1
|
Ivanov VV, Sotnikov VI, Kindel JM, Hakel P, Mancini RC, Astanovitskiy AL, Haboub A, Altemara SD, Shevelko AP, Kazakov ED, Sasorov PV. Implosion dynamics and x-ray generation in small-diameter wire-array Z pinches. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:056404. [PMID: 19518573 DOI: 10.1103/physreve.79.056404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2008] [Revised: 02/06/2009] [Indexed: 05/27/2023]
Abstract
It is known from experiments that the radiated x-ray energy appears to exceed the calculated implosion kinetic energy and Spitzer resistive heating [C. Deeney, Phys. Rev. A 44, 6762 (1991)] but possible mechanisms of the enhanced x-ray production are still being discussed. Enhanced plasma heating in small-diameter wire arrays with decreased calculated kinetic energy was investigated, and a review of experiments with cylindrical arrays of 1-16 mm in diameter on the 1 MA Zebra generator is presented in this paper. The implosion and x-ray generation in cylindrical wire arrays with different diameters were compared to find a transition from a regime where thermalization of the kinetic energy is the prevailing heating mechanism to regimes with other dominant mechanisms of plasma heating. Loads of 3-8 mm in diameter generate the highest x-ray power at the Zebra generator. The x-ray power falls in 1-2 mm loads which can be linked to the lower efficiency of plasma heating with the lack of kinetic energy. The electron temperature and density of the pinches also depend on the array diameter. In small-diameter arrays, 1-3 mm in diameter, ablating plasma accumulates in the inner volume much faster than in loads of 12-16 mm in diameter. Correlated bubblelike implosions were observed with multiframe shadowgraphy. Investigation of energy balance provides evidence for mechanisms of nonkinetic plasma heating in Z pinches. Formation and evolution of bright spots in Z pinches were studied with a time-gated pinhole camera. A comparison of x-ray images with shadowgrams shows that implosion bubbles can initiate bright spots in the pinch. Features of the implosions in small-diameter wire arrays are discussed to identify mechanisms of energy dissipation.
Collapse
Affiliation(s)
- V V Ivanov
- Department of Physics, University of Nevada, Reno, Nevada 89506, USA
| | | | | | | | | | | | | | | | | | | | | |
Collapse
|
2
|
Chittenden JP, Jennings CA. Development of instabilities in wire-array Z pinches. PHYSICAL REVIEW LETTERS 2008; 101:055005. [PMID: 18764402 DOI: 10.1103/physrevlett.101.055005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2008] [Indexed: 05/26/2023]
Abstract
3D resistive MHD simulations are used to show how the properties of the "fundamental" mode of modulated ablation in wire-array Z pinches, are consistent with the growth of a modified m=0-like instability. The modulation wavelength, structure, and evolution is found to be governed by the magnetic topology and is largely independent of the initial conditions. The perturbation amplitude as a function of wire number is shown to be consistent with experimental x-ray power scaling. Simulations of an array of helical wires show a substantial reduction in the amplitude of the instability.
Collapse
Affiliation(s)
- J P Chittenden
- Blackett Laboratory, Imperial College, London, United Kingdom
| | | |
Collapse
|
3
|
Mazevet S, Lambert F, Bottin F, Zérah G, Clérouin J. Ab initio molecular dynamics simulations of dense boron plasmas up to the semiclassical Thomas-Fermi regime. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:056404. [PMID: 17677179 DOI: 10.1103/physreve.75.056404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2006] [Indexed: 05/16/2023]
Abstract
We build an "all-electron" norm-conserving pseudopotential for boron which extends the use of ab initio molecular dynamics simulations up to 50 times the normal density rho0. This allows us to perform ab initio simulations of dense plasmas from the regime where quantum mechanical effects are important to the regime where semiclassical simulations based on the Thomas-Fermi approach are, by default, the only simulation method currently available. This study first allows one to establish, for the case of boron, the density regime from which the semiclassical Thomas-Fermi approach is legitimate and sufficient. It further brings forward various issues pertaining to the construction of pseudopotentials aimed at high-pressure studies.
Collapse
Affiliation(s)
- S Mazevet
- Département de Physique Théorique et Appliquée, CEA/DAM Ile-de-France, BP12, 91680 Bruyères-le-Châtel Cedex, France
| | | | | | | | | |
Collapse
|
4
|
Sarkisov GS, Rosenthal SE, Struve KW. Thermodynamical calculation of metal heating in nanosecond exploding wire and foil experiments. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2007; 78:043505. [PMID: 17477658 DOI: 10.1063/1.2712938] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
A method of thermodynamical calculation of thin metal wire heating during its electrical explosion is discussed. The technique is based on a calculation of Joule energy deposition taking into account the current wave form and the temperature dependence of the resistivity and heat capacity of the metal. Comparing the calculation to a set of exploding tungsten wire experiments demonstrates good agreement up to the time of melting. Good agreement is also demonstrated with resistive magnetohydrodynamics simulation. A similar thermodynamical calculation for Mo, Ti, Ni, Fe, Al, and Cu shows good agreement with experimental data. The thermodynamical technique is useful for verification of the voltage measurements in exploding wire experiments. This technique also shows good agreement with an exploding W foil experiment.
