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

Abstract

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.