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Annihilation model of the Tormac sheath

Description: A one-dimensional, steady state fluid model is developed to describe the boundary layer between plasma and magnetic field that occurs in the Tormac sheath. Similar systems which may be treatable by the same model are tokamaks with divertors and reversed field mirrors. The model includes transport across the magnetic field as well as mirror losses along the field, the latter being represented as annihilation terms in the one-dimensional equations. The model equations are derived from the two-dimensional, time dependent hierarchy of equations generated by taking velocity moments of the kinetic equation including collisions.
Date: February 1, 1979
Creator: Hammer, J.H.
Partner: UNT Libraries Government Documents Department

Reconnection in Spheromak formation and sustainment

Description: The Spheromak is a magnetic confinement device that is being explored in both the US and Japanese fusion programs. It is a member of the Compact Torus family of magnetic structures characterized by a set of closed, nested toroidal flux surfaces but without any coils, transformer cores, etc. protruding through the hole in the torus. The Speromak is closely elated to the Reversed Field Pinch (RFP) in that most of the magnetic field is produced by plasma currents flowing along the magnetic field lines (a near force free field) rather than by external coils. The Spheromak has magnetic field components of comparable strength in both the toroidal (azimuthal) and poloidal (in the plane perpendicular to the azimuthal unit vector) directions. The large internal magnetic energy in the Spheromak makes it rich in magnetohydrodynamic phenomena and reconnection, in particular, plays an important role in the formation, resistive decay and instability processes.
Date: December 12, 1983
Creator: Hammer, J.H.
Partner: UNT Libraries Government Documents Department

Mass streams for spacecraft propulsion and energy generation

Description: A speculative propulsion concept is presented, based on accelerating a spacecraft by impact of a stream of matter in relative motion with respect to the spacecraft. To accelerate the stream to the needed velocity the stream mass is contained in a transit vehicle, launched at low velocity and hence low energy cost, and then sent on a trajectory with near encounters of the planets for gravitational assist. The mass arrives at Earth or wherever the propellant is needed at much higher velocity and kinetic energy, where it is released into an extended stream suitable for propulsion. The stream, moving at a relative velocity in the range of 10 to 30km/s, should be capable of both high thrust and high specific impulse. Means of limiting the transverse expansion of the stream during release and for the {approx}1000 seconds duration of impact are a critical requirement for practicality of the concept. The scheme could potentially lead to a virtually unlimited energy source. One can imagine using a portion of one stream to launch another, larger payload on a similar trajectory. This creates, in effect, an energy amplifier extracting energy from the orbital motions of the planets. The gain of the energy amplifier is only limited by the capacity to prepare mass in transit vehicles.
Date: August 31, 2005
Creator: Hammer, J H
Partner: UNT Libraries Government Documents Department

Analytic Expressions for Optimal ICF Hohlraum Wall Density and Wall Loss

Description: Solutions to the radiation diffusion equation predict the absorbed energy (''wall loss'') within an inertial confinement fusion (ICF) hohlraum. Comparing supersonic vs. subsonic solutions suggests that a high Z metallic foam as hohlraum wall material will reduce hydrodynamic losses, and hence, net absorbed energy by {approx}20%. We derive an analytic expression for the optimal density (for any given drive temperature and pulse-length) that will achieve this reduction factor and which agrees well with numerical simulations. This approach can reduce the cost of a reactor driver. Radiation heat waves, or Marshak waves, play an important role in energy transport and in the energy balance of laser, z-pinch and heavy ion beam hohlraums for ICF and high energy density physics experiments. In these experiments, a power source, e.g. a laser, delivers energy to the interior of a high Z cavity that is converted to x-rays. Typically, most of the energy is absorbed in a thin, diffusively heated layer on the hohlraum interior surface, and re-emission from the heated layer sets the radiation temperature T achieved in the hohlraum. In our recent paper, (henceforward referred to as HR) we developed an analytic theory of Marshak waves via a perturbation theory using a small parameter {var_epsilon} = {beta}/(4 + {alpha}) where the internal energy varies as T{sup {beta}} and the opacity varies as T{sup -{alpha}}. A consistent theory was built up order-by-order in {var_epsilon}, with the benefits of good accuracy and order-by-order energy conservation. We first derived analytic solutions for supersonic Marshak waves, which remarkably allowed for arbitrary time variation of the surface temperature. We then solved the full set of subsonic equations, though specialized to the case that the surface temperature varies as t{sup k}, where self-similar solutions can be found. Our solutions compared very well with exact analytic solutions (for the specialized ...
Date: May 25, 2004
Creator: Rosen, M D & Hammer, J H
Partner: UNT Libraries Government Documents Department

