LAUSR

The charge relaxation of accumulated charge patches in insulating straight capillaries is investigated theoretically. The model assumes that charges accumulate only at the inner and outer insulator-vacuum interface of the capillary but not in the bulk. We give an analytical solution to the coupled equations that describe the surface charge dynamics at both interfaces. We provide a tool to calculate easily the characteristic relaxation times in a straight capillary of any dimension, possibly surrounded by a conducting cylinder. The latter allows for different scenarios found in experimental setups, and is applicable to both nanocapillaries and macrocapillaries. We propose an original experimental technique to monitor the charge relaxation in a straight glass capillary and show how to use the presented model to extract the bulk and surface conductivity of the insulator from the measured data. In the Supplemental Material, we provide a script in mathematica that allows the reader to compute comfortably the decay rates for all straight insulating capillaries the reader is interested in.