Noise Spectrum of Electron Beam in Longitudinal Magnetic Field: Part I -The Growing Noise Phenomenon

W h e n ail RF probe is moved along a magnetically-focused electron b e a m in a drift region, t h e noise power is at first found to v a r y periodically with distance f r o m t h e electron gun. 1 F o r a sufficiently long beam, however, t h e periodic p a t t e r n is succeeded by an exponential rise, culminating in an irregular p l a t e a u . T h i s so-called " g r o w i n g noise" phenomenon has been extensively investigated by its discoverers, L. Smullin and his colleagues at t h e M . I . T . Research L a b o r a t o r y of E l e c t r o n i c s . 2 , 3 T h e y h a v e established t h a t this noise will begin to grow at a plane nearer t h e gun, a n d t e n d to grow at a faster rate, for electron b e a m s (a) of higher perveance, (b) w i t h less space-charge neutralization by positive ions, and (c) issuing f r o m convergent, partly-shielded guns, r a t h e r t h a n those immersed in t h e magnetic field. T h e growth of microwave noise power in d r i f t i n g b e a m s h a s h a m p e r e d t h e development of high-power, traveling-wave t u b e s w i t h acceptably low noise figures, as such devices generally h a v e convergent, p a r t l y shielded electron guns. T h e problem h a s been evaded in t h e design of low-noise, low-power traveling-wave tubes, by resort to confined-flow, parallel beams. Several theories h a v e been proposed to explain t h e growing-noise wave: (1) E x c i t a t i o n of higher-order modes w i t h complex propagation cons t a n t s , b y electrons t h r e a d i n g t h e b e a m transversely; 4 (2) Slipping-stream amplification, d u e to either longitudinal or transverse velocity gradients; 5 (3) R i p p l e d - b e a m amplification; 0 , 7 ' 8 a n d (4) Electron-electron interactions leading eventually to equipartition of t h e r m a l energy, and t h u s an increase in longitudinal velocity fluctuations.