Bent Marshak Waves

Description: Radiation driven heat waves (Marshak Waves) are ubiquitous in astrophysics and terrestrial laser driven high energy density plasma physics (HEDP) experiments. Generally, the equations describing Marshak waves are so nonlinear, that solutions involving more than one spatial dimension require simulation. However, in this paper we show how one may analytically solve the problem of the two-dimensional nonlinear evolution of a Marshak wave, bounded by lossy walls, using an asymptotic expansion in a parameter related to the wall albedo and a simplification of the heat front equation of motion. Three parameters determine the nonlinear evolution, a modified Markshak diffusion constant, a smallness parameter related to the wall albedo, and the spacing of the walls. The final nonlinear solution shows that the Marshak wave will be both slowed and bent by the non-ideal boundary. In the limit of a perfect boundary, the solution recovers the original diffusion-like solution of Marshak. The analytic solution will be compared to a limited set of simulation results and experimental data.
Date: October 11, 2005
Creator: Hurricane, O A & Hammer, J H
Partner: UNT Libraries Government Documents Department

Stability Of Plasma Configurations During Compression

Description: Magnetized Target Fusion (MTF) efforts are based on calculations showing that the addition of a closed magnetic field reduces the driver pressure and rise time requirements for inertial confinement fusion by reducing thermal conductivity. Instabilities that result in convective bulk transport at the Alphen time scale are of particular concern since they are much faster than the implosion time. Such instabilities may occur during compression due to, for example, an increase in the plasma-magnetic pressure ratio {beta} or, in the case of a rotating plasma, spin-up due to angular momentum conservation. Details depend on the magnetic field topology and compression geometry. A hard core z pinch with purely azimuthal magnetic field can theoretically be made that relaxes into a wall supported diffuse profile satisfying the Kadomtsev criterion for the stability of m = 0 modes, which is theoretically preserved during cylindrical outer wall compression. The center conductor radius and current must also be large enough to keep the {beta} below stability limits to stabilize modes with m > 0. The stability of m > 0 modes actually improves during compression. A disadvantage of this geometry, though, is plasma contact with the solid boundaries. In addition to the risk of high Z impurity contamination during the (turbulent) relaxation process, contact thereafter can cause plasma pressure near the outer surface to drop, violating the Kadomtsev criterion locally. The resultant m = 0 instability can then convect impurities inward. Also, the center conductor (which is not part of the Kadomtsev profile) can go m = 0 unstable, convecting impurities outward. One way to mitigate impurity convection is to instead use a Woltjer-Taylor minimum magnetic energy configuration (spheromak). The sheared magnetic field inhibits convection, and the need for the center conductor is eliminated. The plasma, however, would likely still have to be wall supported ...
Date: October 27, 2006
Creator: Ruden, E L & Hammer, J H
Partner: UNT Libraries Government Documents Department

