  We investigate the full-cycle operation of a coaxial Packed Bed Dielectric
Barrier Discharge (PB-DBD) reactor operating in pure $\mathrm{CO_{2}}$. The
reactor is packed with high permittivity dielectric rods and is analyzed with a
two-dimensional (2D) self-consistent plasma model. We show that the PB-DBD
operation is governed by both glow and volume/surface streamer discharges,
forming alternatively and non-uniformly inside the gas volume. The presence and
surface charging of the dielectric rods and dielectric layer is crucial for the
initiation, propagation, annihillation and afterglow of these microdischarges.
Our calculations show maximum electron and $\mathrm{CO_{2}^{+}}$ densities in
the order $10^{20}$ $\mathrm{m^{-3}}$, an average discharge power of 353.42
W/m, microdischarge peak currents in the order of 50-400 A/m, total half-cycle
plasma charge of around 6 $\mathrm{\mu}$C/m. Dominant negative ions are found
to be $\mathrm{CO_{3}^{-}}$. CO molecules and O atoms are mainly formed during
the MDs development and the streamer-surface ionization waves. Molecular oxygen
($\mathrm{O_{2}}$) is preferentially formed during the glow, current-decaying
and afterglow phase of each microdischarge. The spatially average reduced
electric field inside the reactor lies in the 20-100 Td range. Each MD,
presents distinct non-uniform and non-repeatable glow and volume/streamer
discharges owed to the non-uniform surface charging processes which dictate the
complex spatial distribution of produced neutral (and ion) species. These
detailed results shed light on crucial, largely non-uniform plasma
spatiotemporal characteristics that can help design efficient PB-DBD reactors
for $\mathrm{CO_{2}}$ splitting and beyond, while emphasizing the important
insights obtained by 2D simulations which can not be captured with 0D-global or
1D models.
