A Simple ODE Model for ICF Gain by Volume Ignition

There are several basic fuel configurations for ICF. Hot spots aim to reach high gain by propagating a burn wave into surrounding cold fuel. The small hot spot size means they are optically thin and the required temperature is >5 keV. Volume ignition has fuel in a single phase and relies on the trapping of radiation. This reduces the required temperature to ~2 keV, allowing high gain.

The model includes energy deposition by alpha particles as instantaneous but non-local. The radiation loss smoothly transitions from pure bremsstrahlung to blackbody. Degeneracy effects are included and found to be significant.

Verification of the model against detailed simulations from literature indicates good accuracy. The critical trade-off between self-heating time and confinement time is captured. Confinement time is eventually the limiting factor. Were it possible to increase the confinement time without deleterious additional effects, required temperature can be reduced to <1keV.

Finally, constraints coming from reactor design are related back to the plasma properties. The union of parameter space where no constraint applies is called the “island of viability” and it is shown that for this island to exist, a very high coupling efficiency of 2% is required.