Cyclotron maser instability for general magnetic harmonic number

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Abstract
The cyclotron maser instability for general magnetic harmonic number transverse electric (TE) and transverse magnetic (TM) waveguide modes in a conducting cylinder of radius Rc are examined. The analysis is carried out for a hollow electron beam (radius R0) propagating parallel to a uniform axial magnetic field B0êz. It is assumed that ν/γ0≪1, where ν is Budker’s parameter and γ0mc2 is the electron energy in a frame of reference moving with the beam axial velocity βbcêz. One of the most important features of the analysis is that the instability growth rate for magnetic harmonic numbers s=2,3,... is comparable to the growth rate of the fundamental (s=1) mode, particularly for moderate electron energy [β0= (1−1/γ20)1/2≳0.4]. Moreover, it is shown that the instability growth rate can be maximized by appropriate choice of the geometric parameter R0/Rc.