Increased Ion Temperature and Neutron Yield Observed in Magnetized Indirectly Driven D_{2}-Filled Capsule Implosions on the National Ignition Facility

The application of an external 26 Tesla axial magnetic field to a D_{2} gas-filled capsule indirectly driven on the National Ignition Facility is observed to increase the ion temperature by 40% and the neutron yield by a factor of 3.2 in a hot spot with areal density and temperature approaching what is required for fusion ignition [1]. The improvements are determined from energy spectral measurements of the 2.45 MeV neutrons from the D(d,n)^{3}He reaction, and the compressed central core B field is estimated to be ∼4.9  kT using the 14.1 MeV secondary neutrons from the D(T,n)^{4}He reactions. The experiments use a 30 kV pulsed-power system to deliver a ∼3  μs current pulse to a solenoidal coil wrapped around a novel high-electrical-resistivity AuTa_{4} hohlraum. Radiation magnetohydrodynamic simulations are consistent with the experiment.

Optimization of current waveform tailoring for magnetically driven isentropic compression experiments

The Thor pulsed power generator is being developed at Sandia National Laboratories. The design consists of up to 288 decoupled and transit time isolated capacitor-switch units, called "bricks," that can be individually triggered to achieve a high degree of pulse tailoring for magnetically driven isentropic compression experiments (ICE) [D. B. Reisman et al., Phys. Rev. Spec. Top.-Accel. Beams 18, 090401 (2015)]. The connecting transmission lines are impedance matched to the bricks, allowing the capacitor energy to be efficiently delivered to an ICE strip-line load with peak pressures of over 100 GPa. Thor will drive experiments to explore equation of state, material strength, and phase transition properties of a wide variety of materials. We present an optimization process for producing tailored current pulses, a requirement for many material studies, on the Thor generator. This technique, which is unique to the novel "current-adder" architecture used by Thor, entirely avoids the iterative use of complex circuit models to converge to the desired electrical pulse. We begin with magnetohydrodynamic simulations for a given material to determine its time dependent pressure and thus the desired strip-line load current and voltage. Because the bricks are connected to a central power flow section through transit-time isolated coaxial cables of constant impedance, the brick forward-going pulses are independent of each other. We observe that the desired equivalent forward-going current driving the pulse must be equal to the sum of the individual brick forward-going currents. We find a set of optimal brick delay times by requiring that the L2 norm of the difference between the brick-sum current and the desired forward-going current be a minimum. We describe the optimization procedure for the Thor design and show results for various materials of interest.

Understanding fuel magnetization and mix using secondary nuclear reactions in magneto-inertial fusion

Magnetizing the fuel in inertial confinement fusion relaxes ignition requirements by reducing thermal conductivity and changing the physics of burn product confinement. Diagnosing the level of fuel magnetization during burn is critical to understanding target performance in magneto-inertial fusion (MIF) implosions. In pure deuterium fusion plasma, 1.01 MeV tritons are emitted during deuterium-deuterium fusion and can undergo secondary deuterium-tritium reactions before exiting the fuel. Increasing the fuel magnetization elongates the path lengths through the fuel of some of the tritons, enhancing their probability of reaction. Based on this feature, a method to diagnose fuel magnetization using the ratio of overall deuterium-tritium to deuterium-deuterium neutron yields is developed. Analysis of anisotropies in the secondary neutron energy spectra further constrain the measurement. Secondary reactions also are shown to provide an upper bound for the volumetric fuel-pusher mix in MIF. The analysis is applied to recent MIF experiments [M. R. Gomez et al., Phys. Rev. Lett. 113, 155003 (2014)] on the Z Pulsed Power Facility, indicating that significant magnetic confinement of charged burn products was achieved and suggesting a relatively low-mix environment. Both of these are essential features of future ignition-scale MIF designs.

