a constant current, region 2. Region 3 and 4 are caused by ion avalanche as explained by the Townsend discharge mechanism. Friedrich Paschen established the relation between the breakdown condition to breakdown voltage. He derived a formula that defines the breakdown voltage () for uniform field gaps as a function of gap length () and gap pressure (). Paschen also derived a relation between the minimum value of pressure gap for which breakdown occurs with a minimum voltage. and are constants depending on the gas used. Corona breakdown Partial breakdown of the air occurs as a corona discharge on high voltage conductors at points with the highest electrical stress. Conductors that have sharp points, or balls with small radii, are prone to causing dielectric breakdown, because the field strength around points is higher than that around a flat surface. High-voltage apparatus is designed with rounded curves and grading rings to avoid concentrated fields that precipitate breakdown. Appearance Corona is sometimes seen as a bluish glow around high voltage wires and heard as a sizzling sound along high voltage power lines. Corona also generates radio frequency noise that can also be heard as ‘static’ or buzzing on radio receivers. Corona can also occur naturally as "St. Elmo's Fire" at high points such as church spires, treetops, or ship masts during thunderstorms. Ozone generation Corona discharge ozone generators have been used for more than 30 years in the water purification process. Ozone is a toxic gas, even more potent than chlorine. In a typical drinking water treatment plant, the ozone gas is dissolved into the filtered water to kill bacteria and destroy viruses. Ozone also removes the bad odours and taste from the water. The main advantage of ozone is that any residual overdose decomposes to gaseous oxygen well before the water reaches the consumer. This is in contrast with chlorine gas or chlorine salts, which stay in the water longer and can be tasted by the consumer. Other uses Although corona discharge is usually undesirable, until recently it was essential in the operation of photocopiers (xerography) and laser printers. Many modern copiers and laser printers now charge the photoconductor drum with an electrically conductive roller, reducing undesirable indoor ozone pollution. Lightning rods use corona discharge to create conductive paths in the air that point towards the rod, deflecting potentially-damaging lightning away from buildings and other structures. Corona discharges are also used