MEASUREMENT OF ELECTRON-BEAM NOISE

R 553 Philips Res. Repts 20, 349-356, 1965 MEASUREMENT OF ELECTRON-BEAM NOISE by W. KUYPERS and M. T. VLAARDINGERBROEK Abstract The beam-noise parameters Sand Il have been measured by means of a sealed-off three-cavity klystron. No moveable cavities were necessary for the method described. The results compare very well with Hammer's measurements when the gun potentials are adjusted for low-noise figures. If this is not done the values of Sand n are completely different. It appears that in low-noise beams there is a positive correlation between the convection current and the velocity fluctuations. 1. Introduction In the past decade noise propagation along electron streams has been the subject of an intensive theoretical and experimental study. Although much understanding has been obtained, it has not proved possible to discover the mechanism that gives rise to the recently obtained ultra-low noise figures in travelling-wave tubes and backward-wave amplifiers 1). The noise fluctuations in an electron beam are caused by the random emission of electrons by the cathode, giving rise to convection-current and -velocity fluctuations, which are not mutually correlated 2). The major difficulty in the study of noise in electron streams lies in the fact 'that it is impossible to trace the propagation of these noise fluctuations by the beam"in the region immediately in front of the cathode either experimentally or theoretically. In this region the velocity spread ofthe beam is comparable with its d.c. velocity and the noise propagation is non-linear. Furthermore, when the gun voltages are adjusted for low-noise figures the multi-velocity region is extended and the current and velocity distribution across the beam is very inhomogeneous 3). Behind this multi-velocity region there is the high-voltage region, where the velocity spread is small compared to the d.c. velocity. The signal and noise propagation in this region is well understood. To describe the noise propagation in this region Haus 4) obtained from the self- and cross-power density spectra two parameters Sand n which determine the minimum-noise figure of beamtype tubes. These parameters are invariant in the high-voltage region. The inhomogeneous current distribution has little influence on these statements. If Sand Tl were also invariant in the multi-velocity region in front of the cathode we would measure a noise figure of 6 4 db. Yet much lower noise figures have been obtained experimentally. Since the potential distribution in the electron gun under circumstances favorable for low-noise figures causes an extended multi-velocity region 3) it is likely that noise reduction results from the prop-

350 w. K~ERS and M. T. VLAARDINGERBROEK erties of this region. In this paper we present measurements of the noise parameters Sand II as they exist in our low-noise beams. The measurements were performed on a tube with three fixed' cavities. By using three cavities moving interaction circuits could be avoided, which led to a simple construction and the possibility to bake and to seal off the tube. The gun used was developed for low-noise travelling-wave tubes having a wide dynamic range. With a beam voltage of 600 V and a current of 120 (.LAthe tubes have a saturation output power of mw, and a noise figure of 4 5-5 db. 2. Measuring method A sketch of the measuring tube is shown in fig. 1. All three cavities can be tuned over a small frequency range (RI 0 Mc/s). The drift lengths between the interaction gaps are equal. The cavities are machined in one block and consequently they are at the same potential. We first measure the plasma wavelength along the beam using the first and the third cavity. The second cavity is then detuned to such an extent as to insure that it has no influence on the signal coupled into the beam by the first cavity..by changing the cavity voltage we can adjust the power output of the third cavity to a minimum. Then the distance between the first and the third gap is equal to n times the half plasma wavelength. The highest voltage found in this way corresponds to n = 1. This voltage, Vc, is kept constant during the further Fig. la. Sketch of the tube. The output coaxiallines are machined in the same blocks as the cavities but turned over 120 0 with respect to' each other. This also holds for the tuning rods. "'. I. 30mm J Fig. lb. Sketch of the low-noise gun and the drift tubes.

