Applications. Sami G. Tantawi, Stanford Linear Accelerator Center, Stanford University, CA 94025, USA

Transcription

1 SLAC-PUB-9142 April 2004 A Novel Circular TE 01 -Mode Bend for Ulra-High-Power Applicaions Sami G. Tanawi, Sanford Linear Acceleraor Cener, Sanford Universiy, CA 94025, USA Absrac Fuure Linear Colliders and Acceleraors require rf sysems and componens ha are capable of handling hundreds of megawas power levels a x-band frequencies and higher. Sandard rf componens ha have been in use for a long ime such as waveguide bends, direcional couplers and hybrids, can no be used because of peak field consideraions. Indeed, one has o reinven mos of hese componens aking ino accoun he consrains imposed by ulra-high-power operaion. Here, we presen a new design for circular waveguides bends propagaing he low-loss TE 01 mode. The bend has smooh walls and low field levels. We presen a simple synhesis process for designing such device. The general philosophy of his echnique can be applied o oher componens as well. We describe he deailed design of he bend and compare our design wih finie elemen simulaions and experimenal daa. The bend has very low ohmic losses, and he TE 01 mode is ransmied wih virually perfec mode puriy. The Auhor is wih Sanford Linear Acceleraor Cener (SLAC), Menlo Park, CA He is also wih he communicaions and elecronics Deparmen, Cairo Universiy, Giza, Egyp. Work suppored in par by he Deparmen of Energy conrac DE-AC03-76SF00515.

2 I. INTRODUCTION Recenly, ulra-high-power rf sysems a X-band and above have received a lo of aenion in differen laboraories around he world because of he desire o design and consruc a fuure linear collier. For a review of hese aciviies he reader is referred o [1-2]. These sysems are required o generae and manipulae hundreds of megawas. Sandard rf componens ha have been in use for a long ime such as waveguide bends, direcional couplers and hybrids, can no be used direcly because of peak field consideraions. Indeed, one has o reinven mos of hese componens while aking ino accoun he consrains imposed by ulra-high-power operaion. Usually mos of hese compors are made wih oxygenfree high-conduciviy copper and he operaion akes place under ulra-high vacuum condiions. Experimenal work a x-band showed ha peak elecric fields should no exceed 500 kv/cm[3]. Peak magneic field should be limied so ha he pulsed surface heaing does no exceed 30 C o [4] For hese sysems he TE 01 mode in circular waveguide is very aracive because i has low loss properies, and here are no elecrical field lines ha erminae on he walls of he waveguide. The low-loss TE 01 mode in circular waveguide has been uilized for several decades. I was used in several applicaions including communicaion sysems, anenna feeds and rf sysems for high energy acceleraors. Waveguide bends are imporan componens for waveguide rf circuis and ranspor lines. The firs analysis for bends in circular guides carrying he TE 01 mode is found in [5]. Since hen several design conceps have been inroduced o for hese bends [6,7,8]. However, none of hese designs are really suiable for ulra-high-power operaions. Here, we presen a new idea for perurbing he cross secion of he waveguide smoohly o allow ulra high power operaion. There are several numerical echniques for he analysis of waveguide bends, see for example [9]. However, since here are several consrains on he design including mode puriy, hese are no convenien for he design process. We presen a simple synhesis process for designing such bends ha guaranees mode puriy. We laer verify our resuls wih finie elemen simulaions and experimenal daa.

3 II. DESIGN METHODOLOGY AND SYNTHESIS PROCESS The bend design is shown in Fig. 1. The bend comprises wo circular o square apers, wo adiabaic apers from square o recangular cross secion, and a connecing recangular waveguide bend. Z -Axes Square o recangular aper lengh Lengh: of λ The dimensions of he recangular guide is λ x1.452λ a =2.916 λ Circular o square aper of a lengh Lengh: of λ. The dimensions of square he square waveguide are λ x1.355 λ b =4.049 λ Circular waveguide wih a Diameer: diameer of λ h =1.452 λ Figure 1. Bend Geomery. All dimensions are given in erms of free space wavelengh. A. The Circular o Square Taper In [10] i was noed ha smooh ransiions from recangular o circular waveguide preserve heir common reflecion symmeries. The S-marix of he ransiion connecs modes of he same symmery class, and for a sufficienly adiabaic ransiion preserves heir TE (or TM) characer. I is hen also nonreflecing and, in he absence of degeneracy, is modal connecions are one o one and order preserving. These properies enable us o carry ou all of he RF manipulaions in he more easily handled over-moded recangular waveguide. For he circular o square aper presened here he circular waveguide diameer is chosen such ha all modes wih cu-off frequency above ha of he TE 01 mode do no propagae. The square waveguide is jus large enough o allow boh TE 20 and TE 02 modes o propagae. However, i does no allow he propagaion of TE 22 and TM 22 modes. Because of reflecion symmeries, only he wo degenerae modes, TE 20 and TE 02, are exied in he recangular guide when he TE 01 mode is inciden in he circular waveguide. Using a finie elemen code, he design process for his aper is done by simply increasing he lengh unil he

