FENNECS 3D: A three-dimensional particle-in-cell code for non-neutral plasma dynamics and diocotron instability simulations

This work presents the three-dimensional (3D) extension of the FENNECS code, a particle-in-cell framework developed to simulate the dynamics of non-neutral plasmas in complex geometries. The development is motivated by the study of spontaneous electron cloud formation in gyrotron electron guns, which can induce parasitic currents and lead to operational disruptions. The inclusion of 3D effects allows the modeling of the diocotron instability, which plays a major role in limiting the cloud density and driving electron losses. These features are inherently absent from the previous 2D version, where the axisymmetric assumption suppresses all azimuthal dynamics. The 3D capabilities are verified in simplified configurations. Simulations of the diocotron instability in an axially uniform annular electron cloud are found to be in excellent agreement with analytical linear theory. Finite-length effects are also investigated by simulating a cloud confined in a Penning–Malmberg trap, with the code reproducing the expected trends predicted by a linear model. FENNECS 3D is then used to simulate the TRapped Electrons eXperiment, a dedicated setup designed to reproduce the trapping conditions of gyrotron electron guns. Simulations performed under experimentally realistic conditions demonstrate the periodic, self-consistent growth and disruption of the electron cloud due to the diocotron instability. The simulated currents agree quantitatively with experimental measurements in both frequency and amplitude. This work establishes a robust and versatile framework for investigating electron trapping phenomena in gyrotrons and other devices where similar mechanisms are present and represents a significant step forward in the numerical modeling of non-neutral plasmas.