Power coupling. 1 Introduction: basic concepts and coupler classification. D. Alesini LNF, INFN, Frascati, Italy

Transcription

1 Power couplig D. Alesii LNF, INFN, Frascati, Italy Abstract Power couplig is the subject of a huge amout of literature ad material sice for each particular RF structure it is ecessary to desig a coupler that satisfies some requiremets, ad several approaches are i priciple possible. The choice of oe coupler with respect to aother depeds o the particular RF desig expertise. Nevertheless some desig criteria ca be adopted ad the scope of this paper is to give a overview of the basic cocepts i power coupler desig ad techiques. We illustrate both the cases of ormalcoductig ad supercoductig structures as well as the cases of stadigwave ad travellig-wave structures. Problems related to field distortio iduced by couplers, pulsed heatig, ad multipactig are also addressed. Fially a couple of desig techiques usig electromagetic codes are illustrated. The paper brigs together pictures, data, ad iformatio from several works reported i the refereces ad I would like to thak all the authors of the papers. 1 Itroductio: basic cocepts ad coupler classificatio Power couplers ca geerally be defied as etworks desiged to trasfer power from a RF power source to a cavity, as illustrated i Fig. 1(a). Geerally speakig, they are realized with slots, widows, or ateas that couple the electromagetic (e.m.) field of the power trasfer lie to the cavity e.m. field. For this reaso, a first classificatio (foud i the literature) of couplers is betwee magetic or electric, depedig o what type of field they couple. I some cases, evertheless, this classificatio caot be applied because they couple both the E ad the H field, as discussed i the followig. Aother possible classificatio of couplers ca be betwee waveguide type ad coaxial type couplers, depedig o the particular geometry used to couple the power with the cavity field. Both types of coupler have advatages ad drawbacks i terms of desig, power hadlig capacity, ad tuability. If ecessary, special trasitios betwee waveguide ad coaxial lies (or vice-versa) ca be itegrated i the coupler itself (as a example, the power trasfer lie ca be a waveguide ad the fial coupler ca be coaxial); i this case a special trasitio has to be itegrated i the coupler itself. The desig of the particular coupler depeds o the cavity type: ormal-coductig (NC) or supercoductig (SC), stadig-wave (SW) or travellig-wave (TW) as show i Fig. 1(b) where all pricipal combiatios are give. The desig has to be orieted ot oly to the right power trasfer but it has to iclude other importat techical aspects. First of all, sice, i geeral, trasmissio lies (coaxial or waveguide), are usually filled with gas, couplers have to icorporate vacuum barriers (RF widows) to preserve the cavity s operatio uder ultra-high vacuum coditios. This is, i particular, a critical poit for SC cavities where vacuum cotamiatio ca seriously damage the structures. Moreover, i the case of SC cavities, a iput coupler must serve as a low-heat-leak thermal trasitio betwee the room-temperature eviromet outside ad the cryogeic temperature (from 2 to 4.5 K). Thermal itercepts ad/or active coolig i the coupler desig might be ecessary. Fially, the coupler desig caot be idepedet of beam dyamics cosideratios. It itroduces, i fact, a asymmetry i the electromagetic field distributio which ca deteriorate the beam quality. Special measures, such as double symmetric couplers or compesatig stubs, may be required ad itegrated i the coupler itself. I recet years the RF desig of the couplers has bee eormously aided by computer codes. These codes allow complete modellig of the field distributio i the couplers ad cavities avoidig the use of the cut-ad-try techique used i the past. The codes allow miimizatio i the desig procedure of the pulsed heatig ad multi-pactig pheomea that ca seriously limit coupler performace.

2 Fig. 1: (a) Coceptual sketch of a source power trasfer lie coupler cavity system; (b) schematic represetatio of possible combiatios of coaxial ad waveguide couplers with differet types of cavity 2 Couplig to stadig-wave cavities Stadig-wave cavities ca be excited usig slots o waveguides or loops ad ateas i coaxial couplers. The geeral problem of couplig betwee a power trasfer lie ad a cavity is ot trivial ad oly perturbative aalytical approaches ca be followed [T1 T4]. The problem is that couplig slots or ateas chage the cavity ad waveguide geometry ad, whe the field ito the cavity starts to icrease, the cavity itself radiates ito the waveguide through the same slot or atea. I steady state, ad at a give frequecy of operatio, there is equilibrium betwee the power flowig ito the cavity, that dissipated ito the walls, ad that radiated from the cavity back ito the power trasfer lie. The aalytical, exact solutio of such a problem is i geeral impossible. Before itroducig the approximated aalytical formulae that allow the modellig of this couplig, let us start with a ituitive ad qualitative approach to the subject. 2.1 Slots o waveguides Let us cosider, for the sake of simplicity, the case of the excitatio of the TM 010 acceleratig mode of a simple pillbox cavity by a waveguide coupled to the cavity with a slot. Lookig at the magetic field lies of a short-circuited waveguide ad cavity [Fig. 2(a)], it is straightforward to ote that there are two possible simple solutios to couple the magetic field of the waveguide with the magetic field lies of the mode ad they are give i Figs. 2(b) ad 2(c). If the liear dimesios of the aperture are small compared with the wavelegth, it is possible to use a perturbative approach i which the aperture is equivalet to a magetic dipole ( M slot ), whose dipole momet is proportioal to the tagetial magetic field o the slot ( H slot ). This dipole is the source of the field ito the cavity ad the source of the field radiated back from the cavity ito the waveguide. As discussed i the ext paragraphs the fial amplitude of the mode ito the cavity is proportioal to the scalar product H slot H cavity, where H cavity is the magetic field ito the closed cavity (without the slot). From the formula it is easy to ote that, i order to have mode excitatio, both from zero ad o orthogoal. H cavity ad H slot must be differet

