Q, break-even and the n/spl tau//sub E/ diagram for transient fusion plasmas

Q, break-even and the n/spl tau//sub 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 n/spl tau//sub E/ diagram can be interpreted for transient plasma conditions. This discussion shows that there are two mathematically correct methods to describe the n/spl tau//sub 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/sub fusion//P/sub aux/ with the plasma energy confinement time for the n/spl tau/ diagram given by /spl tau//sub E/*=W/sub p//P/sub heat/ where W/sub p/ is the total plasma kinetic energy and P/sub heat/=P/sub aux/+P/sub alpha/-P/sub brem/ is the net power heating the plasma. In the Lawson/TFTR definition break-even (P/sub fusion/=P/sub aux/) occurs at Q=1, ignition occurs at Q=infinity and the n/spl tau//sub 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/sub fusion//(P/sub aux/-dWp/dt) and /spl tau//sub E/=Wp/(P/sub heat/-dWp/dt). This method produces the confusing result that break-even requires Q*=P/sub aux//(P/sub aux/-dWp/dt) which is >1 for many cases of interest. In addition, the n/spl tau//sub 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.