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Assuming that the wire acts as an ion source, the current i applied to the wire is used to maintain the space charge as follows:

where Z is the ion mobility. Substituting Equation 5.17(5) in 5.17(4) and solving the resultant differential equation yields the following equation:

where C is a constant of integration which depends on corona voltage, current, and the inner and outer cylinder diameters and r is the radial distance from the wire. For large values of i and r, Equation 5.17(6) reduces to E = (2i/Z)1/2, implying a constant field strength over most of the cross section away from the inner electrode.

The following equation gives an approximation of the corona current i (White 1963):

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