This paper examines the negativehyphen;mass stability properties of anElayer for transverse electric (TE) and transverse magnetic (TM) waveguide modes in a conducting cylinder. The analysis is carried out for a relativistic nonhyphen;neutralElayer aligned parallel to a uniform axial magnetic fieldB0ecaret;z, within the context of the assumptions that the electron motion is ultrarelativistic (ggr;0Gt;1) and that (ngr;/ggr;0)1/3Lt;1, where ngr; is Budkerrsquo;s parameter and ggr;0mc2is the electron energy. One of the most important features of the analysis is that the axial energy spread can have a large influence on the stability behavior for both the TE and TM waveguide modes. By an appropriate choice of system parameters, it is shown that the spectrum of microwave radiation generated by the negativehyphen;mass instability can be very narrowband.
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