A new form of the space charge distribution inside the channel corona sheath that represents a generalization of previously adopted or calculated space charge densities is numerically analyzed. On one hand, the use of appropriate parameter values produces the previously established corona charge densities as special cases of this generalized distribution. On the other hand, the influence of the new space charge distribution on the corona sheath dynamics can be examined. The simulations showed that the new generalized function possesses excellent features regarding flexibility in modeling of different corona sheath charge distribution. Besides, it proved to be simple and easy to calculate. Although it is applied in the generalized traveling current source model in this study, it could also be readily implemented in transmission-line type return stroke models.