Experimental demonstration of fusion-relevant conditions in magnetized liner inertial fusion

This Letter presents results from the first fully integrated experiments testing the magnetized liner inertial fusion concept [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)], in which a cylinder of deuterium gas with a preimposed 10 Taxial magnetic field is heated by Z beamlet, a 2.5 kJ, 1 TW laser, and magnetically imploded by a 19 MA, 100 ns rise time current on the Z facility. Despite a predicted peak implosion velocity of only 70 km = s, the fuel reaches a stagnation temperature of approximately 3 keV, with T(e) ≈ T(i), and produces up to 2 x 10(12) thermonuclear deuterium-deuterium neutrons. X-ray emission indicates a hot fuel region with full width at half maximum ranging from 60 to 120 μm over a 6 mm height and lasting approximately 2 ns. Greater than 10(10) secondary deuterium-tritium neutrons were observed, indicating significant fuel magnetization given that the estimated radial areal density of the plasma is only 2 mg = cm(2).

Observations of modified three-dimensional instability structure for imploding z-pinch liners that are premagnetized with an axial field

Novel experimental data are reported that reveal helical instability formation on imploding z-pinch liners that are premagnetized with an axial field. Such instabilities differ dramatically from the mostly azimuthally symmetric instabilities that form on unmagnetized liners. The helical structure persists at nearly constant pitch as the liner implodes. This is surprising since, at the liner surface, the azimuthal drive field presumably dwarfs the axial field for all but the earliest stages of the experiment. These fundamentally 3D results provide a unique and challenging test for 3D-magnetohydrodynamics simulations.

Penetrating radiography of imploding and stagnating beryllium liners on the Z accelerator

The implosions of initially solid beryllium liners (tubes) have been imaged with penetrating radiography through to stagnation. These novel radiographic data reveal a high degree of azimuthal correlation in the evolving magneto-Rayleigh-Taylor structure at times just prior to (and during) stagnation, providing stringent constraints on the simulation tools used by the broader high energy density physics and inertial confinement fusion communities. To emphasize this point, comparisons to 2D and 3D radiation magnetohydrodynamics simulations are also presented. Both agreement and substantial disagreement have been found, depending on how the liner's initial outer surface finish was modeled. The various models tested, and the physical implications of these models are discussed. These comparisons exemplify the importance of the experimental data obtained.

Measurements of magneto-Rayleigh-Taylor instability growth during the implosion of initially solid Al tubes driven by the 20-MA, 100-ns Z facility

The first controlled experiments measuring the growth of the magneto-Rayleigh-Taylor instability in fast (∼100  ns) Z-pinch plasmas are reported. Sinusoidal perturbations on the surface of an initially solid Al tube (liner) with wavelengths of 25-400  μm were used to seed the instability. Radiographs with 15  μm resolution captured the evolution of the outer liner surface. Comparisons with numerical radiation magnetohydrodynamic simulations show remarkably good agreement down to 50  μm wavelengths.

Planar wire-array Z-pinch implosion dynamics and X-ray scaling at multiple-MA drive currents for a compact multisource hohlraum configuration

An indirect drive configuration is proposed wherein multiple compact Z-pinch x-ray sources surround a secondary hohlraum. Planar compact wire arrays allow reduced primary hohlraum surface area compared to cylindrical loads. Implosions of planar arrays are studied at up to 15 TW x-ray power on Saturn with radiated yields exceeding the calculated kinetic energy, suggesting other heating paths. X-ray power and yield scaling studied from 1-6 MA motivates viewfactor modeling of four 6-MA planar arrays producing 90 eV radiation temperature in a secondary hohlraum.

Fully kinetic particle-in-cell simulations of a deuterium gas puff z pinch

We present the first fully kinetic, collisional, and electromagnetic simulations of the complete time evolution of a deuterium gas puff z pinch. Recent experiments with 15-MA current pinches have suggested that the dominant neutron-production mechanism is thermonuclear. We observe distinct differences between the kinetic and magnetohydrodynamic simulations in the pinch evolution with the kinetic simulations producing both thermonuclear and beam-target neutrons. The kinetic approach demonstrated in this Letter represents a viable alternative for performing future plasma physics calculations.

