DK2041_09 - FUNDAMENTAL ASPECTS OF GASEOUS BREAKDOWN-!! W e...

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Unformatted text preview: FUNDAMENTAL ASPECTS OF GASEOUS BREAKDOWN-!! W e continue the discussion of gaseous breakdown shifting our emphasis to the study of phenomena in both uniform and non-uniform electrical fields. We begin with the electron energy distribution function (EEDF) which is one of the most fundamental aspects of electron motion in gases. Recent advances in calculation of the EEDF have been presented, with details about Boltzmann equation and Monte Carlo methods. The formation of streamers in the uniform field gap with a moderate over-voltage has been described. Descriptions of Electrical coronas follow in a logical manner. The earlier work on corona discharges has been summarized in several books 1 ' 2 and we shall limit our presentation to the more recent literature on the subject. However a brief introduction will be provided to maintain continuity. 9.1 ELECTRON ENERGY DISTRIBUTION FUNCTIONS (EEDF) One of the most fundamental aspects of gas discharge phenomena is the determination of the electron energy distribution (EEDF) that in turn determines the swarm parameters that we have discussed briefly in section (8.1.17). It is useful to recall the integrals that relate the collision cross sections and the energy distribution function to the swarm parameters. The ionization coefficient is defined as: (9.1) N W \m in which e/m is the charge to mass ratio of electron, F(c) is the electron energy distribution function, e the electron energy, Cj the ionization potential and Qj(s) the ionization cross section which is a function of electron energy. Other swarm parameters are similarly defined. It is relevant to point out that the definition of (9.1) is quite general and does not specify any particular distribution. In several gases Qi(s) is generally a function of 8 according to (Fig. 8.4), Substitution of Maxwellian distribution function for F(s), equation (1.92) and equation (9.2) in eq. (9.1) yields an expression similar to (8.11) thereby providing a theoretical basis 3 for the calculation of the swarm parameters. 9.1.1 EEDF: THE BOLTZMANN EQUATION The EEDF is not Maxwellian in rare gases and large number of molecular gases. The electrons gain energy from the electric field and lose energy through collisions. In the steady state the net gain of energy is zero and the Boltzmann equation is universally adopted to determine EEDF. The Boltzmann equation is given by 4 : <-», v,0 + a • V v F(r,v,0 + v • V r F(r,v,f) = J[F(r,v,0] (9.3) where F is the EEDF and J is called the collision integral that accounts for the collisions that occur. The solution of the Boltzmann equation gives both spatial and temporal variation of the EEDF. Much of the earlier work either used approximations that rendered closed form solutions or neglected the time variation treating the equation as integro-differential. With the advent of fast computers these are of only historical importance now and much of the progress that has been achieved in determining EEDF is due to numerical methods.is due to numerical methods....
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DK2041_09 - FUNDAMENTAL ASPECTS OF GASEOUS BREAKDOWN-!! W e...

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