3 It is also straightforward to ote that the excitatio of the field iside the cavity, i the case of Fig. 2(c), ca be varied (for a fixed couplig slot aperture) by chagig the distace d betwee the shortcircuit plae ad the slot itself. The distace d, i fact, varies the amplitude of the fial H slot. Fig. 2: Magetic couplig betwee a waveguide ad a SW cavity: (a) magetic field lies o a short-circuited waveguide ad cavity operatig o the TM 010 mode; (b) first solutio of magetic couplig betwee the waveguide ad the cavity; (c) secod solutio for magetic couplig (the distace d, i this case, allows chagig the excitatio of the mode) 2.2 Loops o coaxial Magetic couplig ca be also realized usig loops, as show i Fig. 3. I this case also it is possible, for small loop dimesios, to use a perturbative approach. The loop excites ito the cavity a magetic dipole whose itesity is proportioal to the loop area ad coaxial iput power, while the amplitude of the excited mode is proportioal to the scalar product betwee this magetic dipole ad the magetic field of the excited mode i the loop regio ( M loop H cavity ). It is straightforward to ote that, also i this case, the amplitude of the mode ca be varied (for a fixed loop dimesio) by chagig the loop orietatio. 2.3 Atea o coaxial Fig. 3: Magetic couplig betwee a loop ad a SW cavity: the excitatio of the mode ca be varied by chagig the orietatio of the loop Electric couplig ca be realized by a atea i the case of coaxial couplers. The typical situatio is illustrated i Fig. 4. I this case the ier coductor of the coaxial is iserted ito the cavity ad the electric

4 curret o its surface is coupled with the electric field of the mode i the cavity. If the liear dimesios of the atea are small with respect to the wavelegth, it is possible to use, also i this case, a perturbative approach i which the ier is equivalet to a electric dipole ( P atea ), whose dipole momet is proportioal to the tagetial desity curret o the ier itself. This dipole is the source of the field ito the cavity ad, vice-versa, whe the cavity field starts to icrease, it is the source of the field radiated back ito the coaxial from the cavity. As illustrated i the followig paragraph, i this case the amplitude of the excited mode is proportioal to the scalar product Patea Ecavity. Fig. 4: Electric couplig betwee a coaxial ad a SW cavity: the excitatio of the mode ca be varied by chagig the peetratio of the ier 2.4 Basics of the theory of couplig to stadig-wave cavities The theory of cavity excitatio has bee extesively treated usig several equivalet approaches. Without eterig ito the details of the rigorous treatmets that ca be foud i the previous refereces, we summarize i the followig the basic results. Let us cosider first the case of a sigle, closed, metallic cavity without exteral couplig. The resoat modes i such a cavity ca be expaded i a series. To have a complete expasio we eed both soleoidal modes (with zero divergece ad o-zero curl) ad irrotatioal modes (with zero curl but ozero divergece). I most practical cases we deal with the first type of modes ad, i the frequecy domai, we ca cosider the followig expasio of modes i a closed, ideal (without losses), metallic cavity: Ee He jt jt e E e h H e where e ad h are the mode amplitudes (complex i geeral ad frequecy-depedet) while the eigefuctios E, H are solutios of the followig equatios: jt jt,, (1) E k E 0 H k H 0 i the volume of the cavity V, E 0 H 0 o the surface of the cavity S, E 0 H 0 i V ad o S. (2) The first equatios are the well-kow Helmoltz equatios ad k are the eigevalues of the problems, related to the resoat frequecy of the mode by the usual relatio = k () -1/2. The eigefuctios ad the eigevalues ca be chose real ad orthoormal. This meas that E Em m H Hm m, (3) V where the Kroecker delta m = 0 if m ad m = 1 if = m. The relatioship betwee the eigefuctios E ad H ad betwee e ad h are give by Maxwell s equatios. It ca be demostrated that V E k H H k E. (4)

5 It is easy to demostrate that i a source-free cavity with perfectly coductig walls, e 0 if ad oly if = ad that I this case, therefore, the field ca be expaded i the followig sum: Ee He h j e. (5) jt jt e E e h H e The case of wall losses ca be treated usig a perturbative approach startig from the case of a source-free cavity with lossy walls. I this case it is possible to demostrate that the coefficiets e ad h are differet from zero if ad oly if satisfies this equatio: where the quality factor Q 0 is defied as: Q 0 j t j t 1 1 j, 2Q 2Q 0 0 W Pd Rs H ds W H dv E dv (8) P d cavity walls,. cavity volume cavity volume where P d ad W are the average dissipated power ito the cavity walls ad the average electromagetic eergy stored i the cavity. I Eq. (8) R s is the surface resistivity, defied as: R s cavity wall coductivity. (9) 2 Equatio (7) shows that the frequecy of free oscillatio slightly differs from the o-loss resoat frequecy ad, i additio, there is a dampig costat. Let us ow cosider the case of a cavity coupled exterally with a waveguide or a coaxial. These cases are illustrated i the previous Figs Followig, also i this case, a perturbative approach, the excitatios of a mode i a cavity ca be modelled by a equivalet electric ( J ) or magetic ( J ) desity curret represetig the sources of the modes. The equivalet magetic sources are, for example, the magetic field o a couplig slot betwee the waveguide ad the cavity (Fig. 2) ad the magetic field geerated by a loop coupled with a cavity (Fig. 3), while the equivalet electric sources are the currets o a small atea coupled with the cavity (Fig. 4). It ca be demostrated that, if the frequecy of the exteral excitatio (), is very ear to a particular mode resoat frequecy, all coefficiets i the expasio (1) are small with respect to the coefficiets e, h related to the -mode ad these latter coefficiets are give by h e Q Q k J E j J H j J E J H 0 0 m electric magetic k electric magetic m couplig couplig couplig couplig regio regio regio regio j k k 1 1 jq0 Q0 Q0 Q0 j J E k J H J E j J H k m m electric magetic electric magetic couplig couplig couplig couplig regio regio regio regio k 2 2 k 1 j 1 Q0 1 jq 0. m (6) (7) (10)

