As we now turn our attention from fusion physics to fusion energy, we have to introduce Big Q, as distinct from little q. Little q, as you remember, is the “quality”

factor in toruses like tokamaks and stellarators. It is the reciprocal of the rotational transform, which is the number of times a helical field line encircles the minor axis each time it goes around the whole torus. The variation of q with radius r, or q(r), is perhaps the most important feature in the design of toroidal magnetic bottles. Big Q, on the other hand, has to do with how much energy a fusion reactor will produce. It is the ratio of the fusion energy produced to the energy required to make the plasma:

q _ Fusion energy Input energy

In Chap. 3, we showed this equation for the DT reaction:

D + T ® a + n +17.6 MeV,

where a is an alpha particle (a helium nucleus) and n is a neutron. Most of the 17.6 MeV of energy released is carried by a 14.1 MeV neutron, and the other 3.5 MeV is carried by the alpha particle.11 The neutron energy is the part used to produce the electrical output of the power plant, and the alpha energy is used to keep the plasma hot. Since the a’s are charged, they are confined by the magnetic field, and the hope is to hold them long enough that they can transfer their energies to the DT plasma, keeping it at a steady temperature. But since the a’s have only one-fifth of the fusion energy, Q has to be at least 5 for this to happen. This is called ignition. The plasma is “burning” by itself. The reaction cannot run away as in fission because some instability will quench the plasma as soon as the operational limits are exceeded.

The first milestone is to achieve Q = 1, which is called scientific breakeven, which assumes that the whole 17.6 MeV is equal to the input energy. The next milestone is to get to ignition at Q=5. To produce net energy, you have to count also the energy needed to make the magnetic fields and the plasma currents, as well as all the electric­ity needed to run the power plant (even the lights!) and the energy used to transmit the power to where it is used. This means that Q has to be at least 10. Figure 8.20 is a Lawson diagram (Chap. 5) plotting nrE vs. T and showing what different tokamaks have achieved in DD and DT plasmas. The heavy curve is for Q = 1 in DT, and we see that this has been reached in JET. The yellow region is ignition at Q greater than 5. The diagonal dashed lines are for constant values of the triple product. The obvious next significant step is to get to ignition, and that is the story of ITER.