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CERN-TOTEM-NOTE-2013-003June 2013

RF Characterization of the New TOTEM Roman Pot

Nicola Minafra

The aim of the present work is the optimization of the Roman Pot (RP) design to minimize thebeam-coupling impedance, in particular when the RP is inserted very close to the beam. Indeed, inthe first period of running of the LHC a rise in temperature due to RF has been observed both in theALFA and TOTEM RP [1] [2]. After the LS1 the LHC beam current will increase and the equipmentsthat can interact with the beam need to be optimized; moreover, new detectors for the TOTEM upgradeprogram require a longer longitudinal dimension of the RP. A new RP design has been proposed [3] anddeveloped [4] by the TOTEM collaboration; this work will describe the studies done to optimize thebeam-coupling impedance of the new design.

A moving charged particle perturbs its surroundings creating an electromagnetic field (wake field)that affects other charges. This phenomenon is particularly important in a particle accelerator, wherea beam of charged particles generates a field that interacts with the vacuum pipe, collimator and allunshielded equipments and with the beam itself. A RP is a movable section of the vacuum pipe that canapproach the beam at very small distances and can severely interfere with the beam.

Transverse and longitudinal impedance at very low frequencies will be used to estimate the insta-bilities introduced on the beam. The part of the energy of the beam that is transferred to the equipmentdepends on the real part of the longitudinal impedance. This energy is then converted into heat in theresistive surface of the device; thus, a correct estimation is also needed to design the cooling system.

Various geometrical configurations of the vacuum pipe housing the RP have been simulated toidentify what most influence the impedance. The RF performance of the present RP (BoxRP) and of aRP with the present shape rotated by 90 (LongBoxRP) will be computed. Also a new cylindrical design(CylindricalRP) will be proposed and analyzed.

The development of an optimized RP has gone through several iterations and improvement to takeinto account mechanical, vacuum and technological constraint. The solution presented here can also bemanufactured within time and cost limits imposed by the TOTEM collaboration.

1 Impedance simulationsThe impedance seen by a beam of particles is due to the shape of the vacuum chamber (geometricalimpedance) and by the finite conductivity of the material used for its construction. If needed, this resistivecontribution can be reduced by coating the cavity with a good conductor, like copper or beryllium. Thiswork deals with the optimization of the geometrical contribution.

Since the impedance of an equipment facing the beam can be very difficult to be computed analyt-ically, we use here CST Particle Studio® [5] which is a software that performs a time domain simulationof the induced wake field: the software simulates the passage of a charge distribution (source charge)inside a cavity and computes the field felt by a longitudinally displaced second charge (test charge). Thepotential felt by this second charge is then used to compute the impedance using Fourier Transforms. Thesoftware allows to define the total charge and its longitudinal space distribution. Even if the impedanceshould not depend on all beam parameters, to reproduce the LHC environment, a charge of 10−9 C lon-gitudinally distributed over a Gaussian with σ = 50 mm that travels at the speed of light has been usedin this work.

1.1 Beam induced heatThe real part of the calculated longitudinal impedance can be used to estimate the power transmitted bythe beam to the resistive wall of the cavity, producing heat. The heating depends on the amount of thebeam present and on its power spectrum.

Figure 1: Power spectrum measured on the LHC before LS1, in October 2012 [6]. It should be noted that thespectrum is more than 37 dB attenuated above 1.2 GHz.

The power spectrum is strongly dependent on the overall characteristics of the beam, like thenumber of bunches, the bunch spacing, the number of particles per bunch and the bunch shape which isnot easily described a priori and can vary during the run.

We use here a power spectrum (Fig. 1) measured in one of the past runs of the LHC, with a bunchspacing of 50 ns [6]. One observes that the power emitted above 1.2 GHz is already attenuated morethan 30 dB. Even if the power spectrum can be different depending on the run conditions [7], the maincontribution to the heating is given by resonances at frequency below 1.5 GHz.

The formula to compute the power lost by the beam is [6] [8]:

Ploss = 2 I2∑

p=1, ...,∞PS(pM ′frev)<[Zlong(pM ′ frev)] (1)

where,

– PS(f) is the power spectrum;– frev is the revolution frequency, 11245 Hz for the LHC;– M ′ is the number of buckets, 1782 for the LHC with a bunch spacing of 50 ns;– I = MeNBfrev is the beam current, with M number of bunches, e charge of the proton, NB

number of protons per bunch;– Zlong is the simulated longitudinal impedance.