6 The secod equalities are valid sice, i geeral Q 0 >> 1 ad i the umerator ca be approximated with. I other words, the amplitudes of the electric ad magetic field excited ito the cavity have a typical resoat behaviour as a fuctio of the frequecy of the excitatio ad are differet from zero oly if. If i the couplig regio the electric ad magetic fields of the modes are sufficietly small ad ca be approximated by their values i the cetre of the coupler regio ad the itegrals of the desity currets ca be substituted by their equivalet dipole momets, Eq. (10) becomes h e 2 k M H jk P E j k k 1 Q0 2 P E jk M H j k k 1 Q0 For a give coupler geometry ad SW cavity, it is, i geeral, very difficult to fid a aalytical expressio for Eqs. (10) (11) ad oly approximated treatmets ca be doe. The previous cosideratios allow oe to obtai, evertheless, some importat practical results as illustrated i the followig sectio. 2.5 Equivalet circuit of the couplig betwee a stadig-wave cavity ad a power trasfer lie ad defiitio of the couplig coefficiet Equatios (10) ad (11) state that, at a give frequecy, the mode excitatio is proportioal to the equivalet source desity currets ( J, J ) or dipole momets ( P, M ) ad these sources are proportioal, obviously, to m the field i the coupler regio. As usual, we ca associate to the field ito the cavity ad to the field ito the waveguide (or coaxial) a equivalet voltage ad curret proportioal to the correspodig electric ad magetic fields or, more precisely, to their itegrals over a give path. Let us cosider, for example, the case represeted i Fig. 2(b) ad let us idicate with V cav the equivalet cavity voltage ad with V waveg ad I waveg the equivalet voltage ad curret ito the waveguide i the coupler regio, give by the superpositio of a icidet wave (V + ) ad a reflected oe (V - ). From Eqs. (10) (11) the cavity voltage is proportioal to the magetic field i the hole aperture ad therefore to I waveg ad, i the limit of a small couplig hole, the reflected wave V - will be give by the superpositio of the reflected wave from the short-circuited plae at the ed of the waveguide ad the radiated field from the cavity through the couplig hole. Let us write these relatioships: Vcav V V R V V R Vcav Iwaveg 1 jq 0 Z 0 1 jq0 where we have take ito accout Eqs. (10) (11) i the cavity voltage expressio ad where we have itroduced the waveguide characteristic impedace Z 0 ad two quatities ad R. The first oe is a adimesioal quatity that relates the cavity voltage to the radiated voltage from the cavity ito the waveguide; i other words if, at a certai time, we switch off the excitatio, the cavity radiates ito the waveguide ad the ratio betwee the radiated voltage ad the cavity voltage is 1/. The other quatity is R/ (ohm) ad it relates the waveguide magetic curret to the maximum amplitude of the cavity voltage, whe the cavity is excited perfectly o resoace ( = 0). From Eqs. (12) it is easy to uderstad that the couplig betwee a waveguide ad a cavity ca be modelled by the circuit give i Fig. 5. The cavity is modelled with a equivalet lumped RLC circuit, the RF source by the curret geerator, while the trasformer models the coupler. I this equivalet circuit the RLC circuit must have the same quality factor as the resoat mode ad the same resoat frequecy. This meas that., (11) (12)

7 1 C ; Q o R. (13) LC L I Eq. (13) ad from ow o we cosider just a sigle resoat mode ad we idicate with f res ( res ) ad Q 0 its resoat frequecy ad quality factor. value: Fig. 5: Equivalet circuit of a cavity coupled with a RF source From the geerator poit of view the cavity ca be see as a termial impedace with the followig Z cav 2 R. (14) 1 jq O the other had, the eergy stored i the cavity (W) is dissipated ito the cavity walls (P cav ) ad is also radiated through the coupler ad dissipated ito the matched load of the geerator (P ext ). Therefore the geerator ca be see from the cavity poit of view as a extra-load ad we ca defie the followig quatities: a) The loaded quality factor that takes ito accout the total dissipated power: resw QL. P P While Q 0 is called the uloaded quality factor, ad P T is the total average power dissipated ito the cavity ad ito the exteral load. b) The exteral quality factor Q E defied as The quality factors are related by the followig relatioship: c) The couplig coefficiet is defied as From the previous relatios it is possible to obtai that Q E cav P T 0 ext (15) resw. (16) P 0 ext (17) Q Q Q L E P Q R ext 0. (18) 2 Pcav QE Z0 Q Q 1 The reflectio coefficiet see by the source uder the assumptio of zero legth power lie is the 0 L. (19)

8 1 jq 1 ;. 1 1 cav 0 jq cav f fres 0 From the previous equatios it is straightforward to ote that the couplig fixes the reflectio coefficiet at the iput port, the resoace badwidth, ad the ratio betwee the power dissipated ito the cavity ad exteral load. It plays a importat role i the desig of a cavity, ad the choice of its value depeds o several parameters such as the beam loadig ad the available iput power from the source. It is possible, i geeral, to chage it by chagig the geometry of the coupler as give i Fig. 6. The particular case of = 1 is called critical couplig ad, i this case, i the steady-state regime, we have o reflected power to the geerator because there is a perfect destructive iterferece betwee the power reflected from the waveguide (or coaxial) termiatio ad that radiated back by the cavity through the hole. The case with < 1 is called udercouplig while the case with > 1 is called overcouplig. As a example the reflectio coefficiet at the coupler iput port, ear the cavity resoat frequecy, is give i Fig. 7 with the assumptio f res = 1 GHz, Q 0 = ad for three differet values of the couplig. (20) Fig. 6: Typical geometry modificatios to chage the couplig: (a) slot aperture; (b) short-circuit termial plae; (c) atea peetratio; (d) loop orietatio Fig. 7: Reflectio coefficiet at the coupler iput port for a cavity resoatig at f res = 1 GHz with Q 0 = for three differet value of the couplig coefficiet: (a) absolute value; (b) complex plae I the desig procedure (by, for example, a electromagetic code) it is possible to calculate ad tue the couplig coefficiet followig these two steps: a) Establish if we are uder-coupled or over-coupled. To do this it is sufficiet to look at the reflectio coefficiet at the coupler iput port (as a fuctio of frequecy) i the complex plae. Out of resoace the reflectio coefficiet has a absolute value equal to 1 ad, therefore, it describes a circle with radius equal to 1. At resoace it describes a circle towards the origi of the complex plae. It is easy to demostrate that, if the circle icludes the origi of the complex plae we are overcoupled, if ot we are udercoupled. If the circle crosses the origi we are i critical couplig.

9 b) Oce we have established if we are over- or udercoupled, we ca calculate the couplig by the formulae simply derived from Eqs. (20): 1 1 cav cav (overcoupled), Here cav is the absolute value of the reflectio coefficiet at resoace. (21) 1 cav (udercoupled) Advatages ad disadvatages of waveguide ad coaxial couplers cav Table I illustrates the mai advatages ad disadvatages of waveguide ad coaxial couplers (well discussed i [S4]). Table 1: Advatages ad disadvatages of waveguide ad coaxial couplers Type Advatages Drawbacks Waveguide Higher power hadlig Larger size capability Easier to cool More difficult to make variable Higher pumpig speed Bigger heat leak Simpler desig: it does ot require a trasitio betwee the waveguide, which usually carries the output power of the RF sources, ad the cavity iterface. Lower atteuatio Coaxial Easier to make variable More complicated desig More compact Worse power hadlig Smaller heat leak Higher atteuatio Multipactig levels easier to maage Smaller pumpig speed More difficult to cool (coaxial ier) Couplers o waveguide are preferred at high frequecy (>1 GHz) ad for high-gradiet ad high-power structures likes TW liacs ad ormal-coductig RF gus. Couplers o coaxial are preferred for lowfrequecy structures (<1 GHz) ad whe the couplig has to be varied, for example, for supercoductig structures (due also to the smaller heat leak). The aalysis of the coupler i the followig sectios will clarify some of these features. 3 Iput couplers for ormal-coductig stadig-wave cavities: a aalysis of the critical features We will illustrate the mai critical poits i the desig of iput couplers for ormal-coductig stadigwave cavities lookig at some practical examples. 3.1 Normal-coductig stadig-wave cavities: RF gus Normal-coductig RF gus are the first stage of acceleratio of e - i the liacs for FELs [G1]. They are, i geeral, 2 3 cell SW acceleratig structures operatig o the mode at frequecies of the order of a few GHz. Required couplig coefficiets are betwee 1 ad 2. The operatio of RF gus is, i geeral, pulsed