Effects of mass ablation on the scaling of X-ray power with current in wire-array Z pinches

X-ray production by imploding wire-array Z pinches is studied using radiation magnetohydrodynamics simulation. It is found that the density distribution created by ablating wire material influences both x-ray power production, and how the peak power scales with applied current. For a given array there is an optimum ablation rate that maximizes the peak x-ray power, and produces the strongest scaling of peak power with peak current. This work is consistent with trends in wire-array Z pinch x-ray power scaling experiments on the Z accelerator.

Radiation energetics of ICF-relevant wire-array Z pinches

Short-implosion-time 20-mm diameter, 300-wire tungsten arrays maintain high peak x-ray powers despite a reduction in peak current from 19 to 13 MA. The main radiation pulse on tests with a 1-mm on-axis rod may be explained by the observable j x B work done during the implosion, but bare-axis tests require sub-mm convergence of the magnetic field not seen except perhaps in >1 keV emission. The data include the first measurement of the imploding mass density profile of a wire-array Z pinch that further constrains simulation models.

Wire initiation critical for radiation symmetry in z-pinch-driven dynamic hohlraums

Axial symmetry in x-ray radiation of wire-array z pinches is important for the creation of dynamic hohlraums used to compress inertial-confinement-fusion capsules. We present the first evidence that this symmetry is directly correlated with the magnitude of the negative radial electric field along the wire surface. This field (in turn) is inferred to control the initial energy deposition into the wire cores, as well as any current shorting to the return conductor.

Demonstration of radiation pulse shaping with nested-tungsten-wire-array pinches for high-yield inertial confinement fusion

Nested wire-array pinches are shown to generate soft x-ray radiation pulse shapes required for three-shock isentropic compression and hot-spot ignition of high-yield inertial confinement fusion capsules. We demonstrate a reproducible and tunable foot pulse (first shock) produced by interaction of the outer and inner arrays. A first-step pulse (second shock) is produced by inner array collision with a central CH2 foam target. Stagnation of the inner array at the axis produces the third shock. Capsules optimized for several of these shapes produce 290-900 MJ fusion yields in 1D simulations.

Theoretical z -pinch scaling relations for thermonuclear-fusion experiments

We have developed wire-array z -pinch scaling relations for plasma-physics and inertial-confinement-fusion (ICF) experiments. The relations can be applied to the design of z -pinch accelerators for high-fusion-yield (approximately 0.4 GJ/shot) and inertial-fusion-energy (approximately 3 GJ/shot) research. We find that (delta(a)/delta(RT)) proportional (m/l)1/4 (Rgamma)(-1/2), where delta(a) is the imploding-sheath thickness of a wire-ablation-dominated pinch, delta(RT) is the sheath thickness of a Rayleigh-Taylor-dominated pinch, m is the total wire-array mass, l is the axial length of the array, R is the initial array radius, and gamma is a dimensionless functional of the shape of the current pulse that drives the pinch implosion. When the product Rgamma is held constant the sheath thickness is, at sufficiently large values of m/l, determined primarily by wire ablation. For an ablation-dominated pinch, we estimate that the peak radiated x-ray power P(r) proportional (I/tau(i))(3/2)Rlphigamma, where I is the peak pinch current, tau(i) is the pinch implosion time, and phi is a dimensionless functional of the current-pulse shape. This scaling relation is consistent with experiment when 13 MA < or = I < or = 20 MA, 93 ns < or = tau(i) < or = 169 ns, 10 mm < or = R < or = 20 mm, 10 mm < or = l < or = 20 mm, and 2.0 mg/cm < or = m/l < or = 7.3 mg/cm. Assuming an ablation-dominated pinch and that Rlphigamma is held constant, we find that the x-ray-power efficiency eta(x) congruent to P(r)/P(a) of a coupled pinch-accelerator system is proportional to (tau(i)P(r)(7/9 ))(-1), where P(a) is the peak accelerator power. The pinch current and accelerator power required to achieve a given value of P(r) are proportional to tau(i), and the requisite accelerator energy E(a) is proportional to tau2(i). These results suggest that the performance of an ablation-dominated pinch, and the efficiency of a coupled pinch-accelerator system, can be improved substantially by decreasing the implosion time tau(i). For an accelerator coupled to a double-pinch-driven hohlraum that drives the implosion of an ICF fuel capsule, we find that the accelerator power and energy required to achieve high-yield fusion scale as tau(i)0.36 and tau(i)1.36, respectively. Thus the accelerator requirements decrease as the implosion time is decreased. However, the x-ray-power and thermonuclear-yield efficiencies of such a coupled system increase with tau(i). We also find that increasing the anode-cathode gap of the pinch from 2 to 4 mm increases the requisite values of P(a) and E(a) by as much as a factor of 2.

