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1 Doument downloaded from: This paper must be ited as: Gonzalez Iglesias, D.; Soto Paheo, P.; Anza Hormigo, S.; Gimeno Martinez, B.; Boria Esbert, VE.; Viente Quiles, CP.; Gil Raga, J. (0). Multipator suseptibility harts for ridge and multiridge waveguides. IEEE Transations on Eletron Devies. ():0-0. doi:0.0/ted.0.. The final publiation is available at Copyright Institute of Eletrial and Eletronis Engineers (IEEE) Additional Information 0 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any urrent or future media, inluding reprinting/republishing this material for advertising or promotional purposes, reating new olletive works, for resale or redistribution to servers or lists, or reuse of any opyrighted omponent of this work in other works.

2 Page of Multipator Suseptibility Charts for Ridge and Multi-Ridge Waveguides D. González-Iglesias, P. Soto, Member, IEEE, S. Anza, B. Gimeno, Member, IEEE, V. E. Boria, Senior Member, IEEE, C. Viente, Member, IEEE, J. Gil, Member, IEEE Abstrat The aim of this letter is to study the multipator RF breakdown voltage in several ridge and multi-ridge waveguide onfigurations. Firstly, multipator suseptibility harts for several types of ridged waveguides have been omputed using the ommerial software FESTD. Next, these harts have been used to predit multipator threshold values for a band-pass filter and a quasi low-pass filter both ontaining ridge waveguide setions. Furthermore, multipator simulations using FESTD are arried out to alulate the multipator threshold of the aforementioned strutures. A good agreement between preditions and simulations has been found for both filter examples. Index Terms Ridge waveguide, Multi-ridge waveguide, Multipator effet, RF breakdown. I. INTRODUCTION Multipator is a vauum disharge phenomenon that takes plae on devies operating under high-power radio frequeny (RF) eletromagneti fields []. It an appear in a wide variety of senarios, suh as satellite ommuniation devies, klystrons and aelerator strutures []-[]. The multipator effet ours when an RF eletri field aelerates free eletrons inside the devie impating on the metalli walls of the devie. When eletron impat energy is suh that the seondary emission yield oeffiient (SEY), δ of the material is higher than unity, new seondary eletrons are released []. Under ertain resonant onditions, new seondaries get synhronized with the RF eletri field produing an exponential growth of the eletron population. One the number of eletrons beomes very high, an eletrial urrent is established between the walls of the omponent. This RF disharge an produe several negative effets that degrade the devie performane: inrease of signal noise and refleted power, heating up of the devie walls, outgassing, detuning of resonant avities, vauum window failure and even the total destrution of the omponent. Multipator has been deeply studied for many different kinds of geometries suh as parallel-plate []-[], oaxial [0]- [], retangular []-[], mirostrip [], irular []-[], and elliptial [] waveguides. Despite all these past efforts, D. González-Iglesias and B. Gimeno are with the Departamento de Físia Apliada, Instituto de Cienia de Materiales, Universidad de Valenia, 00- Burjasot(Valenia), Spain. P. Soto and V.E. Boria are with the Departamento de Comuniaiones, Instituto de Teleomuniaiones y Apliaiones Multimedia, Universidad Politénia de Valenia, 0-Valenia, Spain. S. Anza, C. Viente and J. Gil are with Aurora Software and Testing, S.L., Business Development Building, Universidad Politénia de Valenia, 0- Valenia, Spain. and to the authors knowledge, multipator in ridge and multiridge waveguides has not been studied yet. Single- and multi-ridged waveguides have found many appliations in mirowave and millimeter-wave devies. Among their main advantages we find that they inlude large singlemode broad-band operation, large dominant utoff wavelength, and low impedane harateristis. They are widely used for both high-power and low-power appliations suh as band-pass and quasi low-pass filters [0]. These filters are very appropriate andidates for some spae and terrestrial ommuniations appliations due to their ompat size and good stop-band performane. For instane, they an be used as preseletor filters before the input multiplexer, or as harmoni suppression filters after RF transmitters or amplifiers, partiulary as on board satellite omponents. In this work, we have omputed multipator suseptibility harts for several ridge and multi-ridge waveguide onfigurations. First, setion II desribes the proedure arried out to perform the requested multipator simulations in order to generate the suseptibility harts. In setion III, ridge, double-ridge and multi-ridge waveguide multipator harts are presented for both symmetrial and asymmetrial onfigurations. These results are used in setion IV for prediting the multipator threshold values of an evanesent-mode filter, and of a waffle-iron filter, both ontaining ridge-waveguide setions. In addition, and with the aim of verifying the derived suseptibility harts, a omplete FESTD multipator analysis has been performed for both filter strutures. Finally, in setion V some relevant onlusions are outlined. II. MULTIPACTOR ANALYSIS METHODOLOGY The ommerial software FESTD [] has been used to perform multipator simulations within the analyzed ridged waveguides. This ode allows -D traking of a set of eletrons immersed into a region under RF eletri and magneti fields. An eletromagneti solver based on full-wave modal tehniques [] and mirowave network theory alulates these fields with high auray and effiieny, even for omplex passive mirowave omponents. The strutures are exited from the input port with its fundamental mode. Differential equations of eletrons motion are numerially solved using a Leap-Frog method, as desribed in []. The interations of the eletrons with the metal boundaries are modeled to onsider eletron elasti refletion, absorption or reation of seondaries after eah primary eletron impat. The SEY is modeled using a modified version of the Vaughan s formula []. All

