On the Divergence of the Legendre Expansion of the Electron Velocity Distribution

  • W. P. Allis
Part of the NATO Advanced Science Institutes Series book series (NSSB, volume 89a)


In this chapter, we consider the velocity distribution of free electrons in a gas of stationary molecules subjected to an electric field E = - ma/e but with no density gradients. We first discuss the distribution ϕ (\(v\)) when the electrons disappear, by attachment or recombination, at each collision, and then introduce the scat-tered-in electrons as a separate source function S(v,f) to evaluate the full distribution f(\(v\)). It will be seen that the functions ϕ are a recognizable part of the function f. They describe the collision-less “streaming” of the fast electrons in front of the swarm which gain energy from the field and effectively disappear on collision, whereas the bulk of the distribution is determined by the balance between energy gained from the field and lost to recoil or inelastic collisions.


Electron Velocity Inelastic Collision Electron Velocity Distribution Loss Cross Section Computer Printout 


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Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • W. P. Allis
    • 1
    • 2
  1. 1.Joint Institute for Laboratory AstrophysicsBoulderUSA
  2. 2.Laboratoire de Physique des Gas et des PlasmasOrsayFrance

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