size. This represents a tip radius of curvature of 1 µm for a 200-
µm long spheroid and 0.33-µm radius for a 600-µm long particle
(300-µm major radius). These are very small tip radii, small
enough that a dielectric such as XLPE is not highly homogeneous
on this scale, which will increase the statistical variability
of failure statistics, as discussed subsequently.
Figure 6 shows a computation of the critical background field
at room temperature (300°K) required to produce a space charge
limited field extent of 1, 1.5, and 2 µm as a function of particle
length for a constant particle diameter of 10 µm, which is near
the worst case. Based on Figure 6 and assuming that failure is
likely if the space charge limited field extends beyond 1.5 µm
from the defect tip, a background field of 24 kV/mm would be
required to cause failure for a 100-µm long particle, decreasing
to about 14.5 kV/mm for a 200-µm long particle. These data
suggest that the maximum tolerable particle length is in the range
of 150 to 200 µm at room temperature, given typical maximum
operating fields in the range of 15 to 18 kV/mm.