There is widespread belief amongst physicists in the laser ICF community that high compression densities (~100x solid) are necessary in order to achieve fusion gain. That belief is based on two assumptions:
- fusion yields must be constrained below some maximum yield to prevent the surface of the blast chamber from being vaporized (due to radiation fluxes that exceed the wall’s rate of cooling through thermal conduction)
- the mass necessary to produce a given burn efficiency scales inversely with the density squared for targets that have the same \rho r confinement parameter.
Those are mainstream ICF assumptions, unsuitable for BSF, for the following reasons:
- When assessing the blast of nuclear explosions, one should keep in mind that fusion energy is released in the form of high velocity particles (neutrons, ions) and photons, carrying relatively low momentum (mv) per unit of energy (\frac{1}{2} mv^2). A nuclear blast is therefore only about \frac{1}{1000} as strong as a chemical explosion that release this same amount of energy in the form of gases with much lower velocities. Most of the energy (80%) gets deposited as neat (neutron heat), spread over several cubic meters of molten FLiBe. In addition, because FLiBe blocks x-rays, the wall of a BSF reactor is protected against melting/vaporization. Also See: max survivable yield calc.
- The usefulness of the \rho r confinement parameter was derived under the assumption that there is no physical mechanism to confine an ICF plasma except its own mass inertia. Gas dynamics tells us that the plasma sphere will expand as a rarefaction wave moving outward into the vacuum at the speed of sound. In BSF, the fuel is confined by more than just its inertia. To escape, it must first push outward against a dense wall of molten salt that is converging inward at high velocity.
- The method of confinement used by BSF extends both self-heating and burnup times. This enables higher gains to be achieved in a way that is not directly based on \rho r.
- In a BSF reactor, the fuel sits deep inside a transparent liquid blanket. Radiant energy cannot leave the fuel unless the surrounding FLiBe is transparent at that wavelength, creating an energy barrier at the fuel–liquid interface—a greenhouse‑like effect. The fuel first absorbs narrow‑band laser light from rare‑earth dopants in the FLiBe, then reradiates in a broad spectrum. Because the fuel and FLiBe have different transparency profiles, much of this reradiated energy is deposited at their boundary. The resulting heating and ionization smooth Rayleigh–Taylor instabilities, and the liberated electrons add to the local pressure, tightening the containment grip like a boa constrictor. Even when the fuel emits wavelengths that pass through FLiBe, no cooling takes place unless that radiation also escapes a second barrier: the reflective sphere, which continually returns electromagnetic energy to the fuel. This allows ignition at a lower Ideal Ignition Temperature. In this way, BSF’s method of trapping radiant energy enables higher fusion gains independent of 𝜌𝑟.
Dimensional Analysis, for a uniform sphere of D-T plasma:
- mass ∝ M
- volume ∝ L^3
- density ∝ ML^{-3}
- Energy ∝ M ← energy to heat plasma
Assuming ICF, plasma in vacuum:
- \tau_{ICF} ∝ L ← inertial confinement \approx R_f/4c_s
- Yield_{ICF} ∝ M^2L^{-2} ← given <\sigma v> ∝ 1 and yield = <\sigma v>n^2V\tau
- Gain_{ICF} = \frac{yield}{energy} ∝ ML^{-2}
Assuming BSF, plasma in FLiBe:
- \tau_{BSF} ∝ L^2 ← random walk diffusion model
- Yield_{BSF} ∝ M^2L^{-1} ← given <\sigma v> ∝ 1 and yield = <\sigma v>n^2V\tau
- Gain_{BSF} = \frac{yield}{energy} ∝ ML^{-1}
Suppose we are given a plasma that satisfies the 100x solid density requirement mentioned at the top of this post. Starting in comparison to that base case, we want to know if, given 10x the energy, we can create a lower-densiy plasma with equal (or better) performance.
Let’s run new numbers, for mildly compressed BSF plasma:
- with 10x energy we heat 10x mass
- we mildly compress to 10x radius
- the resulting plasma will be 1000x volume
- the resulting plasma will be 0.01x density ← AKA solid density
- the resulting plasma would produce 10x fusion yield
- and resulting plasma would have no change in gain
Conclusion:
High-densities (>solid) are NOT required for BSF.