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Formation, Compression, and Acceleration of Magnetized Plasmas
Abstract
Compression and acceleration of magnetized plasmas is relevant to fusion for two reasons. Certain types of magnetized plasmas can be compressed and accelerated without fluid instability growth. These are magnetized plasmas rings or compact toroids1,2. Because of their stability, they can be compressed and accelerated over meters of distance and several microseconds of time, enabling economic scaling to much higher energy operation. Other types of implosions and compressions, e.g., Z-pinches, are limited by instability growth3 to much shorter acceleration distances (a few cm) and times (less than 100 nanoseconds), making it very expensive to scale their operating energies to the fusion regime. An important second advantage of magnetized plasmas is that discussed by Lindemuth and Kirkpatrick in their magnetized target fusion (MTF) concept4. Reduced electron thermal conduction losses and increased alpha energy deposition result in reduced requirements of fuel density-radius product for achieving fusion ignition. In this paper, we discuss two experimental efforts at the Phillips Laboratory relevant to this topic. These are our Compact Toroid2,5,6,7 and Solid Liner/Working Fluid8,910,11 efforts. Though these efforts have potential fusion application, their present support is for the applications of intense X-ray generation and achieving high density and pressure in the laboratory, respectively.
This paper discusses some aspects of dense plasma focus (DPF) operation relevant to its extrapolation to hundreds of MJ energy storage. Experiments show, that the main fusion production mechanism is based on the plasma target-beam interaction i.e.: the pinch and the expanding column form hot and dense plasma target, that confines the hundred keV ion beams, produced during the column instability phase. Using a new compilation of neutron yield scaling with capacitor bank energies (Wo) it is expected that the scientific break-even will occur for Wo of a few hundreds of MJ, not less than Wo=50 MJ, assuming that plasma parameters will evolve in the same manner as for the existing DPF machines.
Strength of DPF research program lies in the fact that, it is based on two complementary and realistic lines of R&D actions. The first line of action considers two independent scaling tests of DPF performance at ten MJ energy level in Russia and USA. Both tests can use existing energy storages and chambers. The scaling tests will additionally demonstrate the operation of DPF in the insulator free version and the use of inductive storage. The second line of action (already implemented) is to use the DPFs, as intense and pulsed sources of neutrons, X-rays and ion beams. Selected examples of 100 kJ class DPF (and below) are shown to demonstrate the potentials of industrial applications and near-term payoffs.
In the worldwide controlled thermonuclear fusion research effort, ignition of a magnetically confined plasma is yet to be achieved. Consequently, it is not known whether a plasma's approach to ignition is associated with a change (degradation or enhancement) of the confinement of plasma energy. Knowledge of this, however, can have a significant impact on the design criteria (and thus cost) of the planned International Thermonuclear Experimental Reactor (ITER). Fast adiabatic compression for producing short-timescale ignited toroidal plasmas is proposed as a means to gain this knowledge using existing resources.
Research on forming, compressing, and accelerating milligram‐range compact toroids using a meter diameter, two‐stage, puffed gas, magnetic field embedded coaxial plasma gun is described. The compact toroids that are studied are similar to spheromaks, but they are threaded by an inner conductor. This research effort, named marauder (Magnetically Accelerated Ring to Achieve Ultra‐high Directed Energy and Radiation), is not a magnetic confinement fusion program like most spheromak efforts. Rather, the ultimate goal of the present program is to compress toroids to high mass density and magnetic field intensity, and to accelerate the toroids to high speed. There are a variety of applications for compressed, accelerated toroids including fast opening switches, x‐radiation production, radio frequency (rf) compression, as well as charge‐neutral ion beam and inertial confinement fusion studies. Experiments performed to date to form and accelerate toroids have been diagnosed with magnetic probe arrays, laser interferometry, time and space resolved optical spectroscopy, and fast photography. Parts of the experiment have been designed by, and experimental results are interpreted with, the help of two‐dimensional (2‐D), time‐dependent magnetohydrodynamic (MHD) numerical simulations. When not driven by a second discharge, the toroids relax to a Woltjer–Taylor equilibrium state that compares favorably to the results of 2‐D equilibrium calculations and to 2‐D time‐dependent MHD simulations. Current, voltage, and magnetic probe data from toroids that are driven by an acceleration discharge are compared to 2‐D MHD and to circuit solver/slug model predictions. Results suggest that compact toroids are formed in 7–15 μsec, and can be accelerated intact with material species the same as injected gas species and entrained mass ≥1/2 the injected mass.
