Halbritter, J.

Hietschold, R.

Kneisel, P.

Schopper, H.

English

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April 1968Institut für Experimentelle KernphysikCoupling los ses and the :rneasurement of Q-valuesof superconducting cavitiesJ. Halbritter, R. Hietschold, P. Kneis el. H. SchopperKFK 758G M. B. H.KERNFORSCHUNGSZENTRUM KARLSRUHEApril 1968Institut für Experimentelle Kernphysikder Universität (TH) Karlsruhe und desKernforschungszentrums KarlsruheCoupling losses and the measurement ofQ-values of superconducting cavitiesJ. Halbritter, R. Hietschold, P. Kneiseland H. SchopperGesellschaft rur Kernforschung m.b.H. KarlsruheKFK 758throughmight oeeurof the cavityFor the investigation of the surface resistance of superconductorsat high frequencies the Q-value of resonating cavities is usuallymeasured. This is done by observing the decay time of the energystored in the cavityo The decay time is inversely proportional tothe losses in the cavity walls.In order to fill the cavity and to .observe the deeay time, eouplingelements have to be provided which, however, give rise to additionallosses. These consist of two parts. First energy is lostthe coupling apperture by radiation. Second ohmie lossesin the eoupling elements. Usually the quality faetor Qowithout eoupling has been determined from the relation(1 )where QL is the loaded Q-value. The coupling coefficient ß can bedetermined by a measurement of the reflected power at the cavityinput by using the relationp11-ß'12 P 4ß2r e= or K ;: (1+ßfP. \ 1+ß)J. 1.where P. is the incident, P is the reflected power and P is the1. r eemitted power at t = t' (fig.1).During our measurements we made the experience that a reliable de-termination of ß is rather difficult1~ince it requires a perfectmatehing of the network which is used to couple power into theeavity and to observe the decay time. Therefore a method will bedescribed here which permits to determine the Q-value of the un-loaded cavity without measuring ß. Furthermore it will be shown howthe radiative and ohmic losses can be determined independently. Itwas found that the ohmic lasses are not negligible, if coupling loopsare used.- 2 -1)J. Halbritter, P. Kneisel, Ext.Bericht 3/67-3, 1967, Institut fürExp.Kernphysik, Karlsruhe2We start by observing that the losses are proportional to the inverseof the quality factor. By adding up the individuallosses we obtainthe relation=1+Q'o1lir(3)with QM =~ w where ~ 1s the measured decay time. Q isofactor of the cavity which We want to determine. (1/Qr)to the radiation losses and C1/QK) indicates the lossesing system.The radiation losses can be written asthe qua.litycorrespondsin the coupl-= ßQ'o= G (4)In accordance with equ. (1) we find that QM = QL' if the losses inthe coupling system are negligible. It can be shown that ß/Q' = Gois a quantity which depends only on the geometrical dimensions ofthe coupling system.The cavity can be connected to the generator and the measuring deviceeither by a wave guide26r a coaxial cable~ )3Je prefered the secondpossibility since it is most convenient as far as cryogenic and va-cuum technique is concerned and it allows to change the couplingcoefficient. A coupling loop is usually used to couple the cavityfields to the fields in the coaxial line. If the coupling loop doesnot protrude into the cavity but is withdrawn into the tube of thecoaxial line a cut-off mode will build up in the couplingtube withan exponentially decreasing field. By changing the position of thecoupling loop in this field the coupling coefficient ß can easily bechanged over a large range of values. In this case one has- 3 -2)P.B. Wilson, Nucl.Instr. and Methods 20 (1963), 336-3403)Hahn et al, Measurement of Q of Superconducting TE j~ Cavities byFrequency Sweep Technique (Paper presented at the gtli Internat.Conf.on High Energy Ace., Cambridge, Sept. 11-15, 19ß7)" G(z) = Go3-20:. zewhere z gives the position of the loop. The constant 0:. ina firstapproximation does not depend on the frequencyand is given by0:. = j11/a where a is the radius of the coupling tube+. Of courseequ. (5) will hold