10 with high peak iput power (from a few up to 15 MW), pulse legth from a few s up to oe ms, ad repetitio rate from a few Hz up to khz. Because of the high-frequecy, high-acceleratig gradiet ( MV/m), high-iput-power operatio, ad fixed couplig, these structures are fed by slots o waveguides, as illustrated i Fig. 8. The mai critical poits i the desig, realizatio, ad operatio of such couplers are related to the field distortio itroduced by couplers ad pulsed heatig i the coupler regio Field distortio Fig. 8: Sketch of a RF gu with iput coupler Because of the relatively low eergy of the electro beams (from 0 up to few MeV) a excellet uiformity is required for the acceleratig field to preserve the beam quality. Stadard couplig slots itroduce a distortio i the field distributio ad multi-pole compoets of the field ca appear ad affect the beam dyamics [BD1]. The mai mechaism that guides such field distortio is sketched i Fig. 9 where the magetic field lies of a pure pillbox cavity ad those of a cavity with a sigle ad a double iput coupler are show. It is quite clear that i the first case the coupler itroduces both a distortio of the field i terms of dipole compoet o axis ad higher order compoets (quadrupole, sextupole, etc.), while i the case of a symmetric feedig, the odd magetic field compoets of the field (like dipole, sextupole, etc.) are suppressed but we still ca have eve compoets (like quadrupoles, octupoles, etc.). More precisely we ca develop the magetic field ear the beam axis as follows: 1 B r,, z Ao z r A z cos r, (22) where z is the logitudial coordiate, r is the radial oe ad is the azimuthal agle, as illustrated i Fig. 9. The A compoets are, i geeral, complex fuctios ad deped o the logitudial coordiate z. The dipole compoet correspods to the term A 1, the quadrupole oe to the term A 2, ad so o. I the case of a symmetric feedig oly the eve compoets remai. The mai techiques to miimize such field distortio are show i Fig. 10. The simple way to partially compesate the dipole field is to itroduce a symmetric compesatig slot opposite to the RF iput oe [Fig. 10 (a)]. The opposite slot is ot fed by RF power ad ca be used, for example, by pumpig the structure (as reported i the same figure where the picture of the SLAC-UCLA-BNL gu is show [G2]). I this case the field is partially compesated i the sese that the eve compoets still remai ad also the odd compoets have a residual amplitude o axis, due to the fact that the power is still eterig from oe side oly. To suppress the odd compoets the straightforward way is to use a symmetric feed [Fig. 10 (b)]. I this case a double feed is eeded ad it ca be realized with a splitter that splits the mai iput power ito two braches. Of course this system itroduces a further complicatio ad a icrease i the cost of the complete realizatio due to the presece of the splitter itself. Nevertheless, also i this case the quadrupole 1

11 compoet still survives ad the oly way to suppress it is by the use of a deformed profile of the cells (racetrack profile [G4, G5]) [as give i Fig. 10 (c)]. This cell deformatio complicates further the machiig of the cell that caot be fabricated by lathe but eeds a computer-cotrolled millig machie. Fig. 9: Sketch of the magetic field lies i a pure pillbox cavity (a), i a cavity with sigle iput coupler (b), ad i a cavity with double iput coupler (c) Fig. 10: Mai techiques to miimize the field distortio itroduced by the coupler: (a) compesatig slot ([G2]); (b) dual feed; (c) dual feed ad deformed iteral profile of the cell High magetic field i couplers ad pulsed heatig As metioed before, RF gus are structures fed by typical RF pulses of several MW. High peak electric field (>100 MV/m) ca be easily reached ad breakdow pheomea ca occur. These ca be drive also by a high magetic field i the coupler regio, as reported i [B0, B1]. I fact, RF power eters the structure through the slots, the surface currets flow alog the edges of the slots, ad these edges are a place where local currets are sigificatly amplified. The high currets ca give localized losses that ca create hot spots ad drive breakdow pheomea damagig the coupler itself. The pulse temperature rise ΔT ca be calculated usig a 1D model [B2] ad is give by 2 H t T, (23) ' ck where t is the pulse legth, σ is the electrical coductivity, δ the ski depth, ρ the desity, c the specific heat, ad k the thermal coductivity of the metal. For copper it is possible to use the followig formula: 2 T C 127 H MA/m f GHz t μs. (24) As a geeral experimetal rule, if this pulsed heatig exceeds 100 o C serious damage to the coupler regio has a high probability of occurrece, below 50 o C damage to the couplers is practically avoided while i the iterval o C there is some probability of coupler damage. RF

12 The possible solutios to reduce the high magetic field i the couplers are show i Fig. 11. The strategy is to icrease the curvature radius of the coupler slot. I particular the so-called z-couplig was the fial solutio adopted at SLAC for the LCLS gu [G4, G5]. Figure 11 (b) gives, for example, the pulsed heatig as a fuctio of the iteral curvature radius of the z-coupler itself with the parameters of the LCLS gu give i the figure captio. Fig. 11: (a) Possible solutios to reduce the high magetic field i the couplers; (b) pulsed heatig as a fuctio of the iteral radius of curvature of the z-coupler itself with the parameters of the LCLS gu [G5] (f RF = GHz, t = 3 s, E cathode = 120 MV/m) O-axis coaxial couplig To simultaeously suppress the multipole compoets of the field ad to strogly reduce the magetic field i the coupler regio, a ew type of coupler for RF gus has bee proposed ad implemeted [GA0, GA1, GA2]. The couplig is coaxial ad o-axis coaxial as show i Fig. 12. The TE 11 mode of the waveguide is coverted ito a TEM mode of a coaxial lie (i the so-called door-kob trasitio) ad the coaxial lie excites, o-axis, the acceleratig field i the gu. The excitatio is both electric ad magetic sice o-axis there are both field compoets. All mode asymmetries i the door-kob trasitio are suppressed i the coaxial lie ad the excitatio of the cavity is purely 2D symmetric without multipole compoets [BD2]. It is also easy to verify that, i this case, the magetic field i the coupler regio (ad therefore the pulsed heatig) is strogly reduced sice there are o sharp edges or couplig slots. O the other had, this type of coupler complicates the coupler desig ad gu realizatio. The gus of the Free Electro Laser i Hamburg (FLASH) ad of the Photoijector Test Facility at DESY i Zeuthe (PITZ) are based o this priciple. Fig. 12: O-axis coaxial couplig for RF gus (FLASH RF gu [GA1])

