Non-Laplacian ion trajectories in mutually interacting corona discharges

Ion drift in a single-source corona discharge occurs along trajectories which deviate relatively little from the Laplacian field direction. This allows the Deutsch approximation to be used with low errors as in the Popkov model. For coronas from more than one source, the interaction of the space-charge electric fields can cause significant trajectory distortion. Measurements of positive coronas from twin- wire systems make it possible to quantify the Deutsch error. A charge expansion model is used to calculate the ion trajectories at the corona boundaries. The Popkov model predicts, in agreement with measurements, that the normalization of the current density and electric field profiles with respect to the maximum values (J(max) and E-max) yields unique curves independent of the magnitude of the applied voltage. However, the shapes of the profiles of current density and electric field for small wire displacements give poor simulations because of the effect of the proximity of the interacting coronas. In practice this would lead to failure of the Kaptsov condition at the wire surface. The charge expansion model avoids the difficulties of the Popkov model's assumptions. A finite-difference procedure of the charge-expansion model has been outlined and applied to the position of maximum current density (theta = 0) where the ion path is known. This confirms the failure of the Kaptsov approximation of the field at the corona conductor. Application of the charge-expansion model to the position of minimum current density (theta = 90 degrees) has been also possible in order to estimate the drift path length. This trajectory is non-Laplacian in shape and the results indicate that, along this path, a position of minimum field is encountered rather than the monotonic field found at theta = 0.