Integrated 3D fully kinetic simulation of field-reversed-configuration formation with embedded coils

We present an integrated, three-dimensional, fully kinetic particle-in-cell simulation of field-reversed-configuration (FRC) formation at the device scale. To our knowledge, this is the first fully kinetic model of whole-device FRC formation. The model embeds the drive coils directly inside the computational domain as physical conductors, advancing them self-consistently with the plasma on a single explicit grid and coupling them in closed loop to an external circuit. We apply this unified framework to the Yingguang-1 $\theta$-pinch. Unlike the magnetohydrodynamic and hybrid models used previously, our framework advances the electrons as kinetic particles rather than a fluid, capturing fast magnetic reconnection and electron heating from first principles. The simulation reproduces the complete formation sequence, from reversed-bias lock-in through reconnection to the emergence of a closed-flux FRC, reaching a peak ion density ${\sim}2.2\times10^{22}\,\mathrm{m^{-3}}$ consistent with experiment. The compressed core is electron-dominated, with $T_e\approx1.7\,$keV exceeding $T_i\approx1.2\,$keV, and is pinched to a separatrix radius $r_s\approx1\,$cm, several times below the equilibrium-inferred value, indicating that the plasma never relaxes to a pressure-balanced equilibrium within the microsecond pulse. The model further reproduces a non-axisymmetric, four-fold ($m=4$) deformation of the compressed column, matching the square cross-section recorded by the experiment's end-on framing camera, a feature beyond the reach of the two-dimensional models previously applied to this device. Running on modest GPU hardware, this work brings integrated, first-principles kinetic modeling of fusion-relevant FRCs within reach.