In dc discharge, most of potential drop is within a spatial length (called sheath thickness). the sheath thickness depends on the various parameters. at constant pressure. It strongly depends on the applied discharge voltage and reduces as we increase the applied voltage. it should be noted that with decrease in sheath thickness, electric field gradient of sheath field is also increased. In this process, one can notice the change in potential contour around the cathode. my first question is that how this contour get changed with increase in the voltage drop across sheath thickness? is possibility that field at sheath edge may change or remain same for any voltage drop?  if you have any link regarding such work then please suggest me.