  A significant fraction of white dwarfs (WDs) exhibit signs of ongoing
accretion of refractory elements at rates $\sim10^3$--$10^7$ kg s$^{-1}$, among
which, 37 WDs were detected to harbor dusty debris disks. Such a concurrence
requires not only fertile reservoirs of planetary material, but also a high
duty cycle of metal delivery. It has been commonly suggested that this material
could be supplied by Solar System analogs of Main Belt asteroids or Kuiper Belt
objects. Here we consider the primary progenitors of WD pollutants as a
population of residual high-eccentricity planetesimals, de-volatilized during
the stellar giant phases. Equivalent to the Solar System's long-period comets,
they are scattered to the proximity of WDs by perturbations from remaining
planets, Galactic tides, passing molecular clouds, and nearby stars. These
objects undergo downsizing when they venture within the tidal disruption limit.
We show quantitatively how the breakup condition and fragment sizes are
determined by material strength and gravity. Thereafter, the fragments'
semi-major axes need to decay by at least $\sim$6 orders of magnitude before
their constituents are eventually accreted onto the surface of WDs. We
investigate the orbital evolution of these fragments around WDs and show that
WDs' magnetic fields induce an Alfv\'en-wave drag during their periastron
passages and rapidly circularize their orbits. This process could be
responsible for the observed accretion rates of heavy-elements and the
generation of circum-WD debris disks. A speculative implication is that giant
planets may be common around WDs' progenitors and they may still be bound to
some WDs today.
