Measurements and modelling of stray magnetic fields and the simulation of their impact on the Compact Linear Collider at 380 GeV
C. Gohil, P. N. Burrows, N. Blaskovic Kraljevic, D. Schulte, B. Heilig
AA Model for Simulating Stray Magnetic Fields inLinear Colliders
C. Gohil , P. N. Burrows , N. Blaskovic Kraljevic ∗ , D. Schulte , and B.Heilig John Adams Institute, University of Oxford, Oxford, United Kingdom European Organization for Nuclear Research, Geneva, Switzerland Mining and Geological Survey of Hungary, Tihany, Hungary(September 4, 2020)
Abstract
Future linear colliders target nanometre beam sizes at the collision point. Real-ising these beam sizes requires the generation and transport of ultra-low emittancebeams. Dynamic imperfections can deflect the colliding beams, leading to a collisionwith a relative offset. They can also degrade the emittance of each beam. Both ofthese effects can significantly impact the luminosity of a collider. In this paper, weexamine a newly considered dynamic imperfection: stray magnetic fields. Measure-ments of stray magnetic fields in the Large Hadron Collider tunnel are presentedand used to develop a statistical model that can be used to realistically generatestray magnetic fields in simulations. The model is used in integrated simulations ofthe Compact Linear Collider including mitigation systems for stray magnetic fieldsto evaluate their impact on luminosity.
There are currently two projects that propose a TeV-scale linear electron-positron collider:the International Linear Collider (ILC) [1, 2] and the Compact Linear Collider (CLIC) [3,4]. CLIC incorporates a staged approach with three centre-of-mass energies: 380 GeV,1.5 TeV and 3 TeV. In this paper, we derive a model for stray magnetic fields and applyit to the 380 GeV stage of CLIC.
Dynamic imperfections in a linear collider can deflect the beams, which leads to a collisionwith a relative offset, and causes emittance growth. Linear colliders target extremely smallbeam sizes to maximise the luminosity [5]. This makes the beams in a linear colliderparticularly sensitive to these effects. ∗ Present address: European Spallation Source, Lund, Sweden. a r X i v : . [ phy s i c s . acc - ph ] S e p eams in linear colliders are generated in pulses. Dynamic imperfections influenceconsecutive pulses differently. This makes them difficult to correct. The main tool formitigating the impact of dynamic imperfections is a beam-based feedback system, whichmeasures and corrects the beam offset. Often the beam-based feedback system, whosebandwidth is inherently limited by the beam repetition frequency, is not enough to mit-igate the imperfection to the desired level. Dedicated studies are necessary to devise amitigation strategy for dynamic imperfections. In this paper, we look at the impact ofstray magnetic fields and their mitigation. Stray magnetic fields, or simply stray fields, are external dynamic magnetic fields, whichinfluence the beam. They can be classified in terms of their source: natural, environmentaland technical [6, 7, 8]. stray fields are from non-man-made objects, e.g. the Earth’s magnetic field. Areview of natural stray fields can be found in [9]. Natural stray fields have large amplitudesat low frequencies, which can mitigated with a beam-based feedback system [11]. At higherfrequencies the amplitude is small enough that they can be ignored.
Environmental stray fields are from man-made objects, which are not part of theaccelerator. This includes stray fields from the electrical grid, such as power lines andpower stations, and nearby transport infrastructure, such as train and tram lines.The electrical grid is typically the largest stray field source. In Europe, the electricalgrid operates at 50 Hz. This motivates the choice of 50 Hz for the repetition frequency forCLIC. Stray fields at 50 Hz have the same impact on a train-by-train basis. Therefore,stray fields at 50 Hz (and higher-order harmonics) appear as if they are static to the beamand can be removed during beam-based alignment [4].
Technical stray fields are from elements of the accelerator, e.g. magnets, RF systems,power cables, etc. These stray fields are the biggest concern because of their proximityto the beam. Measurements at live accelerator facilities, which include stray fields fromtechnical sources are presented in Sec. 2.3.
Linear colliders are sensitive to extremely small stray fields. CLIC has a sensitivity downto 0.1 nT [7, 8, 12, 13] and the ILC is sensitive to stray fields on the level of 1 nT [1]. Thesevalues are several orders of magnitude lower than the typical level of stay fields found inaccelerator environments. Therefore, they are a serious consideration in the design andoperation of a linear collider.A realistic model that can be used to simulate stray fields is needed to evaluate theeffectiveness of different mitigation strategies. In this paper, we work towards developingsuch a model.
The magnetic field sensors used in this work are described in Sec. 2.1. The calculation ofuseful quantities to characterise stray fields is described in Sec. 2.2.2easurements in a realistic magnetic environment for an accelerator are presented inSec. 2.3. These measurements were taken in the Large Hadron Collider (LHC) tunnel. TheLHC [14] is a circular proton-proton collider that uses superconducting bending magnets.It is housed approximately 100 m underground.
Four fluxgate magnetometers (Mag-13s) produced by Bartington Instruments, UK [15]were used in the measurements. The key specifications of these sensors are summarisedin Table 1. Further details can be found in [16, 17].
