Session TO7: Magneto-Inertial Fusion II

Progress on Scaling the Sheared-Flow Stabilized Z-Pinch: The Fusion Z-Pinch Experiment "FuZE"

The sheared-flow-stabilized (SFS) Z-pinch ZaP experiment was constructed based on calculations [1] showing stabilization of the kink and sausage instabilities with sufficient flow shear. ZaP experimentally demonstrated production and sustainment of an SFS Z-pinch for a wide range of plasma parameters, with densities up to $n=5\times10^{22}$ m$^{-3}$ and a pinch radius of $a$=1~cm. [2-4] The follow-on ZaP-HD (high density) experiment demonstrated scaling of the SFS Z-pinch to 2-3x smaller radii and 10x higher densities than ZaP, with up to 1~keV temperatures. [5] Based on the successful results of ZaP and ZaP-HD, the Fusion Z-pinch Experiment (FuZE) project is experimentally and computationally studying scaling the plasma performance toward fusion conditions, with the target of a smaller radius, $a$=1 mm, and higher density, $n=2\times10^{24}$ m$^{-3}$. Initial FuZE experimental results show several hundred eV ion temperatures, with pinch currents of 100--200~kA and a few mm radius. 2D kinetic calculations show stabilization of instabilities at moderate sheared flows, and 3D kinetic calculations are in progress. 1. Shumlak PRL 1995 2. Shumlak PRL 2001 3. Golingo PoP 2005 4. Shumlak NF 2009 5. Shumlak PoP 2017   

A Reactor Development Scenario for the FuZE Sheared-Flow Stabilized Z-pinch

We present a conceptual design, scaling calculations, and development path for a pulsed fusion reactor based on a flow-stabilized Z-pinch. Experiments performed on the ZaP [1] and ZaP-HD [2] devices have largely demonstrated the basic physics of sheared-flow stabilization at pinch currents up to 100 kA. Initial experiments on the FuZE device [3], a high-power upgrade of ZaP, have achieved $\sim$20 usec of stability at pinch current 100-200 kA and pinch diameter $\sim$few mm for a pinch length of 50 cm. Scaling calculations based on a quasi-steady-state power balance show that extending stable duration to $\sim$100 usec at a pinch current of $\sim$1.5 MA and pinch length of 50 cm, results in a reactor plant Q$\sim$5. Future performance milestones are proposed for pinch currents of: 300 kA, where Te and Ti are calculated to exceed 1-2 keV; 700 kA, where DT fusion power would be expected to exceed pinch input power; and 1 MA, where fusion energy per pulse exceeds input energy per pulse. [1]U. Shumlak, et. al., Nucl. Fusion 49 (2009) 075039. [2]U. Shumlak, et. al., Phys. Plasmas 24 (2017) 055702. [3]B.A. Nelson, et. al., this meeting.   

Characterizing an octant of a spherically imploding plasma liner as an MIF driver

Spherically imploding plasma liners formed by merging supersonic plasma jets are a proposed compression driver for magneto-inertial fusion (MIF)\@. The Plasma Liner Experiment-ALPHA (PLX-$\alpha$) aims to demonstrate the formation of sub-fusion-scale plasma liners ($\sim 150$-kJ kinetic energy) via dozens of merging supersonic plasma jets (with initial ion density $\sim 10^{16}$~cm$^{-3}$, velocity $\approx$ 50~km/s, mass $\sim 1$~mg, and use of various gas species). In this talk, we summarize experimental findings on the formation of an octant of spherically imploding plasma liners by merging up to six plasma jets. Experimental data from gated fast-framing-cameras, survey and high-resolution visible spectrometers, and a multi-chord interferometer have been analyzed to assess (i) ion heating (and associated liner-Mach-number degradation) due to collisional shock formation between merging jets, and (ii) liner uniformity upon jet merging. These data are being used to benchmark code calculations, which will set requirements on the allowable shock heating and nonuniformity for scaled-up plasma liners to be an effective MIF compression driver. We also describe plans to field a $4\pi$ imploding plasma liner experiment.   

The PLX-$\alpha$ Plasma Guns: Progress and Plans

The ALPHA coaxial plasma guns are being developed to support a 60-gun scaling study of spherically imploding plasma liners as a standoff driver for plasma-jet-driven magneto-inertial fusion (PJMIF) [1]. Seven complete guns have been delivered to LANL with 6 guns currently undergoing simultaneous test firings on PLX. The guns are designed to operate over a range of parameters: 0.5-5.0 mg of Ar, Ne, N2, Kr, and Xe; 20-60 km/s; $\sim$ 2 $\times$ 10$^{16}$~cm$^{-3}$ muzzle density; and up to 7.5 kJ stored energy per gun. Each coaxial gun incorporates a fast dense gas injection and triggering system, a compact low-weight pfn with integral sparkgap switching, and a contoured coaxial gap to suppress the blow-by instability [2]. Optimizing parameter scans performed at HyperV have achieved : $\sim$4 mg at $>$50 km/s and length of $\sim$10 cm. Peak axial density 30 cm from the muzzle is $\sim 2 \times 10^{16}$ cm$^{-3}$. We will provide an overview of the experimental results, along with plans for further improvements in reliability, maintainability, fabricability, and plasma jet performance, with the latter focused on further improvements in the fast gas valve and the ignitors. [1] Hsu et al., IEEE Trans. Plasma Sci.~{\bf 40}, 1287 (2012). [2] Witherspoon et al., Rev. Sci. Instr. \textb   