13 3.2 Coaxial-loop couplers for stadig-wave, ormal-coductig cavities: DANE cavity A example of the coaxial-loop coupler is the case of the DANE cavity at LNF-INFN, Frascati, Italy [G7]. A sketch of the cavity ad a detail of the loop mechaical drawig are give i Fig. 13. The cavity operates at 368 MHz with a maximum iput power of 100 kw. The coupler itegrates a trasitio betwee the rectagular waveguide ad the coaxial. The loop ca be rotated, chagig the couplig coefficiet from 0 to 10, ad water coolig is itegrated i the loop itself. Fig. 13: (a) Sketch of the DANE cavity ad picture of the coaxial-loop coupler; (b) detail of the coupler mechaical drawig 4 Iput couplers for supercoductig stadig-wave cavities: a aalysis of the critical features Supercoductig cavities are used for both electro ad heavy particle acceleratio i a extremely wide rage of applicatios. Owig to the low surface resistace (about 10 at 2 K), their quality factors may exceed ; this meas that oly a tiy fractio of the icidet RF power is dissipated i the cavity walls ad most of it is either trasferred to the beam or reflected ito the source load. The iput power ca be from a few kw up to a few MW. Supercoductig cavities allow CW operatio ad i pulsed regime ad this affects the coupler desig. The trasiet ature of pulsed power itroduces thermal ad mechaical stress i critical compoets that have to be evaluated. O the other had, CW operatio requires special solutios for power hadlig ad coupler coolig. Several excellet reviews o couplers for supercoductig cavities ca be foud i the literature [S1 S4]. I the case of supercoductig cavities the mai fuctio of the coupler, providig power, has to be merged ad itegrated with other importat requiremets like vacuum, cryogeic ad couplig tuability. Both waveguides ad coaxial couplers ca be used for supercoductig cavities. I both cases the couplig is realized o oe side of the cavity structure ad the profile of the cells is a purely symmetric 2D. This is doe to avoid the opeig of slots o the acceleratig cells that ca create magetic hot spots i the cells themselves with additioal desig complicatios ad potetial problems i the cavity operatio at high gradiet. I coaxial-type couplers the couplig stregth depeds o the logitudial locatio ad size of the couplig port ad ca be varied by chagig the isertio of the ier. As a example, the mechaical drawig of the coupler for the TESLA Test Facility (TTF) cavities [S7, S8] is give i Fig.14. The TESLA cavity is a ie-cell stadig-wave structure of about 1 m legth whose lowest TM mode resoates at 1300 MHz. The cavity is made of solid iobium ad is cooled by superfluid helium at 2 K. Each ie-cell cavity is equipped with its ow titaium helium tak ad with a coaxial RF power coupler capable of trasmittig more tha 200 kw [S6].

14 Fig. 14: Coaxial coupler of the TESLA cavity [S8] The mechaical drawig allows us to illustrate may critical compoets i the desig of the coaxial couplers for supercoductig cavities. As clearly show i the figure the coupler itegrates several compoets: a) Waveguide to coaxial trasitio. b) Bellows for Q EXT tuability. For may accelerators it is ecessary to tue the couplig by chagig the peetratio of the atea i the pipe. I geeral Q EXT ca vary from about 10 7 to about 10 5 depedig o the applicatio, ad to chage such couplig coefficiet the coupler has to be iserted (or extracted) by several mm at operatig frequecies aroud 1 GHz. This peetratio has to be compesated by the bellows. c) Vacuum barriers (widows). They prevet cotamiatio of the SC structure ad are made, i geeral, from Al 2 O 3. These barriers are ecessary also i ormal-coductig accelerators but the requiremet o the quality of the vacuum ad reliability of the widows is much more striget for SC structures. For this reaso more tha oe vacuum barrier ca be itegrated i the coupler. I the example show there are two widows. The first oe is itegrated i the waveguide-to-coaxial trasitio ad is at room temperature, the secod is a cold oe. From the RF poit of view the widows must be desiged to be trasparet to the electromagetic field. Coaxial widows ca be of several geometries: plaar, cylidrical, or coical. Active pumpig ear the widows is desirable to avoid discharge problems durig out-gassig evets associated with varyig power levels. As discussed i Sectio 6, multipactig pheomea ca occur at the widow locatio ad ca be particularly dagerous sice a large amout of power ca be deposited i small areas of the dielectric, leadig to potetial failures. Careful choice of geometry ad coatig with low-secodary-electro-emissiocoefficiet materials ca mitigate this pheomeo. Aother potetial problem for RF widows is the exposure to radiatio that ca also lead to chargig pheomea at the widow surface ad to damage of the widow itself. Geometrical protectio ad metallic films of proper thickess ca be used to decrease the icidece of this problem. d) Thermal barrier. The RF power must be fed ito the cold supercoductig cavity ad i the coupler we cross the boudary betwee the room-temperature ad the low-temperature eviromet. This aspect imposes very tight requiremets o geometries ad a delicate balace betwee static ad dyamic heat loads placed o the refrigerator system. Special thermal barriers have to be itegrated i the coupler which must avoid the heatig of the supercoductig part of the cavity. Thermal simulatios are also ecessary for a complete ad safe desig of the coupler.