Direct experimental evidence for current-transfer mode operation of nested tungsten wire arrays at 16-19 MA

Nested tungsten wire arrays (20-mm on 12-mm diam.) are shown for the first time to operate in a current-transfer mode at 16-19 MA, even for azimuthal interwire gaps of 0.2 mm that are the smallest typically used for any array experiment. After current transfer, the inner wire array shows discrete wire ablation and implosion characteristics identical to that of a single array, such as axially nonuniform ablation, delayed acceleration, and trailing mass and current. The presence of trailing mass from the outer and the inner arrays may play a role in determining nested array performance.

Characteristics and scaling of tungsten-wire-array z -pinch implosion dynamics at 20 MA

We present observations for 20-MA wire-array z pinches of an extended wire ablation period of 57%+/-3% of the stagnation time of the array and non-thin-shell implosion trajectories. These experiments were performed with 20-mm-diam wire arrays used for the double- z -pinch inertial confinement fusion experiments [M. E. Cuneo, Phys. Rev. Lett. 88, 215004 (2002)] on the Z accelerator [R. B. Spielman, Phys. Plasmas 5, 2105 (1998)]. This array has the smallest wire-wire gaps typically used at 20 MA (209 microm ). The extended ablation period for this array indicates that two-dimensional (r-z) thin-shell implosion models that implicitly assume wire ablation and wire-to-wire merger into a shell on a rapid time scale compared to wire acceleration are fundamentally incorrect or incomplete for high-wire-number, massive (>2 mg/cm) , single, tungsten wire arrays. In contrast to earlier work where the wire array accelerated from its initial position at approximately 80% of the stagnation time, our results show that very late acceleration is not a universal aspect of wire array implosions. We also varied the ablation period between 46%+/-2% and 71%+/-3% of the stagnation time, for the first time, by scaling the array diameter between 40 mm (at a wire-wire gap of 524 mum ) and 12 mm (at a wire-wire gap of 209 microm ), at a constant stagnation time of 100+/-6 ns . The deviation of the wire-array trajectory from that of a thin shell scales inversely with the ablation rate per unit mass: f(m) proportional[dm(ablate)/dt]/m(array). The convergence ratio of the effective position of the current at peak x-ray power is approximately 3.6+/-0.6:1 , much less than the > or = 10:1 typically inferred from x-ray pinhole camera measurements of the brightest emitting regions on axis, at peak x-ray power. The trailing mass at the array edge early in the implosion appears to produce wings on the pinch mass profile at stagnation that reduces the rate of compression of the pinch. The observation of precursor pinch formation, trailing mass, and trailing current indicates that all the mass and current do not assemble simultaneously on axis. Precursor and trailing implosions appear to impact the efficiency of the conversion of current (driver energy) to x rays. An instability with the character of an m = 0 sausage grows rapidly on axis at stagnation, during the rise time of pinch power. Just after peak power, a mild m = 1 kink instability of the pinch occurs which is correlated with the higher compression ratio of the pinch after peak power and the decrease of the power pulse. Understanding these three-dimensional, discrete-wire implosion characteristics is critical in order to efficiently scale wire arrays to higher currents and powers for fusion applications.

