An estimate of the resistive losses in the LHC dipole beam screen is given from cold surface resistance measurements using the shielded pair technique. Several beam screen samples have been evaluated, with different copper coating methods, including a sample with ribbed surface envisaged to reduce electron cloud losses thanks to its low reflectivity. Experimental data, derived by a proper analysis of the measured Q-factors and including error estimates are compared with theoretical predictions of the anomalous skin effect

Caspers, Friedhelm

Morvillo, M

Ruggiero, F

Tan, J

Tsutsui, H

CERN Document Server

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHEuropean Laboratory for Particle PhysicsSURFACE RESISTANCE MEASUREMENTS OFLHC DIPOLE BEAM SCREEN SAMPLESF. Caspers, M. Morvillo, F. Ruggiero, J. Tan and H.TsutsuiAn estimate of the resistive losses in the LHC dipole beam screen is given from cold surface resistancemeasurements using the shielded pair technique. Several beam screen samples have been evaluated,with different copper coating methods, including a sample with ribbed surface envisaged to reduceelectron cloud losses thanks to its low reflectivity. Experimental data, derived by a proper analysis of themeasured Q-factors and including error estimates are compared with theoretical predictions of theanomalous skin effect.PS, SL DivisionsPresented at the Seventh European Particle Accelerator Conference  (EPAC 2000)26-30 June 2000, Vienna, AustriaGeneva, Large Hadron Collider ProjectAdministrative SecretariatLHC DivisionCERNCH - 1211 Geneva 23SwitzerlandLHC Project Report 410Abstract14 August 20001SURFACE RESISTANCE MEASUREMENTS OF LHC DIPOLE BEAMSCREEN SAMPLESF. Caspers, M. Morvillo, F. Ruggiero, J. Tan, H.Tsutsui, CERN, Geneva, SwitzerlandAbstractAn estimate of the resistive losses in the LHC dipolebeam screen is given from cold surface resistancemeasurements using the shielded pair technique. Severalbeam screen samples have been evaluated, with differentcopper coating methods, including a sample with ribbedsurface envisaged to reduce electron cloud losses thanksto its low reflectivity. Experimental data, derived by aproper analysis of the measured Q-factors and includingerror estimates are compared with theoretical predictionsof the anomalous skin effect.1  INTRODUCTIONOne of the undesirable phenomena that contribute to thethermal load on the cold LHC beam screen is the beam-induced resistive wall heating. The key element to thiseffect is the surface resistance which is frequencydependent and which is sensitive to the coatingpreparation technique, and in particular to the surfaceroughness. For that purpose a resonator was developed tomeasure the surface resistance in the range 150 – 2300MHz at room temperature as well as in a cryostat. Thisdevice, however, is susceptible to a significant amountof technical parameters, which are discussed section 2.Improvements brought to the test stand [1] are describedin a chronological sequence and the user will be givenpractical hints and guidelines for future measurementcampaigns. The results of cold measurements (withoutmagnetic field) performed with the latest version of theresonator are presented section 3. They agree withtheoretical predictions in the anomalous skin effectregime, contrary to previous results obtained by anearlier version of the resonator [2].2  TEST SET-UP2.1  Measurement PrincipleTwo cylindrical inner conductors are placed in parallelinside a tube, which is the Device Under Test (DUT).The measurement principle consists in exciting even andodd Transverse Electromagnetic Modes (TEM) with aVector Network Analyser (VNA) and in evaluating thecorresponding Q-values. From these two parameters wederive the effective resistance of the DUT and of theinner conductors, assumed identical. As shown in [1],the phase-shift between the inner conductors, 0° (evenmode) and 180° (odd mode), is obtained by an externalhybrid circuit.  Basically in a coaxial resonator, the fundamental modeis determined by the length of the inner conductor, here925 mm which is equal to λ0/2 and gives a resonantfrequency of f0 = c/λ0 = 162 MHz, if one neglects theinfluence of the end capacity of the rods. The followingharmonics are given by fn = n×f0 where n is an integer.Note that at half the resonator the electric field is zerofor odd harmonic number, and maximum for evenharmonic numbers.  