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High current pulsed-power generators efficiently store and deliver magnetic energy to z-pinch targets. We review applications of magnetically driven implosions (MDIs) to inertial confinement fusion. Previous research on MDIs of wire-array z-pinches for radiation-driven indirect-drive target designs is summarized. Indirect-drive designs are compared with new targets that are imploded by direct application of magnetic pressure produced by the pulsed-power current pulse. We describe target design elements such as larger absorbed energy, magnetized and pre-heated fuel, and cryogenic fuel layers that may relax fusion requirements. These elements are embodied in the magnetized liner inertial fusion (MagLIF) concept [Slutz “Pulsed-power-driven cylindrical liner implosions of laser pre-heated fuel magnetized with an axial field,” Phys. Plasmas, 17, 056303 (2010), and Stephen A. Slutz and Roger A. Vesey, “High-Gain Magnetized Inertial Fusion,” Phys. Rev. Lett., 108, 025003 (2012)]. MagLIF is in the class of magneto-inertial fusion targets. In MagLIF, the large drive currents produce an azimuthal magnetic field that compresses cylindrical liners containing pre-heated and axially pre-magnetized fusion fuel. Scientific breakeven may be achievable on the Z facility with this concept. Simulations of MagLIF with deuterium-tritium fuel indicate that the fusion energy yield can exceed the energy invested in heating the fuel at a peak drive current of about 27 MA. Scientific breakeven does not require alpha particle self-heating and is therefore not equivalent to ignition. Capabilities to perform these experiments will be developed on Z starting in 2013. These simulations and predictions must be validated against a series of experiments over the next five years. Near-term experiments are planned at drive currents of 16 MA with D2 fuel. MagLIF increases the efficiency of coupling energy (=target absorbed energy/driver stored energy) to targets by 10-150X relative to indirect-drive targets. MagLIF also increases the absolute energy absorbed by the target by 10-50X relative to indirect-drive targets. These increases could lead to higher fusion gains and yields. Single-shot high yields are of great utility to national security missions. Higher efficiency and higher gains may also translate into more compelling (lower cost and complexity) fusion reactor designs. We will discuss the broad goals of the emerging research on the MagLIF concept and identify some of the challenges. We will also summarize advances in pulsed-power technology and pulsed-power driver architectures that double the efficiency of the driver.

Negative conductors in vacuum transmission lines used in multiterrawatt applications emit electrons freely. These lines are efficient only because the self‐magnetic field of the power flow forces the electrons to flow parallel to the electrodes. Excepting numerical simulations, dynamic modeling of systems of these transmission lines has generally either ignored electron flow, or has included only those electrons that cross immediately to the anode at the front of the forward wave. In this paper we describe an analytic model that includes flowing electrons and the effects of these flows on line voltage and on the reduction of magnetic flux. Axial electron currents are modeled using simple, measurable, and calculable parameters. Transverse electron currents are modeled using general patterns found empirically from simulation data. These currents are in turn related by an expanded set of Telegrapher equations. An example of the use of the model is compared to two‐dimensional, time‐dependent particle‐in‐cell simulations.

In modern pulsed power systems the electric field stresses at metal surfaces in vacuum transmission lines are so high that negative surfaces are space‐charge‐limited electron emitters. These electrons do not cause unacceptable losses because magnetic fields due to system currents result in net motion parallel to the electrodes. It has been known for several years that a parameter known as flow impedance is useful for describing these flows. Flow impedance is a measure of the separation between the anode and the mean position of the electron cloud, and it will be shown in this paper that in many situations flow impedance depends upon the geometry of the transmission line upstream of the point of interest. It can be remarkably independent of other considerations such as line currents and voltage. For this reason flow impedance is a valuable design parameter. Models of impedance transitions and voltage adders using flow impedance will be developed. Results of these models will be compared to two‐dimensional, time‐dependent, particle‐in‐cell simulations.

We have developed a semianalytic expression for the total energy loss to a vacuum transmission-line electrode operated at high lineal current densities. (We define the lineal current density j' � B=� 0 to be the current per unit electrode width, where B is the magnetic field at the electrode surface and � 0 is the permeability of free space.) The expression accounts for energy loss due to Ohmic heating, magnetic diffusion, jB work, and the increase in the transmission line's vacuum inductance due to motion of the vacuum-electrode boundary. The sum of these four terms constitutes the Poynting fluence at the original location of the boundary. The expression assumes that (i) the current distribution in the electrode can be approximated as one-dimensional and planar; (ii) the current Iðt Þ¼ 0 for t< 0, and Iðt Þ/ t for t � 0; (iii) j' � 10 MA=cm; and (iv) the current-pulse width is between 50 and 300 ns. Under these con- ditions we find that, to first order, the total energy lost per unit electrode-surface area is given by Wtðt Þ¼ �tB � ðt Þþ �tB � ðtÞ, where BðtÞ is the nominal magnetic field at the surface. The quantities � , � , � , � , � , andare material constants that are determined by normalizing the expression for WtðtÞ to the results of 1D magnetohydrodynamic MACH2 simulations. For stainless-steel electrodes operated at current densities between 0.5 and 10 MA=cm, we find that � ¼ 3:36 � 10 5 , � ¼ 1=2, � ¼ 2, � ¼ 4:47 � 10 4 , � ¼ 5=4, and � ¼ 4 (in SI units). An effective time-dependent resistance, appropriate for circuit simulations of pulsed-power accelerators, is derived from WtðtÞ. Resistance-model predictions are compared to energy-loss measurements made with stainless-steel electrodes operated at peak lineal current densities as high as 12 MA=cm (and peak currents as high as 23 MA). The predictions are consistent with the measurements, to within experimental uncertainties. We also find that a previously used electrode-energy-loss model overpredicts the measurements by as much as an order of magnitude.

