodynamic (MHD) fluid equations. However there are several key phases in z-pinch behavior when kinetic effects are important. Runaway electrons can occur close to the axis especially in an m = 0 neck or during the subsequent disruption. Large ion-Larmor orbits can, if sufficiently collisionless, lead to stabilizing effects. During a disruption, ion beams can be produced. For deuterium discharges, the interaction of an ion beam with the ambient plasma can lead to a significant neutron yield. If the drift velocity of the current-carrying electrons exceeds a threshold for generating microinstabilities (lower-hybrid or ion-acoustic instabilities), this leads to anomalous resistivity. This can occur not only during a disruption, but also in the low-density (usually outer) plasma boundary of an equilibrium or dynamic pinch. Related to this is the open question of whether current reconnection can occur in fully developed magneto-Rayleigh-Taylor instabilities in the low-density coronal plasma. Two other kinetic effects are new to z pinches. First, there are the collisions of low-density energetic ions from a wire array as they pass close to the axis to form a precursor plasma. Second, there is the possible erosion and ablation of wire cores in the necks of m = 0 coronal current-carrying plasma by flux-limited heat flow with its attendant deviation from a Maxwellian of the isotropic part of the distribution function.

Experiments to study plasma formation and implosion dynamics of wire array z pinches performed on MAGPIE generator (1.4 MA, 240 ns) at Imperial College are reviewed. Data from laser probing and X-ray radiography show that heterogeneous plasma structure with dense wire cores surrounded by low-density coronal plasma persists in wire arrays for a significant part of the implosion. Early implosion of the coronal plasma produces a precursor plasma column on the array axis, parameters of which depend on the rate of radiative cooling. The seeding of perturbations on the dense core of each wire is provided by nonuniform sweeping of the low-density coronal plasma from the cores by the global J X B force. The spatial scale of these perturbations ( 0.5 mm for Al, 0.25 mm for W) is determined by the size of the wire cores ( 0.25 mm for Al, ∼0.1 mm for W). A qualitative change in implosion dynamics, with transition to 0-D-like trajectory, was observed in Al arrays when the ratio of interwire gap to wire core size was decreased to ∼3. In experiments with nested wire arrays, two different modes of operation were identified, both giving significant sharpening of the X-ray pulse ( 10 ns) in comparison with a single array, despite the small number of wires in the arrays (16 outer, 16 inner) and the long implosion time (260 ns).

A series of specialized multidimensional resistive magnetohydrodynamic (MHD) models have been developed to tackle the different phases of evolution of wire array z-pinch implosions. Two-dimensional (r–z) “cold-start” or “wire initiation” simulations of single wires indicate the persistence of a two-component structure with a cold, dense core embedded within a much hotter, low density, m = 0 unstable corona. Cold-start simulations with similar conditions to wires in an array show a general trend in the plasma structure from discrete wires with large m = 0 perturbation amplitudes to partially merged wires with smaller perturbation amplitudes as the number of wires is increased. Two-dimensional (r–θ) simulations then show how the persistence of dense wire cores results in the injection of material between the wires into the interior of the array, generating radial plasma streams which form a precursor plasma upon reaching the axis. Higher-resolution 2-D (r–θ) simulations show similar behavior for large number wire arrays in use at Sandia National Laboratories. This model is also used to predict which modes of implosion are in operation in nested wire array experiments. Separate r–θ plane simulations of the flux of plasma imploding towards the axis from the outer array and the bombardment of the inner array by this flux are presented. Finally, 2-D (r–z) simulations of the Rayleigh–Taylor instability during the final implosion phase are used to illustrate the effect upon the power and duration of the radiation output pulse. The results of low-resolution 3-D resistive MHD simulations are also presented. The need for much higher resolution 3-D simulations of certain aspects of wire array evolution is highlighted.

A series of one-, two-, and three-dimensional (1-D, 2-D, and 3-D) resistive magnetohydrodynamic models are used to build up a composite model of the different phases of wire array Z-pinch implosions. 1-D(r) and 2-D(r,z) “cold-start” simulations of single wire experiments are used to illustrate some of the important processes in the plasma formation phase of wire arrays. Detailed comparison of the simulation results with data from single wire experiments provides an excellent method of code verification. 2-D simulations in the r–θ or x–y plane show how the combination of the core–corona structure of the wire plasmas and the magnetic field topology result in the formation of radial plasma streams and a precursor plasma on axis well before the implosion phase commences. The same 2-D(x–y) model is also used to illustrate how the implosion trajectories of nested wire arrays are controlled by the levels of momentum, energy, and magnetic flux which are transferred during their collision. Preliminary results showing the evolution of a single wire in the array in 3-D are presented. These results suggest that the dynamics and structure of imploding wire arrays at Imperial College can potentially be explained in terms of the current breaking through the wire cores rather than in terms of the Rayleigh–Taylor instability.

