ABSTRACT
T h is expression fo r the charged partic le s ' density d istribu tion nix) then can be app lied to find the second approx im ation o f the elec tric field d is tribu tion E(x), using the M axw ell equation fo r the case o f cy lindrica l sym m etry:
T he M axw ell equation can be easily in tegrated , tak ing in to account that the e lec tric field d is tribu tion should fo llow E quation 9.1 w ith the critical value o f voltage Vn. (co rrespond ing to co rona ign ition) at the low curren t lim it i —> 0. T h is in tegration y ie lds the elec tric field d is tribu tion , w hich takes into account cu rren t and, thus, the space charge:
A lso , the d is tribu tion (E quation 9 .19) is valid only in the case o f sm all elec tric field pertu rbations due to the space charge ou ts ide the active co rona volum e. E xpressions s im ilar to E quation 9 .19 describ ing the influence o f elec tric cu rren t and space charge on the elec tric field d is tribu tion could be derived for o ther corona configu ra tions.264
In tegration o f the expression fo r the elec tric field E quation 9 .19 over the rad ius x, tak ing into accoun t tha t in m ost o f the co rona d ischarge gap .r2 » r2, gives the relation betw een cu rren t (per unit length) and voltage o f the d ischarge, w h ich is the c u rren t-v o ltag e characteristic o f co ro n a genera ted around a thin w ire:
