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

Abstract

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 τE, 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 τE, 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.

Physics basis for the Wisconsin HTS Axisymmetric Mirror (WHAM)

“…Equation (3.4) is well supported by the historical record of fast ion confinement shown in figure 1 in minimum-B mirrors (Coensgen et al. 1975; Post 1987; Wurzel & Hsu 2022). Historically, the data collection ended when the US mirror program was cancelled in 1986.…”

Tritium burn efficiency in deuterium–tritium magnetic fusion

“…It is expected that the first commercial FPPs will utilize the deuterium-tritium (D-T) fusion cycle. D-T fusion has well-known advantages over other fusion fuels, including a ∼100× higher reactivity at experimentally achieved plasma temperatures (∼10-20 keV), and access to ignition and high gain (Q p ) at lower T and lower nτ E product [3] due to its high reactivity and significant energy release per reaction (17.6 MeV). The D-T reaction creates two particles: a helium ion (or alpha, α) and a free neutron (n).…”

Prospects for a high-field, compact break-even axisymmetric mirror (BEAM) and applications

“…Appendix A introduces a direct energy converter (DEC)geometry that could be tested in BEAM and would be appropriate for an axisymmetric mirror. This potential is not fully captured by or even the metrics as put forth by Wurzel & Hsu (2022).…”

“…That may not be necessary, however, for the mirror because its geometry allows the plasma energy losses out of the ends to be directly recovered in an efficient manner. This can be an enormous advantage for fusion energy systems that can employ it (see Ribe (1975) and more recently Wurzel & Hsu (2022)). Appendix A introduces a direct energy converter (DEC)geometry that could be tested in BEAM and would be appropriate for an axisymmetric mirror.…”

“…For example, if process heat is chosen as an application, a quantity like a heat-pump coefficient of performance or Wurzel's wall-plug might be used (Wurzel & Hsu 2022). For a fusion system which utilizes only the high-quality heat from a blanket for process heat, this would be where the numerator represents the heat from the blanket and the denominator represents the electrical power input required from the grid to heat the plasma and operate the plant.…”