Collapse
|
5
|
Stygar WA, Cuneo ME, Vesey RA, Ives HC, Mazarakis MG, Chandler GA, Fehl DL, Leeper RJ, Matzen MK, McDaniel DH, McGurn JS, McKenney JL, Muron DJ, Olson CL, Porter JL, Ramirez JJ, Seamen JF, Speas CS, Spielman RB, Struve KW, Torres JA, Waisman EM, Wagoner TC, Gilliland TL. Theoretical z -pinch scaling relations for thermonuclear-fusion experiments. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:026404. [PMID: 16196715 DOI: 10.1103/physreve.72.026404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2004] [Revised: 03/07/2005] [Indexed: 05/04/2023]
Abstract
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.
Collapse
Affiliation(s)
- W A Stygar
- Sandia National Laboratories, Albuquerque, New Mexico 87185-1196, USA
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
6
|
Sarkisov GS, Rosenthal SE, Cochrane KR, Struve KW, Deeney C, McDaniel DH. Nanosecond electrical explosion of thin aluminum wires in a vacuum: experimental and computational investigations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:046404. [PMID: 15903791 DOI: 10.1103/physreve.71.046404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2004] [Revised: 08/31/2004] [Indexed: 05/02/2023]
Abstract
Experimental and computational investigations of nanosecond electrical explosion of a thin Al wire in vacuum are presented. We have demonstrated that increasing the current rate leads to increased energy deposited before voltage collapse. The experimental evidence for synchronization of the wire expansion and light emission with voltage collapse is presented. Hydrocarbons are indicated in optical spectra and their influence on breakdown physics is discussed. The radial velocity of low-density plasma reaches a value of approximately 100 km/s. The possibility of an over-critical phase transition due to high pressure is discussed. A one-dimensional magnetohydrodynamic (MHD) simulation shows good agreement with experimental data. The MHD simulation demonstrates separation of the exploding wire into a high-density cold core and a low-density hot corona as well as fast rejection of the current from the wire core to the corona during voltage collapse. Important features of the dynamics for the wire core and corona follow from the MHD simulation and are discussed.
Collapse
Affiliation(s)
- G S Sarkisov
- Ktech Corporation, Albuquerque, New Mexico 87123, USA.
| | | | | | | | | | | |
Collapse
|
7
|
Mazevet S, Desjarlais MP, Collins LA, Kress JD, Magee NH. Simulations of the optical properties of warm dense aluminum. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:016409. [PMID: 15697737 DOI: 10.1103/physreve.71.016409] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2004] [Indexed: 05/24/2023]
Abstract
Using quantum molecular dynamics simulations, we show that the optical properties of aluminum change drastically along the nonmetal metal transition observed experimentally. As the density increases and the many-body effects become important, the optical response gradually evolves from the one characteristic of an atomic fluid to the one of a simple metal. We show that quantum molecular dynamics combined with the Kubo-Greenwood formulation naturally embodies the two limits and provides a powerful tool to calculate and benchmark the optical properties of various systems as they evolve into the warm dense matter regime.
Collapse
Affiliation(s)
- S Mazevet
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | | | | | | | |
Collapse
|
8
|
Stygar WA, Ives HC, Fehl DL, Cuneo ME, Mazarakis MG, Bailey JE, Bennett GR, Bliss DE, Chandler GA, Leeper RJ, Matzen MK, McDaniel DH, McGurn JS, McKenney JL, Mix LP, Muron DJ, Porter JL, Ramirez JJ, Ruggles LE, Seamen JF, Simpson WW, Speas CS, Spielman RB, Struve KW, Torres JA, Vesey RA, Wagoner TC, Gilliland TL, Horry ML, Jobe DO, Lazier SE, Mills JA, Mulville TD, Pyle JH, Romero TM, Seamen JJ, Smelser RM. X-ray emission from z pinches at 10 7 A: current scaling, gap closure, and shot-to-shot fluctuations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:046403. [PMID: 15169102 DOI: 10.1103/physreve.69.046403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2003] [Indexed: 05/24/2023]
Abstract
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.
Collapse
Affiliation(s)
- W A Stygar
- Sandia National Laboratories, Albuquerque, New Mexico 87185-1196, USA
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Collapse
|
9
|
Lebedev SV, Beg FN, Bland SN, Chittenden JP, Dangor AE, Haines MG, Pikuz SA, Shelkovenko TA. Effect of core-corona plasma structure on seeding of instabilities in wire array Z pinches. PHYSICAL REVIEW LETTERS 2000; 85:98-101. [PMID: 10991168 DOI: 10.1103/physrevlett.85.98] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2000] [Indexed: 05/23/2023]
Abstract
We present the first measurements by x-ray radiography of the development of instabilities during the implosion phase of wire array Z pinches. The seeding of perturbations on the dense core of each wire is provided by nonuniform sweeping of the low-density coronal plasma from the cores by the global JxB force. The spatial scale of these perturbations ( approximately 0.5 mm for Al and approximately 0.25 mm for W) is determined by the size of the wire cores ( approximately 0.25 mm for Al and approximately 0.1 mm for W). A qualitative change in implosion dynamics, with transition to 0D-like trajectory, was observed in Al arrays when the ratio of interwire gap to wire core size was decreased to approximately 3.
Collapse
Affiliation(s)
- SV Lebedev
- The Blackett Laboratory, Imperial College, London, SW7 2BZ, United Kingdom
| | | | | | | | | | | | | | | |
Collapse
|