3 Page of Fig.. Symmetrial strutures on the left olumn and asymmetrial strutures on the right olumn. From top to bottom: ridge, double-ridge and multi-ridge waveguides. simulated strutures are silver-plated. The SEY parameters for silver, whih are desribed in [], are: the first ross-over, W = 0 ev; the maximum SEY oeffiient, δ max =.; and the impat kineti energy for δ max, W max = ev. The seondary eletron veloities have been omputed using a ev mean and ev standard deviation Maxwellian distribution. III. MULTIPACTOR SUSCEPTIBILITY CHARTS Ridge, double-ridge and multi-ridge waveguides (see Fig. ) with housing dimensions of a standard WR retangular (a =.0 mm, b =. mm) have been analyzed. Symmetrial and asymmetrial onfigurations have been onsidered. In suseptibility harts, the RF multipator voltage threshold is depited as a funtion of the frequeny gap f d. Multipator disharge is always expeted to our in the narrowest waveguide zone, where eletri field beomes higher. Aording to this, the existing gap between metal ridges is the ritial zone for the appearane of a multipator disharge. Thus, an equivalent voltage is numerially omputed using the following expression: d V eq = E dl () 0 where E is the RF eletri field of the fundamental mode in the ridge gap, and dl is the differential vetor parallel to the transversal omponent of the eletri field. It an be heked numerially that for double-ridge waveguides the equivalent voltage is the same at both symmetrial ridges, whereas for multi-ridge waveguides (with an odd number of ridges) the voltage is higher at the entral one. In Figs. and Fig. the eletri field lines are depited for the different waveguide geometries. Fig.. Eletri field lines for symmetrial onfigurations. From top to bottom: ridge, double-ridge and multi-ridge waveguides. Fig. shows the voltage threshold as a funtion of the waveguide length for both symmetrial and asymmetrial single-ridge waveguides. Multipator simulations show that multipator threshold strongly depends on the waveguide length value, i.e. l/λ g in Fig.. In fat, the voltage threshold raises up for short waveguide lengths as a result of the axial drift that allows eletrons leaving the ridge gap. Thus, in order to ounterat the lost eletrons a higher rate of seondaries generation is needed, whih is obtained by means of an inrease of RF power. Similar results were obtained for the different multi-ridge topologies. In the next multipator suseptibility harts, a waveguide length in the flat zone of the graphi has been always onsidered (i.e. l/λ g > 0.). Two different kinds of harts are presented. First, RF voltage threshold for several ridge widths is depited in Figs. and for symmetrial and asymmetrial onfigurations, respetively. As it an be shown, there are slight variations on voltage threshold with the ridge width for eah figure. However, it an be observed that the narrower the ridge the higher the voltage threshold. An explanation of this phenomenon is that lower w/a values allow eletrons to esape from the gap region, so an extra voltage is needed in order to ompensate this phenomenon. Similar multipator behavior is found for waveguide irises []-[], where the power threshold inreases when the h/l ratio is higher (h is the gap height and l is the iris length). Two different mehanisms for eletron loss were proposed for an iris senario. On the one

4 Page of Fig.. Eletri field lines for asymmetrial onfigurations. From top to bottom: ridge, double-ridge and multi-ridge waveguides. Fig.. Multipator voltage threshold as a funtion of the normalized waveguide length for symmetrial and asymmetrial single-ridge waveguides. Gap is d = 0. mm (d/b = 0.0), b/a = and w/a = 0.. RF frequeny is GHz and λ g is the wavelength in the guide. hand, fringing eletri field aelerates eletrons out of the iris. On the other hand, a random drift due to the axial omponent of the initial veloity of the seondary emitted eletrons may push many eletrons away from the gap region. In our ridge waveguide ase, both effets are supposed to at but in the transverse plane to the wave propagation, speifially parallel to the ridge width of value w. For a better understanding of the fringing phenomenon in Fig.. Multipator voltage threshold for several ridge widths in symmetrial onfigurations. From top to bottom: ridge, double-ridge and multi-ridge waveguides. Gap length is d = 0. mm, d/b = 0.0 and b/a =. ridged waveguides, an study of the voltage threshold dependane with the ratio of ridge width to gap, w/d, has been performed. It overs a wider range of w/d values than the previous w/a analysis. Results are presented in Fig. for a symmetrial single ridge waveguide but similar behavior an be found for asymmetrial and/or multi-ridge waveguides. It is observed than fringing effet raises up voltage threshold as w/d ratio redues. This behavior beomes more important when w/d is lose to unity or lower. On the other hand, for w/d values higher than unity, threshold variations beome

