RF Cavities Y. Papaphilippou, N. Catalan Lasheras

Transcription

1 RF Caviis Y. Papaphilippou, N. Caala Lashas RF Caviis. USPAS, Ju 5 USPAS, Coll Uivsiy, Ihaa, NY h Ju s July 5

2 How o podu a RF fild RF Caviis. USPAS, Ju 5 I f spa, h lomagi wav has li ad magi fild vos ppdiula o h diio of popagaio. I boudd mdia, wh h bouday is a pf oduo, suh a wav yp is o possibl baus h bouday odiios ao b saisfid. O h bouday, h agial ompo of h li fild, as wll as h omal ompo of h magi fild B, hav o b o. Ths odiios a saisfid if h wav has o of h fild ompos i h diio of popagaio. If i is h li fild ompo, h wav yp is alld asvs magi TM; if i is h magi fild ompo B h wav yp is alld asvs li T. I agula aviis h idx idia h umb of half wavs i h x ad y diio, spivly. A hid subsip idias h umb of half wavs i h diio. T ml o TM ml W us lomagi wavs i poply boudd mdia o ala h bam. Thy d b syhoid wih h passag of h pail.

3 RF Caviis. USPAS, Ju 5 3 Ragula wavguids I Rmid: Fom Maxwll quaios w obaid ha i a mdium wihou u o hags h popagaio of a lomagi wav is dsibd h by h gal wav quaio W spaa h im ad spaial dpd ad w obai: Baus w wa a alaio, w d a lial fild i h diio of movm. W osid oly h -ompo of h fild. Usig a ial soluio x,y,xx Yy Z givs: B B i T, wih y x / / / Z Z Y y Y X x X

4 RF Caviis. USPAS, Ju 5 4 Ragula wavguids II Fo his quaio o hold fo al valus x, y, a alld h wavumbs ad hy a oupld I paiula, h soluio fo h li fild i h popagaig diio will b a wav If is omplx h ampliud falls xpoially dampig If is al h wav popagas x y is h wavumb of h fis popagaig wav ad is alld h u-off wavumb Th fuios Xxad Yy will b dfid by h boudais wih,,, y x i y Y x X y x wih / ; / ; / Z Z Y y Y X x X y x y x

5 RF Caviis. USPAS, Ju 5 5 Cylidial wavguids Cylidial wavguids a usd as alaig suus. I ylidial oodias, h wav quaio has h followig xpssio: Spaaig ow RΦφZT,Th soluios fo Z ad T a simila as i h agula as. Φφ -iφ. Fo h adial fuio dpd, w obai Th soluios a giv by h Bssl fuios of od : W will pla h malli boudais a h os of h Bssl fuios φ m 443 i J φ

6 RF Caviis. USPAS, Ju 5 6 Mods i ylidial wavguids, θ,h ad H θ a b divd fom his ; ' ; ; ' i i i i i B J J i B J J B J i θ θ θ θ θ θ

7 Cylidial aviis RF Caviis. USPAS, Ju 5 Th spd of h s is alld h phas vloiy v > Th phas vloiy is abov h vloiy of ligh. If w wa syhoism w d o slow dow h phas vloiy!! W a do ha by addig daps i h wavguid. Th wav will b fld ad w will hav a sadig wav Tha adds aoh bouday ad ow pπ i l Wh l is h si of h aviy i h logiudial diio. TM mods hav ow h idxs idiaig h umb of os i ah diio, φ, ad Th u-off wavub will ow b: ph p π l 7

8 Th pill box aviy Th simpls aviy osiss of a ylidial wavguid of lgh l ad adius a losd a boh ds Th bouday odiios a θ θ fo fo a ad l l a RF Caviis. USPAS, Ju 5 Th simpls soluio is h mod TM wih oly h ompos J i J ' i Bθ i J ' ad hus h fquy is fixd by h dimsios of h aviy J a a.45 i i 8

