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The spherical pinch: Generalized scaling laws and experimental verification of the stability of imploding shock waves in spherical geometry

Published online by Cambridge University Press:  09 March 2009

D. P. Singh ,
M. A. Harith ,
V. Palleschi ,
G. Tropiano ,
M. Vaselli ,
N. Salingaros  and
E. Panarella
D. P. Singh
Affiliation:
Istituto di Fisica Atomica e Molecolare del C.N.R., Via del Giardino, 7, 56100 Pisa, Italy
M. A. Harith
Affiliation:
Istituto di Fisica Atomica e Molecolare del C.N.R., Via del Giardino, 7, 56100 Pisa, Italy
V. Palleschi
Affiliation:
Istituto di Fisica Atomica e Molecolare del C.N.R., Via del Giardino, 7, 56100 Pisa, Italy
G. Tropiano
Affiliation:
Istituto di Fisica Atomica e Molecolare del C.N.R., Via del Giardino, 7, 56100 Pisa, Italy
M. Vaselli
Affiliation:
Istituto di Fisica Atomica e Molecolare del C.N.R., Via del Giardino, 7, 56100 Pisa, Italy
N. Salingaros
Affiliation:
Division of Mathematics, The University of Texas, San Antonio, TX 78285U.S.A.
E. Panarella
Affiliation:
Advanced Laser and Fusion Technology, Inc., P.O. Box 8763, Alta Vista Terminal, Ottawa, Canada K1G 3J1
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Extract

The Spherical Pinch (SP) is a particular variation of the inertial confinement scheme, in that the two criteria required for plasma fusion breakeven condition, namely the attainment of a sufficiently high plasma temperature and of a product nτ in excess of 1014 cm-3. sec, are satisfied through two separate mechanisms. The advantage of this approach is that the scaling laws for breakeven are easier to satisfy than in the classical inertial confinement scheme. The first derivation of the scaling laws for spherical pinch experiments (Panarella & Savic 1983; Panarella 1987) was obtained under the simplifying assumption of an infinitely small central plasma in a sphere reaching the required high temperature for fusion, and of an undefined time delay Δt between the creation of such central plasma and the launching of the peripheral shock waves used to contain the central plasma. The analysis reported in this paper removes these assumptions and derives scaling laws which are generalized in their parameters, in that they explicitly contain the radius Rp of the central plasma and the time delay Δt.

Type
Research Article
Information
Laser and Particle Beams , Volume 8 , Issue 1-2 , January 1990 , pp. 253 - 263
Copyright
Copyright © Cambridge University Press 1990

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References

Ahlborn, B. & Key, M. H. 1981 Plasma Phys. 23, 435.CrossRefGoogle Scholar
Cornolti, F., Giammanco, F. & Giulietti, A. 1977 Lett. Nuovo Cim. 19, 165.CrossRefGoogle Scholar
Cornolti, F. et al. 1986 Opt. Comm. 57, 249.CrossRefGoogle Scholar
Gardner, J. H., Book, D. L. & Bernstein, I. B. 1982 J. of Fluid Mech. 114, 41.CrossRefGoogle Scholar
Gatti, M. et al. 1988 Opt. Comm. 69, 141.CrossRefGoogle Scholar
Giulietti, A., Vaselli, M. & Giammanco, F. 1980 Opt. Comm. 33, 257.CrossRefGoogle Scholar
Giulietti, A. et al. 1983 Opt. Comm. 47, 131.CrossRefGoogle Scholar
Harith, M. A. et al. 1988 Opt. Comm. 71, 76.CrossRefGoogle Scholar
Kidder, R. E. 1969 Proc. Varenna School on Physics of High Energy Density,Varenna,14–26 July.Google Scholar
Linhart, J. G. 1961 Proc. Conf. on Plasma Physics and Controlled Nuclear Fusion Research,Salzburg,4–9 September.Google Scholar
Linhart, J. G. 1986 Proc. 4th Intern. Conf. on Emerging Nuclear Energy Systems,Madrid,30 June-4 July.Google Scholar
Nuckolls, J. et al. 1972 Nature 239, 139.CrossRefGoogle Scholar
Panarella, E. 1969 C.A.S.I. (Canadian Aeronautics and Space Institute) Transactions 2, 21.Google Scholar
Panarella, E. 1980 Can. J. Phys. 58, 983.CrossRefGoogle Scholar
Panarella, E. 1987 J. Fusion Energy 6, 285.CrossRefGoogle Scholar
Panarella, E. & Savic, P. 1983 J. Fusion Energy 3, 199.CrossRefGoogle Scholar
Takayama, K., Kleine, H. & Grönis, H. 1987 Exp. in Fluids 5, 315.CrossRefGoogle Scholar
Tuck, J. L. 1958 Proc. 2nd Conf. on Peaceful Uses of Atomic Energy 32, 3.Google Scholar