A critical review of resistive losses in the LHC beam screen, taking into account anomalous skin effect and surface roughness, has triggered a programme of surface resistance measurements at different temperatures, frequencies and magnetic field intensities. The aim is to establish a realistic heating budget for the LHC cryogenic system and to optimize the fabrication process for the copper coating of the beam screen. Preliminary results at cryogenic temperatures (without magnetic field) indicate a surface resistance about a factor two larger than previously estimated: an absolute measurement precision of a few per cent is reached by comparing the quality factors of even and odd TEM modes in a cylindrical structure with two inner conductors

Caspers, Friedhelm

Morvillo, M

Ruggiero, F

CERN Document Server

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHEuropean Laboratory for Particle PhysicsSurface Resistance Measurements for the LHC Beam ScreenCaspers, F.; Morvillo, M.; Ruggiero, F.A critical  review of resistive  losses in the LHC beam screen, taking into account  anomalous  skineffect and  surface  roughness,  has  triggered  a programme of surface  resistance  measurements  atdifferent  temperatures, frequencies and magnetic field  intensities.  The aim is to establish a realisticheating budget for the LHC cryogenic system and to optimize the  fabrication  process for the coppercoating of the beam screen.  Preliminary  results at cryogenic temperatures  (without magnetic field)indicate a surface  resistance about a factor two larger than previously estimated: an absolutemeasurement precision of a few per cent is reached by comparing the quality factors of even and oddTEM modes in a cylindrical structure with two inner conductors.SL-APPSPresented at 1997 Particle Accelerator Conference, Vancouver, 12-16 May 1997.Geneva, 12 juin 1997Large Hadron Collider ProjectAdministrative SecretariatLHC DivisionCERNCH - 1211 Geneva 23SwitzerlandLHC Project Report 115AbstractSurface Resistance Measurements for the LHC Beam ScreenF. Caspers, M. Morvillo and F. Ruggiero, European Laboratory for Particle Physics (CERN)AbstractA critical review of resistive losses in the LHC beamscreen, taking into account anomalous skin effect and sur-face roughness, has triggered a programme of surface resis-tance measurements at different temperatures, frequenciesand magnetic field intensities. The aim is to establish a re-alistic heating budget for the LHC cryogenic system and tooptimize the fabrication process for the copper coating ofthe beam screen. Preliminary results at cryogenic tempera-tures (without magnetic field) indicate a surface resistanceabout a factor two larger than previously estimated: an ab-solute measurement precision of a few per cent is reachedby comparing the quality factors of even and odd TEMmodes in a cylindrical structure with two inner conductors.1 INTRODUCTIONThe LHC beam screen is a stainless steel pipe (for mechan-ical strength during quench) with a 50 m copper layercoated on its inner surface. It is cooled at a temperatureranging from 5 to 20 K. The purpose of the copper coatingis to reduce the surface resistanceRs, i.e., the ratio betweenlongitudinal component of the electric field at the wall sur-face and beam-induced wall current. This is important tominimize at the same time transverse resistive wall insta-bility (a relatively low frequency phenomenon) and beam-induced wall heating. At top energy and for nominal beamparameters, the classically computed resistive wall heatingof the LHC beam screen is 75mW/m. Owing to the anoma-lous skin effect, this value should increase by 11%, but ac-cording to surface resistance measurements performed onsamples of the SSC beam tube, the increase could be sig-nificantly larger [1].For a circular screen of radius b, the parasitic heatingpower per unit length is given by                                                                                           VNWATEFLON++ +++- +-TEFLONl d2-2000 MHz2-2000 MHzHYBRID0°/180°HYBRID0°/180°Figure 