5 Page of Fig.. Multipator voltage threshold for several ridge widths in asymmetrial onfigurations. From top to bottom: ridge, double-ridge and multi-ridge waveguides. Gap length is d = 0. mm, d/b = 0.0 and b/a =. slighter. Next, the effet of ridge gap variation on voltage threshold was also studied for both symmetrial and asymmetrial topologies (see Figs. and, respetively). Like in the previous performed studies, it is observed a very slight variation of the voltage threshold in terms of the gap for higher w/d values onsidered. Finally, multipator voltage threshold omparison among single, double and multi-ridge waveguide is presented for the symmetrial ase in Fig. 0. As it was pointed out in Figs. Fig.. Multipator voltage threshold for several values of ridge width to gap ratio for single ridge symmetrial waveguide. Gap length is d = 0. mm, d/b = 0.0 and b/a =. and, RF voltage threshold inreases as the ridge width beomes smaller. Multi-ridge waveguide has the narrowest ridges and therefore the higher threshold values, as it an be expeted. IV. MULTIPACTOR PREDICTION USING SUSCEPTIBILITY CHARTS In this setion, a simple multipator predition method for omplex mirowave devies ontaining ridge waveguide setions is presented. This proedure does not require any additional multipator simulation. Only the eletromagneti field distribution inside the struture at the operating frequeny is needed. One the eletromagneti fields are omputed, the eletri field must be integrated in order to alulate the voltage aross the ridge gap setions using (). As the eletri field typially varies with the axial diretion [], suh voltage must be evaluated for several axial points along the ridge length. As a result, the highest voltage V eq at eah ridge in the struture for an RF power input exitation, i.e. P in = W, is found. For eah frequeny value, the devie input power is proportional to the square of the ridge voltage. Aordingly, the multipator input power threshold P th at the input port of the devie related to a partiular ridge setion will be P th = V eq th V eq P in () where the voltage threshold V eq th depends on the frequeny gap f d of eah partiular setion, whih an be extrated from the previously omputed multipator suseptibility harts. Multipator power threshold in the full struture is the lowest power value obtained among all studied ridges. We detail this method through the two following examples. A. Evanesent mode filter The first analyzed struture is an evanesent mode filter extrated from []. Fig. shows the filter topology, and their dimensions are summarized in Table I. Input and output

6 Page of Fig.. Multipator voltage threshold for several gap lengths in symmetrial topologies. From up to down: ridge (width w/a = 0.), double-ridge (w/a = 0.) and multi-ridge (w/a = 0.) waveguides. In all ases, b/a =. ports are implemented with WR waveguide (a in =. mm, b in =.0 mm). The operation frequeny is hosen to be entered in the passband of the filter, namely f =. GHz. Sine the onsidered struture onsists of five idential ridges, the frequeny gap produt is f d =.0 GHzmm for all of them. First, eletromagneti analysis of the full struture is performed, assuming P in = W exitation at the input port. The equivalent voltage over the gap has been omputed for Fig.. Multipator voltage threshold for several gap lengths in asymmetrial topologies. From up to down: ridge (width w/a = 0.), double-ridge (w/a = 0.) and multi-ridge (w/a = 0.) waveguides. In all ases, b/a =. several axial points along the ridge setions (see Fig. ). Ridges are numbered from the input port to the output port as indiated in Table I. From these results, multipator threshold an be predited as follows. Sine the ridge setions have the very same gap values, the voltage threshold V eq th will be the same for all of them. Therefore, the greatest voltage among all the ridge setions must be found. From suh a voltage value and the voltage threshold extrated from symmetrial waveguide harts, multipator power threshold

