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Q, Break-even and the Lawson Diagram for Transient Fusion Plasmas
Author: Dale M. Meade
Q, break-even and the Lawson [n(tau)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 Lawson diagram can be interpreted for transient plasma conditions. This discussion shows that there are two mathematically correct methods to describe the Lawson 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 = Pfusion/Paux with the plasma energy confinement time for the n(tau) diagram given by (tau)E* = Wp/ Pheat where Wp is the total plasma kinetic energy and Pheat = Paux + Palpha - Pbrem is the net power heating the plasma. In the Lawson/TFTR definition break-even (Pfusion = Paux) occurs at Q = 1, ignition occurs at Q = infinity and the n(tau)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* = Pfusion/(Paux - dWp/dt) and (tau)E = Wp/(Pheat - dWp/dt). This method produces the confusing result that break-even requires Q* = Paux/(Paux - dWp/dt) which is >1 for many cases of interest. In addition, the Lawson 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.