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# Interaction of imploding shock waves with expanding central plasma in spherical pinch experiments: Simulation analysis

Department of Elecrical and Computer Engineering University of Tennessee 37990-2100 Knoxville TN
(Impact Factor: 0.99). 01/1990; 9(4):513-516. DOI: 10.1007/BF01588289

ABSTRACT

In the spherical pinch scheme, the hot D-T plasma produced in the center of the high pressure spherical vessel is confined by means of imploding shock waves launched from the periphery of the vessel for a time sufficiently long to achieve break-even conditions for plasma fusion. Theoretical studies on spherical pinch made so far have been limited up to the conditions of substantial expansion of the central plasma and the well-defined time delay between the creation of central plasma and the launching of the peripheral shock which led to the conclusion that, in realistic situations of SP experiments, negative time delays should be adopted, i.e., the launching of the imploding shock wave should precede the formation of the central plasma. However, the interaction of converging shock wave with the central plasma causing an additional heating and compression of the central plasma favoring plasma fusion conditions was not taken into account. Starting from the hydrodynamic equations of the system, the proposed simulation code deals with the propagation of converging shock waves and its interaction with the expanding central plasma. Considering the above-mentioned interaction in a self-consistent manner, the temporal evolution of temperature of central plasma is studied. Some results of the numerical simulation on the dynamics of shock wave propagation are also compared with the predictions of point strong explosing theory.

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• ##### Article: Scaling laws for spherical pinch experiments
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ABSTRACT: Spherical pinch experiments are characterized by a central discharge in a spherical vessel followed by an inductive discharge in the vessel's peripheral shell gas. An analysis is carried out of the evolution of the imploding shock waves produced by the shell explosion in order to find out if the central discharge can be contained and compressed by the converging shocks, so as to maintain its temperature for a time sufficiently long for breakeven. The analytical model adopted is essentially that of the recent paper of Ahlborn and Key (Plasma Phys. 23: 435, 1981). One finds that the converging shocks are indeed capable of containing and compressing the central plasma. In addition, if the central spark reaches the critical temperatureT L = 2.58 keV by the deposition of an energy density of 1.86108 Jg–1, the scaling law required in order to contain such a plasma for breakeven is 0 R(Es/Ms)1/2 1.96106, where 0 is the initial fill gas density,R is the radius of the spherical vessel, andE s is the energy deposited in the peripheral shell massM s . The general applicability of the model to other fusion devices based on the implosion principle is discussed.
Journal of Fusion Energy 05/1983; 3(3):199-214. DOI:10.1007/BF01052556 · 0.99 Impact Factor

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##### Conference Paper: Simulation analysis of the spherical pinch for neutron and hardX-ray generation in a 1 MJ experiment
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ABSTRACT: Summary form only given. A 1-D Lagrangian hydrodynamic and heat transfer code has been used to derive the design parameters for a 1 MJ experiment of neutron and hard X-ray generation from the Spherical Pinch. The numerical simulation analysis has been performed on the basis of the indications provided by the scaling laws governing the phenomenon. The experiment will make use of 200 condensers of 5 kJ energy, each operating at 60 kV in a special facility of the National Research Council of Canada. The parameters that need to be optimized are neutron and hard X-ray outputs for such industrial applications as nondestructive material radiography. The numerical simulation provides a strong indication that the Spherical Pinch can become a useful source of radiation for material radiography as well as for fusion energy studies
Plasma Science, 1993. IEEE Conference Record - Abstracts., 1993 IEEE International Conference on; 07/1993
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