X-ray emission from z pinches at 10 7 A: current scaling, gap closure, and shot-to-shot fluctuations

We have measured the x-ray power and energy radiated by a tungsten-wire-array z pinch as a function of the peak pinch current and the width of the anode-cathode gap at the base of the pinch. The measurements were performed at 13- and 19-MA currents and 1-, 2-, 3-, and 4-mm gaps. The wire material, number of wires, wire-array diameter, wire-array length, wire-array-electrode design, normalized-pinch-current time history, implosion time, and diagnostic package were held constant for the experiments. To keep the implosion time constant, the mass of the array was increased as I2 (i.e., the diameter of each wire was increased as I), where I is the peak pinch current. At 19 MA, the mass of the 300-wire 20-mm-diam 10-mm-length array was 5.9 mg. For the configuration studied, we find that to eliminate the effects of gap closure on the radiated energy, the width of the gap must be increased approximately as I. For shots unaffected by gap closure, we find that the peak radiated x-ray power P(r) proportional to I1.24+/-0.18, the total radiated x-ray energy E(r) proportional to I1.73+/-0.18, the x-ray-power rise time tau(r) proportional to I0.39+/-0.34, and the x-ray-power pulse width tau(w) proportional to demonstrate that the internal energy and radiative opacity of the pinch are not responsible for the observed subquadratic power scaling. Heuristic wire-ablation arguments suggest that quadratic power scaling will be achieved if the implosion time tau(i) is scaled as I(-1/3). The measured 1sigma shot-to-shot fluctuations in P(r), E(r), tau(r), tau(w), and tau(i) are approximately 12%, 9%, 26%, 9%, and 2%, respectively, assuming that the fluctuations are independent of I. These variations are for one-half of the pinch. If the half observed radiates in a manner that is statistically independent of the other half, the variations are a factor of 2(1/2) less for the entire pinch. We calculate the effect that shot-to-shot fluctuations of a single pinch would have on the shot-success probability of the double-pinch inertial-confinement-fusion driver proposed by Hammer et al. [Phys. Plasmas 6, 2129 (1999)]. We find that on a given shot, the probability that two independent pinches would radiate the same peak power to within a factor of 1+/-alpha (where 0< or =alpha<<1) is equal to erf(alpha/2sigma), where sigma is the 1sigma fractional variation of the peak power radiated by a single pinch. Assuming alpha must be < or =7% to achieve adequate odd-Legendre-mode radiation symmetry for thermonuclear-fusion experiments, sigma must be <3% for the shot-success probability to be > or =90%. The observed (12/2(1/2))%=8.5% fluctuation in P(r) would provide adequate symmetry on 44% of the shots. We propose that three-dimensional radiative-magnetohydrodynamic simulations be performed to quantify the sensitivity of the x-ray emission to various initial conditions, and to determine whether an imploding z pinch is a spatiotemporal chaotic system.