15 e) Actuator for Q EXT tuig. To tue Q EXT the peetratio of the ier coductor is chaged by a exteral actuator. I the coupler, pumpig ports for vacuum are also iserted as i the waveguides or coaxial for ormal-coductig structures. Waveguide couplig is coceptually simpler, sice it does ot require a trasitio betwee the waveguide, which usually carries the output power of the RF sources, ad the cavity. Figure 15 shows two pictures of the CESR-B sigle-cell cavity with waveguide couplig [S9]. O the other had, the size of the coupler is geerally larger tha the coaxial oe ad, because of this larger size, the cotributio to the heatig of the cryogeic eviromet is usually larger. Ceramic widows are also itegrated i the waveguide but geerally they are more difficult to maufacture tha the coaxial oes. As already discussed, the couplig stregth ca be chaged by chagig the size of the couplig iris or the logitudial locatio of the waveguide with respect to the cavity ed-cell, or by chagig the locatio of the termiatig short of the waveguide itself. Multipactig occurs i waveguides as well ad ca be moderated by the use of magetic field biasig. A good review of some of these issues ca be foud i Ref. [S10]. I case of CW operatio the requiremets for higher average power are demadig for the desig of a coolig system. Usually the cetral atea ad the bellows ca be water, gas, or air cooled. Attetio must also be paid to the thermal characteristics of the gaskets if the flage regio proves to be a hot zoe. For certai materials (like alumiium, for example) it is possible to have vacuum leaks startig from ~150 degrees. I this case copper gaskets are recommeded. The last importat parameter to be cotrolled (as i the case of NC cavities) is the trasverse kick iduced by the coupler ad the multipole field compoets that ca deteriorate the beam quality. The remedy is to compesate this effect by alteratig the coupler isertio o both sides of the beam propagatio axis ad, i the desig phase, by reducig the ratio betwee the coupler ad cavity diameters. Of course this problem is more serious for SC RF gus ad for low-eergy beams [BD3]. Fig. 15: CESR-B sigle-cell cavity with waveguide couplig [S9] 5 Couplers for travellig-wave structures Travellig-wave structures are ormal-coductig structures used for electro acceleratio. They have a iput coupler, may acceleratig cells (~80), ad a output coupler, as show i Fig. 16. Because of the high gradiet (from ~25 MV/m i S Bad up to MV/m i X Bad) ad high iput power (~100 MW) the structures are fed by waveguides. Several types of coupler have bee proposed for TW structures. They ca be divided ito two big families: the slot-type coupler, as show i Fig.16, ad the mode coverter coupler [T1], show i Fig.17. I the first case the coupler is realized by coectig the waveguide ad the first acceleratig cell through a slot o the waveguide, as illustrated i Fig. 16. The travellig-wave acceleratig mode (TM 01 -like) is magetically excited by the TE 10 mode of the waveguide. Matchig is obtaied by tuig the radius of the first acceleratig cell (R c ) ad the slot aperture (w). Electromagetic codes are, i geeral, used to desig these couplers ad a possible tuig procedure is described i the fial sectio of this paper.

16 I the secod type of coupler the TE 10 mode of the coupler is coverted ito the TM 01 mode of the circular waveguide ad this circular mode is the coverted ito the TM 01 -like mode of the structure. The sketch of this coupler is give i Fig. 17 (a). The first matchig is obtaied by tuig the dimesio of the two bumps, for example, while the circular waveguide mode is coverted ito the acceleratig mode by tuig the radius ad the iris aperture of the first acceleratig cell. A more compact versio of such a coupler is the waveguide coupler [show i Fig. 17 (b)]. I this case the waveguide is directly coected to the acceleratig sectio ad the TE 10 mode is coverted ito the acceleratig mode by tuig the first iris aperture ad the radius of the first cell. Fig. 16: Slot-type coupler for a TW structure Fig. 17: (a) Mode coverter coupler; (b) waveguide coupler [T1 The differet couplers have advatages ad drawbacks. The first oe is of course that of beig more compact sice just oe acceleratig cell is sacrificed for the matchig. O the other had, a high magetic field ca occur i the slot regio if it is ot sufficietly rouded ad, if oly oe slot is used for couplig, a strog dipole compoet of the field ca occur i the coupler cell. Couplers of the secod type are less compact, they eed a splitter for symmetric feed but they completely cacel the problem of high magetic field ad pulsed heatig. Let us go ito the details of such problems. 5.1 Field distortios As observed i the case of SW cells, the couplers for TW sectios itroduce asymmetries i the field distributio i terms of multipole compoets of the field. Let us cosider the case of slot-type couplers. If oly oe slot is used, the most importat distortio is give by the dipole term. Several compesatio techiques are possible: they are illustrated i Fig. 18. The first oe [Fig. 18(a)] is to itroduce a trasverse offset of the couplig cell i order to make the magetic cetre coicidet with the beam axis [T2]. This techique does ot give a perfect compesatio of the kick i the sese that power still flows ito the structure from oe ubalaced side ad the imagiary ad real parts of the dipole field caot be perfectly compesated at the same poit. The secod solutio is the dual feed [Fig. 18(b)]. I this case the dipole compoet is perfectly compesated but, of course, oe eeds a

17 splitter, which complicates the desig. Possible solutios with a splitter itegrated i the coupler have also bee suggested [T3]. The last possibility of dipole kick compesatio is the use of the so-called J-type coupler, proposed a few years ago [T4]. The sketch of this coupler is give i Fig. 18(c). The waveguide follows the profile of the coupler cell ad two slots are opeed o opposite sides. The dimesios ad legths of the waveguide aroud the coupler are tued to have a perfect field i phase o the two slots. I the case of mode coverter couplers the dipole compoet is completely compesated but a stroger quadrupole compoet of the field ca occur [T5]. I such a type of coupler, i fact, the rectagular geometry of the waveguide is directly iserted o the circular geometry of the acceleratig field, as sketched i Fig. 19, ad multipole compoets of the field ca occur. A careful evaluatio of such compoets must be doe i order to ivestigate the effect o the beam dyamics. The itegratio of a splittig system i the waveguide coupler, as show i Fig. 20, is easier. Fig. 18: Possible compesatio techiques for dipole kick compesatio i slottype couplers for TW structures Fig. 19: Sketch of the magetic field lies o a mode coverter coupler Fig. 20: Sketch of the itegratio of the power splittig system i a waveguide coupler

