title: Theoretical z -pinch scaling relations for thermonuclear-fusion experiments.
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.
authors.affiliation: Sandia National Laboratories, Albuquerque, New Mexico 87185-1196, USA.
authors.forename: W A
authors.initials: WA
authors.lastname: Stygar
authors.forename: M E
authors.initials: ME
authors.lastname: Cuneo
authors.forename: R A
authors.initials: RA
authors.lastname: Vesey
authors.forename: H C
authors.initials: HC
authors.lastname: Ives
authors.forename: M G
authors.initials: MG
authors.lastname: Mazarakis
authors.forename: G A
authors.initials: GA
authors.lastname: Chandler
authors.forename: D L
authors.initials: DL
authors.lastname: Fehl
authors.forename: R J
authors.initials: RJ
authors.lastname: Leeper
authors.forename: M K
authors.initials: MK
authors.lastname: Matzen
authors.forename: D H
authors.initials: DH
authors.lastname: McDaniel
authors.forename: J S
authors.initials: JS
authors.lastname: McGurn
authors.forename: J L
authors.initials: JL
authors.lastname: McKenney
authors.forename: D J
authors.initials: DJ
authors.lastname: Muron
authors.forename: C L
authors.initials: CL
authors.lastname: Olson
authors.forename: J L
authors.initials: JL
authors.lastname: Porter
authors.forename: J J
authors.initials: JJ
authors.lastname: Ramirez
authors.forename: J F
authors.initials: JF
authors.lastname: Seamen
authors.forename: C S
authors.initials: CS
authors.lastname: Speas
authors.forename: R B
authors.initials: RB
authors.lastname: Spielman
authors.forename: K W
authors.initials: KW
authors.lastname: Struve
authors.forename: J A
authors.initials: JA
authors.lastname: Torres
authors.forename: E M
authors.initials: EM
authors.lastname: Waisman
authors.forename: T C
authors.initials: TC
authors.lastname: Wagoner
authors.forename: T L
authors.initials: TL
authors.lastname: Gilliland