Microwave Tubes
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IEEE rRANSACTI0N.S ON ELECTRON DEVICES, VOL. ED-32, NO. 11, NOVEMBER 1985
A Model for the, Klystron .Cavity Gap
J. RODNEY M. VAUGHAN,
FELLOW, IEEE
radius of curvature r,,. This was recognized by the workers during World War I1 [l], [2] ,who observed that the “perfectly sharp” gap could be solved by the method of conformal transformation, and yielded a sin-’ variation of the potentia2 across the gap when g/a was either very small or very large. The assumption that this solution was also reasonably good in the middle range of g/a led to the proposal [2] to use J0(S/2) instead of sin (8/2)/(8/2) in (1). This was equivalent to saying that the sharp gap case corresponded to a blunt gap about 25 percent longer, since Jo(x) is a good approximation to sin 1.25d1.25~ over the -1. INTRODUCTION range of values that occur (up to about 4 radians transit HE GAP of a klystron cavity is shownin Fig. 1. Fie.ds angle). developedby an RF voltage VRF across the gap of In reality, the gap is neither perfectly sharp nor perlength g will interact with an electron beam of radiuc. b fectly blunt. Kosmahl and Branch [3] adopted the cosh passing at velocity uo through thetunnel of radius a. Under function to represent the field across the gap in the form large signal conditions, an integral of the form 1E.J dv is E&, a) = Eo cash (mz), (-g/2 < z < g/2) required to compute the interaction accurately. But, uric-er small-signal conditions, which apply for all but the Past =0 ( 2 > g/2). 11 (2) few cavities of a multicavity tube, the interaction can be represented by a coupling factor M: this is the factor 3y The parameter m, which has the dimension of an inverse which the energy exchange is reduced from that due te a length, describes the sharpness of the gap noses, but asdc voltage change equal to the peak RF voltage. It is ba.- signing a value to it is a matter of some difficulty for the sically a transit-time factor, but the fringing of the fiel’js design engineer. Kosmahl
IEEE rRANSACTI0N.S ON ELECTRON DEVICES, VOL. ED-32, NO. 11, NOVEMBER 1985
A Model for the, Klystron .Cavity Gap
J. RODNEY M. VAUGHAN,
FELLOW, IEEE
radius of curvature r,,. This was recognized by the workers during World War I1 [l], [2] ,who observed that the “perfectly sharp” gap could be solved by the method of conformal transformation, and yielded a sin-’ variation of the potentia2 across the gap when g/a was either very small or very large. The assumption that this solution was also reasonably good in the middle range of g/a led to the proposal [2] to use J0(S/2) instead of sin (8/2)/(8/2) in (1). This was equivalent to saying that the sharp gap case corresponded to a blunt gap about 25 percent longer, since Jo(x) is a good approximation to sin 1.25d1.25~ over the -1. INTRODUCTION range of values that occur (up to about 4 radians transit HE GAP of a klystron cavity is shownin Fig. 1. Fie.ds angle). developedby an RF voltage VRF across the gap of In reality, the gap is neither perfectly sharp nor perlength g will interact with an electron beam of radiuc. b fectly blunt. Kosmahl and Branch [3] adopted the cosh passing at velocity uo through thetunnel of radius a. Under function to represent the field across the gap in the form large signal conditions, an integral of the form 1E.J dv is E&, a) = Eo cash (mz), (-g/2 < z < g/2) required to compute the interaction accurately. But, uric-er small-signal conditions, which apply for all but the Past =0 ( 2 > g/2). 11 (2) few cavities of a multicavity tube, the interaction can be represented by a coupling factor M: this is the factor 3y The parameter m, which has the dimension of an inverse which the energy exchange is reduced from that due te a length, describes the sharpness of the gap noses, but asdc voltage change equal to the peak RF voltage. It is ba.- signing a value to it is a matter of some difficulty for the sically a transit-time factor, but the fringing of the fiel’js design engineer. Kosmahl
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