18 5.1 High magetic field ad pulse heatig Sharp edges i slot-type couplers ca give a strog icrease of the surface magetic field. The criteria to reduce this magetic field are similar to those discussed i Sectio 3 ad they are based o a strog coupler roudig. For the mode coverter coupler this problem is completely overcome ad the pulsed heatig of the coupler is similar to that of the sigle cell of the structure. 6 Multipactig i couplers Multipactig is a pheomeo of resoat electro multiplicatio. Several theoretical approaches have bee developed to simulate this pheomeo [M1 M6]. Electros are emitted from the walls because of the presece of high electric field. At a specific level of iput power (field) the electros ca be accelerated, hit aother wall (or the same wall) ad force the emissio of more electros. If the Secodary Emissio Yield (SEY) is bigger tha 1, a large umber of electros ca build up a electro avalache, leadig to remarkable power losses ad heatig of the walls, so that it becomes impossible to icrease the cavity fields by icreasig the icidet power ad damage to the surfaces ad materials ca also appear. Multipactig is strogly ehaced i couplers by the presece of the ceramic widows because ceramic materials have a high SEY that stimulates the multipactig activity. Also bellows ca drive multipactig because of the very high field zoes. I coaxial couplers the multipactor threshold varies followig a (f RF D) 4 or a ZD 4 law where f RF is the frequecy, Z is the coaxial impedace, ad D the exteral diameter of the coaxial coupler. Followig these criteria ad by a proper electromagetic desig it is possible to fid shapes ad cofiguratios that miimize the multipactig activity. To fight the multipactig pheomea, bias voltage o the cetral ier of the coaxial couplers ca be implemeted i order to shift the resoat coditio [M8]. I waveguides the same effect is obtaied by applyig a magetic field. Coatig (of some teths of m) o ceramic RF widows with a low SEY material (usually Ti or TiN) ca also be implemeted ad, i some cases, is madatory [M9, M10]. 7 Desig techiques usig electromagetic codes The desig of couplers for SW ad TW structures is performed, owadays, usig 3D electromagetic codes. I the two cases the methods are differet ad, i the followig, we discuss a couple of possible desig techiques. 7.1 Desig of couplers for travellig-wave structures Several techiques have bee proposed for TW structure desig [D1, D3, TW1]. Let us cosider the case of a slot-type coupler. I this case the dimesios of the slot ad of the coupler cell have to be desiged so as to miimize the reflected power at the waveguide iput/output ports. Several geometrical parameters ca be used for this purpose. The most effective are the radius of the cell ad the width of the slot. Sice by e.m. codes it is ot possible to cosider a ifiite umber of TW cells, i order to desig the coupler oe has to cosider a TW structure with iput ad output couplers ad a few TW cells. I this case it is possible to desig the couplers by chagig their dimesios miimizig the reflectio coefficiet at the waveguide iput port ad verifyig that also the phase advace per cell i the TW structure is costat ad equal to the omial oe. There are, i fact, cases i which the reflectios at the iput ad output ports compesate each other ad oe has a miimum reflectio coefficiet eve if the couplers are mismatched. This procedure is, i geeral, very time cosumig. Aother techique is give i Ref. [D1] ad is based o the equivalet circuit show i Fig. 21. I the figure the two port etworks with scatterig matrix [S] correspod to the couplers that match the iput/output waveguides to the disc loaded structure. Each cell of the TW structure is modelled by a two-port

19 etwork. A perfectly matched coupler has the first elemet of the coupler scatterig matrix (S 11 ) equal to zero. Based o this equivalet circuit ad eglectig the losses i the coupler ad cell it is possible to demostrate that 2 1 S 0 e (with 1), s s j2 11 s s 1 s where () is the reflectio coefficiet at the coupler iput port whe the structure is short circuited ( is the positio of the short-circuited cell) ad is the phase advace per cell i the TW structure. A typical situatio of short-circuited cells is show i Fig. 22. Without goig ito details, widely discussed i Ref. [D1], i order to tue the coupler it is eough to vary oly two of the iput coupler dimesios (two parameters) util Eq. (25) is satisfied. This techique is much easier ad faster sice oly oe port ad few cells eed to be simulated. As a example, the fial reflectio coefficiet at the structure iput port for a seve-cell X-Bad structure is reported i Fig. 23. The coupler i this example has bee tued at GHz. The fiite umber of reflectio coefficiet miima is give by the resoat SW patters geerated i the structure by the reflectios at the iput ad output couplers. I fact, the coupler has a fiite badwidth (typically 50 MHz at 11 GH Z ) ad, over this, there are reflectios of the travellig wave from the iput ad output couplers. The miima are located i the pass-bad of the periodic structure ad their umber is equal to the umber of cells. By icreasig the umber of cells we progressively icrease the umber of miima i the pass-bad. (25) Fig. 21: Equivalet circuit of a TW structure with couplers Fig. 22: Short-circuited cells for coupler matchig Fig. 23: Reflectio coefficiet at the coupler as a fuctio of frequecy i the case of a seve-cell structure operatig at 11 GHz

20 7.2 Desig of couplers for ormal-coductig stadig-wave structures I this case oe has to desig the couplig slot i order to obtai the desired couplig coefficiet without modifyig the acceleratig field distributio ad the resoat frequecy of the structure. Let us cosider the case of a multicell structure desiged to operate at a give frequecy with a certai field flatess [Fig. 24 (a)]. The isertio of the coupler i the cetral cell of the structure [Fig. 24(b)] detues the couplig cell thus chagig the resoat frequecy ad the field flatess. The waveguide iput coupler, i fact, detues the coupler cell because it icreases its volume. To retue the structure oe has to reduce the radius of the couplig cell itself [Fig. 24 (c)]. Sice it is ot possible to evaluate the couplig coefficiet before the retuig of the couplig cell (because it depeds o the field level ito the couplig cell itself), i order to desig the coupler oe has to follow a iterative procedure: 1. fix the slot dimesio, 2. simulate the structure retuig the coupler cell, 3. calculate the couplig coefficiet, 4. if the couplig is ot the desired oe, start agai from 1. To simplify the desig it is possible to simulate the coupler cell oly with the proper boudary coditios (perfect H for the acceleratig mode), as give i Fig. 25. Lookig at the defiitio of the couplig coefficiet, oe has to tue the slot ad the radius of the cell i order to have a couplig coefficiet equal to N times (N = total umber of acceleratig cells i the full structure) the desired couplig coefficiet with a resoat frequecy exactly equal to the resoat frequecy of the structure without coupler. As a example the reflectio coefficiet at the coupler iput port for the seve-cell structure is give i Fig. 26 as a fuctio of frequecy. The differet miima are the SW modes of the structure that ca be excited from the coupler, ad the coupligs to these modes are, of course, differet sice they deped o the mode cofiguratio. The workig oe has, i this example, = 1. Fig. 24: Steps i the desig of a coupler for a SW multicell cavity Fig. 25: Coupler cell of a multi-cell structure with the proper boudary coditios for acceleratig mode