Sound velocity and elastic moduli in $alpha$-plutonium at pressures to 50 KBAR

Description: The elastic moduli, bulk modulus, and shear modulus were measured in polycrystalline $alpha$-plutonium at pressures to 50 Kbar. An ultrasonic technique enabled measurement of both longitudinal and shear wave velocities in a girdled-piston high pressure cell. The average pressure derivatives were 14.3 and 4.3 m/s/kbar for the longitudinal and shear velocities, respectively. Bulk and shear moduli were calculated from the sound velocity data. The average pressure derivatives for the moduli were 14 and 3.5, respectively. Poisson's ratio was calculated directly from the ratio of longitudinal and shear velocities and increased from 0.17 at atmospheric pressure to 0.28 at 50 kbar. (auth)
Date: January 1, 1974
Creator: Merz, M.D.; Hammer, J.H. & Kjarmo, H.E.
Partner: UNT Libraries Government Documents Department

Analytical and numerical calculations of field-reversed theta-pinch equilibria based on a generalized Hill's vortex model

Description: We have been investigating methods for numerically extending the analytic solutions of field reversed theta pinch equilibria so that the results may be used in various stability and dynamics studies. We have used generalizations of elliptical Hill's vortex equilibria which accomodate separatrices with more rectangular shapes and which allow plasma to exist outside the separatrix. Although the equilibria are specified analytically inside the plasma surface, numerical techniques are required to generate the solution in the vacuum region. Two computer codes have been used in sequence. The first determines a set of external coils and their currents so that they match the known coil field inside the plasma. Then, given this coil field, we compute the contribution from the plasma currents to the fields in the vacuum region.
Date: October 1, 1981
Creator: Anderson, D.V.; Hammer, J.H. & Barnes, D.C.
Partner: UNT Libraries Government Documents Department

Recent results of studies of acceleration of compact toroids

Description: The observed gross stability and self-contained structure of compact toroids (CT's) give rise to the possibility, unique among magnetically confined plasmas, of translating CT's from their point of origin over distances many times their own length. This feature has led us to consider magnetic acceleration of CT's to directed kinetic energies much greater than their stored magnetic and thermal energies. A CT accelerator falls in the very broad gap between traditional particle accelerators at one extreme, which are limited in the number of particles per bunch by electrostatic repulsive forces, and mass accelerators such as rail guns at the other extreme, which accelerate many particles but are forced by the stress limitations of solids to far smaller accelerations. A typical CT has about a Coulomb of particles, weighs 10 micrograms and can be accelerated by magnetic forces of several tons, leading to an acceleration on the order of 10/sup 11/ gravities.
Date: March 2, 1984
Creator: Hammer, J.H.; Hartman, C.W. & Eddleman, J.
Partner: UNT Libraries Government Documents Department

Acceleration of compact torus plasma rings in a coaxial rail-gun

Description: We discuss here theoretical studies of magnetic acceleration of Compact Torus plasma rings in a coaxial, rail-gun accelerator. The rings are formed using a magnetized coaxial plasma gun and are accelerated by injection of B/sub theta/ flux from an accelerator bank. After acceleration, the rings enter a focusing cone where the ring is decelerated and reduced in radius. As the ring radius decreases, the ring magnetic energy increases until it equals the entering kinetic energy and the ring stagnates. Scaling laws and numerical calculations of acceleration using a O-D numerical code are presented. 2-D, MHD simulations are shown which demonstrate ring formation, acceleration, and focusing. Finally, 3-D calculations are discussed which determine the ideal MHD stability of the accelerated ring.
Date: May 16, 1985
Creator: Hartman, C.W.; Hammer, J.H. & Eddleman, J.
Partner: UNT Libraries Government Documents Department

