The admittance expressions of small signal electron beam in the 2π-mode double-gap output cavity are derived by analytic method in this paper

and a formula of starting oscillation current is obtained based on the condition of forming monotron oscillation in a double-gap output cavity.The circuit admittance of a 2π-mode double-gap outqut cavity loaded with rectangular waveguide is calculated quantitatively by 3D simulation method

then the starting oscillation current and the frequency of monotron oscillation in the 2π-mode double-gap output cavity are determined.These calculations results show that under the condition of invariant accelerative voltage of electron beam

when beam current is increased to a certain value

a harmful monotron oscillation will be brought on in the double-gap output cavity.Moreover

the monotron oscillation frequency has complicated relationships with the accelerative voltage and the current of electron beam.Meanwhile

the possibility of forming monotron oscillation in the double-gap output cavity has been demonstrated further using the MAGIC PIC simulation program

and the starting oscillation current is obtained.The results of particle simulation are consistent with the results of analytic method.These research conclusions about forming process and regularities of harmful monotron oscillations in a double-gap output cavity will have a vital significance for improving the stability of double-gap cavity output circuits of klystrons.