The sum can be computed for 0 < pM ′ frev < 2.7 GHz, since the measurement of the powerspectrum at larger frequencies is dominated by noise.

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The formula (1) shows an explicit dependence on the square of the beam current I and, withinthe hypothesis of a power spectrum that is not varying, the same computation can be scaled for differentvalues of the beam intensity. However, for different beam configuration, i.e. bunch spacing of 25 ns, thepower spectrum changes and it must be modified accordingly.

All the heating computation in the present work have been done for a beam current of 0.6 A, usingthe measured power spectrum shown in Fig. 1.

One of the purpose of the RF optimization is to reduce the power induced by the beam and dis-sipated by the resistive walls of the cavity. The first step is to find, if possible, a geometry withoutresonances below 1.5 GHz. If resonances are still present, they may be damped, as usual, using properlypositioned ferrite materials to reduce the Q-factor of a resonance and the heating computed with formula(1). A few different ferrite materials are available and currently used for LHC equipment; however, thepurpose of this work is the optimization of the geometry of the RP, hence, all simulation will be doneusing the same ferrite material: 4s60 by Ferroxcube [9].

1.2 Low frequency behaviorThe simulated impedance is also used to compute the effective transverse and longitudinal impedance,which are correlated with transverse and longitudinal instabilities of the beam and should also be kept ata minimum.

It is possible to define ZEff , the impedance effectively felt by the beam:

Zeff =

∑f

Z(f)σ(f)∑f

σ(f)(2)

where σ(f) is a weighting function determined by the bunch profile.

The imaginary part of the effective longitudinal impedance (=Zlong/n)eff , where n = f/frev isthe harmonic number, is an indication of the dispersion of the beam through the cavity: if (=Zlong/n)eff =0 the longitudinal shape of the beam remains the same.

It is possible to compute the slope of the imaginary part of the longitudinal impedance at lowfrequency and assume this slope constant:

=Z0long(f) =

d=Zlong(f)

df

∣∣∣∣f=0

f (3)

Hence1:=Z0

long

n= lim

f→0frev

d=Zlong(f)

df= const (4)

Fig. 2 shows that below ∼ 1 GHz, =Zlong(f) ≤ =Z0long(f). If this condition is verified, from eq.

(2): (=Zlong

n

)eff

=

∑f

=Zlong

n σ(f)∑f

σ(f)<

=Z0long

n

∑f

σ(f)∑f

σ(f)==Z0

long

n(5)

Hence, =Z0long/n is an overestimation of (=Zlong/n)eff . The simulated value for =Zlong/n will

be compared with the measured value for (=Zlong/n)effLHC = 90mΩ [10].

1With a time domain simulation it is really difficult to compute values for very low frequency; for this reason, the derivativeis not directly computed for f = 0 and the limit is explicit.

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Figure 2: Imaginary part of the simulated longitudinal impedance =Zlong for the present RP. The dashed line isthe computed value for =Z0

long(f): =Zlong(f) ≤ =Z0long(f) for f < 1 GHz.

Similarly, one computes the effective transverse impedanceZEfftrans which is related to the impedance

seen by particles of the beam that are transversally displaced from the ideal trajectory. If ZEfftrans = 0 the

transverse shape of the beam is not modified by the passage through the cavity.

As anticipated, the wake potential is computed using 2 charge distributions: a source charge thatgenerates the wake field and a test charge that measures it. It is possible to compute the driving (ordipolar) impedance and relate it to the transverse impedance [11]:

=Zdrivingt =

∂=Zt

∂tsource(6)

where t = x, y and tsource represents a small transverse displacement of the source charge from thenominal position. The value is usually constant at low frequency (< 500 MHz).

The impedance is then normalized with a factor depending on the optics to easily compare it withother equipments in the LHC: the βt, with t = x or y, at the position of the simulation divided by theaverage on the full LHC ring, 〈βt〉 = 70 m.

ZEfftrans = ZEff

trans

βt〈βt〉

= lims→0

d=[Ztrans]

ds

βt〈βt〉

(7)

Since we are studying a RP which will be in the horizontal plane, only t = x will be consideredhere. In particular, for the β∗ = 0.55 m optics, 〈βx〉 = 70 m; βx depends on the position of the RP andis 97.56 m at 200 m from the interaction point (IP5) and decreases with distance. The worst case value,βx = 98 m, is used here.

