The Lawson criterion is a key concept in the pursuit of fusion energy, relating the fuel density $n$, pulse duration $\tau$ or energy confinement time $\tau_E$, 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 $n$, $\tau$ or $\tau_E$, 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. 

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

Overview of C-2W: High-temperature, steady-state beam-driven field-reversed configuration plasmas

An inductive pulsed plasma thruster (IPPT) operates by pulsing high current through an inductor, typically a coil of some type, producing an electromagnetic field that drives current in a plasma, accelerating it to high speed. The IPPT is electrodeless, with no direct electrical connection between the externally applied pulsed high-current circuit and the current conducted in the plasma. Several different configurations were proposed and tested, including those that produce a plasma consisting of an accelerating current sheet and those that use closed magnetic flux lines to help confine the plasma during acceleration. Specific impulses up to 7000 s and thrust efficiencies over 50% have been measured. The present state-of-the-art for IPPTs is reviewed, focusing on the operation, modeling techniques, and major subsystems found in various configurations. Following that review is documentation of IPPT technology advancement paths that were proposed or considered.

https://www.mdpi.com/2226-4310/7/8/105/pdf

State-of-the-Art and Advancement Paths for Inductive Pulsed Plasma Thrusters

Observation of self-organized FRC formation in a collisional-merging experiment

https://absimage.aps.org/image/DPP14/MWS_DPP14-2014-000706.pdf

High Performance Field Reversed Configurations

TAE Technologies' research is devoted to producing high temperature, stable, long-lived field-reversed configuration (FRC) plasmas by neutral-beam injection (NBI) and edge biasing/control. The newly constructed C-2W experimental device (also called "Norman") is the world's largest compact-toroid (CT) device, which has several key upgrades from the preceding C-2U device such as higher input power and longer pulse duration of the NBI system as well as installation of inner divertors with upgraded electrode biasing systems. Initial C-2W experiments have successfully demonstrated a robust FRC formation and its translation into the confinement vessel through the newly installed inner divertor with adequate guide magnetic field. They also produced dramatically improved initial FRC states with higher plasma temperatures (Te ~250+ eV; total electron and ion temperature g1.5 keV, based on pressure balance) and more trapped flux (up to ~15 mWb, based on rigid-rotor model) inside the FRC immediately after the merger of collided two CTs in the confinement section. As for effective edge control on FRC stabilization, a number of edge biasing schemes have been tried via open field-lines, in which concentric electrodes located in both inner and outer divertors as well as end-on plasma guns are electrically biased independently. As a result of effective outer-divertor electrode biasing alone, FRC plasma diamagnetism duration has reached up to ~9 ms which is equivalent to C-2U plasma duration. Magnetic field flaring/expansion in both inner and outer divertors plays an important role in creating a thermal insulation on open field-lines to reduce a loss rate of electrons, which leads to improvement of the edge and core FRC confinement properties. Experimental campaign with inner-divertor magnetic-field flaring has just commenced and early result indicates that electron temperature of the merged FRC stays relatively high and increases for a short period of time, presumably by NBI and ExB heating.

https://iopscience.iop.org/article/10.1088/1741-4326/ab0be9/pdf

Formation of hot, stable, long-lived field-reversed configuration plasmas on the C-2W device

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Formation of hot, stable, long-lived field-reversed configuration plasmas on the C-2W device