The device is a 1.2 m long (length of the DUT) and39.2 mm diameter cylindrical resonator with two copper-coated inner conductors of 16 mm diameter each. Thecoating technique of the DUT results from the co-lamination of a sheet of copper and a sheet of stainlesssteel (SS), which was then rolled and welded to form atube. Details of the tube fabrication process areextensively described in Ref. [2].Figure 1: Schematic test set-up; port1=left; port2=right.  The technical choice for non-superconducting materialfor the inner conductors is motivated by• the requirement to be tested in a high DC magneticfield,• the absence of quench phenomena,• its versatile handling,• the capability to work on a wide temperature range,• an acceptable price for the hardware. The inner conductors are held by three identical internalteflon supports (ε’ = 2, loss factor tan(δ) = 10-4). Eachdisk-like support is fixed by two nylon pins which areinserted in the inner conductors. The two end sidesupports are placed 1 mm from the rods end side. Thegap between the centre of the inner conductors is set to2a = 19 mm. Finally the resonator is coupled to the VNAvia two pairs 17 mm-long semi-rigid SMA cables, eachone being terminated by a 3 mm-long antenna.  The cables are connected to the hybrid devices (AnzacH-9, range 2-2000 MHz) in a given excitationconfiguration, e. g. starting with the ∆-mode (see Fig. 1).A  more detailed representation of the test stand in theodd mode is given in [1, 2]. Then S-parameters andloaded Q’s are recorded from the fundamental frequencyto the highest harmonic achievable, without running intowave-guide modes (Higher Order Modes = HOM).Thereafter the hybrids are connected from ∆ to Σexcitation. All together the relevant S-parameters S11(input reflection), S21 (transmission from port 1 to port 2)and S22 (output reflection) are recorded for the Σ- and ∆-modes.2.2 Data AnalysisIn a two-port resonator, the loaded quality factor Qload atresonance ω0 is related to the dissipated power in thecavity walls Pwall, to the losses P1 and P2 in the couplingports, and to the stored energy U0 by the followingequation:210021 1111QQQUPPPQ wallwallload++=++=ω.    (1)With the so-called coupling factor βi [i=1,2] defined aswalliiwalli PPQQ==β ,                     (2)Eq. (1) turns into211 ββ ++=loadwallQQ.                     (3)At resonance βi is related to the reflection coefficient |ρi|by1111−−+−=iii ββρ .                           (4)RF quantities measured in a given mode at a givenresonance frequency are Qload , S11, S22 and S21. From Sparameters one gets |ρi|. Deducing βi ‘s gives Qwall.  More explicitly, Pwall is the total power dissipated by theinner conductors and by the outer conductor. Withrespect to both excitation modes one obtains:where Rsi and Rso are the surface resistances of the innerand of the outer conductors, Γi,∆, Γo,∆, Γi,Σ and Γo,Σ aregeometrical factors. The last four quantities which arealso frequency dependent have to be computed [3] tosolve the system of two equations with two unknowns Rsiand Rso, assuming that the two inner conductors haveidentical coating characteristics. The variation versusfrequency of the surface resistance of both innerconductors and DUT is obtained by solving this systemfor each TEM mode. The function Rso(ω) is then used tocalculate the parasitic power dissipation per unit lengthin a circular beam screen :( ) ( )∫∞ ⋅⋅⋅⋅⋅=02022~ωωωλπdlRfMcILP soav  [W/m],   (7)where Iav is the average beam current, M the number ofbunches, f0 the revolution frequency, c the velocity oflight l the perimeter of the beam screen cross section and( )ωλ~  the bunch spectrum.2.3 Sensitivity on Tolerances and MeasurementErrorsThe surface resistance is obtained by combination of  themeasured Q-values of the odd and the even modes withcoefficients as a function of the geometrical parametersof pure TEM-modes. Sources of errors are the errors ofthe measured Q-values and the geometrical errors of thecross section. The accuracy in Q measurement for boththe odd and the even mode is estimated to be 0.5% bytaking into account the correction for external loadingvia S11 and S22. The Q-value is lowered by the dielectricloss in the vinyl (nylon) screws, which tie the innerconductor to the teflon support [1]. To reduce the effect,the vinyl screws are positioned in regions of smallelectric field. A very important source of problems was the modecoupling with the undesired TEM-like modes in thecoupler region at either side, which