Research on the formation of a hot hydrogen working fluid, which may be used in multiple concentric solid‐density liner implosions, is reported. In such implosions, an axisymmetric outer liner is driven by a multi‐megamp axial discharge, and a coaxial inner liner is driven by a working fluid contained between the liners. The fluid is shocklessly compressed to high pressure as the outer liner implodes around it. In the work reported here a 10 to 100 Torr pressure, hydrogen filled coaxial gun discharge was used to inject plasma into a diagnostic chamber simulating an interliner volume. Spectroscopically determined electron densities of between 1017 and 1018 cm-3 and electron temperatures in the 0.5–2.0 eV range were obtained with a fair degree of reproducibility and symmetry. Two‐dimensional, time‐dependent magnetohydrodyna‐ mic computer simulations of the working fluid formation experiment have been performed, and the computations suggest that the present experiment achieves electron number densities and temperatures at the lower extreme of these limits, and neutral densities ∼ 0.3–1.0 ×1019 cm-3. The simulations further suggest that the upper range, and beyond, can be achieved in a more energetic version of the present experiment.
First Page of the Article
We have magnetically driven a tapered-thickness spherical aluminum shell implosion with a 12.5 MA axial discharge. The initially 4 cm radius, 0.1 to 0.2 cm thick, +/- 45o latitude shell was imploded along conical electrodes. The implosion time was approximately 15 musec. Radiography indicated substantial agreement with 2D-MHD calculations. Such calculations for this experiment predict final inner-surface implosion velocity of 2.5 to 3 cm /musec, peak pressure of 56 Mbar, and peak density of 16.8 g /cm3 ( >6 times solid density). The principal experimental result is a demonstration of the feasibility of electromagnetic-driven spherical liner implosions in the cm /musec regime.
form only given, as follows. A compact toroid (CT) formation experiment is discussed. The device has coaxial electrode diameters of 0.9 m (inner) and 1.25 m (outer) and an electrode length of ~1.2 m, including an expansion drift section. The CT is formed by a 0.1-0.2-T initial radial magnetic field embedded coaxial puff gas discharge. The gas puff is injected with an array of 60 pulsed solenoid driven fast valves. The formation discharge is driven by a 108-μF, 40-100-kV, 86-540-kJ, 2-5-MA capacitor discharge with ~20-nH initial total discharge inductance. The hardware includes transmission line connections for a Shiva Star (1300-μF, up to 120-kV, 0.4-MJ) capacitor bank driven acceleration discharge. Experimental measurements include current and voltage; azimuthal, radial, and axial magnetic field at numerous locations; fast photography and optical spectroscopy; and microwave, CO2 laser, and He-Ne laser interferometry. Auxiliary experiments include Penning ionization gauge, pressure probe, and breakdown gas trigger diagnostics of gas injection, and Hall probe measurements of magnetic field injection
Electromagnetic implosions of shaped cylindrical aluminum liners that remain at solid density are discussed. The approximate liner parameters have an initial radius of 3 to 4 cm, are 4 cm in height, and are nearly 0.1 cm thick. The liners are driven by the Shiva Star 1300-μf capacitor bank at an 84-kV charging voltage and an nearly 30-nH total initial inductance (including implosion load). The discharge current travels along the length of the liner and rises to 14 MA in nearly 8 μs. The implosion time is nearly 12 μs. Diagnostics include inductive current and capacitive voltage probes, magnetic probes, and radiography. Both right-circular cylinder and conical liner implosion data are displayed and discussed. Radiography indicates implosion behavior substantially consistent with two-dimensional magnetohydrodynamic calculations, which predict inner surface implosion velocities exceeding 20 km/s, and compressed density of two to three times solid density. Less growth of perturbations is evident for the conical liner (nearly 1% thickness tolerance) than for the right-circular cylindrical liner (nearly 3% thickness tolerance). 12 refs., 8 figs.
The spontaneous generation of reversed fields in toroidal plasmas is shown to be a consequence of relaxation under constraints. With perfect conductivity a topological constraint exists for each field line and the final state is not unique. With small departures from perfect conductivity, topological constraints are relaxed and the final state becomes unique. The onset of the reversed field and other features of this model agree well with observations on ZETA.
Described here is a collective accelerator based on magnetically confined plasma rings. Typical rings which have been produced and which have 10-kJ magnetic energy and 0.1 to 10 C of nuclei are predicted to be accelerated magnetically to 10 MJ or higher in acceleration lengths of 100 m. Applications are discussed of current drive in tokamak fusion reactors, fueling and heating magnetic fusion reactors, transuranic element synthesis, and, for focused rings, a high-energy density driver for inertial confinement fusion.