Numerical Modeling of Plasma-Liner Formation and Implosion for PLX-{\$}$\backslash $alpha{\$}

Numerical simulations of spherically imploding plasma liners formed by merging hypersonic plasma jets have been performed using the FronTier and smooth particle hydrodynamics (SPH) codes in support of the PLX-{\$}$\backslash $alpha{\$} project. The physics includes radiation, Braginskii thermal conductivity and ion viscosity, and tabular EOS (LTE and non-LTE). Solid-angle-averaged and standard deviation of liner ram pressure and Mach number reveal variations in these properties during formation and implosion. Spherical-harmonic mode-number analysis of spherical slices of ram pressure at various radii and times provide a quantitative means to assess the evolution of liner non-uniformity. Simulations of 6 and 7 jets support near-term experiments, and synthetic spectra and line-integrated densities are compared with experimental data.   

Magnetothermodynamics: Measuring the equations of state in a relaxed MHD plasma for magneto-inertial fusion

The estimation of the equations of state (isothermal or adiabatic) for any set-up is necessary to envisage its behavior as the theoretical models and numerical simulations rely on them. In this talk, we will present compression experiments in which we generate parcels of magnetized, relaxed plasma (called Taylor states$^1$) and compress them in a closed volume. We call these experiments magnetothermodynamics. The compressed plasma parameters are measured in a compression volume and a PV diagram is produced which shows ion heating during plasma compression. The magnetohydrodynamic and the double adiabatic (i.e., Chew, Goldberger and Low) equations of state are tested under several experimental conditions. The results from these experiments show that the parallel component of double adiabatic equation of state fit our data best. The compression of this magnetized, relaxed plasma is being investigated as an eventual target for magneto-inertial fusion reactors. $^1$Gray \textit{et. al.}, Phys. Rev. Lett. 110, 085002 (2013)   

Acceleration of Taylor plumes on SSX for magneto-inertial fusion

We have added two pinch coils to the glass extension of the SSX plasma wind tunnel device in order to accelerate Taylor plumes to over $100~km/s$. We have characterized velocity ($40~km/s$), density ($0.4~\times 10^{16}~cm^{-3}$), proton temperature ($20~eV$), and magnetic field ($0.2~T$) of relaxed, unaccelerated helical Taylor states $[1]$. Our goal is to accelerate the Taylor states to over $100~km/s$ and compress to small volumes by stagnation. Compression by a factor of ten to increase both density and temperature will put the Taylor state in a suitable parameter regime as a magneto-inertial fusion target. One prototype pinch coil operates at $1~kJ$ ($1.3~\mu F, 40~kV$) and the other operates at $2~kJ$ ($3~\mu F, 40~kV$). Both have quarter-cycle rise times of less than $1~\mu s$. Results from both prototype units will be presented. [1] Gray, et al, PRL {\bf 110}, 085002 (2013).   

Instability control in a Staged Z-pinch, using an axial-magnetic field and target plasma

Experiments on Zebra at UNR, and COBRA at Cornell, show evidence of a uniform pinch by the inclusion of low-Z target plasma (H, or D) inside a hollow gas shell of high-Z (Ar, or Kr) liner plasma. Adding an axial magnetic field of 1 - 2 kG improves the pinch stability. Numerical simulation is conducted using the 2-1/2 D radiation-MHD code MACH2. During implosion, magnetosonic-type shock waves propagate radially inward at different speeds in the liner and target plasmas, producing a shock front at the liner - target interface and a conduction channel ahead of the liner that preheats the target. This secondary conduction channel remains stable throughout the compression, even as the outer surface of the liner becomes Rayleigh-Taylor (RT) unstable. An axial magnetic field reduces the growth of the RT instability and enhances the secondary conduction channel. And in some cases reverses the effects of the RT instability, resulting in a uniform pinch. Simulations reveal that $B_z$ field "piles-up" at the liner-target interface, instead of compressing uniformly over the entire volume. This scenario confines the target plasma in a magnetic well resulting in a high-$\beta$, stable plasma.   

Staged Z-pinch Experiments on Cobra and Zebra

A Staged Z-pinch (SZP), configured as a pre-magnetized, high-Z (Ar, or Kr) annular liner imploding onto a low-Z (H, or D) target, was tested on the Cornell University, Cobra Facility and the University of Nevada, Reno, Zebra Facility; each characterized similarly by a nominal 1-MA current and 100-ns risetime while possessing different diagnostic packages. XUV-fast imaging reveals that the SZP implosion dynamics is similar on both machines and that it is more stable with an axial (B$_z$) magnetic field, a target, or both, than without. On Zebra, where neutron production is possible, reproducible thermonuclear (DD) yields were recorded at levels in excess of 10$^9$/shot. Flux compression in the SZP is also expected to produce magnetic field intensities of the order of kilo-Tesla. Thus, the DD reaction produced tritions should also yield secondary DT neutrons. Indeed, secondaries are measured above the noise threshold at levels approaching 10$^6$/shot.   

