Home made High voltage Capacitors
Yes it is corona discharge.

Corona discharges are a particular example of partial discharges : a dielectric breakdown in a part only of the electric insulation. This appears when a sufficient high voltage appears across a gap (most often air gap), which triggers the breakdown, and the corresponding light emission.

You can see this phenomenon occurring on AC, because on AC a capacitive current exists through the entire insulation and is able to periodically charge the equivalent capacitor across the aforementioned airgap. Thus, periodically, the air gap is charged, and then discharged by the breakdown.

In DC, the small capacitor is only charged once, so you won't see light.

To prevent this phenomenon, high voltage devices are impregnated with liquid ("oil") or solid (wax, resins) dielectrics, which have a much higher dielectric strength than gases (air).

Edit: actually, this might not be exactly corona discharges, as these kind of discharges occur with very non homogeneous electric fields (around cables, spikes...). This can perhaps be more directly classified as surface discharges (at the boundary of different insulation materials). Anyway, these are all partial discharges.