Magnetohydrodynamic simulations are used to predict which modes of implosion are in operation in nested wire array experiments. Separate r–θ plane simulations of the flux of plasma imploding towards the axis from the outer array and the bombardment of the inner array by this flux are presented. The different implosion modes are distinguished by the level of momentum transfer and magnetic flux compression during collision. For typical configurations, large interwire gaps (>1.5 mm) are required in the inner array in order to access the advantageous mode where the outer array material passes through.

Results of particle transport analysis are presented for both low and high charge impurity species in JET optimized shear plasmas. The impurity content in the plasma centre is sensitive to the strength of the internal transport barrier. In a strong transport barrier plasma, the diffusion coefficient in the centre is about an order of magnitude lower than that in plasmas with weak transport barriers. Impurity transport is close to the neoclassical transport prediction in the centre of the plasma, whereas it is much higher than the neoclassical theoretical value in the plasma edge. A convection term in the vicinity of the transport barrier was required in order to account for the measurements. These data support theories of turbulence suppression by the E × B shearing rate.

Poloidally asymmetric distributions of nickel ions have been observed experimentally in Joint European Torus optimized shear tokamak plasmas following nickel laser injection experiments. Two types of asymmetries occur. In the first type of asymmetry, which has earlier been observed in high-confinement mode plasmas, nickel ions accumulate on the outboard side of the poloidal cross section. This can be explained well by fast toroidal plasma rotation driven by neutral beam injection. The second type of asymmetry was opposite in position: In a radio frequency heated optimized shear plasma, nickel ions have been seen to accumulate on the inboard side of the poloidal cross section.

A study of a 2 kJ, 200 kA, table top plasma focus device as an intense x-ray source is reported. The x-ray yield from a number of gases, (deuterium, nitrogen, neon, argon, and xenon) is measured as a function of filling pressure and in neon as a function of anode length. In gases with Z

Optical emission from xenon plasma in a hollow cathode has been recorded over a wide range of wavelengths extending from vacuum ultraviolet to the visible band 100-590 nm. The cathode was operated in direct current discharge mode with a continuous flow of xenon ~13 cc min -1 at 70 Torr. A column of neutral xenon gas (~21.2 cm long) existed in-between the active plasma column (~1 cm long) source and the detector. The observed spectra show that strong Xe II and impurity (Ba, Al and Ca) lines are superimposed on a weak continuum. Xenon I lines have not been observed. A subsidiary broadened continuum band within the far vacuum ultraviolet range 100-200 nm supports the evidence that the emission due to the transitions by the excited molecular dimer/excimer species is also involved. In the present work, bremsstrahlung emission has been used to estimate the plasma electron temperature Te = 1.1 eV. The resulting electron density ne = 1014 cm-3 is then obtained using the Saha formulation for the ratio of the discrete lines. The radiative properties and the validity of the various plasma equilibrium models within the hollow cathode have also been discussed.

Recent success on the Saturn [C. Deeney et al., Phys. Rev. E 56, 5945 (1997)] and Z [R. B. Spielman et al., Phys. Plasmas 5, 2105 (1998)] accelerators at Sandia National Laboratories have demonstrated the ability to scale Z-pinch parameters to increasingly larger current pulsed power facilities. Next generation machines will require even larger currents (>20 MA), placing further demands on pulsed power technology. To this end, experiments have been carried out on Saturn operating in a long pulse mode, investigating the potential of lower voltages and longer implosion times while still maintaining pinch fidelity. High wire number, 25 mm diam tungsten arrays were imploded with implosion times ranging from 130 to 240 ns. The results were comparable to those observed in the Saturn short pulse mode, with rise times on the order of 4.5–6.5 ns. Experimental data will be presented, along with two-dimensional radiation magnetohydrodynamic simulations used to explain and reproduce the experiment.