Specification Value Unit
Frequency range 0-3 kHzNoise level (at 1 Hz) < √ HzResolution (24-bit DAQ) 6 pTMagnetic field range ± µ TTable 1:
Mag-13 specifications [16].
The sensors require a power supply unit (PSU) [18], which is also provided by Bart-ington Instruments. The Mag-13 sensors output an analogue voltage. A National Instru-ments (NI) data acquisition system was used to digitise the signal. This was a 24-bit NI9238 module [19]. The data was recorded using a NI LabVIEW script [20] running on alaptop [21].A schematic diagram of the full measurement setup is shown in Fig. 1. All devicesare powered using batteries to ensure currents from the mains do not contaminate themeasurement. The setup is highly portable, which is necessary for surveying stray fields. BatteryNI DAQs PSUs Mag - Laptop
Figure 1:
Full measurement setup for survey stray fields.
There are two useful quantities that can be used to characterise stray fields: the powerspectral density (PSD) and correlation. The PSD is the average power density as afunction of frequency. This is useful for characterising the amplitude of stray fields. Thecorrelation describes the phase difference as a function of frequency and location. This isuseful for characterising the spatial variation of stray fields.3 .2.1 PSD
The magnetic field sensors output a voltage v ( t, s ), which is measured as a function oftime t and location s . A periodogram can be estimated as p V ( f, s ) = 1∆ f V ∗ ( f, s ) V ( f, s ) , (1)where V ( f, s ) is the normalised Fast Fourier Transform (FFT) of the signal v ( t, s ), ∆ f = f s /N is the frequency bin width of the FFT, f s is the sampling frequency, N is the numberof data points in v ( t, s ) and ∗ denotes the complex conjugate.A FFT assumes a signal is repeated infinitely many times. This often leads to disconti-nuities that the interface between repetitions, which causes spectral leakage. A windowingtechnique is applied to the voltage v ( t, s ) to minimise spectral leakage [22]. In this work,we apply a Hann window [22] to all voltage measurements.A FFT describes a signal in the frequency domain over the range [ − f s / , f s / V ∗ ( − f ) = V ( f ). Therefore, negative frequenciesare redundant. In this paper, the FFT and PSD of a signal will only be defined for positivefrequencies.PSDs were calculated using Welch’s method [23]. Here, the signal v ( t, s ) is split into M overlapping segments. Each segment contains a 50% overlap with its neighbours. Aperiodogram is calculated for each segment p ( m ) V ( f ). The estimate for a PSD is calculatedby averaging each periodogram, P V ( f, s ) = 1 M M (cid:88) n =1 p ( m ) V ( f, s ) . (2)The PSD of the voltage is converted into a PSD of the magnetic field by using the transferfunction of the magnetometer S ( f ), which was provided by the manufacturer. The PSDof the magnetic field is given by P B ( f, s ) = P V ( f, s ) | S ( f ) | . (3)A property of a PSD is that its integral gives the variance, σ B ( s ) = (cid:90) ∞ P B ( f, s ) d f. (4)In this paper, we normalise PSDs such that Eq. (4) is true. The square root of Eq. (4)is the standard deviation. To examine the frequency content of a signal, it is useful tocalculate the standard deviation as a function of frequency range, σ B ( f, s ) = (cid:115)(cid:90) ∞ f P B ( f (cid:48) , s ) d f (cid:48) . (5) A correlation spectrum can be calculated for two simultaneous measurements at differentlocations v ( t, s ) and v ( t, s ), where s is a reference location. The correlation for eachfrequency and location is given by C B ( f, s ) = C V ( f, s ) = Re { P V ( f, s , s ) } (cid:112) P V ( f, s ) P V ( f, s ) , (6)4here P V ( f, s , s ) is the cross spectral density of v ( t, s ) and v ( t, s ), which can be calcu-lated using Welch’s method by averaging correlograms, p V ( f, s , s ) = 1∆ f V ∗ ( f, s ) V ( f, s ) . (7)The correlation describes whether two signals are moving in phase or anti-phase. Signalswith a phase difference of 0 ◦ ( C B ( f, s ) = 1) are said to be highly correlated, signals witha phase difference of 90 ◦ ( C B ( f, s ) = 0) or signals that vary independently are said to beuncorrelated and signals with a phase difference of 180 ◦ ( C B ( f, s ) = −
1) are said to beanti-correlated.
The ambient magnetic field was measured near the Compact Muon Solenoid (CMS) de-tector [24]. Specifically, the measurements were taken in LSS5, which is a long straightsection that precedes the detector. The measurements were taken on 29/04/2019, duringlong shutdown 2, over the course of one hour.The measurements were taken at a time where accelerator elements were operational.This includes magnets, vacuum pumps, cooling, ventilation, cryogenics, lighting, etc. Ofinterest in this work is the stray field seen by the beam. Therefore, measurements shouldbe taken with the sensor inside the beam pipe. However, measuring inside the beam pipeis impractical due to the limited space and access. Accurately positioning and moving thesensors inside a beam pipe is also difficult. The measurements presented in this sectionwere taken outside of the beam pipe. All known stray field sources are located outside ofthe beam pipe in an accelerator.
