HOM Couplers at DESY Jacek Sekutowicz** 2000 Hamburg 52, West-Germany

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1 ntroduction HOM Couplers at DESY Jacek Sekutowicz** DESY, MHF, NotkestraBe Hamburg 52, West-Germany UiMEL computation and beadpull measurements showed that a 4-cell, 500 MHz HERA cavity has five parasitic mode families with high R/Q which must be damped by HOM couplers. To reduce induced power in cavity,qext of these resonances should be low due to the fact that maximum design current of the HEM electron ring is b = 58 ma. During the last two years couplers based on two inductive stubs were developed and tested in SC version. The two stubs construction of HUM couplers was chosen as a relatively simple cryogenic solution for the cooling of all inner components of the coupler. n November 1987 a test of the complete accelerating modul consisting of two 4- cell cavities, two fundamental mode couplers and six HOM couplers will be carried out. Each 4-cell cavity is equipped with a set of three HOM couplers: one mainly for reducing Q of TMoii family (coupler TM) and two for loading the most dangerous dipole modes and TMoi2 family (couplers ''Ej. Table 1 presents a list of higher order modes with high R/Q and &xt as measured for copper model of 3 HOM couplers attached to a 4-cell cavity: TMo i i TMi l i jtm * For dipole modes R/Q is computed and measured 5 cm out of beam axis. ** on leave of absence from NS, Otwock-Swierk, Poland

2 More detailed information about the measured data of the copper model is presented in (2). Two Stub HOM Couulers t can be seen from Table 1 that most dangerous modes have resonant frequencies below 1.5 GHz. That is why a coaxiel line technique was chosen as more useful compared to waveguide technique for coupler design. nteraction between cavity and electric antenna coupler can be analyzed with the help of the lumped element circuit of fig. 1 (1,s). 1 ) ;cc ; CCz C' Transforming par+ cavity a b- load. antenna Fig. 1 Lumped elements representation of the interaction between cavity and electric antenna coupler. Here the elements b, Lo, CO represent a resonator. The coupling condenser Cc corresponds to the part of the electric field lines terminated at the antenna tip. CS is the stray capacitor of the coaxial line in the region of the antenna tip. Both Cc and CS represent the electric antenna. The transforming part of the coupler is a microwave circuit, the function of which will be discussed below. The elements Ro, Lo, CO, Cc in general are different for different modes. To reduce Q one ought to shunt the parallel resonator RoLoCo with a low resistor in the plane a-a. This is required for all resonance modes except for the fundamental-for each HOM resonance, low resistance in the plane a-a can be obtained by proper transformation of the load resistor 3 towards the cavity in a way that the imaginary part of the impedance in the plane b-b compensates reactance of both capacitors, equal:-j/w((+c ). The coupling condenser Cc << CS, then as the first order 5 c approximation we assume that the imaginary part Zitb of the impedance in the plane b-b should be j/oc S instead of j/w(~,+~c).

3 For the fixed geometry of the antenna tip an "ideal" transforming part ought to realize compensation in the whole range of HOM frequencies, as shown in fig. 2 by solid line: Fig. 2 " " reactance ----" reactance realized by two stub coupler type TE ' -X-X" reactance realized by two stub coupler type TM Since Z ibb is positive, it has character of an inductance, the reactance of which is proportional t03/~. This is just opposite to the normal behaviour of an inductor (impedance ).Two stub transforming part of couplers TE and TM are designed to approximate the curve of Fig. 2 in the region TEiii, TMoii and TMoiz families by the coupler TE and in the region of TMoii passband by the coupler TM. Fig. 3 a, b show the transforming part of the HOM coupler based on two inductive stubs and its microwave replacement circuit. inductive stubs inner <outer conductor Fig. 3 a) Two stub transforming part b) Replacement circuit of two stub transforming part

4 The microwave function of both inductances which are separated uy a piece of coaxial line, is as showri on the Smith chart below: Fig. 4 1 ) ''ransiormatic~n for i~ 2) Transformaticln Tor f2 For two frequencies fi < f2 one can choose a vaiue of the irlductance L2 and distance d so that the impedance ZA, belng the result of the transformation (1) 1 L2 to the plane of L1, is high ana (6 ~ ~ + 4 ' ~ ) w,lq ' & For higher krequency fz transformation gives small impedance Zs (as shown in fig. 4 and then(d/u2~,+.?~b)-~~e<u)+~4 The complete replacement circuit, including fundamental mode filter and output system is shown in Big. 5.

5 CL L1 CL L2 CL FMF CL OS CL Fig. 5 Lumped element representation of HOM coupler CL - coaxial line FMF - fundamental mode filter CS,CS ' - stray capacitors OS - output system The frequency broadband characteristic behaviour of the couplers was computed with help of the computer program written especially for synthesis of coupler components. Computed transfer curves were checked for each succeeding coupler version by two types of broadband characteristic measurement: with the coupler mounted onto a piece of beam tube with damping material inside and with the couplers mounted onto 50 Ohm coaxial line. The second measurements were used as a calibration of the transfer curves obtained with the first measurements to get a relation between dissipated power in coupler load R and electric field at the antenna tip for each HOM frequency. The electric field in a cavity can be computed with a code like URMEL. Having an electric field at the coupler position one can rescale the power dissipated in the load and then find Qext. This method was used for monopole modes and several initial couplers before the copper model of 1- and 4-cell cavity was done. Qext values differed by less than an order of magnitude from the values measured directly afterwards on 1- and 4-cell cavities. Picture 1 shows the coaxial line employed for these measurements and the set of subelements used for construction of coupler models. An example of computed and measured transfer curves of the coupler TE is performed in Fig. 6.

6 Pic. 1 Coaxial line employed for broadband characteristic measurements and subelements used for coupler models. Fig. 6 Transfer curve of coupler TE a - measured curve b - computed curve

7 Cold Test Results The SC version of both kinds of couplers is shown in Pic. 2. Pit. 2: Coupler TE (left), coupler TM (right) The construction of HOM couplers allows correction of machining errors after couplers are welded to the cavity. Damping of HOM is optimized with output coupling condenser C2 apd end stray condenser CS' (Fig. 5). The power of the fundamental mode dissipated in the load of a coupler is minimized by tuning of condenser C1 which is part of the fundamental mode filter. Eight HOM couplers ( 3 TM and 5 TE) were tested in SC version, two with l-cell cavity and six with 4-cell cavities (6,7). Damping of all HOM was as for the copper models (Table 1). Qext of fundamental mode was in the worst case 1.2 X t means that with Eacc = 5 MV/m fundamental mode dissipated power was 6.7 W.

8 Acknowlednements want to thank my colegues E. Haebel from CERN, B. Dwersteg and D. Proch from DESY for the fruitful collaboration during studying and developing this type of HOM couplers. References ) R.N. GHOSE, Microwave Circuit Theory and Analysis 2j E. HAEBEL, J. SEKUTOWCZ, Higher Order Mode Coupler Studies At DESY, DESY M ) D. PROCH, private communications 4 ) H. UWERSTEG, private comrnunications 5) E. HAEBEL, P. MARCHAND, B. TUECKMANTEL, Proc. of Second Workshop on RF Superconductivity, Geneva ) Lab. note, DESY/MHF-SL-1/87 '7) Lab. note, besy/mhf-sl, to be published

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