9 Mod fquy ah mod has is soa fquy dfid by h gomy of h pillbox aviy RF Caviis. USPAS, Ju 5 9

10 Caviy Paams Sod gy: U ε μ dv H dv Th li ad magi sod gy osilla i im 9 dgs ou of phas. I pai, w a us ih h li o magi gy usig h pa valu. Pow dissipaio: Rs P H ds; Rs ; σδ δ. σμ RF Caviis. USPAS, Ju 5 wh R s is h sufa sisa, σ is h d oduiviy ad δ is h si dph Qualiy fao: Q U aviy sod gy P avag pow disspad

11 Th pill box aviy II Sod gy: U π ε la J.45 Pow dissipaio: ε P π ars J.45[ l a] μ RF Caviis. USPAS, Ju 5 Qualiy fao: Q U P μ R.45 a l s

12 Loadd aviis his W add a piodiiy o h suu ad hag h bouday odiios No a sigl mod bu a whol spum is popagad hough h aviy Th soluio is ow xpssd i modifid Bssl fuios. W a hav avlig wav alaos ad sadig wav alaos RF Caviis. USPAS, Ju 5

13 Oh aviy yps Dis-loadd lia Sid-oupld lia RF Caviis. USPAS, Ju 5 Dif ub lia DTL 3

14 Th RFQ I Th RFQ uss oly li fild o ala ad fous h bam Th wav quaio a b plad wih h Lapla quaio i ylidial oodias U U U θ θ Th gal soluio RF Caviis. USPAS, Ju 5 U V, θ, A os θ A l li l os θ wih l p p,,,v/ h lod poial, I is h modifid Bssl fuio of od ad π/βλ Taig oly h low od soluio U [ A os A I os ] V, θ, θ osl 4

15 Th RFQ II Th fis m is h poial of a li quadupol fousig m; h sod, will ga a logiudial alaig li fild. Cosas A ad A a dmid by imposig h volag i h lods A A m I a m, a I ma [ A I a ]. χ a RF Caviis. USPAS, Ju 5 Iasig m o gs mo alaio Dasig a o gs mo fousig 5

16 Th RFQ III Th opaio of h RFQ a bs b udsood by osidig a log li quadupol wih a alaig volag o i, Pails movig alog h -axis ad sayig isid h RFQ fo sval piods of h alaig volag, would b xposd o a alaig gadi fousig RF Caviis. USPAS, Ju 5 If h ips of h lods a o fla bu 'modulad' a pa of h li fild is 'dviad' io h logiudial diio ad his fild a b usd o buh ad ala pails 6

17 Fdig ad uig h aviy RF Caviis. USPAS, Ju 5 Th asmissio of h pow bw h gao ad h aviy is do hough a oaxial li sho disas, low pow < W hough a wavguid. Low losss. Ca b oold Th oio bw h wavguid ad h aviy is do wih a sho oaxial li wih viually o-losss A ami widow isid h oaxial abl spaas h wavguid fom h aviy To big h aviy io h soa odiio, uig is do usig uig plugs 7

18 Bibliogaphy Th physis of Pail Alaos. A ioduio, Klaus Will Oxfod uivsiy pss ISBN Ioduio o Lia Alaos, Thomas P. Wagl. LA-UR Pail Alao Physiss II, H. Widma Spig 999 Dyamis ad Alaio i lia suus, J. l Duff ad Covioal RF Sysms Dsig, M. Puglisi i CRN Alao Shool: 5h Gal alao physis ous, CRN 94- Fudamal of Io Lias M. Wiss, i CRN Alao Shool: Cyloos, lias ad hi appliaios, CRN 96- RF Caviis. USPAS, Ju 5 8

19 Cu-off fquy Dispsio o Billoui diagam As is fixd by h gomy w a lf wih h quaio of a hypbola. Th miimum fquy popagaig i h aviy is alld h u-off fquy RF Caviis. USPAS, Ju 5 9