The Z pinch is enjoying a renaissance as the world’s most powerful yet efficient soft x-ray source which can energize large volume hohlraums for indirectly driven inertial confinement fusion. It has the advantages of being efficient and having high energy and power density. Its early history will be traced from the 18th century to the present day. The most notable feature of the Z pinch is its instability. The various regimes of stability analysis will be reviewed, including resistive and finite ion Larmor radius effects. Work in the last 10 years on single fibres, especially of cryogenic deuterium, gave neutrons that were of the same origin, namely, beam–plasma interactions, as reported by Kurchatov. The renaissance has come about through the implosion of arrays of fine wires. Research at Sandia National Laboratory has shown that by using more and finer wires, the x-ray radiation emitted at stagnation increased in power and decreased in pulse width. The understanding of these results has been advanced considerably by theory, simulation and smaller-scale, well diagnosed experiments showing the early uncorrelated m=0 instabilities on each wire, the inward jetting of plasma to the axis, the global Rayleigh–Taylor instability and the mitigating effect of nested arrays.

Two different modes of nested wire array implosion driven by a 1-MA, 240-ns current pulse were observed, determined by the fraction of total current induced in the inner array. Penetration by the outer array through the inner with switching of current occurred if current in the inner array was initially suppressed. Simultaneous implosion of arrays with apparent compression of magnetic flux between the arrays was observed if $\ensuremath{\sim}20%$ of the current was in the inner array. In both cases the x-ray pulse rise time of $\ensuremath{\sim}10\mathrm{ns}$ (for 260-ns implosion time) was considerably smaller than for a single array.

High wire number, 25-mm-diameter tungsten wire arrays have been imploded on the 8-MA Saturn generator [R. B. Spielman et al., AIP Conference Proceeding 195, 3 (American Institute of Physics, Woodbury, NY 1989)], operating in a long-pulse mode. By varying the mass of the arrays from 710 to 6140 μg/cm, implosion times of 130–250 ns have been obtained with implosion velocities of 50–25 cm/μs, respectively. These Z-pinch implosions produced plasmas with millimeter diameters that radiated 600–800 kJ of x-rays, with powers of 20–49 TW; the corresponding pulsewidths were 19–7.5 ns, with risetimes ranging from 6.5 to 4.0 ns. These powers and pulsewidths are similar to those achieved with 50-ns implosion times on Saturn. Two-dimensional, radiation-magnetohydrodynamic calculations indicate that the imploding shells in these long implosion time experiments are comparable in width to those in the short-pulse cases. This can be due to lower initial perturbations. A heuristic wire array model suggests that the reduced perturbations, in the long-pulse cases, may be due to the individual wire merger occurring well before the acceleration of the shell. The experiments and modeling suggest that 150–200 ns implosion time Z-pinches could be employed for high-power, x-ray source applications.

The modified Fokker–Planck collision operator for partially degenerate electrons was derived in an earlier paper [J. Plasma Phys.58, 577 (1997)]. This is now employed to study linear electron transport for a partially degenerate, magnetized plasma. Because polynomial expansions can yield incorrect transport coefficients owing to lack of resolution of the small fraction of low-energy unmagnetized electrons, a numerical discrete-ordinate scheme is employed. The inclusion of electron–electron collisions advances the model beyond that of Lee and More, and in the classical limit agrees with the results of Epperlein and Haines.

Comparisons of measured total radiated x-ray power from annular wire-array z-pinches with a variety of models as a function of wire number, array mass, and load radius are reviewed. The data, which are comprehensive, have provided important insights into the features of wire-array dynamics that are critical for high x-ray power generation. Collectively, the comparisons of the data with the model calculations suggest that a number of underlying dynamical mechanisms involving cylindrical asymmetries and plasma instabilities contribute to the measured characteristics. For example, under the general assumption that the measured risetime of the total-radiated-power pulse is related to the thickness of the plasma shell formed on axis, the Heuristic Model [IEEE Trans. Plasma Sci. 26, 1275 (1998)] agrees with the measured risetime under a number of specific assumptions about the way the breakdown of the wires, the wire-plasma expansion, and the Rayleigh–Taylor instability in the r–z plane, develop. Likewise, in the high wire-number regime (where the wires are calculated to form a plasma shell prior to significant radial motion of the shell) the comparisons show that the variation in the power of the radiation generated as a function of load mass and array radius can be simulated by the two-dimensional Eulerian-radiation- magnetohydrodynamics code (E-RMHC) [Phys. Plasmas 3, 368 (1996)], using a single random-density perturbation that seeds the Rayleigh–Taylor instability in the r–z plane. For a given pulse-power generator, the comparisons suggest that (1) the smallest interwire gaps compatible with practical load construction and (2) the minimum implosion time consistent with the optimum required energy coupling of the generator to the load should produce the highest total-radiated-power levels.