1: Experimental setup: a vector network analyser (VNWA) is used in conjunction with two hybrids, yielding eithereven (++) or odd (+-) mode excitation for a 1 m long cylindrical cavity with two inner conductors, held by 3 teflon supports.The near degeneracy of even and odd modes is removed by two teflon splitters placed between the inner conductors.PL=I2avMf0c2Z10~(!)2Rs(!)2bd!; (1)where Iavis the average beam current, M the number ofbunches, f0the revolution frequency, c the velocity of lightand ~(!) the bunch spectrum, which for the relatively shortLHC bunches at 7 TeV (7.5 cm, r.m.s.) will cover a widehigh frequency region (637 MHz, r.m.s.).Since the parasitic heating scales with the square of Iav,for the ultimate beam intensity of 850 mA, it may be-come comparable to the synchrotron radiation power lossof 326 mW/m. Reliable data for the surface resistance upto a few GHz is therefore needed to establish a realisticheating budget for the cryogenic system and to optimizethe fabrication process for the copper coating of the beamscreen. The situation is complicated by the fact that theanomalous skin effect is accompanied by a strong magneticfield and by phenomena associated with the surface rough-ness. There is no valid theory for estimating the surfaceresistance in this complex environment and this has trig-gered a programme of surface resistance measurements onseveral samples of the LHC beam screen.2 EXPERIMENTAL SETUPTo measure the surface resistance at several temperaturesand with an 8.4 T magnetic field, we decided to avoid us-ing supercondutors. With the experimental setup shown inFig. 1, we measure the quality factors Q++ and Q+  ofeven and odd modes excited in a 1 m long cylindrical TEMmode cavity with two inner conductors. Relying on theonly assumption that Rsbe the same for the two inner con-ductors, we then obtain the surface resistance of both innerconductors and outer tube in steps of about 150 MHz.0.5 1 1.5 20246810121416o o ox x x+ + +b baa* ** * *XXXXOOOO OO OOOOa)Rs[m] IN (RRR'200, (300 K) = 2 10 8m)frequency [GHz]0.5 1 1.5 20246810121416o oox xx+ ++b baa* * ***XXXXOOOOO OOOOOb)Rs[m] OUT (RRR'50, (300 K) = 3:2 10 8m)frequency [GHz]0.5 100.511.522.533.5oo oxx x++ +bbaa*****c)Rs[m] IN (RRR'200, (4 K) = 10 10m)frequency [GHz]0.5 100.511.522.533.5oooxxx+++b baa** ***d)Rs[m] OUT (RRR'50, (4 K) = 6:4 10 10m)frequency [GHz]0.5 1 1.500.511.522.533.5oooooooe)Rs[m] IN (RRR'200, (4 K) = 10 10m)frequency [GHz]0.5 1 1.500.511.522.533.5ooooooof)Rs[m] OUT (RRR'50, (4 K) = 6:4 10 10m)frequency [GHz]Figure 2: Surface resistance measured for the thermally treated inner conductors (a, c, e) having a dc RRR'200, andfor the outer tube (b, d, f) with no thermal treatment and a dc RRR'50, compared to the predictions in the classic (solidline) and anomalous regime (dot-dashed lines: 40 K, dashed lines: 4 K). Figures (a) and (b) show data measured at roomtemperature, either before (“X”) or after cryogenic measurements using shorter coupling networks (“O”), at 40 K, eitherbefore (“b”) or after (“a”) injection of He gas during cool down (leading to a sudden thermalisation of the inner conductors,otherwise thermally insulated) or with external heating (“*”), at 20 K (“+”), at 10 K (“x”) and at 4 K (“o”). Somemeasurements at 40 K have a large temperature spread from top to bottom of the outer tube. The data at room temperatureis best fitted assuming a resistivity (300 K) = 2 10 8m for the inner conductors and (300 K) = 3:2 10 8m forthe outer tube. Figures (c) and (d) are a magnification of (a) and (b), respectively, showing only measurements at cryogenictemperatures. The data in (e) and (f) has been obtained at 4 K with shorter coupling networks, to allow measurements ina wider frequency range: data above 1.2 GHz, however, has been discarded due to strong or badly corrected coupling.0.5 1 1.500.511.522.533.5ooooooooo++++++++a)Rs[m] IN (RRR'200, (4 K) = 1:35  10 10m)frequency [GHz]0.5 1 1.500.511.522.533.5oooooo oooo+++ +++++b)Rs[m] OUT (RRR'200, (4 K) = 1:6 10 10m)frequency [GHz]Figure 3: Surface resistance