Progress toward fusion energy breakeven and gain as measured against the Lawson criterion

The Lawson criterion is a key concept in the pursuit of fusion energy, relating the fuel density $n$, pulse duration $τ$ or energy confinement time $τ_E$, and fuel temperature $T$ to the energy gain $Q$ of a fusion plasma. The purpose of this paper is to explain and review the Lawson criterion and to provide a compilation of achieved parameters for a broad range of historical and contemporary fusion experiments. Although this paper focuses on the Lawson criterion, it is only one of many equally important factors in assessing the progress and ultimate likelihood of any fusion concept becoming a commercially viable fusion-energy system. Only experimentally measured or inferred values of $n$, $τ$ or $τ_E$, and $T$ that have been published in the peer-reviewed literature are included in this paper, unless noted otherwise. For extracting these parameters, we discuss methodologies that are necessarily specific to different fusion approaches (including magnetic, inertial, and magneto-inertial fusion). This paper is intended to serve as a reference for fusion researchers and a tutorial for all others interested in fusion energy.