Analysis of the Fusion Breakeven Conditions for D-T Plasmas of Prescribed Temperature Evolution

Abstract

In the past several years, the Lawson criteria (Proc. Phys. Soc. B70, 6, 1957) have provided guidelines to the fusion community on the conditions required for energy breakeven from a hot plasma. These criteria state that, in a pulsed system, breakeven can be achieved if the plasma temperature exceeds a certain critical number (30 million °K for deuterium-tritium reactions), and the reaction is sustained for a sufficient time τ_E such that nτ_E > 10¹⁴ cm⁻³ sec, where n is the particle density. In the present study, the complete pulsed system is analyzed from which breakeven is required, i.e., source from which energy flows into a plasma sink, and plasma sink from which energy returns to the source. The case is considered where the a particles escape from the plasma, and the alternative case where they are retained. The analysis departs from the conventional one because it introduces conduction losses from heat transfer theory rather than through the 3nkT/03C4;_E term, and therefore the containement time τ_E does not play an explicit role in the breakeven conditions. These are now determined by particle density, temperature temporal profile, and dimension of the plasma. The analysis confirms the requirement of a threshold temperature for breakeven. However, it adds another threshold element, a particle density in excess of 10¹⁶ cm⁻³, below which breakeven cannot be achieved under realistic reactor conditions. Although a spherical geometry is considered here, such as the spherical pinch plasma configuration (J. Fusion Energy 13, 45, 1994), the analysis can be extended to the toroidal or other plasma geometries, when the appropriate heat conduction loss term is introduced.

In light of these results, the analysis of Lawson and successive interpretations have been re-examined. It is found that they have limited validity for a pulsed system, but are better suited for steady-state reactor operation.