4 reflecion coefficien for he TE 01 mode in he circular guide is small enough. Because of degeneracy he combinaion beween he wo modes in he square waveguide could be regarded as one single mode. When exciing he circular guide wih he TE 21 mode, again, i couples o he same wo recangular modes TE 02 and TE 20. However, he phase beween hem is a 180-degree differen from he previous case, i.e., when hey are excied wih he TE 01 mode in he circular guide. B. The Square To Recangular Taper For reasons ha will become clear in he nex subsecion we needed o perform he bend in a recangular waveguide raher han a square one. To ge o he cross secion of he recangular guide we used an adiabaic aper. The recangular cross secion of he guide sill propagaes boh TE 02 and TE 20 modes. However, hey are no longer degenerae. A sraigh recangular cross secion is insered afer he aper o adjus he phase difference beween he TE 20 and he TE 02 modes C. The Recangular Bend The modes in a recangular waveguide bend are well known, see for example [11]. The modes are referenced as TE or TM o he Z direcion; where he Z direcion is normal o he bend plane; see Fig. 1. For TE modes one can wrie he z componen of he magneic field explicily as H jφ ( r, φ, z) = AY [ ( k a) J ( k r) J ( k a) Y ( k r) ] sin z e ; (1) z nπ h where J (.) is he Bessel funcion of firs kind and order, Y (.) is Neumann s funcion of order, a is he bend s inner radius, h is he bend heigh, n is an ineger, Y and J means derivaives of hese funcion wih respec o he argumen, and k is he ransverse wave number given by, 2 k + 2 nπ h 2 ω = c ; (2) where ω is he rf angular frequency and c is he speed of ligh in free space.

5 The inciden field of he TE 20 mode in he recangular guide has wo variaions along he Z-direcion. Because he bend is uniform along he Z-direcion he excied fields in he bend mus respec he symmeries of he inciden field, hence one mus choose n =2. Eq. (1) indeed saisfies he boundary condiion of H z = 0. To saisfy he boundary condiions a he ouer radius of he bend b, one mus choose he order such ha H z = 0 ; i.e, Y ( ) ( ) ( ) ka J kb J ka Y ( kb) = 0. (3) Similarly for TM o Z modes one can wrie H r r=a r n jφ ( r, φ, z) = AY [ ( k a) J ( k r) J ( k a) Y ( k r) ] cos z e. (4) z π h Applying similar argumens o he case of he TE modes, because he inciden TE 20 mode has no variaion along he Z-direcion one mus choose n=0. The boundary condiion of E = 0 is saisfied by Eq. (3). To saisfy he boundary condiions a he ouer radius of he bend b, one mus choose he order such ha E = 0 ; i.e, z r=b Y ( ka) J ( kb) J ( ka) Yυ ( kb) = 0 (5) One can choose he dimensions of he bend such ha only wo TE modes wih n=2 can propagae. A he same ime, one can also choose hese dimensions so ha only wo TM modes wih n=0 can propagae. This gives us a oal of four modes ha can propagae and are excied because of an inciden TE 01 mode in he circular guide. Because of reciprociy, if he relaive phases and ampliudes of hese four modes are he same a he inpu and oupu of he recangular bend, hen one has o excie a pure TE 01 mode a he oupu circular guide if a pure TE 01 mode is exied a he inpu circular guide. The recangular bend is relaively compac and he four modes will propagae hrough i wih negligible loss, hence, he ampliudes of hese modes are he same a he beginning and end. However, one mus adjus he bend dimensions o phase hem for proper recombinaion a he oupu r=b z r=a

6 Le he four modes have azimuhal propagaion consans 1 hrough 4. The oal phase shif for each mode i around he bend is given by i φ0 ; where φ 0 is he bend angle. In his paper we give a design and experimenal resuls for a o 90 bend, i.e., / 2 φ = 0 π. The necessary and sufficien condiions for he relaive phases o be equal a boh ends of he bend are ha he difference beween he oal phase shifs for all he modes be a muliples of 2 π. For a compac bend, wih oally differen propagaion consans for all four modes his implies, φ = φ + π = φ + 4π = φ 6π (6) Eq.(6) represens hree condiions o be saisfied by 1 hrough 4. Since we have hree degrees of freedom, namely he inner radius a, he ouer radius b and he bend heigh h, one can hope, using Eqs. (3) and (4), o find a se of dimensions ha saisfy Eq. (6). This is possible, and he dimensions are shown in Fig. 1. An HFSS[12] simulaion of he aper is shown in Fig. 2 where he colors represens he relaive elecrical field srengh. Figure 2. HFSS simulaion shows a ime snap sho of he relaive elecrical field srengh a boh circular pors and a he middle plane of he bend. Because of symmery only one half of he bend is simulaed III. EXPERIMENTAL RESULTS We buil four copies of he bend design shown in Fig.1. The dimensions were chosen so ha he cener frequency is GHz; he Nex Linear Collider (NLC) frequency [1]. The TE 01 mode was excied using a wrap-around mode converer [3]. We used an HP8510C nework analyzer for hese measuremens. The resuls of he measured ransmission hrough he bends are also shown in Fig. 3. This figure shows a near perfec ransmission hrough his bend. For comparison, he resuls of he HFSS simulaion are shown in