Analytic electrical-conductivity tensor of a nondegenerate Lorentz plasma

We have developed explicit quantum-mechanical expressions for the conductivity and resistivity tensors of a Lorentz plasma in a magnetic field. The expressions are based on a solution to the Boltzmann equation that is exact when the electric field is weak, the electron-Fermi-degeneracy parameter Theta>>1, and the electron-ion Coulomb-coupling parameter Gamma/Z<<1. (Gamma is the ion-ion coupling parameter and Z is the ion charge state.) Assuming a screened 1/r electron-ion scattering potential, we calculate the Coulomb logarithm in the second Born approximation. The ratio of the term obtained in the second approximation to that obtained in the first is used to define the parameter regime over which the calculation is valid. We find that the accuracy of the approximation is determined by Gamma/Z and not simply the temperature, and that a quantum-mechanical description can be required at temperatures orders of magnitude less than assumed by Spitzer [Physics of Fully Ionized Gases (Wiley, New York, 1962)]. When the magnetic field B=0, the conductivity is identical to the Spitzer result except the Coulomb logarithm ln Lambda(1)=(ln chi(1)-1 / 2)+[(2Ze(2)/lambdam(e)v(2)(e1))(ln chi(1)-ln 2(4/3))], where chi(1) identical with 2m(e)v(e1)lambda/ variant Planck's over 2pi, m(e) is the electron mass, v(e1) identical with (7k(B)T/m(e))(1/2), k(B) is the Boltzmann constant, T is the temperature, lambda is the screening length, variant Planck's over 2pi is Planck's constant divided by 2pi, and e is the absolute value of the electron charge. When the plasma Debye length lambda(D) is greater than the ion-sphere radius a, we assume lambda=lambda(D); otherwise we set lambda=a. The B=0 conductivity is consistent with measurements when Z greater, similar 1, Theta greater, similar 2, and Gamma/Z less, similar 1, and in this parameter regime appears to be more accurate than previous analytic models. The minimum value of ln Lambda(1) when Z> or =1, Theta> or =2, and Gamma/Z< or =1 is 1.9. The expression obtained for the resistivity tensor (B not equal 0) predicts that eta( perpendicular )/eta( parallel ) (where eta( perpendicular ) and eta( parallel ) are the resistivities perpendicular and parallel to the magnetic field) can be as much as 40% less than previous analytic calculations. The results are applied to an idealized 17-MA z pinch at stagnation.

Double Z-pinch hohlraum drive with excellent temperature balance for symmetric inertial confinement fusion capsule implosions

A double Z pinch driving a cylindrical secondary hohlraum from each end has been developed which can indirectly drive intertial confinement fusion capsule implosions with time-averaged radiation fields uniform to 2%-4%. 2D time-dependent view factor and 2D radiation hydrodynamic simulations using the measured primary hohlraum temperatures show that capsule convergence ratios of at least 10 with average distortions from sphericity of <Delta r>/r<or=30% are possible on the Z accelerator and may meet radiation symmetry requirements for scaling to fusion yields of >200 MJ.

Analytic models of high-temperature hohlraums

A unified set of high-temperature-hohlraum models has been developed. For a simple hohlraum, P(S)=[A(S)+(1-alpha(W))A(W)+A(H)]sigmaT(4)(R)+(4Vsigma/c)(dT(4)(R)/dt), where P(S) is the total power radiated by the source, A(S) is the source area, A(W) is the area of the cavity wall excluding the source and holes in the wall, A(H) is the area of the holes, sigma is the Stefan-Boltzmann constant, T(R) is the radiation brightness temperature, V is the hohlraum volume, and c is the speed of light. The wall albedo alpha(W) identical with(T(W)/T(R))(4) where T(W) is the brightness temperature of area A(W). The net power radiated by the source P(N)=P(S)-A(S)sigmaT(4)(R), which suggests that for laser-driven hohlraums the conversion efficiency eta(CE) be defined as P(N)/P(Laser). The characteristic time required to change T(4)(R) in response to a change in P(N) is 4V/c[(1-alpha(W))A(W)+A(H)]. Using this model, T(R), alpha(W), and eta(CE) can be expressed in terms of quantities directly measurable in a hohlraum experiment. For a steady-state hohlraum that encloses a convex capsule, P(N)=[(1-alpha(W))A(W)+A(H)+[(1-alpha(C))A(C)(A(S)+alpha(W)A(W))/A(T)]]sigmaT(4)(RC), where alpha(C) is the capsule albedo, A(C) is the capsule area, A(T) identical with(A(S)+A(W)+A(H)), and T(RC) is the brightness temperature of the radiation that drives the capsule. According to this relation, the capsule-coupling efficiency of the baseline National Ignition Facility hohlraum is 15-23 % higher than predicted by previous analytic expressions. A model of a hohlraum that encloses a z pinch is also presented.