Swarming Electrons
Posted: Tue Sep 29, 2009 9:18 am
Sent by one of my correspondents:
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http://rspa.royalsocietypublishing.org/ ... /436.short
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http://rspa.royalsocietypublishing.org/ ... /436.short
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Electron clouds rotating in axially symmetric magnetic fields have been known for a long time, but the agreement between theory and experiment is still very unsatisfactory. The discrepancy appears to be due to the interaction of electrons. Before approaching this difficult problem it is desirable to possess a more complete theory of stationary swarms without interaction. In the present paper the distribution density is calculated on the basis of classical statistical mechanics. It is shown that electrons injected at any point with very small initial velocities will distribute themselves with a density inversely proportional to the distance from the axis, in a certain annular space. Only the limits of this space, not the distribution inside it, will be dependent on the electric or magnetic fields. The uniform or nearly uniform distributions calculated by previous authors are singular solutions, inconsistent with any degree of statistical disorder. Other laws of density distribution can be realized by simultaneous injection of electrons at several points. These offer a possibility to realize dispersing electron lenses and corrected electron optical systems. It is shown that the ring current produced by the rotating electron cloud can reduce the magnetic field at the axis very considerably in devices of practicable dimensions. It appears also possible to produce clouds of free electrons with densities sufficient for observable optical effects.