Inertial Confinement Fusion with Lasers or Particle Beams

Abstract

Controlled fusion of light nuclei for energy production occurs at hight temperatures, kT≳10keV. In order to obtain efficient burn the fuel has to be confined for a minimum time τ which is inversely proportional to the fuel density (Nuckolls, 1982). At low particle densities the fuel can be confined and kept in a steady state by magnetic fields. At densities higher than n ≅ 10¹⁷ cm⁻³ matter can be confined only by its own inertia, and so burn has to be achieved in a very short time; the less thermonuclear fuel is involved the shorter this will be. The principle of ICF is simple (Fig.1). A pellet of radius R, uniform density n and temperature T burns according to (Duderstadt, Moses, 1982)

$$\frac{d}{{dt}}\frac{n}{2} = \frac{{{n^2}}}{2} \left\langle \sigma \right.\left. v \right\rangle $$

(1.1)

where < σv > is the reaction rate of one fuel perticle averaged over its velocity distribution function. Owing to the high temperature the pellet disassembles with the rarefaction wave the edge of which moves inward at sound speed s = (kT/${\bar m_i}$)^½, where ${\bar m_i}$ stands for the average fuel ion mass. Keeping in mind thet 60% of the mass is contained the outer shell of thickness R/4 an adequate expression for the confinement time is τ = R/4s. With this the fractional burn η = 1 − n(τ)/n₀ is obtained by integrating eq. (1.1)

$$\eta = \frac{{\rho R}}{{\rho R + \delta }}, \delta = 8{({\bar m_i}kT)^{1/2}}/ < \sigma v >= \delta (T).$$

(1.2)

The parameter δ is a function of temperature only.