High efficiency ICF driver employing magnetically confined plasma rings

Description: We discuss the possibility of achieving energy, power and power density necessary for ICF by magnetically accelerating plasma confined by a compact torus (CT) field configuration. The CT, which consists of a dipole (poloidal) field and imbedded toroidal field formed by force-free, plasma current, is compressed and accelerated between coaxial electrodes by B/sub THETA/ fields as in a coaxial railgun. Compression and acceleration over several meters by a 9.4 MJ capacitor bank is predicted to give a 5.7 cm radius, 0.001 gm CT 5 MJ kinetic energy (10/sup 7/ m/sec). Transport and focussing several meters by a disposable lithium pipe across the containment vessel is predicted to bring 4.8 MJ into the pellet region in 0.5 cm/sup 2/ area in 0.3 ns. The high efficiency (approx.50%) and high energy delivery of the CT accelerator could lead to low cost, few hundred MW power plants that are economically viable.
Date: March 4, 1985
Creator: Meeker, D.J.; Hammer, J.H. & Hartman, C.W.
Partner: UNT Libraries Government Documents Department

Linear pinch driven by a moving compact torus

Description: In principle, a Z-pinch of sufficiently large aspect ratio can provide arbitrarily high magnetic field intensity for the confinement of plasma. In practice, however, achievable field intensities and timescales are limited by parasitic inductances, pulse driver power, current, voltage, and voltage standoff of nearby insulating surfaces or surrounding gas. Further, instabilities may dominate to prevent high fields (kink mode) or enhance them (sausage mode) but in a nonuniform and uncontrollable way. In this paper we discuss an approach to producing a high-field-intensity pinch using a moving compact torus. The moving torus can serve as a very high power driver and may be used to compress a pre-established pinch field, switch on an accelerating pinch field, or may itself be reconfigured to form an intense pinch. In any case, the high energy, high energy density, and high velocity possible with an accelerated compact torus can provide extremely high power to overcome, by a number of orders of magnitude, the limitations to pinch formation described earlier. In this paper we will consider in detail pinches formed by reconfiguration of the compact torus.
Date: April 25, 1984
Creator: Hartman, C.W.; Hammer, J.H. & Eddleman, J.L.
Partner: UNT Libraries Government Documents Department

High-power RF compressor

Description: We discuss here the possibility of rapidly compressing resonant RF fields in a coaxial cavity with a moving, magnetically confined plasma ring. The possibility of accelerating a plasma ring and various acceleration configurations was discussed earlier. Since the ring velocity can be high, compression to high energy density and high power can be achieved before significant resistive loss or vaporization of the cavity walls occurs. An example is given of compressing 10/sup 5/ J of lambda = 15 cm stored energy to 2 x 10/sup 6/ J of lambda = 1.0 cm RF energy with the energy released in 3 nsec for a maximum power of 6 x 10/sup 14/ W. A proof of principle plasma ring accelerator experiment could provide a significant test by compressing 125 joules of 14 cm RF to 1.25 kJ of 1.4 cm radiation, released in 5 nsec for a very respectable peak power of 2.5 x 10/sup 11/ W.
Date: March 30, 1984
Creator: Hartman, C.W.; Hammer, J.H. & Meeker, D.
Partner: UNT Libraries Government Documents Department

Charged particle driver for ICF using an accelerated, focused compact torus

Description: We report the status of evaluating an accelerated and focused compact torus as a driver for ICF. We are studying the acceleration and focusing aspects experimentally in the RACE facility, a recently completed ring generator coupled to a 260 kJ acceleration bank. Compact torus and ICF target interaction is being investigated with PIC codes and LASNEX, a 2D magneto-hydrodynamics code. Final conditions required of the CT are discussed as well as coupling issues such as superthermal electron production. We conclude with an economic evaluation of a few 100 MW reactor driven by a compact torus. 9 refs., 5 figs., 1 tab.
Date: June 1, 1986
Creator: Meeker, D.J.; Hammer, J.H. & Hartman, C.W.
Partner: UNT Libraries Government Documents Department