7 his figure. We aribue he small differences o manufacuring olerances and he measuremen accuracy. The apers were made wih manufacuring olerances of 100 microns. The measuremen accuracy is mainly affeced by he accuracy of he algorihm used o remove he mode converers response from he measuremens. However, he level of losses in hese bends is remarkably small, and he measuremens agree well wih he simulaion db -0.4 Bend 1 Bend Simulaion Bend Bend Frequency (GHz) Fig. 3 Measured Transmission hrough wo TE 01 mode converers and he 90 degree bend. Cener Frequency is GHz, and he measuremens are performed over a 1% bandwidh. IV. CONCLUSION We presened a novel idea for a waveguide bend ha suppors he TE 01 mode in circular waveguides. This bend is suiable of ular-high-power operaions. Boh simulaions and experimenal resuls showed very good resuls. The design mehodology could be used o produce bends wih deferen angles. V. ACKNOWLEDGMENTS The auhor would like o hank Dr. David Farkas, Prof. Norman Kroll, and Prof. Ron Ruh for many useful discussions. We also hank Gordon Bowden for his advice on his manuscrip.

8 REFERENCES [1] Physics And Technology Of The Nex Linear Collider: A Repor Submied To Snowmass '96. By NLC ZDR Design Group and NLC Physics Working Group (S. Kuhlman e al.). SLAC-R-0485, BNL , FERMILAB-PUB , LBL-PUB-5425, LBNL-PUB-5425, UCRL-ID , Jun pp. See also BOOKS subfile under call-number: QCD191:S861:1996. Presened a 1996 DPF / DPB Summer Sudy on New Direcions for High-Energy Physics (Snowmass 96), Snowmass, Colorado, 25 Jun - 12 Jul [2] Sami G. Tanawi New Developmen in rf Pulse Compression, LINAC2000-WE203, Aug pp., Invied Talk a he 20 h Inernaional Linac Conference (Linac 2000), Monerey, California, Aug [3] Sami G. Tanawi, e. al. The Generaion Of 400-MW RF Pulses A X Band Using Resonan Delay Lines,, IEEE Trans. on Microwave Theory and Techniques, Vol 47, No. 12, December, 1999, p [4] V.A. Dolgashev, High Magneic Fields in Couplers of X-Band Acceleraing Srucures Proceedings of he 2003 Paricle Acceleraor Conference, Porland, Oregon U.S.A., May 12-16, 2003, pp [5] M. Jougue Effec of Curvaure on he propagaion of elecromagneic waves in guides of circular cross secions, Cables e Transmission (Paris), Vol. 1, No. 2, pp , July This analysis can also be found in Leonard Lewin, David C. Chang, and Edward F. Kueser, Elecromagneic waves and curved srucures, P. Peregrinus, [6] S. Tanawi e. al., The Nex Linear Collider Tes Acceleraor s RF Pulse Compression and Transpor Sysems, Proc. of he 5h European Paricle Acceleraor Conference (EPAC96), Siges, Spain, Jun 1996, p [7] Jeffery W Waarren, Compac bend for TE01 mode circular overmoded waveguide, U.S. paen #: 5,151,673, July 29, 1992.

9 [8] C. Nanisa (SLAC), N.M. Kroll, E.M, Design Of A 90-Degrees Overmoded Waveguide Bend,. SLAC-PUB-6141, Apr pp. Presened a 1993 Paricle Acceleraor Conference (PAC 93), Washingon, DC, May Published in IEEE PAC 1993: [9] A. Weisshaar, M. Mongiardo and V. K. Tripahi, Accurae and efficien CAD-oriened modeling of circular waveguide bends, IEEE MTT-S In. Symp. Dig., Denver 1997, pp [10] S. G. Tanawi, N. M. Kroll, And K. Fan, Rf Componens using Over-moded Recangular Waveguides for he Nex Linear Collider Muli-Moded Delay Line RF Disribuion Sysem, Proc. Of The IEEE Paricle Acceleraor Conference, New York Ciy, March 29h - April 2nd, 1999, p [11] Mahmoud, S.F., "Elecromagneic Waveguides: Theory and Applicaion", IEE Publicaions, Elecromagneic Series, Vol.32, Peregrinus Ld., 1991, and he reference cied herein. [12] HP High Frequency Srucure Simulaor, Version 5.4, Copyrigh , Hewle-Packard Co.