Charge separation, azimuthal instabilities and radial transport in two-dimensional-r z r z $rz$ and three-dimensional magnetic mirror simulations

Fully kinetic, energy-conserving electrostatic particle-in-cell (PIC) simulations are employed to quantify how geometry and two-dimensional (2-D- r z r z $rz$ ) and three-dimensional (3-D) effects modify confinement, acceleration and cross-field transport by comparing our results with previous 1-D simulations in an open magnetic mirror. The bulk of the simulations are performed using an explicit scheme at a plasma density of approximately 10 Superscript 16 Baseline normal m Superscript negative 3 10 16 m − 3 10¹⁶\,m⁻³ . In addition to being computationally accessible to explicit PIC, this regime has a relatively large Debye length and therefore emphasises charge-separation effects important in 2-D and 3-D simulations. Starting from a 2-D axisymmetric (2-D- r z r z $rz$ ) model and extending to three dimensions, we isolate finite-ion-Larmor-radius (FLR) effects and azimuthal instabilities. In the 2-D- r z r z $rz$ case, FLR effects partially decouple ions from magnetised electrons, producing charge separation near the plasma edge and modest radial ion leakage to the wall, while the near-axis density, potential and acceleration profiles remain close to those in the reduced 1-D model. Full 3-D simulations demonstrate azimuthal modes that induce radial currents, broaden radial density profiles and reduce the confining potential and the total axial potential drop. At low ion temperature, a coherent azimuthal mode of low frequency and low mode number m equals 2 m = 2 $m=2$ is observed. At high ion temperature, fluctuations shift toward higher mode numbers m asymptotically equals 4 m ≃ 4 m 4 – 5 5 $5$ and higher frequencies, with a broadband turbulent spectrum. The particle and energy (for ions and electrons) radial and axial losses are studied in detail. We show that for 3-D cases, radial ion losses account for approximately