The Fusion Cross Section
The energy-dependent probability that two colliding nuclei fuse, the microscopic input to all reaction rates.
What a cross section is
The cross section sigma(E) is the effective target area a nucleus presents for a given reaction; multiplied by flux it gives the reaction probability. For fusion it is written in terms of the astrophysical S-factor to separate the smoothly varying nuclear physics from the steep Coulomb-tunneling dependence:
sigma(E) = S(E) / E * exp(-b / sqrt(E))The exponential is the Gamow tunneling factor; the 1/E is a quantum geometric factor; S(E) captures the nuclear reaction strength and any resonances. This form makes the cross section easy to extrapolate and tabulate.
Resonances
The D-T reaction has a broad resonance near 64 keV (a state of helium-5), which greatly enhances its cross section and is a major reason D-T is so much easier than other fuels. Other reactions lack such favorable low-energy resonances.
From cross section to rate
- Average sigma(E) v over the Maxwellian to get the reactivity
- Peak reaction contribution comes from the Gamow-peak energy
- Measured cross sections are fit (Bosch-Hale) for use in codes
How it is used
Evaluated cross-section data (from measurement and nuclear theory) are the fundamental input. Codes do not recompute them; they use validated parameterizations to get reactivities as functions of temperature, then reaction rates as n_1 n_2
Kronos fuels
The large, resonance-enhanced D-T cross section supports the Hyperion breeder design point (88.7 MW, Q 3.424). The D-3He cross section peaks at higher energy and yields mostly charged products with a small neutron fraction, which is why the Kronos burner is a higher-temperature D-3He design with 5.44 percent neutron fraction. All figures are for design and simulation studies.