MEASUREMENT OF ELECTRON-BEAM NOISE 351 s b ~ Icath = 0p.A r-, ~2 = 60V." ~ =0V 4 ~, <, ~ 2 ~ r-, ~ -';'=9"/1~ 4 2 I"-. l"'l 840 0 K - i N -111 (V) 20 Icaih = 0PA "['--... ~ = 15V ~3 = 60V 1"'- ~ r-, r-, I'-....._ r-, <, <, r- 7C=840_lK- 7ëJ9!K- -VS (V) 20_ Fig. 2. Iso-current characteristics for two sets of values of VA2 and VA3. measurements, while VA2 and VA3 (cf. fig. 2b) are set at arbitrary values. The beam current is then chosen and kept constant with VB and VAl. Theiso-current characteristics of our gun are shown in fig. 2. In the bend of the characteristics the beam grows hollow and a virtual cathode forms in the space between cathode and first anode 3). This is of great importance for the noise behaviour of the beam. The voltage of the two drift tubes, VDl and VD2, and VA4 are adjusted so that we get minimum noise output from the second cavity (cf. fig. I). From the first cavity we then automatically obtain maximum noise output, since it is located a quarter space-charge wavelength away. Due to the fact that the two cavities are tuned outside each other's resonance region there will be no influence of the first cavity on the output of the second cavity. On the other hand the frequency difference 11/is too small to be of any importance in the beam-noise spectra (11/= 15 Mc/s; Qo cavity = 1500; Jo = 4000 Mc/s). For the output of a matched tuned cavity we can write 5) M2_ P=-qq*, 4gc where P = output power, M = beam-gap coupling coefficient,

352 W. KUYPERS and M. T. VLAARDINGERBROEK.. ge = unloaded-cavityadmittance, q = current-density modulation. The noise output from the first cavity is given by (1) where Sfis the receiver bandwidth (small compared to the cavity bandwidth). The last form in eq. (1) defines lj'max. Since the second cavity is detuned with respect to the first one and a quarter plasma wavelength apart, its output must be With the well-known formula 4) where Zo is the caracteristic -beam impedance, we obtain 4Z02gclgc2 PIP2A PIP2A S2 = -- = G-I -- - M4 47T2Sf2 47T 2 Sf2 ' where G is the power gain from first to second cavity. The power measurements are done by comparing the noise output from the cavity with that produced by a gas-discharge noise standard. When matched, the noise standard supplies a noise power Ps = kts Sj, where k = Boltzmann's constant and Ts = known equivalent noise temperature of the standard. Since the receiver bandwidth Sf (150 kc/s) is sufficiently small compared to the cavity bandwidth (~ 2 Mc/s) the noise spectra from cavity and noise standard are measured over the same bandwidth. We now tune the second cavity to the same frequency as the first cavity. The noise output from the second cavity will become higher as a result of the influence of the first cavity on the beam. This change in noise output is a measure of Il/S as can be calculated in the following way 5,6). If we have at the input of the first gap a noise current modulation ql and a velocity modulation VI,given by the kinetic potential VI, then we get at the output of this gap: and VI' = VI-- M2 2gcl ql' :;:ql, ql-mvg (3) (4)

MEASUREMENT OF ELECTRON-BEAM NOISE where -_ VIVO VI=--, 7J 7J = charge-to-mass ratio of the electron, 4kTS! IVul2 = -- = noise voltage on the gap due to the noise of the 2gcl input system, k = Boltzmann's constant, Vo = d.c. beam velocity, T = cavity temperature. From the second cavity we then get a noise output M2 P2B = - q2q2*. 4gc2 Since the distance between first and second gaps is equal to one quarter of the plasma wavelength, we can put V'. I q2=j-, Zo (5) and M2 1 P2B = - - VI'VI'* 4g c 2 Z02 and with some calculation we find from eqs (2) and (6) (6) with and where II is defined as 3. Results and conclusions and M2 m= --- 2Z 0 g cl 1 II = - (Vq* + V*q). 8rrS! Using the method described we measure Sand II as a function of VB' with VAl adjusted so as to keep the beam current constant; VA2 and VA3 could be chosen arbitrarily, but since they can still influence the multi-velocity region the values of Sand II will depend on these voltages. In fig. 3 we have plotted the results of the measurements for a beam current of 0 (J.A. It appears that the beam noisiness, S _ Tl, is lower when VA2 =

