INVESTIGATION OF CHARGED GAS INSTABILITY IN TWO–DIMENSIONAL MODEL OF LIGHTNING DISCHARGE O. V. KRAVCHENKO 1 *, V. I. PUSTOVOIT 2 1 Bauman Moscow State Technical University, Moscow, 105005, Russia 2 Scientific and Technological Center of Unique Instrumentation RAS, Moscow, 117342, Russia *olekravchenko@gmail.com ABSTRACT The present paper is an extension of previous re- search related to the problem of the leader of light- ning formation. It was introduced earlier that a homogenous charged media could become unsta- ble under some initial conditions in [1], [4] in one dimensional case. We present here an investiga- tion of such kind instability in two dimension case also. 1. INTRODUCTION Since the middle of the last century problems of stability of charged jet flow occupy the central place in EHD. But, the fluid equations are difficult to handle because of their nonlinearity and mathe- matical complexity as a result. One of the approaches is to study the influence of an electric field on a velocity field. E. Moreau and O.Vallee considered in [2] an electric field as an elastic term of force for some model plasma prob- lem. An analytic resolution of a one dimensional problem faced in ionised media was proposed, when the electric field is dominant in front of the magnetic field (electro hydrodynamical approach). This situation could be appeared for example in electric discharges or electric arcs studies. For this purpose, E. Moreau and O.Vallee considered a constant electric field applied to a plasma in which it was assumed the existence of a constant electron flow (created for example by electrodes system and depending of applied electric field), which may be interpreted as a source term. More- over, the plasma was assumed to be composed of electrons and motionless ions. After some reasoning a one dimensional Burgers like equation of the local electric field E loc was appeared with an elastic forcing term ∂ t E loc = ν∂ xx E loc + E loc ∂ x E loc − xS + c(t). Finally the possibility to derive a new equation of evolution for the electric field held to the Poisson equation was shown. It seems interesting that probably the first appear- ance of the Burgers like equation in plasma model of instability saturation by resonant mode cou- pling was considered by E. Ott, W. M. Manheimer, D. L. Book and J. P. Boris in [3]. Their model was in general form: ∂ t u + α 1 u∂ x u + M (u)=0, where M (u) is a linear operator given by ∞  -∞ M (u)e -ikx dx = iω(k) ∞  -∞ ue -ikx dx, where ω(k) is a dispersion relationship. It was no- ticed that in case ω(k)= i(α 3 − k 2 α 2 ), a Burgers like equation was obtained in the fol- lowing form ∂ t u + α 1 u∂ x u − α 2 ∂ xx u − α 3 u =0. A variety of different instabilities that can be stabi- lized nonlinearly by resonant mode coupling were examined. A steady state behaviour of Burgers like equation was examined by a phase plane anal- ysis also.