only, if the coupling loop does not distort thefields of the cut-off mode.Ohmic losses in the coupling system will arise in the coupling loopand in the walls of the coupling tube. It seems reasonable to assumethat the losses in the loop are proportional to the square of theelectric field at the loop. Since this field is again determined bythe cut-off mode one can write1QIS.oop=-zo:.zI1:,e (6)The losses in the tube walls are very approximately given by=since beyond the loop one has the coaxial line with practically ne-gligi"ble l()sses.Inserting (5), (6) and (7) into equ. (3) one obtains1wr: = =-zo:.ze (8)This relation isthebasis for adetermination of Q without knowingoß.To this end öne has to measure the decay time L for various .posi-tions of the couplingloop. If one plots the measured value 1/~(or more acurately 1/(1) t) as a function of zone expects a curve thatcan be fitted by a constant term 1/Qo + ~ and an exponential functionwith the slope2o:.. Unfortunately only the sum 1/Qo + ~ canbe deter-minedin this way where KWcorresponds to the total lossesin the tube- 4 -4wall. However, by covering not only the cavity but also the firstpart of the coupling tube with the superconducting material, .KW canbe made small compared to 1/Qo' This is not true for .~ since theloop is not in contact with the cooling bath and hence cannot bemade superconductingwithout great difficulties. However, this doesnot impaire the measurement of Q •oIn order to verify the dependence of. (8) measurements were perform-ed at various temperatures, frequencies and different types of coupl-ing loops. Some examples are shown in Fig. 2 and 3. One sees thatthe measured curves can indeed be decomposed into a constant termand an exponential function whose slope agrees reasonably weIl withthe theoretical expectation. If the coupling loop is made too broadthe field distortion becomes appreciable and a more complicated de-pendence on z is found.Besides Qo one can also determine the coupling losses Go + ·KL - KW'They are given by the value Of the exponential at z = 0, i.e. ifthe coupling loop is positioned right at the cavity wall. A separa-tion of the radiation losses Go and the ohmic losses KL - KW ispossible, if the coupling coefficient ß is measured directly accord-ing to equ. (2). With ß and Q known, G can be calculated from (4).o 0If the coupling tube wall is superconducting one has Kw<K KL andone obtains~ ß1 (1G=oFor our experimental set-up we find at f = 2,46 GHz that the lassesin the coupling loop are comparable with the radiation losses. ~becomes smaller at 20 K since the temperature of the loop changeswhereas G is independent of temperature.oThe authors would like to thank Mr. L. List and Mr. 0. Stoltz for thepreparation of the cavity andthe help during the measurement.timeft =t',....--t =1:......pe-- --~---P,-I------,;;;t=O+P;Fig.l Response Signal of the Cavity at: Resonance11)~7tAJ'(Fig. 2 The Inverse cfMeasured Q as Functionof Loop Positionf :: ,.?!46 GHz(X,th :: 0.378~'- ....... 1)'" ..........."- r-..........~ ~ ...."- . .'Il' 11 I~ = "'-"- 200 -40 0"--.,~r---. /~ ~ ~2 Drt' .-_. .-I'" I'"11 1 -1~ !-,..~Q, 1,.20 . f()6~2°jt-'9'\. 11"- /" /l\. /"- /~ /"l~'", 1/$/01 ~ ""~ xp - q39h/J ...,-o 2 6 8 12 1'1 171m Z10-7+--.....--.....--..,.---..,.---r-----,....--.---------:------------,Fi g. 3 The Inverse ofMeasu~~~rQ asFunctionbf LoopPositionf = 800 HHz;(tth = 0.73T = 4.2o K10-8~--+---+--_+_-_+_--+---+--+--.,.._-.,.._-._-;_-;_-;_-;_--;-1-= -1'1I &0 960 'IOD '.~f- .-1--.\.s+----+--~\----+----+--+_-+--__I_-_+-_j_-__+_-_+_-+--j______+-__;1\\'~10"fo+-_-+-_-+-_-+-_-+I_\--IlIr--+_-+_-+_-+_-?t'"I/_.....,...f._IO_~_'et_I-L-I!'-)(ft_.-:-a-1j-5t._lJ"""-t" /, /5+---t~_+_~t__-+--~-+--__+'---+--+-_____t,,<-/__t~-T-~r___r_~T__---j--_____;" /'KI+--I---+--+--+--+--I---+--+--+--+--I---+-+--+--;--Zo 2 6 8 10 12 1'1- mm

Coupling losses and the measurement of Q-values of superconducting cavities

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Coupling losses and the measurement of Q-values of superconducting cavities

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