measured with shorter coupling networks at 4 K (“o”) and at 20 K (“+”) for the innerconductors (a) and the outer tube (b), both thermally treated at 350 C and having a measured dc RRR'200, comparedto the predictions in the anomalous regime (dashed lines). The corresponding data at room temperature (not shown inthe figure) is best fitted assuming a resistivity (300 K) = 2:7  10 8m for the inner conductors and (300 K) =3:2  10 8m for the outer tube. The slightly higher resistivity attributed to the inner conductors may be due to smallscratches in their copper coating, caused by the sliding teflon supports repeatedly mounted during previous measurements.Indeed the unloaded quality factor of each mode, givenby 1=Q =  IN=RINs+  OUT=ROUTs, is related throughcalculable geometric coefficients [2]  INand  OUTto thesurface resistances RINsand ROUTsof the inner conductorsand of the outer tube. Measuring Q++ and Q+ , there-fore, we can solve a system of two equations in the twounknowns RINsand ROUTs.The two inner cylindrical conductors (of radius 8 mm)and the outer tube (of radius 19.6 mm) are all made out ofstainless steel with a 50 m electrodeposited copper layer,having a surface roughness of a few m. Future measure-ments are planned also with a colaminated copper layer.The distance between the axes of the two inner conduc-tors is 19.5 mm. The distance d between each couplingnetwork and the inner conductors (a few cm) is adjustedto have sufficiently weak coupling coefficients 1(!) and2(!) over the frequency range of interest. We calculatecoupling by measuring reflection coefficients at each cou-pling port, while the loaded quality factor Qload(!) foreach mode is obtained by a transmission coefficient mea-surement. The corresponding unloaded quality factor isthen given byQ(!) = [1 + 1(!) + 2(!)]Qload(!). Thelength l of the coupling networks has been varied from 12down to 4 cm, to allow measurements in a wider frequencyrange (up to about 1.5 GHz). Indeed coupling grows withfrequency, but suddenly drops over a large frequency gapwhose location depends critically on l. This phenomenonseems related to internal resonances of the coupling net-works.3 PRELIMINARY EXPERIMENTAL RESULTSIn Figs. 2 and 3 we present some preliminary surface re-sistance measurements without magnetic field, from roomtemperature down to 4:2 K, compared to the predictions inthe classic and anomalous regime. The inner conductorshave been thermally treated at 350 C and have a measureddc RRR around 200. Fig. 2 refers to an outer tube with nothermal treatment and a dc RRR'50, while Fig. 3 refers toa thermally treated outer tube. The low temperature resis-tivity of the outer tube in the case of Fig. 2 is comparableto that of the LHC beam screen in a magnetic field of 8.4 T,but the measured surface resistance around 1 GHz is almosta factor two larger than previously estimated.Both figures show a slight modulation of the surface re-sistance as a function of frequency; this modulation is anti-correlated for the IN versus OUT data and grows froma few per cent at low frequencies to about 10% beyond1 GHz. We are currently investigating this effect, whichmight be due to the teflon supports, to the teflon splitters,to geometric imperfections or to the coupling networks.4 ACKNOWLEDGEMENTSWe would like to thank several CERN colleagues whogave significant contributions to these measurements and,in particular, A. Poncet and C. Benvenuti for useful discus-sions of the experimental setup, A. Mathewson and N. Kos(beam screen prototypes), S. Sgobba (surface metrologyand welding), C. Reymermier and L. Nikitina (designs),J. Rieubland, G. Ferlin and A. Jacquemot for their con-stant help in the cryolab, L. Walckiers and A. Arn (mea-surements in progress with magnetic field).5 REFERENCES[1] W. Chou and F. Ruggiero, LHC Project Note 2 (1995).[2] G.S. Smith and J.D. Nordga˚rd, IEEE Trans. Microwave The-ory Tech., vol. MTT-28, pp. 887–893, Aug. 1980.

Surface Resistance Measurements for the LHC Beam Screen

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