Development of isentropic loading techniques is a long standing goal of the shock physics community. We have used the Sandia Z Accelerator to produce smoothly increasing pressure loading on planar iron specimens over time durations of 100 ns and for pressures to 300 kbar. Free surface velocity measurements were made on specimens 0.5-mm and 0.8-mm thick that clearly show wave evolution into the well known two-wave structure resulting from the α-e phase transition. The resulting wave profiles are analyzed with a rate-dependent phase transition model to extract information on phase transformation kinetics for isentropic compression of iron. Comparison of the experiments and calculations demonstrate the value of isentropic loading for studying phase transition kinetics.

In a planar crossed-field diode, the steady-state flow in the space-charge-limited regime is governed by a nonlinear integrodifferential equation. We have derived a generalized Fry-Langrnuir equation for the potential which is self-consistent to second order in the normalized magnetic field µ. The small-µ crossed-field potential may be considered as the Fry-Langmuir potential of the corresponding unmagnetized diode, i.e., with the same diode parameters but with zero magnetic field, plus the steady-state second-order perturbation produced by the magnetic field. Owing to the symmetry of the unbounded, planar geometry, there is no first-order perturbation. From four universal functions (the Fry-Langrnuir function and three additional functions we have derived), one can determine the potential and density profiles of any space-charge-limited planar crossed-field diode for which µ is small. It is shown that the crossed-field potential minimum is deepened and shifted toward the anode with respect to the unmagnetized potential minimum.

Applying a perturbation expansion to the self‐consistent Poisson equation for a planar, space‐charge‐limited crossed‐field diode, we have derived four universal diode functions (independent of any particular diode specification), in addition to the usual Fry‐Langmuir function for unperturbed, unmagnetized planar diodes. A crossed‐field diode is completely specified by three external parameters: its normalized width X = xa/λDb, anode voltage V = φa/φTb, and magnetic field Ω = ωc/ωpb. Here a and b, respectively, denote anode and cathode quantities, λDb is the electronic Debye length, ωpb is the plasma frequency, φTb is the electron temperature in volts, and ωc is the electron gyrofrequency. Evaluating the universal functions at abscissas appropriate for a particular set of X, V, and Ω then allows the calculation of the anode noise power (mean square current fluctuation at the anode) as a function of X, V, and Ω. The range of external parameters for which the theory is applicable is specified by a simple con...

Four general functions are presented which determine self‐consistently the potential minimum position and depth in planar space‐charge‐limited crossed‐field electron guns.

Electromagnetic particle simulations of equatorial self‐magnetic‐field‐enhanced ion diodes have been performed. These simulations complement recent experiments on the particle beam fusion accelerator using the pinch ion diode (pid) and the Obi diode. Those experiments are detailed in a companion paper. The simulations have provided useful information concerning the operation of the diode. This paper will describe many of the simulation findings in such areas as current and charge neutralization, virtual cathode formation, diode impedance, ion divergence, and electron temperatures. In addition, a model for ion efficiency has been obtained that is based upon the simulation results. This model is compared to various other efficiency models.

PBFA II is a 100 TW pulsed power accelerator constructed at Sandia National Laboratories for use in the light ion fusion program. The objective of PBFA II is to accelerate and focus upon an inertial confinement fusion (ICF) target a lithium beam with sufficient energy, power, and power density to perform ignition scaling experiments. The technologies used in PBFA II include: primary energy storage and compression with 6 MV, low-inductance Marx generators, pulse forming in water-insulated, water-dielectric lines with self-closing water switches, module synchronization using laser-triggered, 6 MV multistage gas switches, voltage addition in vacuum using self-magnetically-insulated biconic transmission lines, inductive energy storage and pulse compression using a fast-opening plasma erosion switch, beam formation using a magnetically-insulated ion diode, and space-charge and current-neutralized beam propagation to the target in a gas-filled cell. The first multimodule shot was on December 11, 1985.