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.

[1]  R. G. Adams,et al.  Demonstration of radiation symmetry control for inertial confinement fusion in double Z-pinch hohlraums. , 2003, Physical review letters.

[2]  John M. Creedon,et al.  Magnetic cutoff in high‐current diodes , 1977 .

[3]  Computational investigation of single mode vs multimode Rayleigh–Taylor seeding in Z-pinch implosions , 1997 .

[4]  S. Wilks,et al.  Z pinch driven inertial confinement fusion target physics research at Sandia National Laboratories , 1998 .

[5]  T. Nash,et al.  Systematic trends in x-ray emission characteristics of variable-wire-number, fixed-mass, aluminum-array, Z-pinch implosions , 1999 .

[6]  Gordon Andrew Chandler,et al.  Development and Characterization of a Z-Pinch Driven Hohlraum High-Yield Inertial Confinement Fusion Target Concept , 2001 .

[7]  G. M. Oleinik,et al.  Prolonged plasma production at current-driven implosion of wire arrays on Angara-5-1 facility , 2002 .

[8]  R. Bowers,et al.  Characterization of energy flow and instability development in two-dimensional simulations of hollow z pinches , 1998 .

[9]  R. G. Adams,et al.  Radiation symmetry control for inertial confinement fusion capsule implosions in double Z-pinch hohlraums on Z , 2003 .

[10]  R. G. Adams,et al.  Symmetric inertial confinement fusion capsule implosions in a high-yield-scale double-Z-pinch-driven hohlraum on Z , 2003 .

[11]  Norman Rostoker,et al.  Equilibria for Magnetic Insulation , 1973 .

[12]  J. J. Ramirez,et al.  X-ray emission from z pinches at 10 7 A: current scaling, gap closure, and shot-to-shot fluctuations. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  D. S. Bailey,et al.  High yield inertial confinement fusion target design for a z-pinch-driven hohlraum , 1999 .

[14]  L. P. Mix,et al.  Obtaining absolute spatial flux measurements with a time-resolved pinhole camera , 1999 .

[15]  G. O. Allshouse,et al.  Numerical simulations of annular wire-array z-pinches in (x,y), (r,θ), and (r,z) geometries , 1998 .

[16]  J. Porter,et al.  Power enhancement by increasing the initial array radius and wire number of tungsten Z pinches , 1997 .

[17]  J. A. Lott,et al.  Flashover of a vacuum-insulator interface: A statistical model , 2004 .

[18]  Farhat Beg,et al.  One-, two-, and three-dimensional modeling of the different phases of wire array Z-pinch evolution , 2001 .

[19]  G. R. Bennett,et al.  Double Z-pinch hohlraum drive with excellent temperature balance for symmetric inertial confinement fusion capsule implosions. , 2002, Physical review letters.

[20]  G. Chandler,et al.  Radiation science using Z-pinch x rays , 2002 .

[21]  Mosher,et al.  Improved Symmetry Greatly Increases X-Ray Power from Wire-Array Z-Pinches. , 1996, Physical review letters.

[22]  G. M. Oleinik,et al.  Polarity effect for exploding wires in a vacuum. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  G. Chandler,et al.  Optimization of power density by decreasing the length of tungsten wire array Z pinches , 1998 .

[24]  D. Bliss,et al.  Mass-profile and instability-growth measurements for 300-wire Z-pinch implosions driven by 14-18 MA. , 2004, Physical review letters.

[25]  Gordon Andrew Chandler,et al.  Measurement of radiation symmetry in Z-pinch-driven hohlraums , 2001 .

[26]  A. R. Mingaleev,et al.  Density measurements in exploding wire-initiated plasmas using tungsten wires , 1999 .

[27]  R. Spielman,et al.  Two‐dimensional radiation‐magnetohydrodynamic simulations of SATURN imploding Z pinches , 1996 .

[28]  J. Chittenden,et al.  Plasma Formation and Implosion Structure in Wire Array Z Pinches , 1999 .