2 RF performances of the Roman PotThe geometry of the RP installed at present in LHC has been studied; its RF characteristics have beencomputed for both the present BoxRP and for the setup rotated of 90 (LongBoxRP) to have a longerlongitudinal dimension for detector housing. A new cylindrical RP has been proposed to improve thepresent RP configuration.

The dimensions and the exact geometry of all the design is described in the TOTEM upgradeproposal [3] and their material budget have been already studied [12].

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2.1 Box RPThe present Roman Pot (BoxRP) system uses a box shaped container for the detector. A simplified modelhas been developed to simulate the RF interaction with the beam and is shown in Fig. 3: some minordetails of the geometry have a negligible impact on the impedance and have been ignored.

Figure 3: Geometry of the horizontal Roman Pot installed in LHC. The ferrite is shown with a darker color; thetwo charge distributions used in the simulation (see section 1) are indicated by the arrows in the beam line.

The expected heating and the effective longitudinal impedance when the RP is at various distancesfrom the beam are shown in Figs. 5–6. The computed values for the effective transverse impedance arevery small, especially if compared with the total ZEff

trans expected for the LHC; hence, they have beencomputed only for the RP at 1 mm from the beam. Numerical results for the BoxRP and the LongBoxRPare summarized in table 1.

Distance fromthe

beam [mm]

=Z0long

n

[mΩ]

fraction of(=Zlong

n)effLHC

(90 mΩ)

=Zdrivingtrans

[MΩ/m]

fraction of=(Zx)eff

LHC

(25 MΩ/m)

Heating[W]

BoxRP1 1.7 < 1.9% 0.15 < 0.6 % 62

40 (garage) 0.41 < 0.45% 10

LongBoxRP1 2.6 < 2.9% 0.15 < 0.6 % 241

40 (garage) 0.45 < 0.5% 39

Table 1: Main results of the simulation of the present box RP (BoxRP) and the rotated box RP (LongBoxRP). Theeffective impedances are compared with the total value estimated for the present LHC impedances.

The presence of low frequency resonances is the main cause of heating as noted in section 1.1.In the setup installed in LHC, ferrite is used to damp the low frequency modes; nonetheless, to betterunderstand the problems of this configuration, we found it useful to compute the longitudinal impedanceignoring the ferrite. A precise numerical computation of the impedance in presence of resonances thatare not damped is difficult using a time domain approach. Nevertheless, impedances shown in Figs. 7 and8 are useful to understand which part of the design is generating low frequency resonances. Comparingthe impedances shown in Fig. 7 and 8 one can note that the peak at low frequency (∼ 550 MHz) ispresent in both configurations. For the two configurations the frequency at which the peak occurs is verysimilar: this indicates that the resonating cavity is the same in both designs. The results are compatiblewith previous studies [13].

To attenuate the Q-factor of this resonance the cavity between the flange and the RP has to bereduced or removed. Two possibilities are investigated here:

1. change the design building a cylindrical RP to fill the existing cylindrical vacuum chamber;

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Figure 4: Simulated longitudinal impedance for the BoxRP. Both Real and Imaginary part are shown.

Figure 5: Power lost by the beam passing through the RP. Solid circles are for the present setup, solid squaresrefers to the rotated RP.

Figure 6: Effective longitudinal impedance for the box shaped RP. Solid circles are for the present setup, solidsquares refers to the rotated RP.

2. add a radio frequency shield around the present RP.

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Figure 7: Simulated <[Zlong] of the box shaped RP without ferrite. The resonances at 540 MHz and 1380 MHzare due to the cavity between the flange and the box and, because of the power spectrum of the LHC, they are themain problem of this setup. The darkened part of the graph has a small impact on the heating because of the LHCpower spectrum.

Figure 8: Simulated <[Zlong] of the box shaped RP rotated and without ferrite. This graph should be comparedwith the one showed in Fig. 7: the resonance at 575 MHz has a frequency close to the resonance with the non ro-tated RP, but the shunt impedance is higher. The mode at 1380 MHz seems to not be present with this configuration.The darkened part of the graph has a small impact on the heating because of the LHC power spectrum.

(a) Top view of the present setup. (b) Top view of the setup with the rotated RP.