Wire array Z-pinch dynamics are studied in experiments with 16-mm diameter arrays of between 8 and 64, 15-μm diameter aluminum wires, imploded in 200–260 ns by a 1.4-MA current pulse. Side-on laser probing shows early development of noncorrelated m=0-like instabilities with an axial wavelength ∼0.5 mm in individual wires. End-on interferometry (r-θ plane) shows azimuthal merging of the plasma with a density of 1017 cm−3 in 90–65 ns for 8–64 wires, respectively. At the same time low-density plasma reaches the array axis and forms a precursor pinch by 120–140 ns. At 0.7–0.85 of the implosion time a global m=0 instability with a wavelength of 1.7–2.3 mm was detected in soft x-ray gated images, laser probing, and optical streaks. The time when the instability reaches the observable level corresponds to the number of e-foldings for the growth of the classical Rayleigh–Taylor instability of ∫γ dt∼5.6–7. The scaling of this number with the number of wires is consistent with the instability growth from the seed l...

Thomson scattering has recently been introduced as a fundamental diagnostic of plasma conditions and basic physical processes in dense, inertial confinement fusion plasmas. Experiments at the Nova laser facility [E. M. Campbell et al., Laser Part. Beams 9, 209 (1991)] have demonstrated accurate temporally and spatially resolved characterization of densities, electron temperatures, and average ionization levels by simultaneously observing Thomson scattered light from ion acoustic and electron plasma (Langmuir) fluctuations. In addition, observations of fast and slow ion acous- tic waves in two-ion species plasmas have also allowed an independent measurement of the ion temperature. These results have motivated the application of Thomson scattering in closed-geometry inertial confinement fusion hohlraums to benchmark integrated radiation-hydrodynamic modeling of fusion plasmas. For this purpose a high energy 4{omega} probe laser was implemented recently allowing ultraviolet Thomson scattering at various locations in high-density gas-filled hohlraum plasmas. In partic- ular, the observation of steep electron temperature gradients indicates that electron thermal transport is inhibited in these gas-filled hohlraums. Hydrodynamic calcula- tions which include an exact treatment of large-scale magnetic fields are in agreement with these findings. Moreover, the Thomson scattering data clearly indicate axial stagnation in these hohlraums by showing a fast rise of the ion temperature. Its timing is in good agreement with calculations indicating that the stagnating plasma will not deteriorate the implosion of the fusion capsules in ignition experiments.

Increasing the number of wires an order of magnitude from 10 to almost 200 while simultaneously fixing the total wire mass in annular aluminum-wire-array Z-pinch implosions on the 20 TW Saturn generator [Proceedings of the 6th International IEEE Pulsed Power Conference (Institute of Electrical and Electronics Engineers, Piscataway, NJ, 1987), p. 310] demonstrates two separate power-law trends in the measured x-ray characteristics as a function of the initial interwire gap (g). These trends are approximately independent of the array radius. When g decreases from ∼6 to 0.4 mm, the peak total radiated power increases by a factor of 20 and the total energy by a factor of 2. There is a more rapid increase in peak power and energy radiated as g decreases for gaps greater than ∼2 mm. This increase is related to a measured decrease in precursor plasma and to a calculated decreased sensitivity of the implosion to azimuthal asymmetries that occurs when individual wire plasmas begin to merge following their vaporiza...

Fast electron transport in a dense plasma is investigated with one-dimensional particle-in-cell simulations. We show the importance of collisions in the interaction of an ultra-intense ultrashort laser pulse with a solid target. We demonstrate that the fast electron penetration depth and distribution depend on target resistivity. Collisions reinforce the fast electron confinement near the irradiated surface.

A three-dimensional resistive magnetohydrodynamic code has been used to model the reconnection process at the m=1, n=1 surface, in periodic cylindrical geometry. Large current densities are expected at this reconnection layer and an enhancement of the transport properties is expected if the local drift speed exceeds a critical velocity, such as some multiple of the local sound speed. This effect is modeled in these simulations by the local enhancement of the resistivity coefficient where the criterion for micro-turbulence is satisfied. It is found that the reconnection times for this type of simulation are comparable to the reconnection times for a plasma where the resistivity is enhanced everywhere, implying that the reconnection is dominated by the local resistivity value and not its gradient. An analytic scaling law of the reconnection rate for the case when the local electron drift velocity is limited to a multiple of the sound speed is presented. This model predicts that when this multiple is (mi/me)...

