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Concept
Coulomb collision
Summary
A Coulomb collision is a binary elastic collision between two charged particles interacting through their own electric field. As with any inverse-square law, the resulting trajectories of the colliding particles is a hyperbolic Keplerian orbit. This type of collision is common in plasmas where the typical kinetic energy of the particles is too large to produce a significant deviation from the initial trajectories of the colliding particles, and the cumulative effect of many collisions is considered instead. The importance of Coulomb collisions was first pointed out by Lev Landau in 1936, who also derived the corresponding kinetic equation which is known as the Landau kinetic equation.
In a plasma, a Coulomb collision rarely results in a large deflection. The cumulative effect of the many small angle collisions, however, is often larger than the effect of the few large angle collisions that occur, so it is instructive to consider the collision dynamics in the limit of small deflections.
We can consider an electron of charge and mass passing a stationary ion of charge and much larger mass at a distance with a speed . The perpendicular force is at the closest approach and the duration of the encounter is about . The product of these expressions divided by the mass is the change in perpendicular velocity:
Note that the deflection angle is proportional to . Fast particles are "slippery" and thus dominate many transport processes. The efficiency of velocity-matched interactions is also the reason that fusion products tend to heat the electrons rather than (as would be desirable) the ions. If an electric field is present, the faster electrons feel less drag and become even faster in a "run-away" process.
In passing through a field of ions with density , an electron will have many such encounters simultaneously, with various impact parameters (distance to the ion) and directions. The cumulative effect can be described as a diffusion of the perpendicular momentum. The corresponding diffusion constant is found by integrating the squares of the individual changes in momentum.
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