  We have investigated the evolution of a system of sparking discharges in the
inner acceleration region (IAR) above the pulsar polar cap. The surface of the
polar cap is heated to temperatures around $10^6$ K and forms a partially
screened gap (PSG) due to thermionic emission of positively charged ions from
the stellar surface. The sparks lag behind the co-rotation speed during their
lifetimes due to variable $E$x$B$ drift. In a PSG the sparking discharges arise
in locations where the surface temperatures go below the critical level ($T_i$)
for ions to freely flow from the surface. The sparking commences due to the
large potential drop developing along the magnetic field lines in these lower
temperature regions and subsequently the back streaming particles heat the
surface to $T_i$. The temperature regulation requires the polar cap to be
tightly filled with sparks and a continuous presence of sparks is required
around its boundary since no heating is possible from the closed field line
region. We have estimated the time evolution of the sparking system in the IAR
which shows a gradual shift in the spark formation along two distinct
directions resembling clockwise and anti-clockwise motion in two halves of the
polar cap. Due to the differential shift of the sparking pattern in the two
halves, a central spark develops representing the core emission. The temporal
evolution of the sparking process was simulated for different orientations of
the non-dipolar polar cap and reproduced the diverse observational features
associated with subpulse drifting.
