REFLEX OSCILLATORS 677 



We obtain 



p^, = 99.2. (jl4) 



The indications are that oscillations will built up from shot noise rather 

 than from the high frequency transients induced by the pulse. 



The preceding analysis assumes that the full shot noise voltage will 

 appear across the resonator soon enough to override the pulse. The shot 

 noise voltage will reach full amplitude in a time after application of the 

 current of the order of Q/f^ = lirQ/wo . For the values given above 



27r(2/coo = .05 X 10^ 



as this is a considerably smaller time than the .2 microseconds allotted for 

 the buildup of the pulse, the assumption of full shot noise voltage is pre- 

 sumably fairly accurate. 



APPENDIX XI 



Thermal Tuning 



Two extreme conditions may exist 



(1) Cooling is by radiation alone 



(2) CooHng is by conduction alone. 



(1) Radiation Cooling 

 The rate of change of temperature on heating will be given by 



^ = 1 [p, - /cri. (ki) 



Where 



T is the absolute temperature of the expanding element. 



C is the heat capacity of the element. 



K is the radiation loss in watts/ (degree Kelvin) . 



Pi is the power input to the tuner in watts. 



It is assumed that the temperature of the surroundings is constant and the 

 power radiated to the expanding element is included in Pi . Let 



Pi = KT\ and Tr = ^ . (k2) 



Tr is then a reduced temperature since Tg is the temperature which the 

 expanding element would reach at equilibrium for a given power input, i.e. 



(pY' 



r« = I — * 1 . r, is then always less than 1 . 