[29]  G. O. Allshouse,et al.  Wire number doubling in high-wire-number regime increases Z-accelerator X-ray power , 1998 .

[30]  O. Landen,et al.  The physics basis for ignition using indirect-drive targets on the National Ignition Facility , 2004 .

[31]  S. E. Rosenthal,et al.  A simple theory of magnetic insulation from basic physical considerations , 1983 .

[32]  W. Stygar,et al.  Analytic models of high-temperature hohlraums. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  McCall,et al.  Fiber ablation in the solid deuterium Z pinch. , 1989, Physical review letters.

[34]  D. Ryutov,et al.  The physics of fast Z pinches , 1998 .

[35]  Characterization of diagnostic hole-closure in Z-pinch driven hohlraums , 2000 .

[36]  J. Porter,et al.  X-ray spectral power measurements utilizing the diffraction pattern of a slit , 1999 .

[37]  J. M. Foster,et al.  SUPERSONIC JET AND SHOCK INTERACTIONS , 2001 .

[38]  Mordecai D. Rosen,et al.  The science applications of the high-energy density plasmas created on the Nova laser , 1996 .

[39]  M. Basko,et al.  IGNITION ENERGY SCALING OF INERTIAL CONFINEMENT FUSION TARGETS , 1998 .

[40]  G. Chandler,et al.  Tungsten wire-array Z-pinch experiments at 200 TW and 2 MJ , 1998 .

[41]  G. M. Oleinik,et al.  Dynamics of Heterogeneous Liners with Prolonged Plasma Creation , 2001 .

[42]  C. Coverdale,et al.  Optimal wire-number range for high x-ray power in long-implosion-time aluminum Z pinches. , 2002, Physical review letters.

[43]  Implosion dynamics of long-pulse wire array Z pinches , 2000 .

[44]  R. Bowers,et al.  Two‐dimensional modeling of magnetically driven Rayleigh–Taylor instabilities in cylindrical Z pinches , 1996 .

[45]  K. H. Kwek,et al.  Effect of discrete wires on the implosion dynamics of wire array Z pinches , 2001 .

[46]  M. Cuneo,et al.  Equilibrium flow structures and scaling of implosion trajectories in wire array Z pinches , 2004 .

[47]  R. G. Adams,et al.  Symmetric inertial-confinement-fusion-capsule implosions in a double-z-pinch-driven hohlraum. , 2002, Physical review letters.

[48]  E. Yadlowsky,et al.  Evidence for precursor plasma formation resulting from heterogeneous current channels in wire array loads , 1996 .

[49]  M. Cuneo,et al.  Zero-dimensional energetics scaling models for z-pinch-driven hohlraums , 2001 .

[50]  Gordon Andrew Chandler,et al.  Soft x-ray measurements of z-pinch-driven vacuum hohlraums , 1999 .

[51]  Bell,et al.  Plasma formation in metallic wire Z pinches , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[52]  G. R. Bennett,et al.  Characteristics and scaling of tungsten-wire-array z -pinch implosion dynamics at 20 MA. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  R. Lemke,et al.  Wire array implosion characteristics from determination of load inductance on the Z pulsed-power accelerator , 2004 .

[54]  D. Youngs,et al.  Numerical simulation of turbulent mixing by Rayleigh-Taylor instability , 1984 .

[55]  R. Olson.  Target Physics Scaling for Z-Pinch Inertial Fusion Energy , 2005 .

[56]  Haines,et al.  Effect of core-corona plasma structure on seeding of instabilities in wire array Z pinches , 2000, Physical review letters.

[57]  D. Youngs,et al.  Three-dimensional numerical simulation of turbulent mixing by Rayleigh-Taylor instability , 1991 .

[58]  B. M. Marder,et al.  Theory of Wire Number Scaling in Wire-Array Z Pinches , 1999 .

[59]  John Lindl,et al.  Ignition scaling laws and their application to capsule design , 2000 .