Studies of accelerated compact toruses

Description: In an earlier publication we considered acceleration of plasma rings (Compact Torus). Several possible accelerator configurations were suggested and the possibility of focusing the accelerated rings was discussed. In this paper we consider one scheme, acceleration of a ring between coaxial electrodes by a B/sub theta/ field as in a coaxial rail-gun. If the electrodes are conical, a ring accelerated towards the apex of the cone undergoes self-similar compression (focusing) during acceleration. Because the allowable acceleration force, F/sub a/ = kappaU/sub m//R where (kappa < 1), increases as R/sup -2/, the accelerating distance for conical electrodes is considerably shortened over that required for coaxial electrodes. In either case, however, since the accelerating flux can expand as the ring moves, most of the accelerating field energy can be converted into kinetic energy of the ring leading to high efficiency.
Date: January 4, 1983
Creator: Hartman, C.W.; Eddleman, J. & Hammer, J.H.
Partner: UNT Libraries Government Documents Department

Acceleration of magnetized plasma rings

Description: One scheme is considered, acceleration of a ring between coaxial electrodes by a B/sub theta/ field as in a coaxial rail-gun. If the electrodes are conical, a ring accelerated towards the apex of the cone undergoes self-similar compression (focussing) during acceleration. Because the allowable acceleration force F/sub a/ = kappa U/sub m//R (kappa < 1) increases as R/sup -2/, the accelerating distance for conical electrodes is considerably shortened over that required for coaxial electrodes. In either case however, since the accelerating flux can expand as the ring moves, most of the accelerating field energy can be converted into kinetic energy of the ring leading to high efficiency.
Date: November 16, 1982
Creator: Hartman, D.; Eddleman, J. & Hammer, J.H.
Partner: UNT Libraries Government Documents Department

Measurements and Calculations of Halfraum Radiation Drives at the Omega Laser

Description: Thin walled gold halfraums are a common choice for producing x-ray drives in experiments at high-power laser facilities. At the Omega Laser, we use 10 kJ of laser energy in a two-pulse sequence to generate halfraum drive temperatures of 160-190 eV for {approx}3ns. This type of drive is well characterized and reproducible, with characterization of the drive radiation temperature typically performed using the Dante diagnostic. Additionally, calibrated Photoconductive Diamond Detectors (PCDs) are used to measure the drive when it is desirable to utilize the Dante elsewhere in the experiment. Measurements of halfraum drives from both Dante and PCDs are compared with calculations, with good agreement. This agreement lends the calculations a predictive capability in designing further experiments utilizing halfraum drives.
Date: January 6, 2005
Creator: MacLaren, S A; Back, C A & Hammer, J H
Partner: UNT Libraries Government Documents Department

2D radiation-magnetohydrodynamic simulations of SATURN imploding Z-pinches

Description: Z-pinch implosions driven by the SATURN device at Sandia National Laboratory are modeled with a 2D radiation magnetohydrodynamic (MHD) code, showing strong growth of magneto-Rayleigh Taylor (MRT) instability. Modeling of the linear and nonlinear development of MRT modes predicts growth of bubble-spike structures that increase the time span of stagnation and the resulting x-ray pulse width. Radiation is important in the pinch dynamics keeping the sheath relatively cool during the run-in and releasing most of the stagnation energy. The calculations give x-ray pulse widths and magnitudes in reasonable agreement with experiments, but predict a radiating region that is too dense and radially localized at stagnation. We also consider peaked initial density profiles with constant imploding sheath velocity that should reduce MRT instability and improve performance. 2D krypton simulations show an output x-ray power > 80 TW for the peaked profile.
Date: November 6, 1995
Creator: Hammer, J.H.; Eddleman, J.L. & Springer, P.T.
Partner: UNT Libraries Government Documents Department