lowers the Q-valuesand leads to ripples in the curves of Q vs. frequency [2].We made the length of the coupler region shorter so thatthe resonant frequencies of the undesired modes arebeyond our measurement frequency range. For thegeometrical errors of the cross section, the error of thelateral spacing of the inner conductors is estimated to be0.1 mm. From the analysis presented in Refs. [2-3], theresulting total error on the measured surface resistance isbelow 10%. The size of the inner conductors and theirdistance can be optimised from the error analysis. Theoptimised parameters may change if we assumesignificantly different surface resistances for inner andouter conducting surfaces [3].3 MEASUREMENT RESULTSThe surface resistance measured for sample tubes withsmooth and ribbed surface, at room temperature and at)5(111,,, , , ∆∆∆∆∆ Γ+Γ=+=osoisiouterinnerwallRRQQQ)6(111,,, , , ΣΣΣΣΣ Γ+Γ=+=osoisiouterinnerwallRRQQQ3liquid helium temperature (without magnetic field) isshown in Figs. 2 and 3, respectively. The rolling process to form the tubes has an influenceon the RRR. From cold measurements, the initial RRRof flat sheets decreased from 150 to 80 after forming.The fit curves (in the anomalous regime) of the surfaceresistance for the smooth tube are in good agreementwith theory assuming the DC value of the electricalresistivity (1.7 10-8 Ωm).  The forming process of the ribbed structures (withcorrugation depth of 30 microns and 0.5 mm period)increases the DC-resistivity to 2.15 10-8 Ωm. Impuritiesor inclusions contained in the mandrel may havedegraded the copper layer. This rolled tube exhibits aRRR similar to the previous one, i.e. 90 (deduced fromthe anomalous regime). It does not seem to be sensitiveto the saw-tooth structures. Owing to magneto-resistance, the resistivity is described by  the  Kohler law[2]. Using the physical parameters of the ribbed tube andsetting B = 8.386T, one finds ρ(B,T) = 7.69 10-10 Ωm.With nominal LHC beam parameters [2] the RF lossesamount to 104 mW/m for each circulating beam.  The data from the inner conductors are amazinglyreproducible. With a resistivity of 1.7 10-8 Ωm the RRRfound is 35. This fits once again with the interpolationformula in the anomalous regime [2].Surface resistance of the DUTs at room  temperature0510150 500 1000 1500 2000Frequency (MHz)Rs (mΩ)Figure 2: Surface resistance measured at roomtemperature for a sample tube with smooth (∆) andanother with ribbed ( ) surface. The solid line gives thesurface resistance calculated in the classical regime withresistivity ρ(300K)=1.7 10-8 Ωm.Surface resistance of the DUTs at liq. He  temperature01230 500 1000 1500 2000Frequency (MHz)Rs (mΩ)Figure 3: Surface resistance measured at 2K for a samplewith smooth (∆) and another with ribbed ( ) surface.Solid line:RRR=90 from ρ(300K)=2.15 10-8 Ωm,classicalLong dashed:RRR=90, ρ(300K)=2.15 10-8 Ωm, anomal.Dashed line:RRR=80, ρ(300K)=1.7 10-8 Ωm, anomalous.4 CONCLUSIONIt has been demonstrated that the two-wire coaxialresonator technique is a reliable, yet not very easy tool tohandle for measurements of the surface resistance of along tube in a cryogenic environment. The resultsobtained show a remarkable reproducibility on themeasured surface resistance of the inner (=resonator)rods  and gave also a clear indication that the productionprocess has a strong impact on the final performance andthe effective RRR value measured in situ. It turned outthat the ribbed surface structure required to minimisemultiple reflections of the LHC synchrotron light are notof significant influence to the RF losses up to 1.5 GHz.Extrapolating from the measured surface resistancevalues at liquid helium temperatures without magneticfield, we can expect conduction losses of about 100mW/m per beam at 8.4T.5 REFERENCES[1] J. Tan, Technical and Practical Information on theSurface Resistance Measurement Bench Using the ShieldPair Method: Application to the LHC Beam Screen,CERN –SL-2000-002-AP, Jan 2000.[2] F. Caspers, M. Morvillo, F. Ruggiero, J. Tan, SurfaceResistance Measurements and Estimate of the Beam-Induced Resistive Wall Heating of the LHC Dipole BeamScreen, LHC Project Note 307, August 1999.[3] H. Tsutsui,  Optimization of the Shielded PairGeometry for Surface Resistance Measurements of theLHC Beam Screen, LHC Project Note 215, Feb 2000.

Surface Resistance Measurements of LHC Dipole Beam Screen Samples

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