Figure 9: The resonance below 600 MHz is due to the space between the flange and the box; the frequency of thefirst resonance in the two configurations is very similar indeed. The shunt impedance is higher in the case of therotated RP because the cavity is exposed to the beam for a longer time.

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2.2 Cylindrical RPFig. 10 shows the cylindrical design that is considered here.

Figure 10: Simulated design of the new cylindrical RP.

Simulation results, shown in Fig. 11, indicate that low frequency resonances disappear closingthe gap between the detector housing and the flange. However, mechanical constraints require at least2.5 mm gap between the housing and the flange to allow a safe movement of the RP.

Figure 11: Simulated <[Zlong] of the cylindrical RP with no gap between the housing and the flange. However,this design does not allow any movement of the RP. The darkened part of the graph has a small impact on theheating because of the LHC power spectrum.

When a 2.5 mm gap is present, a resonance at 470 MHz appears, as shown in Fig. 12; itsimpedance is nevertheless smaller than with the box configuration. With the insertion of ferrites theQ-factor of the mode is reduced.

The position and the dimensions of the ferrite have been optimized through various iterationsconsidering also vacuum and mechanical construction. The final design consists of a ring-shaped ferriteinstalled near the top flange, as shown in Fig. 13 and has a radial width of 15 mm and a thickness of5 mm. This design is feasible and can be easily integrated in the existing design.

The new configuration of the ferrites reduces the surfaces exposed to the vacuum by an order ofmagnitude. A comparison of the parameters can be found in table 3.

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Figure 12: Simulated <[Zlong] of the cylindrical RP without ferrite. The resonance at 470 MHz is due to the cavitybetween the flange and the detector housing. For mechanical reasons the gap can not be further reduced. Thedarkened part of the graph has a small impact on the heating because of the LHC power spectrum.

Figure 13: The circular ferrite (highlighted with a darker color) has an internal diameter of 150 mm; the surfacefacing the beam is 5 mm long and the thickness is 15 mm. The ferrite is positioned as far as possible from thebeam.

Distance fromthe

beam [mm]

=Z0long

n

[mΩ]

fraction of(=Zlong

n)effLHC

(90 mΩ)

=Zdrivingtrans

[MΩ/m]

fraction of=(Zx)eff

LHC

(25 MΩ/m)

Heating[W]

Box RP1 1.7 < 1.9% 0.15 < 0.6 % 625 1.3 < 1.4% 52

40 (garage) 0.41 < 0.45% 10

Cylindrical RP1 1.1 < 1.2% 0.11 < 0.5 % 135 0.73 < 0.81% 11

40 (garage) 0.18 < 0.20% 4

Table 2: Main results of the simulation of the present box RP (BoxRP) and the cylindrical RP (CylindricalRP).The effective impedances are compared with the total value estimated for the present LHC impedances.

Longitudinal internaldimension

Internal surface Ferrite surface

Box RP 5.0 cm 62 cm2 220 cm2

Cylindrical RP 14.1 cm 156 cm2 23 cm2

Table 3: Comparison of some geometrical details of the presented RP designs.

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Figure 14: Simulated longitudinal impedance for the cylindrical RP. Both Real and Imaginary part are shown.

Figure 15: Power lost by the beam passing through the RP. Solid circles are for the present setup, solid trianglesrefers to the new cylindrical design.

Figure 16: Effective longitudinal impedance for the box shaped RP. Solid circles are for the present setup, solidtriangles refers to the new cylindrical design.

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2.3 Shielded box RPHaving observed a substantial improvement of the RF performance of the new cylindrical design (seesection 2.2), we study a RF shield to improve the impedance of the present BoxRP. The basic idea is touse the same position for the ferrites as the cylindrical RP and to create a thin copper shield to envelopthe box RP, as shown in Fig. 17. The shield should not interfere with the vacuum requirement.

The installation of a RF shield gives the possibility to use the present RP also for higher luminosi-ties. Moreover, the shield can be very thin (∼ 100µm) to keep to a minimum the material budget of thewhole RP. On the lateral surfaces there are 3 rows of 15 circular holes each with a diameter of 1 cm; theshape and the position of the apertures on the surface facing the beam are 3× 12 mm rectangles with thesmaller side rounded with 2 mm radius [?].

The chosen ferrite has the same shape and position as the ferrite used in the cylindrical design (seeFig. 13).

Figure 17: Design of a RF shield for the box RP. The holes have been studied to ensure a good ventilation affectingthe impedance in a negligible way.

