Electrode Bias Propagation in the C-2W Fusion Research Device

TAE Technologies' fifth-generation fusion research device C-2W utilizes neutral beam injection and edge biasing to sustain long-lived, stable field reversed configuration (FRC) plasma embedded within a magnetic mirror. In the C-2W magnetic field topology, a separatrix divides the closed field lines of the core plasma from the open field lines of the surrounding scrape-off layer (SOL) plasma, and the open field lines map onto a set of annular concentric electrodes located at both axial ends of the device. Potentials applied at the electrodes propagate via the field lines into the SOL, driving azimuthal 𝐸⃗ ×𝐵⃗ rotation that counteracts self-generated FRC spin-up and suppresses disruptive rotational instabilities (particularly the 𝑛=2 mode). In an effort to model bias propagation from the electrode plates to the central plasma, the three-fluid Ohm's law (ions, electrons, and neutrals) is utilized to derive a linear, second-order partial differential equation for the electrostatic potential in flux coordinates. This equation is then solved numerically in the biased flux region of C-2W by using plasma parameter outputs from an experimentally informed 2D axisymmetric equilibrium code. Self-consistent boundary conditions are imposed via a sheath model that utilizes experimentally measured currents and voltages on the electrode plates. The resulting solution for electrostatic potential (which also yields the poloidal current density and 𝐸⃗ ×𝐵⃗ rotation velocity) reproduces the O⁵⁺ impurity ion rotation profile measured by Doppler spectroscopy at the mid-plane as well as the H⁺ main ion incident energy measured by retarding‐potential gridded analyzers at the electrode plates. The model predicts that higher neutral densities significantly reduce the effectiveness of bias propagation from the electrode plates to the central plasma, primarily by increasing the fraction of bias potential lost across the sheath directly in front of the electrodes.