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Simple proof of electron beam stability in the deep-potential-well equilibrium

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1 Author(s)
Godfrey, B.B. ; USAF Office of Sci. Res., Bolling AFB, DC, USA

It is well known that a strongly magnetized electron beam propagating in an evacuated conducting pipe can exist in either of two equilibria, one with a shallow potential well and the other with a deep potential well. A Lorentz transformation connecting the two classes of equilibria is derived. Thus, since shallow-potential-well equilibria are known to be stable, the deep-potential-well equilibria must also be. The stability of space charge waves in the two equilibria should follow the same pattern

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Plasma Science, IEEE Transactions on  (Volume:22 ,  Issue: 1 )