Distance fromthe

beam [mm]

=Z0long

n

[mΩ]

fraction of(=Zlong

n)effLHC

(90 mΩ)

=Zdrivingtrans

[MΩ/m]

fraction of=(Zx)eff

LHC

(25 MΩ/m)

Heating[W]

BoxRP1 1.7 < 1.9% 0.15 < 0.6 % 62

40 (garage) 0.41 < 0.45% 10ShieldedRP

1 1.2 < 1.3% 0.2 < 0.8 % 1040 (garage) 0.30 < 0.33% 2

Table 4: Main results of the simulation of the present box RP (BoxRP) and the shielded box RP (ShieldedRP). Theeffective impedances are compared with the total value estimated for the present LHC impedances.

The total surface of the shield is ∼ 68 × 103 mm2 and the openings are ∼ 3.8 × 103 mm2 (∼280 mm2 on the part facing the beam).

3 OutlookIn this work the RF behavior of the present RP has been studied and two methods have been proposedto reduce the beam-coupling impedance. A completely new cylindrical design has been proposed toimprove RF performances and at the same time to increase the space available inside the case; whereas,

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Figure 18: Simulated longitudinal impedance for the shielded box RP (ShieldedRP). Both Real and Imaginary partare shown.

Figure 19: Expectation of the power lost by the beam passing through the RP. Solid stars are for the present setup,solid triangles refers to the shielded design.

Figure 20: Effective longitudinal impedance for the box shaped RP. Solid stars are for the present setup, solidtriangles refers to the shielded design.

a RF shield has been developed to improve the present RP without the need of a fully redesigned project.The feasibility, the cost and the reliability of the proposed improvements have been studied [4].

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In both cases, the beam induced heating has been reduced up to a factor ∼ 6 and the longitudinalimpedance is ∼ 25 % lower. Hence, in any case, the new designs represent an improvement on thepresent RP.

4 AcknowledgmentsI would like to express my gratitude to Joachim Baechler, Dmitry Druzhkin, Marco Bozzo and MarioDeile, from the TOTEM collaboration, for their help and support while writing this note and BenoitSalvant, Elias Metral and Helmut Burkhardt, from the BE-ABP group, for their supervision and for theirinteresting and masterful advices.

Bibliography[1] J. Baechler. LHCC TOTEM Status Report. http://indico.cern.ch/getFile.py/access?

contribId=19&sessionId=1&resId=0&materialId=slides&confId=239117.[2] G. Arduini et al. Very preliminary update on unusual heating in LHC. https://espace.cern.

ch/lhc-machine-committee/Presentations/1/lmc_155/lmc_155c.pptx.[3] TOTEM Collaboration. TOTEM Upgrade Proposal. (CERN-LHCC-2013-009. LHCC-P-007), Jun

2013.[4] Development of a RP for the High Luminosity LHC operations. (TOTEM Note to be published).[5] CST Studio Suite®. http://www.cst.com.[6] B. Salvant et al. Beam induced RF heating. http://indico.cern.ch/getFile.py/access?

contribId=20&sessionId=10&resId=0&materialId=paper&confId=211614.[7] P. Baudrenghien et al. The LHC RF System-Experience with beam operation. Technical report,

2011.[8] N. Minafra. Power loss computation for LHC. http://impedance.web.cern.ch/impedance/

documents/Imp_meeting_06-05-2013/Heating.pdf.[9] Ferroxcube International Holding B.V. http://www.ferroxcube.com.

[10] E. Chapochnikova. First measurements of longitudinal impedance and single-bunch effects in theLHC. https://emetral.web.cern.ch/emetral/ICEsection/2010/Meeting_01-09-10/

Longitudinal%20impedance.pptx.[11] E. Metral. Procedures for frequency and time domain EM simulations in asymmet-

ric structures. http://sps-impedance.web.cern.ch/sps-impedance/documents/

ProceduresForFrequencyAndTimeDomainEMSimulationsInAsymmetricStructures_

EM.pdf.[12] F. Nemes. Geant4 simulations for the TOTEM upgrade program. (CERN-TOTEM-NOTE-2013-

002), Jun 2013.[13] M. Deile and other. Beam Coupling Impedance Measurement and Mitigation for a TOTEM Roman

Pot. arXiv preprint arXiv:0806.4974, 2008.

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