21 Ackowledgemets Fig. 26: Reflectio coefficiet at the coupler iput port for the seve-cell SW structure As metioed i the abstract, the paper brigs together pictures, data, ad iformatio from several works reported i the refereces ad I would like to thak all the authors of the papers. I would like also to thak Miro Preger for careful revisio of the paper. Subject bibliography Geeral theory [T1] R. E. Colli, Foudatios for Microwave Egieerig (McGraw-Hill, New York, 1992). [T2] G. Dôme, Basic RF theory, waveguides ad cavities, CERN Accelerator School: RF Egieerig for Particle Accelerators, Oxford, 1991, CERN 92-03, Vol. I (1992), pp [T3] H. A. Bethe, Phys. Rev. 66 (1944) 163. [T4] J. Gao, Aalytical formula for the couplig coefficiet ß of a cavity waveguide couplig system, Nucl. Istrum. Methods Phys. Res., A 309 (1991) Couplers for ormal-coductig stadig-wave cavities ad RF gus [G1] D. Palmer, The Next Geeratio Photoijector, Ph.D. thesis, Staford Uiversity (Jue 1998). [G2] X. J. Wag, M. Babzie, I. Be-Zvi, X. Y. Chag, S. Pjerov, ad M. Woodle, Desig studies for the LCLS 120 Hz RF gu, BNL 67922, Iformal Report (2000). [G3] G. D Auria et al., The ew photoijector for the Fermi project, Proceedigs of PAC07, Albuquerque, NM, USA, [G4] C. Limborg, Z. Li, L. Xiao, J. F. Schmerge, D. Dowell, S. Gierma, E. Bog, ad S. Gilevich, RF desig of the LCLS gu, LCLS-TN-05-3 (2005). [G5] L. Xiao et al., Dual feed RF gu desig for the LCLS, Proceedigs of 2005 Particle Accelerator Coferece, Koxville, TN, USA, [G6] D. H. Dowell et al., Results of the SLAC LCLS gu high-power RF tests, Proceedigs of PAC07, Albuquerque, NM, USA, [G7] S. Bartalucci et al., The RF cavity for DAFNE, Proceedigs of PAC 1993, Washigto, D.C., USA, RF gu axial couplig [GA0] K. Flottma et al., RF gu desig for the TESLA VUV free electro laser, Nucl. Istrum. Methods Phys. Res., A 393 (1997) [GA1] Jag-Hui Ha ad K. Flottma, Half cell legth optimizatio of photocathode RF gu, Proceedigs of ERL07, Daresbury, UK, [GA2] F. B. Kiewiet et al., A DC/RF gu for geeratig ultra-short high-brightess electro buches, Proceedigs of EPAC 2000, Viea, Austria, 2000.

22 Breakdow ad high magetic field i couplers [B0] V. A. Dolgashev, Experimets o gradiet limits for ormal-coductig accelerators, Proceedigs of LINAC2002, Gyeogju, Korea, [B1] V. A. Dolgashev, High magetic fields i couplers of X-bad acceleratig structures, Proceedigs of the IEEE Particle Accelerator Coferece, Portlad, OR, USA, [B2] D. P. Pritzkau, RF Pulsed Heatig, Ph.D. thesis, Staford Uiversity, SLAC-Report-577 (2001). [B3] V. A. Dolgashev ad S. G. Tatawi, Effect of RF parameters o breakdow limits i high-vacuum X-bad structures, SLAC-PUB (2003). Effect o beam dyamics [BD1] M. Krassilikov, R. Cee, ad T. Weilad, Impact of the RF-gu power coupler o beam dyamics, Proceedigs of EPAC 2002, Paris, Frace, [BD2] R. Cee, M. Krassilikov, S. Setzer, ad T. Weilad, Beam dyamics simulatios for the PITZ RF gu, Proceedigs of EPAC 2002, Paris, Frace, [BD3] M. Dohlus ad D. Jasse, The ifluece of the mai coupler field o the trasverse emittace of a supercoductig RF gu, Proceedigs of EPAC 2004, Lucere, Switzerlad, [BD4] B. Buckley et al., Emittace dilutio due to trasverse coupler kicks i the Corell ERL, Corell ERL (Corell Uiversity, Ithaca, NY, USA, 2006). Couplers for supercoductig cavities [S1] I. E. Campisi, State of the art power couplers for supercoductig RF cavities, EPAC 02, Paris, Frace, [S2] I. E. Campisi, Fudametal power couplers for supercoductig cavities, Proceedigs of 10th Workshop o RF Supercoductivity, Tsukuba, Japa, [S3] A. Variola, High power couplers for liear accelerators, Proceedigs of LINAC 2006, Koxville, TN, USA, [S4] S. Belomestykh, Review of high power CW couplers for supercoductig cavities, Workshop o High-Power Couplers for Supercoductig Accelerators, Jefferso Laboratory, Newport News, VA, USA, [S5] S. Belomestykh, Overview of iput power coupler developmets, pulsed ad CW, Proceedigs of SRF2007, Pekig Uiv., Beijig, Chia, [S6] B. Aue et al., Supercoductig TESLA cavities, Phys. Rev. Spec. Top. Accel. Beams, 3 (2000) [S7] M. Champio et al., TESLA iput coupler developmet, Proceedigs of PAC 1993, Washigto, DC, USA, [S8] B. Dwersteg et al., TESLA RF power couplers developmet at DESY, Proceedigs of SRF 2001, Tsukuba, Japa, 2001, p [S9] S. Belomestykh ad H. Padamsee, Performace of the CESR supercoductig RF system ad future plas, Proceedigs of 10th Workshop o RF Supercoductivity, Tsukuba, Japa, [S10] L. R. Doolittle, Strategies for waveguide couplig for SRF cavities, Liac98, Chicago, IL, USA, 1998, p Couplers for travellig-wave structures [TW1] C. Natista et al., Low-field accelerator structure couplers ad desig techiques, Phys. Rev. Spec. Top. Accel. Beams, 7 (2004) [TW2] SLAC two mile accelerator [TW3] G. Bowde et al., A compact RF power coupler for the NLC liac, Proceedigs of the 1999 Particle Accelerator Coferece, New York, NY, USA, [TW4] C. Suzuki et al., Iput coupler desig for C-bad acceleratig structure, PAC 97, Vacouver, Caada, [TW5] D. Alesii, Desig, realizatio ad low power RF tests of the C-bad structure prototype for SPARC, SPARC-RF-11/002 (2001).