Issues with Strong Compression of Plasma Target by Stabilized Imploding Liner

Strong compression (10:1 in radius) of an FRC by imploding liquid metal liners, stabilized against Rayleigh-Taylor modes, using different scalings for loss based on Bohm vs 100X classical diffusion rates, predict useful compressions with implosion times half the initial energy lifetime [1]. The elongation (length-to-diameter ratio) near peak compression needed to satisfy empirical stability criterion and also retain alpha-particles is about ten. The present paper extends these considerations to issues of the initial FRC, including stability conditions (S*/E) and allowable angular speeds. Furthermore, efficient recovery of the implosion energy and alpha-particle work, in order to reduce the necessary nuclear gain for an economical power reactor, is seen as an important element of the stabilized liner implosion concept for fusion. We describe recent progress in design and construction of the high energy-density prototype of a Stabilized Liner Compressor (SLC) leading to repetitive laboratory experiments to develop the plasma target. [1] P.J. Turchi, S.D. Frese, M.H. Frese, ``Stabilized Liner Compressor for Low-Cost Controlled Fusion at Megagauss Field-Levels,'' IEEE Trans. on Plasma Science, October 2017. *Supported by ARPA-E ALPHA Program   

Experimental investigation of adiabatic compression and heating using collision of an MHD-driven jet with a gas target cloud for magnetized target fusion

We are studying magnetized target fusion using an experimental method where an imploding liner compressing a plasma is simulated by a high-speed MHD-driven plasma jet colliding with a gas target cloud. This has the advantage of being non-destructive so orders of magnitude more shots are possible. Since the actual density and temperature are much more modest than fusion-relevant values, the goal is to determine the scaling of the increase in density and temperature when an actual experimental plasma is adiabatically compressed. Two new-developed diagnostics are operating and providing data. The first new diagnostic is a fiber-coupled interferometer which measures line-integrated electron density not only as a function of time, but also as a function of position along the jet. The second new diagnostic is laser Thomson scattering which measures electron density and temperature at the location where the jet collides with the cloud. These diagnostics show that when the jet collides with a target cloud the jet slows down substantially and both the electron density and temperature increase. The experimental measurements are being compared with 3D MHD and hybrid kinetic numerical simulations that model the actual experimental geometry.   

Cost Modeling and Design of Field-Reversed Configuration Fusion Power Plants

The Inductively Driven Liner (IDL) fusion concept uses the magnetically driven implosion of thin (0.5--1 mm) Aluminum hoops to magnetically compress a merged Field-Reversed Configuration (FRC) plasma to fusion conditions. Both the driver and the target have been studied experimentally and theoretically by researchers at Helion Energy, MSNW, and the University of Washington, demonstrating compression fields greater than 100 T and suitable fusion targets. In the presented study, a notional power plant facility using this approach will be described. In addition, a full cost study based on the LLNL Z-IFE and HYLIFE-II studies, the ARIES Tokamak concept, and RAND power plant studies will be described. Finally, the expected capital costs, development requirements, and LCOE for 50 and 500 MW power plants will be given. This analysis includes core FRC plant scaling, metallic liner recycling, radiation shielding, operations, and facilities capital requirements.   

MEMS-based, RF-driven, compact accelerators

Shrinking existing accelerators in size can reduce their cost by orders of magnitude. Furthermore, by using radio frequency (RF) technology and accelerating ions in several stages, the applied voltages can be kept low paving the way to new ion beam applications. We make use of the concept of a Multiple Electrostatic Quadrupole Array Linear Accelerator (MEQALAC) and have previously shown the implementation of its basic components using printed circuit boards, thereby reducing the size of earlier MEQALACs by an order of magnitude. We now demonstrate the combined integration of these components to form a basic accelerator structure, including an initial beam-matching section. In this presentation, we will discuss the results from the integrated multi-beam ion accelerator and also ion acceleration using RF voltages generated on-board. Furthermore, we will show results from Micro-Electro-Mechanical Systems (MEMS) fabricated focusing wafers, which can shrink the dimension of the system to the sub-mm regime and lead to cheaper fabrication. Based on these proof-of-concept results we outline a scaling path to high beam power for applications in plasma heating in magnetized target fusion and in neutral beam injectors for future Tokamaks.   

Beta > 1 Plasmas

I have suggested that fusion researchers should put more effort into the study of beta > 1 or wall confined plasmas. Magneto-Inertial Fusion and Magnetized Target Fusion projects at Los Alamos National Laboratory are recent examples of this sort of work. Unfortunately, theoretical studies of such systems may be employing overly optimistic models of the magnetic thermal insulation. One might well expect such systems to have stochastic field lines. If that is the case then we might want to employ turbulent thermal insulation as suggested in my papers: Current Science, pg 991, 1988 and Bull. Am. Phys. Soc., Nov. 4, 2009.