Q, Break-even and the ntE Diagram for Transient Fusion Plasmas*

Dale M. Meade

Plasma Physics Laboratory
Princeton University, Princeton, NJ 08543

Q, break-even and the ntE 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 ntE diagram can be interpreted for transient plasma conditions. This discussion shows that there are two mathematically correct methods to describe the ntE diargram for a transient plasma. The 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 nt diagram given by tE* = Wp / Pheat where Wp is the total plasma kinetic energy and Pheat = Paux + Palpha - Pbrem is the net power heating the plasma. In the TFTR definition break-even (Pfusion = Paux) occurs at Q=1, ignition occurs at Q = infinity and the ntE* 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 tE = 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 ntE 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.

*Work supported by U.S. DOE Contract No. DE-AC02-76-CHO3073.