7 Page of Fig. 0. Multipator voltage threshold for symmetrial ridged waveguides. Singe-ridge w/a = 0., double-ridge w/a = 0. and multi-ridge w/a = 0.. Gap is 0. mm (d/b = 0.0) and b/a =. Symmetrial evanesent mode ridge waveguide filter under onsid- Fig.. eration. at the input port an be obtained. Ridge setions have the following dimensions: w/a = 0. and d = 0. mm. The most similar situation in previously omputed suseptibility harts is found in Fig. for w/a = 0. and d/b = 0.0. From there, voltage threshold for the working frequeny is V eq th = 0 V. Moreover, multipator input power threshold is also omputed using FESTD []. Results obtained from both methods are summarized in Table II. The first olumn indiates the number of the ridge setion providing the highest TABLE I DIMENSIONS OF THE EVANESCENT MODE FILTER SHOWN IN FIG. a h b h w h d l = l t = t l = l t = t l = l t.0 mm. mm.00 mm.0 mm 0. mm 0.0 mm 0.0 mm. mm. mm. mm. mm TABLE II SUMMARIZED MULTIPACTOR RESULTS FOR THE EVANESCENT MODE FILTER Ridge V eq (V) P pred (W) P FESTD (W) Fig.. Equivalent voltage over the gap for P in = W on several axial points of the filter. Ridges and in (a), and ridges, and in (b). voltage (and onsequently where breakdown is expeted to our); the seond olumn gives the highest voltage value for P in = W, V eq; the third olumn is the predited input power threshold, P pred ; and the fourth olumn provides the input power threshold omputed by FESTD, P FESTD. It is observed that both simulation and predition math up with the ridge setion where the multipator appears. In addition, power thresholds obtained by two different proedures are very similar, thus demonstrating the feasibility of the predition method. Note that the predited threshold value is always expeted to be less than the simulated one, due to the fat that in the suseptibility harts the ridge waveguides have uniform fields along the axial diretion. In a realisti ase the waveguide is onneted to the adjaent disontinuities, and the voltage along the waveguide varies, as depited in Fig.. This effet raises the multipator threshold above the uniform axial ase. Finally, it must be pointed out the advantage of using the

8 Page of Fig.. Eletri field lines for multi-ridge waveguide setion of the analyzed filter. Fig.. Multipator voltage threshold for the symmetrial multi-ridge waveguide of the waffle-iron filter under onsideration manufatured in opper. new omputed harts instead of the parallel-plate model harts. From ECSS Multipator Tool version. [], power threshold for the onsidered gap at the working frequeny is. W (. V). Comparing this value with the predited one using the new generated harts, it is found that the free-multipator power handling apability of the filter an be inreased in db. In fat, it is well known that parallel-plate model is rather onservative for more omplex waveguide geometries. B. High-Power S-Band Filter The last analyzed struture is a high-power S-band filter whose topology and dimensions are detailed in Fig. of []. The filter onsists of equal multi-ridge setions, eah multiridge transversal ross-setion has symmetrial ridges with d =. mm gap. In Fig. the eletri field lines of the transversal ross-setion of the filter, whih was onstruted in opper, are shown. First, multipator suseptibility harts are omputed for a single -symmetrial multi-ridge waveguide with transversal ross-setion dimensions of the filter. Results for opper are shown in Fig.. For the opper SEY simulations we have used: W = ev, δ max =., and W max = ev. After that, an eletromagneti analysis of the whole devie is performed. Input and output ports are implemented with retangular waveguides of the following dimensions: a =.0 mm, b =. mm. The operation frequeny TABLE III SUMMARIZED MULTIPACTOR RESULTS FOR THE WAFFLE-IRON FILTER Ridge V eq (V) P pred (W) P FESTD (W). Fig.. Equivalent voltage over the gap of the filter ridges for P in = W on several axial points. has been hosen to be. GHz and the frequeny gap produt is f d =. GHzmm for all the ridge setions. Equivalent voltage between ridges was alulated for the entral ridge (where the eletri field is higher), aording to Fig.. From suseptibility hart in Fig., voltage threshold for the working frequeny is V eq th = 0 V. With these data multipator power threshold predition an be done. Table III summarizes the main results (V eq, P pred, P FESTD already defined in the previous subsetion). Good agreement has been found between our predited value and the one provided by FESTD. Comparing the predited power threshold value with the one orresponding to the parallel plate model ( W), there is relevant differene of. db between them. V. CONCLUSIONS In this letter, we have studied the multipator effet in ridged waveguides. Multipator suseptibility harts have been omputed by means of the ommerial software FESTD for several ridge and multi-ridge onfigurations. For eah onfiguration, variation of the voltage threshold as a funtion of the different waveguide dimensions is presented and a qualitative explanation of suh behaviors in terms of the fringing effet is outlined. Afterwards, developed multipator suseptibility harts have been used to predit the RF input power threshold for an evanesent mode filter and for a high-power S-band filter, both ontaining ridges. Predited multipator values have been ompared with FESTD simulations of the entire strutures and a very good agreement has been found in both ases. REFERENCES [] J. Vaughan, Multipator, IEEE Trans. Eletron Devies, vol., no., pp. -, August.

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