Progress toward Fusion Energy Breakeven and Gain as Measured against the Lawson Criterion*

Starting from Lawson’s original 1955 report [1], this tutorial provides a review and re-derivation of the Lawson criterion, which is a key concept in the pursuit of fusion breakeven and gain that relates the fuel density n, confinement time τ, and fuel temperature T to the energy gain Q of a fusion plasma. Extensions to Lawson’s original work use different definitions of τ, e.g., energy confinement time τ_E, in magnetic versus inertial fusion, as will be explained in the tutorial. More than 75 values of the Lawson parameter nτ and T achieved by historical and contemporary fusion experiments, spanning magnetic (MCF), inertial (ICF), and magneto-inertial fusion (MIF), are extracted from the published literature [2]. Unique combinations of nτ and T map directly to unique values of Q; the tutorial will define and describe three versions of energy gain used by the fusion community: fuel gain Q_fuel (relative to energy/power absorbed by the fuel), scientific gain Q_sci (relative to energy/power applied at the vacuum boundary), and engineering gain Q_eng (relative to recirculating electricity). The relationship between Q_sci and Q_fuel depends on the efficiency of absorption of the externally applied energy by the fusion fuel. The tutorial will further describe methodologies for extracting nτ and T from the published literature that are necessarily specific to different fusion approaches, and will discuss major differences in applying the Lawson criterion to MCF versus ICF. Finally, the more-challenging physics requirements for advanced fuels, e.g., D-D, D-³He, and p-¹¹B, compared to D-T fusion will be presented.

[1] J. D. Lawson, Tech. Rep. GP/R 1807, UK Atomic Energy Research Establishment (1955). https://www.euro-fusion.org/fileadmin/user_upload/Archive/wp-content/uploads/2012/10/dec05-aere-gpr1807.pdf .

[2] S. E. Wurzel and S. C. Hsu, https://arxiv.org/abs/2105.10954 .