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Secondary Emission Effects in Retarding-Field SECONDARY EMISSION EFFECTS IN RETARDING-FIELD OSCILLATORS DISSERTATION Presented in Partial I'ulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of the Ohio State University By Richard Arthur Neubauer^ B.S., M.S. The Ohio State University 195U Approved by: < t - Adviser ACKNOWLEDGEMENTS The research described in this dissertation was conducted under contract between the Air Materiel Command, Wright-Patterson Air Force Base and The Ohio State University Research Foundation. The author wishes to express his appreciation to Professor E. M. Boone for his valuable criticism and suggestions in the capacity of adviser and project super­ visor. The author would also like to thank Professor G. E* Mueller and Mr. M. 0. Thurston for many helpful suggestions concerning the theory. Appreciation is expressed for the help given by the other members of the Electron Tube Laboratory. Finally the author would like to express his gratitude to his wife, Norma, for without her help, this graduate work would not have been undertaken. ii A 48129 TABLE OP CONTENTS Pag© Introduction ........................................... 1 Equations of Motion for Primary and Secondary Electrons 5 Ballistics of Primary and Secondary Electrons......... 11 Energy Terms and Conversion Efficiency ........... 50 Performance Curves, Theoretical........................ 81 Experimental Results Using iSealed-Off Tubes........... 95 Experimental Results Using Demountable Tubes ......... Ill Quantitative Check on the Theory ...................... 129 Conclusions................................................ 132 R e f e r e n c e s ................................................ 156 ill LIST OF SYMBOLS a]_, a.g Entrance phase angles for primary electrons for which/3 is equal to regardless of K. d Gap spacing, e Charge of an electron, f Frequency, m Mass of an electron n Number of primary electrons Injected Into the gap per cycle. v^ Instantaneous voltage drop from cathode to repeller. x Displacement of primary electron. xmax dc displacement of primary electron when K is aero. x Velocity of primary electron. x 0 Initial velocity of primary electron. xa Displacement of secondary electron. xs Velocity of secondary electron. Ea Average voltage rise from cathode to nose. Ep Average voltage rise from cathode to repeller. G.£ Reflected load conductance at the gap. G sh Shunt conductance of the cavity. Ia Average anode current. Io Average.beam current. K Vm/vx N Number of primary electrons which have arrived at the repeller at arrival angle ' . iv N Total number of primary electrons which strike the repeller per cycle. Pc Average value of rf power lost in the cavity. Po Average value of rf power delivered to the load. Rsh Shunt resistance of the cavity. V]_ Average gap voltage drop from nose to repeller. Va Average gun voltage drop from nose to cathode. Vm Maximum value of the sinusoidal rf gap voltage. Vr Average voltage drop from cathode to repeller. oC Entrance phase angle for primary electron. *=<s Entrance phase angle for secondary electron. ot | Limiting entrance angles between which primary electrons strike the repeller.. **C Arrival angle of primary electron at the repeller. / Angle at which repeller bombardment begins. Angle at which repeller bombardment stops. Transit angle of primary electron, nose-to-nose. /?o DC transit angle of primary electron. @ s Transit angle of secondary electron, repeller-to-nose. y^os DC transit angle of secondary electron. y ^l/Va, gap spacing factor. cf Average secondary electron yield from repeller tip. Kl Electronic conversion efficiency. © u)t Limiting angles between which the repeller is above cathode potential. v © D Delay angle of production of secondary electron. © h Transit angle of primary electron, nose-to-repeller. Primary transit angle, nose-to-repeller, when «<. is ^ 2 or 2 * A * Wavelength at resonance. ^p Dimensionless velocity of primary electron. Dimensionless impact velocity of primary electron at the repeller. , Dimensionless exit velocity of primary electron p exit 0 0 at the nose. s exit Dimensionless exit velocity of secondary electron at the nose. O5 Dimensionless velocity of secondary electron. Dimensionless displacement of primary electron. Dimensionless displacement of secondary electron. <0 tirf -r if vi Secondary Emission Effects in Retarding-FIeld Oscillators Introduction The retarding-field oscillator, shown in Figure 1, is one member of a family of electron devices used for the generation of microwaves. Some other members of this family are the klystron, the magnetron, and the travelling- wave tube* While the construction of the retarding-field oscillator somewhat resembles that of the reflex klystron, there are important physical and electronic differences between the two. Among these differences are the following: a. The reflector electrode in a reflex klystron is located in an rf field-free region, whereas the repeller in a retarding-field oscillator Is'part of the rf circuit. b. The electrons in a reflex