Vacuum inductive-store, plasma flow switch-driven implosion experiments have been performed using the Shiva Star capacitor bank (1300 {mu}f, 3 nH, 120 kV, 9.4 MJ). A coaxial plasma gun arrangement is employed to store magnetic energy in the vacuum volume upstream of a dynamic discharge during the 3- to 4-{mu}s rise of current from the capacitor bank. Motion of the discharge off the end of the inner conductor of the gun releases this energy to implode a coaxial cylindrical foil. The implosion loads are 5-cm-radius, 2-cm-long, 200 to 400 {mu}g/cm{sup 2} cylinders of aluminum or aluminized Formvar. With 5 MJ stored initially in the capacitor bank, more than 9 MA are delivered to the implosion load with a rise time of nearly 200 ns. The subsequent implosion results in a radiation output of 0.95 MJ at a power exceeding 5 TW (assuming isotropic emission). Experimental results and related two-dimensional magnetohydrodynamic simulations are discussed. 10 refs., 12 figs.
Experiments to form, compress, and accelerate compact toroids are described. A 1-m-diam, two-stage, puffed gas, magnetic field embedded coaxial plasma gun is used. Emphasis is on conical compression. Discharges were in the several mega-ampere, few microsecond rise time range. Magnetic probe data suggest that l/(r{center_dot}{delta}r) compression of the toroid field is achieved, consistent with theoretical prediction. The magnetic field pulse and electron density pulse due to the compact toroid correlate in space and time. The compact toroid species is the injected gas species and precedes electrode plasma by several microseconds. The poloidal magnetic field precedes the azimuthal magnetic field. The time of arrival of the axial magnetic field compared with the axial position is consistent with the mean current axial position trajectory obtained from inductance growth. 8 refs., 6 figs.
Compression by a spherical solid liner of a gold target surrounded by a hydrogen plasma is simulated. Two‐dimensional simulations that treat only a subset of the physics included in the one‐dimensional code were performed in an attempt to assess multidimensional effects. A one‐dimensional numerical code has been developed to study the effects of thermal radiation and conduction. Results of pressure, density, and energy deposited for different initial plasma conditions are presented and discussed. Results from both one‐ and two‐dimensional codes show that the average target density at peak compression is 39–43 g/cm3, using the SHIVA Star facility at 90 kV discharge.
The dynamics of imploding foil plasmas is considered using first‐order theory to model the implosion and to investigate the effects of magnetohydrodynamic instabilities on the structure of the plasma sheath. The effects of the acceleration‐produced magnetohydrodynamic (MHD) Rayleigh‐Taylor instability and a wall‐associated instability are studied for a variety of plasma implosion times for several pulsed power drivers. The basic physics of these instabilities is identified and models are developed to explain both linear and nonlinear behavior. These models are compared with the results of detailed two‐dimensional magnetohydrodynamic simulations. Expressions for linear Rayleigh‐Taylor growth are developed showing its dependence on driving current, plasma conductivity, and density gradient scale length. A nonlinear saturation model, based on magnetic field diffusion, is developed. The model for a wall instability involves the interaction of the plasma sheath with the electrode wall and the material ablated from the electrode. The growth of this instability is shown to be limited by field diffusion. Comparison with two‐dimensional simulations has been excellent.
Experiments to form and accelerate compact toroid (CT) plasmas
have been performed on the 0.4-MJ Shiva Star fast capacitor bank at
Phillips Laboratory. Theoretical investigations of employing a CT as a
very fast opening switch are reported. A particular axisymmetric,
geometrically complex switch design is studied with the help of
2-1/2-dimensional magnetohydrodynamic computer simulations. This design,
called a magnetically-confined-plasma opening switch (McPOS),
accumulates magnetic energy in an inductive store. Because of its
intrinsic stability, the switch can conduct current for ten or more
microseconds and can open in less than 100 ns-substantially less than
the risetime of the capacitively produced electric current. A long
conduction time compact torus plasma opening switch
The formation of a high density working fluid for solid liner implosions
- F M Lehr
- J H Degnan
- D Dietz
- S E Englert
- T J Englert
- J D Graham
- J J Havranek
- T W Hussey
- J M Messerschmitt
- C A Outten
- R E Peterkin
- N F Roderick
- U Shumlak
- P J Turchi
High velocity compact torus injector for the TEXT tokamak
- M R Brown
- P K Loewenhardt
- J Yee
- D R Derkits
- P M Bellan
- MR Brown