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
$10^{16}\,\mathrm{m}^{-3}$
. 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
$m\simeq 4$
–
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
30 percent sign
30
%
$30\,\%$
of the flux injected from the source region. The radial electric field produced by the endplate biasing introduces azimuthal shear that weakens coherent structures and reduces radial losses. Finally, additional simulations at densities of the order
10 Superscript 18 Baseline normal m Superscript negative 3
10
18
m
−
3
$10^{18}\,\mathrm{m}^{-3}$
have been performed with a semi-implicit electrostatic PIC algorithm.