Coulomb Focusing

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Coulomb Focusing

Imagine an incident electron has kinetic energy .

Coulomb focusing gives cross-section.

We want to know how far away an electron with can be aimed and still hit the radius cloud around the ion. This is , the impact parameter. Our collision cross-section . Our angular momentum is conserved, so

We know that , where is the velocity to the original electron velocity. This is a result of it falling toward the ion. Then:

Generally, the Coulomb focusing factor because we want to excite, not ionize. , so:

is the “collisional strength”, and generally is 0 below the threshold, goes to 1 at the threshold, and decreases for increasing , with some occasional spikes. Generally, it is of order 1, with some slight temperature dependency.

2000 K gas. , so . Then