Q, break-even and the nτE diagram for transient fusion plasmas

Q, break-even and the nτ_E diagram are well defined and understood for steady-state fusion plasma conditions. Since many fusion experiments are transient, it is necessary to clarify the definitions for instantaneous Q values and break-even so that the nτ _E diagram can be interpreted for transient plasma conditions. This discussion shows that there are two mathematically correct methods to describe the nτ_E diagram for a transient plasma. The Lawson/TFTR method which is consistent with previous analyses of the Lawson cycle, and prior definitions for Q and break-even describes a transient fusion plasma in terms of Q P_fusion/P_aux with the plasma energy confinement time for the nτ diagram given by τ_E*=W_p/P_heat where W_p is the total plasma kinetic energy and P_heat=P_aux+P _alpha-P_brem is the net power heating the plasma. In the Lawson/TFTR definition break-even (P_fusion=P_aux ) occurs at Q=1, ignition occurs at Q=infinity and the nτ_E* values required to achieve a given Q are the same in transient and steady-state plasmas. The JET/JT-60 method uses the definitions of Q*=P_fusion/(P_aux-dWp/dt) and τ _E=Wp/(P_heat-dWp/dt). This method produces the confusing result that break-even requires Q*=P_aux/(P_aux -dWp/dt) which is >1 for many cases of interest. In addition, the nτ_E value required to achieve break-even depends on dWp/dt and therefore experimental data points with different dWp/dt must be compared to different Q* curves on the Lawson diagram. For a pulsed plasma, this issue can be avoided by using the definition of fusion gain first introduced by Lawson, namely Q=fusion energy per pulse divided by auxiliary plasma heating energy supplied per pulse