354 w. KUYPBRS and M. T. VLAARDINGBRBROBK 60 V then when V.A2= 15 V. According to fig. 2 in the former case the value of VAl at the bend of the iso-current characteristic is lower, which leads to a long multi-velocity region. The measurements in fig. 3a correspond very well to Hammer's measurements 7,8). For comparison we used the same normalization parameter So = kto/27t, where the temperature, To, is 25 "K and So = 2.2.-21 W.s. The actually measured cathode temperatures, Tc, are lower than To as is indicated in the figures. The value of S is highest for the highest cathode temperature, which was to be expected. The importance of choosing the gun adjustment favorable for low-noise conditions is demonstrated in fig. 3b, where VA2 is 15 V. The value of S is now much higher than is the case' in fig. 3a. Also the value of Ill S is lower. Taking SISo to be 2 5 and IllS = 0 1 we obtain a minimum noise figure of 8 db, obtainable with the beam under the conditions of fig. 3b, whereas for the case in fig. 3a we calculate 4 db. This latter figure compares reasonably well with the noise figures obtained with the travelling-wave tubes mentioned in the introduction. The measurements shown might explain the fact that earlier 9) measurements of Sand Il did not exhibit 1 6.) r.,d,9ok ~ f... V ~=B400K <, r- l...- V, o o 1 6 J\..,.oe.. 1i2 l'-.. <, t-- Icath=0pA = 60V lij =1OOV _. 7ë=9oK -I-- IATc=B40oK o o Fig. 3a. Variation of SISo and IIISo with VB at constant beam current.

MEASUREMENT OF ELECTRON-BEAM NOISE 355 - ;... I--- V h1:'9fjok V 1~=840'K V L.o-. 2, 1"- r-... V 1 o o 20 _~ (V) 30 1 IcaiJ,= 1bof.1A. ~ = f5v ~ =60V Va"... o "/ -e- I::;;:o<j..., - k,'trb4fok Y9tfK o Fig. 3b. Same as in fig. 3a for different values of VA2 and VAS. similar results: they were not performed on low-noise beams which are only formed in a gun under very special potential conditions. One of the requirements for a low-noise beam appears to be a low value of VAl and therefore a long multi-velocity region.. Also for higher beam currents (fig. 4) the value of S is generally much higher, and the lowest temperature gives the highest value of S. Probably the cathode comes close to saturation at low température. Negative values of II can occur. An explanation may be found in the resistance ~f the cathode coating, as suggested in ref.. When the beám current is 200 flaand Ta = 9 OK we find a sudden rise in II from a negative value to zero, similar to Hammer's observation. For low-noise beams (fig. 3a) we did not find this rise since we did not consider negative values of VB.. 'Acknowiedgement. The authors are indebted to Mr W. van den Berg for the construction of the tube, and to Mr W. F. van Eyk for performing many of the measurements. Eindhoven, February 1965

356 W. KU PERS and M. T. VLAARDINGERBROEK 7:.=8~olf./" :rcl9joiok ~ -- --0- --~.-~ r/ - -;..- 1C 9tooK -oo o (}5 20 -VB (V) Tt 5,I J Î 0 I-- T,.-9/0 }< -t-ll / -t-- 7ë-~40~ f-- V t-- ~ _- 1--- >-- 1-- -0-?-o-,, -0 5~- -- 7ër-9IoK 30 20 -L11 (V) "'::::: l----l Icc1th =200jlA -- r--.. 1"'--. - " - =500J.lA ~2 =60V <, <, -... ~J =0~... r--- -1...- I r-::::: I--... r--... r-, - -7ë=9oK... <, I'-- I--... I... Î'- o o... --r---- f-]g9tojk 1 7ë,m840oK 30 Fig. 4. Variation of SISo and Ili S with VB and the iso-current characteristic for beam currents of 200 and 500!LA. REFERENCES 1) M. R. Currie, Proc. LR.E. 46, 911, 1958. 2) A. van der Ziel, Noise, Prentice Hall, 1954, p. 370. 3) M. R. Currie and D. C. Forster, J. appl. Phys. 30, 94-3, 1959. 4) H. A. Haus, J. appl. Phys. 26, 560-571, 1955. 5) A. H. W. Beck, Space charge waves, Pergamon Press, 1958, chapter 6. 6) A. Bers, Experimental and theoretical aspects of noise in microwave tubes, Thesis Res. Lab. of Electr., M.LT., 1955. 7) J. 'M. Hammer, Proc. LE.E.E. 51, 390, 1963. 8) J. M. Hammer, J. appl. Phys. 35, 1147-1153, 1964. 9) S. Saito, Trans. LR.E. ED-5, 264-275, 1958. ) A. Zacharias and L. D. Smullin, Tech. Rep. 358, Res. Lab. of Electronics, M.I.T.