Equation of state and optimum compression in inertial fusion energy

Abstract

The inertial confinement fusion (ICF) philosophy is based on high compression. The reasoning is that (a) it is cheaper (energetically) to compress than to heat and (b) nuclear reactions are proportional to density square, therefore the more you compress the better you are in ICF. Of course the only limitations of compression are the hydrodynamic instabilities (like Rayleigh-Taylor, etc). Many of the references in the literature require extremely high compression and in particular the pB11 needs extremely huge compressions. In this paper it is shown that there is an optimum of compression, namely gain G is maximum for a definite compression. The value of this density (for a given fuel mass and particular ICF scheme) depends on the equation of state (EOS). We calculate this value for fast ignition (FI) schemes and compare it with the central spark ignition (CSI) model. The gain calculations are based on the ideal gas for the ions and the Fermi-Dirac EOS for the electrons with an effective alpha, as usually suggested from simulations. The “optimum compression” idea is easily understood from the following argument: From EOS data one needs an infinite energy to compress to an infinite density. Since the energy output is finite it is clear that G is zero for infinite compression. On the other hand for normal density with small fuel mass (~ few mg) the gain is also zero. Therefore a maximum should exist somewhere. For the deuterium-tritium fuel with a mass of few mg one gets an optimum at few hundred g/cc. If you compress more then the gain is going down. So there is a desired maximum compression fixed by EOS. Last but not least, bremsstrahlung losses in degenerate plasma are discussed and the clean fusion (i.e., without neutrons) of proton + B11 → 4α is analyzed.

Heat wave fast ignition in inertial confinement energy

“…The gain G can be analytically estimated [21] . For the cylindrical shell in Figure 5 we use the notation M 0 = initial mass, ρ 0 = density, R 0 = ring radius, ∆R 0 = thickness, L = ring length, R C = final radius of compression, the aspect ratio A r = R 0 /∆R 0 , φ = burning fraction of DT, η C = laser to compression efficiency and W d = driver energy.…”

“…For η C of only 10% and an equation of state parameter α C = 3 [22] we get a gain of G = 100. A similar analytic calculation for the spherical geometry impact fast ignition case has been given [10,21] . In this case, a laser driver with an order of magnitude less energy was suggested.…”

Ultrafast ignition with relativistic shock waves induced by high power lasers

“…The compression of a typical pellet as discussed in the literature [12,47] requires between 100 and 300 kJ of energy, Table 1. The laser is defined by its irradiance I L , pulse duration τ L , energy W L and power P L .…”

Dynamic screening and charge state of fast ions in plasma and solids

“…Since the advent of intense proton and light ion beams generated by intense lasers, this field has experienced a renaissance due to applications ranging from inertial fusion with fast ignition to medical applications (Barriga-Carrasco, 2008;Cook et al, 2008;Eliezer et al, 2007;Evans, 2008;Flippo et al, 2007;Hora, 2007;Romagnani et al, 2008). Regarding the effect of density on the charge state in cold matter, two models with very different views were proposed: the Bohr Lindhard model, (BL) (Bohr & Lindhard, 1954) and the Betz-Grodzins model, (BG) (Betz & Grodzins, 1970).…”