An experimental study of optical probing of a dense z-pinch plasma using the MAGPIE (mega-ampere generator for plasma implosion experiments) generator [I. H. Mitchell et al., Rev. Sci. Instrum. 67, 1533 (1996)] is reported. The generator was operated with a peak current of 1.1 MA rising in 150 ns (10%–90%). The loads were 33 μm diam carbon fibers. Faraday rotation was used to investigate the distribution of the current flowing in the plasma. A measurable Faraday rotation angle was observed only in a time window from 50 to 60 ns after the current start, due to the fact that this effect depends on a combination of the magnetic-field strength and electron number density. A new type of self-referencing cyclic radial shear interferometer was used to evaluate the plasma density profiles which are necessary for the reconstruction of the current distribution. It was calculated that ∼110 kA was flowing in the plasma at 52 ns after the current start. Shadowgraphy was used to study the dynamics of the plasma and to ...

One-dimensional numerical simulations of compressional Z-pinch show that the plasma radius after first compression is oscillating in time. Previous experiments with end-on diagnostics showed no evidence of such behavior but a recent series of experiments with side-on diagnostics on hydrogen plasma has shown that this is indeed the case.

A series of experiments has been carried out on the Mega Ampere Generator for Plasma Implosion Experiments (MAGPIE) generator in order to study the dynamics of carbon fiber Z-pinches. The generator was operated at 1.4 MV, with a peak current of 1 MA, and a rise time of 150 ns. In some shots, a current prepulse of about 30 kA was provided to study its influence on the dynamics of the fiber pinch. Carbon fibers of 7, 33, and 300 /spl mu/m diameter were used during these experiments. The diagnostics employed were a self-referencing interferometer, a two-frame Schlieren system, an optical streak camera, and a four-frame X-ray framing camera. A novel feature of these measurements is the employment of an optical streak camera with a set of four slits arranged along the fiber axis and displaced in the radial direction. This permitted the study of the temporal evolution (axial and radial) of the plasma regions emitting in the visible part of the spectra. Correlation between these regions of the plasma and the location of X-ray hot spots is discussed. In carbon fibers of 33 pm diameter, the radial expansion velocity measured from Schlieren images was 3.6/spl times/10/sup 6/ cm/s and 5.5/spl times/10/sup 6/ cm/s for shots with and without prepulse, respectively. The dominant axial wavelengths of instabilities in the coronal plasma were between 0.05 and 0.2 cm, which correspond to ka values between 10 and 20, where k is the wavenumber of the instability and a is its amplitude. The dynamics of carbon fibers of different diameters are compared.

The latter stages of fiber Z-pinch discharges at current levels up to 1.4 MA with a rise time of 150 ns have been investigated on the MAGPIE generator. Carbon fibers with a diameter of 33 /spl mu/m and deuterated polyethylene (CD/sub 2/) fibers with diameters between 50 and 200 /spl mu/m were used as loads. The detection of hard X-rays and neutrons provide evidence for MeV electrons and ions. The hard X-rays occur around 120-200 ns into the discharge and typically last for between 20 and 100 ns. Beam target neutrons have also been detected at this time with neutron energies of up to 5.2 MeV. Optical and X-ray diagnostics indicate that the dynamic hot spot phase of the pinch is over by this time and that no rapid pinching or expansion of dense plasma is occurring. The pinch is seen to be composed of high density regions along the axis interspersed by tenuous regions where the density is at least two orders of magnitude lower. A conceptual model which is consistent with the experimental data is proposed to explain the energy and duration of the X-ray and neutron pulses.

The quantum Boltzmann collision operator is expanded to yield a degenerate form of the Fokker–Planck collision operator. This is analysed using Rosenbluth potentials to give a degenerate analogue of the Shkarofsky operator. The distribution function is then expanded about an equilibrium Fermi–Dirac distribution function using a tensor perturbation formulation to give a zeroth-order and a first-order collision operator. These equations are shown to satisfy the relevant conservation equations. It is shown that the distribution function relaxes to a Fermi–Dirac form through electron–electron collisions.