358. Thermonuclear reactors. Inertial confinement

I am currently keeping studying thermonuclear fusion and reactors a bit and, I should admit, I’m absolutely in love with HiPER and inertial confinement as an idea – it is so much more elegant than magnetic confinement used in Tokamaks… But before I’ll turn to the discussion of inertial confinement reactors, let me finish with generalities and trivialities (I’ll need them anyway for further reference).

Every thermonuclear reactor is characterized by its fusion energy gain factor equal to the ratio of reactor’s power to power spent for starting and sustaining the nuclear reaction. So far, we were unable to build a reactor with , while what be useful for us in practise to achieve is the gain factor of the order of 20. Why we were so unsuccessful so far (Russians started working on thermonuclear fusion and building Tokamaks from 1960s)? We will discuss associated difficulties in one of the next posts.

It seems that the simplest option for us is to build a reactor working on d-t fuel, the corresponding reaction rate being larger than for any other thermonuclear reactions. The next (but actually more attractive as you’ll see below) possibility is a reactor working on d- fuel. In this case, neutrons can only appear in subsequent d-d and d-t reactions, and associated danger is much lower compared to the usual fission nuclear reactors: there is no need to develop the whole industry dealing with radioactive waste, etc. The main problem associated with d- thermonuclear reactor is almost absolute absence of in Nature. It sounds somewhat funny but we may end up delivering it to Earth from Moon…

(the guy on the video is way too funny )

Ok, finished with generalities and trivialities and let me now get to the interesting part and explain how inertial confinement works physically. There is a lot of interesting and simple associated physics, so probably explanations will take couple of posts but, I think, it’s definitely worth studying.

Contrary to usual idea of magnetic confinement of plasma, plasma in reactors with interial confinement is not really confined – it propagates freely. Conditions for the thermonuclear reaction to start are achieved on the stage of compression of plasma. The systems with inertial confinement are initially designed to be out of equilibrium (a time scale exists characterizing inertial confinement).

Imagine that the plasma of d, t nuclei and electrons with densities , , correspondingly is localized within the sphere of radius . The number of d-t fusion reactions in the corresponding spherical volume is given by

,

where for given species (d or t). (The d-t reaction rate is given as usual by averaging over Maxwell distribution for the given temperature of plasma). Since plasma is not confined, reaction can be only effective during a characteristic kinematic time

,

where is the velocity of the plasma during the state of compression. In the very first approximation, we can estimate it as a speed of sound in the plasma

Therefore, a characteristic number of d (or t) nuclei that entered the reaction as

.

Using the ideal gas approximation for plasma we find

,

where is atomic number of ions in plasma and is their mass. Then,

.

To be continued…