  The formation channel of the tens of compact debris discs which orbit white
dwarfs (WDs) at a distance of one Solar radius remains unknown. Asteroids that
survive the giant branch stellar phases beyond a few au are assumed to be
dynamically thrust towards the WD and tidally disrupted within its Roche
radius, generating extremely eccentric (e>0.98) rings. Here, we establish that
WD radiation compresses and circularizes the orbits of super-micron to cm-sized
ring constituents to entirely within the WD's Roche radius. We derive a closed
algebraic formula which well-approximates the shrinking time as a function of
WD cooling age, the physical properties of the star and the physical and
orbital properties of the ring particles. The shrinking timescale increases
with both particle size and cooling age, yielding age-dependent WD debris disc
size distributions.
