364. Thermonuclear reactors. More on inertial confinement

Last time I did not quite finish with the discussion of physics of inertial confinement, so let me continue…

An important parameter that characterizes plasma in reactors with inertial confinement is the ratio between the geometric size of the region where reactions take place and the mean free path of -particles. It basically determines the ability of thermonuclear reactions in the plasma to self-sustain – if particles are adsorbed faster, plasma is getting warmed up more effectively. In other words, one naturally would want to increase or decrease . How to do that?

We have:

,

i.e., the ratio depends on the density of plasma in the beginning of the experiment and the characteristic size of the plasma (prefactor that we omitted also depends on temperature of the plasma non-trivially). Basically, at characteristic velocity of particles in plasma is about , and the fusion can be only effective at plasma densities of the order or larger. Such densities greatly exceed the ones we deal with in solid state physics, so one needs to really strongly compress plasma to make fusion possible.

Geometrically, the most convenient way to compress plasma is to deal with spherical samples. In this case, we have , so (geometrically, the fastest decrease with which is possible) and .

And that’s how a corresponding fuel microcapsule looks like (inside this capsule is d+t fuel)

It is also clear from the considerations above that we really want to keep the spherical symmetry intact during the whole compression stage – otherwise, the density of the fuel will not achieve maximal possible values. As it turns out, that is the main technical difficulty we face with when we try to start reaction of fusion in an inertial confinement reactor – Rayleigh-Taylor instabilities in the heated fuel lead to breakdown of spherical symmetry. That’s how the problem of thermonuclear fusion is related to the problem of turbulence, but let me leave the discussion of hydrodynamic instabilities to another post…