O-d energetics scaling models for Z-pinch-driven hohlraums

Description: Wire array Z-pinches on the Z accelerator provide the most intense laboratory source of soft x-rays in the world. The unique combination of a highly-Planckian radiation source with high x-ray production efficiency (15% wall plug), large x-ray powers and energies ( &gt;150 TW, {ge}1 MJ in 7 ns), large characteristic hohlraum volumes (0.5 to &gt;10 cm{sup 3}), and long pulse-lengths (5 to 20 ns) may make Z-pinches a good match to the requirements for driving high-yield scale ICF capsules with adequate radiation symmetry and margin. The Z-pinch driven hohlraum approach of Hammer and Porter [Phys.Plasmas, 6, 2129(1999)] may provide a conservative and robust solution to the requirements for high yield, and is currently being studied on the Z accelerator. This paper describes a multiple region, 0-d hohlraum energetic model for Z-pinch driven hohlraums in four configurations. The authors observe consistency between the models and the measured x-ray powers and hohlraum wall temperatures to within {+-}20% in flux, for the four configurations.
Date: June 8, 2000
Partner: UNT Libraries Government Documents Department

Linear stability of an accelerated wire array

Description: The linear stability of an array of a large number of thin wires is considered. The wires form a cylindrical surface which is accelerated towards the axis under the action of a current excited in the array by an external source. General equations governing stability of this system are derived and a complete classification of all the modes present in such a system is presented. In agreement with an earlier analysis by Felber and Rostoker, it is shown that there exist two types of modes: medial modes, in which the wires experience deformation in the rz plane, and lateral modes, in which only a purely azimuthal deformation is present. For a given axial wave number k, the maximum growth rate for medial perturbations corresponds to a mode in which all the wires move �in phase� (an analog of an axisymmetric mode for a continuous cylindrical shell), whereas for the lateral perturbations the maximum growth rate corresponds to the opposite displacements of the neighboring wires. Numerical analysis of a dispersion relation for a broad range of modes is presented: Some limiting cases are discussed. In particular, it is shown that a traditional k�� scaling holds until surprisingly high wave numbers, even exceeding the inverse inter- wire distance. In the limit of long-wavelength perturbations, a model of a continuous shell becomes valid; the presence of the wires manifests itself in this model by a strong anisotropy of electrical conductivity, high along the wires and vanishing across the wires. The resulting modes differ considerably from the modes of a thin perfectly conducting shell. In particular, a new mode of �zonal flows� is identified.
Date: October 15, 1998
Creator: Hammer, J H & Ryutov, D D
Partner: UNT Libraries Government Documents Department

Results from the RACE (Ring ACceleration Experiment) Compact Torus Acceleration Experiment

Description: RACE (Ring ACceleration Experiment) is a proof-of-principle experiment aimed at demonstrating acceleration of magnetically confined compact torus plasma rings to directed kinetic energies well in excess of their magnetic and thermal energies. In the course of the first year of operation the following have been observed: successful formation of rings in the RACE geometry; acceleration of rings with large forces, F/sub accelerate/ approx.F/sub equilibrium/ without apparent degradation of the ring structure; peak velocities of approx. =2.5 x 10/sup 8/ cm/sec; acceleration efficiency of >30% at speeds of 1.5 x 10/sup 8/ cm/sec inferred from trajectory and capacitor bank data; kinetic to magnetic energy ratios approx.10 were observed. Experiments in the near future will be aimed at confirmation of the mass/energy measurements by calorimetry and direct density measurements.
Date: June 1, 1987
Creator: Hammer, J.H.; Hartman, C.W.; Eddleman, J.L. & Kusse, B.
Partner: UNT Libraries Government Documents Department

Compact Torus plasma ring accelerator: a new type driver for inertial confinement fusion

Description: We discuss the acceleration of magnetically-confined plasma rings to provide a driver for ICF. The acceleration of plasma rings is predicted to be efficient and following focusing, to generate ion-bombardment power in the range 10/sup 15/ to 10/sup 16/ W/cm/sup 2/ at a total deposition energy of multimegajoules. The simplicity of plasma ring accelerator suggests that a 5 MJ (on target) driver would cost in the range 1 to 5 $/joule. First experimental tests of the accelerator are described.
Date: August 22, 1986
Creator: Hartman, C.W.; Eddleman, J.L.; Hammer, J.H. & Meeker, D.L.
Partner: UNT Libraries Government Documents Department