klystron remain In the gap for a length of time which is only a small fraction of the period of the rf voltage, but the electrons In a retarding-field oscillator remain in the working gap for a length of time greater than the period of the rf voltage. The retarding-field oscillator is easily tuned over a wide range of frequencies. A two-to-one tuning range is common, and In special cases the range can be considerably greater. The tube is simple in design and therefore ' / / s'y/y/'/'i Model of a C&pacitively Tuned* Demountables 2- U cm Retarding-field Oscillator Figure 1 3 promises to be relatively easy to produce in large quantities. Its power output is good; in the 2.5~to-5-om wavelength region it ranges from about one watt for the planar gap geometry to several watts for the capacitive geometry. Because of its excellent tuning range and power out­ put, the retarding-field oscillator is a good source of microwave energy for measurement purposes. It could also be used as a local oscillator in microwave receivers. High power output under pulsed operation has not been investi­ gated because there are commercial tubes available for this purpose. Rather, the retarding-field oscillator is best adapted to filling the need for a low-voltage, easily tuned microwave energy source which can cover a wide range of frequencies. The basic design for the oscillator studied in this paper was introduced In 1947 by Dr. Oskar Heil^- who was then associated with the Electron Tube Laboratory of the Ohio State University. The original work of developing the oscillator was largely done by J. J. Ebers^- under the supervision of Dr. Hell. The first models operated in the 5-toiO-cm wavelength range. They used the half-size Hell electron gun and loop output coupling. Scaling techniques have since been applied and the oscillator has now been successfully operated in the 7-to-14- mm wavelength region. There is evidence that the tube can b© scaled further if the techniques of fabrication can be refined. Loop output coupling is no longer used, having been replaced by the repeller output coupling and waveguide system shown in Figure 1. The experimental work covered by this paper was performed in the 2.5-to-5-cm wavelength region. Reference to Figure 1 shows that the oscillator consists of an electron gun, a cavity resonator, and a repeller electrode. High velocity primary electrons enter the resonator through an orifice in the nose of the gun assembly. In the working gap between repeller and nose, the electrons reverse direction and return to the nose where they are collected. When conditions are correct, an rf gap voltage will develop, being supported by the resonator with energy obtained from the electron beam. Tuning Is accomplished by moving the repeller, and the frequency of oscillation increases with gap spacing. The cavity and repeller form a coaxial line by means o-f which rf energy may be extracted from the resonator. In normal operation, the injected electrons remain in the working gap for a length of time longer than the period of the rf voltage. Their trajectories are therefore complicated functions of time and entrance phase angle. Some electrons extract energy from the rf field and strike the repeller. Here they give rise to secondary electrons which are accelerated through the gap to the nose. The number of secondary electrons produced depends, among other thingsj upon the shape and surface of the repeller, and upon the energy and number of primary electrons striking it. Both positive and negative repeller currents have been observed. At the low-frequency end of its vd.de timing range, the oscillator is particularly sensitive to the production of secondary electrons. The purpose of this investigation is to determine theoretically and experimentally some of the effects of secondary emission on the operation of planar retarding- field oscillators. The theory is generalized in dimension­ less form and covers not only the range where oscillations are self-sustaining, but also the range where the cavity is driven as in hot admittance measurements or amplifier applications. Equations of Motion for Primary and Secondary Electrons The analysis of the retarding-field oscillator is made with the assumption of planar geometry, uniform electric field intensity (function of time only), and complete coupling to the beam. Figure 2 illustrates the voltages present in the working gap. The force per electron is V1 ■+■ vm 3in (e+oC) z , . — ------------------- e newtons/electron (1) d where e is + 1.601 x 10~^® coulomb/electron, © = ci>t, and FL&ss© of to® Hepollos* BsgEroeoatetdLoa of to© Voltages® PpsoQiat. in to© tJarkisis G©p. Figaro 2 is the entrance phase angle of the primary electron. Newton1s law of motion gives the acceleration as g — — — 2. P V n + V sin (©+oC )*"] meters/second^, (2) ^ 2 m«sl L- -J where m = 9.107 x 10” kilogram/electron. Integration of the acceleration yields the velocity x = - _g j^V-^t - Xg cos (©*<<rj + 0^ (3) When t — 0, x = xQ, the initial velocity of the Injected electrons.
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