Four sensors were placed at different longitudinal positions on a parallel line adjacent tothe beamline (see Fig. 2). They were approximately 1 m away from the beamline axis. Themagnetic field in three orthogonal directions: x , y and z (see Fig. 2) was simultaneouslymeasured for one minute by each sensor. Beam Pipe 1 m xy z
Figure 2:
Placement of the sensors relative to the beam pipe.
In between measurements three sensors were moved to a new position along the beam-line ( s in Fig. 3), mapping out a 40 m section of the beamline at intervals of 1 m. Thefourth sensor was kept stationary as a reference.5 .3.2 Beamline Description A schematic diagram of the elements in the beamline is shown in Fig. 3. The beamlineincludes: • Two roman pots (XRPT), which are particle detectors used for machine protec-tion [25]. • Three vacuum pumps (VAC), which are used to maintain the vacuum inside thebeam pipe. • Two quadrupoles (Q5, Q4). These are the fifth and fourth closest quadrupoles tothe collision point at CMS. • One concrete shielding block (JBCAE). • One collimator (TCL), which is used to collimate the beam before collision. • One beam position monitor (BPTX). s [m] XRPT XRPT XRPTVAC VAC VACQ5 Q4TCLJBCAE
BPTX
XRPT –
Roman Pot
VAC –
Vacuum Pump
Q5, Q4 –
Quadrupole
JBCAE –
Shielding Block
TCL –
Collimator
BPTX –
Beam Position Monitor
HALF CELL 5L5
Figure 3:
Schematic diagram of the elements in LSS5. Relative lengths are to scale.
The PSD of the magnetic field in the x , y and z -direction and total PSD (sum of all threecomponents) is shown in Fig. 4. The amplitude of the x and y -components is relativelyconstant over the length of the beamline. The z -component has the smallest amplitude.The most prominent peaks are at harmonics of 50 Hz, which are from the electrical grid.The standard deviation of the magnetic field as a function of position is shown in Fig. 5. The correlation of the magnetic field in the x , y and z -direction with respect to thereference sensor at s = 30 m is shown in Fig. 6. The magnetic field is highly correlated forlow frequencies (below 10 Hz) in the x and y -direction. In the z -direction, the magneticfield flips direction several times. This is consistent with elements in the beamline with ahigh iron content attracting the magnetic field. The locations of anti-correlated magneticfields coincide with the minima of standard deviation shown in Fig. 5.6 f [Hz] s [ m ] − − − − − P B , x ( f , s ) [ n T H z ] (a) x -direction. f [Hz] s [ m ] − − − − − P B , y ( f , s ) [ n T H z ] (b) y -direction. f [Hz] s [ m ] − − − − − P B , z ( f , s ) [ n T H z ] (c) z -direction. f [Hz] s [ m ] − − − − P B ( f , s ) [ n T H z ] (d) Total. Figure 4:
PSD of the magnetic field P B ( f, s ) (RH scale) vs location s (LH scale) and frequency f . s [m] σ B ( s ) [ n T ] xyz Total
Figure 5:
Standard deviation of the magnetic field σ B ( s ) in the x -direction (blue), y -direction(orange), z -direction (green) and total (red) vs location s . f [Hz] s [ m ] − . − . − . − . . . . . . C B , x ( f , s ) (a) x -direction. f [Hz] s [ m ] − . − . − . − . . . . . . C B , y ( f , s ) (b) y -direction. f [Hz] s [ m ] − . − . − . − . . . . . . C B , z ( f , s ) (c) z -direction. Figure 6:
Correlation of the magnetic field with respect to a reference sensor at s = 30 m C B ( f, s ) (RH scale) vs location s (LH scale) and frequency f . This section develops a two-dimensional PSD model for stray fields based on the LHCmeasurements. There are two characteristics of stray fields that must be accurately cap-tured in the model: the amplitude and the spatial correlation.In this paper, we follow the same approach used to simulate ground motion in linearcolliders described in [26]. Ground motion is modelled as a set of travelling waves ofdiffering wavenumber k and frequency f . The amplitude of each wave is determined by atwo-dimensional PSD P ( f, k ) as a ij = √ σ ij = (cid:115) (cid:90) f i +1 f i (cid:90) k j +1 k j P ( f, k ) d k d f ≈ (cid:113) P ( f i , k j )∆ k ∆ f . (8)The displacement of an accelerator element at a particular location and time is calculatedfrom the superposition of each wave. 8 .1 Amplitude The amplitude of the magnetic field measured in the LHC tunnel was similar in the twotransverse directions to the beam ( x and y in Fig. 4). The y -component measurementswere used to develop the model.The average PSD of the magnetic field in the y -direction measured by the referencesensor is given by P B,y, ref ( f ) = 1 M M (cid:88) i =1 P B,y,i ( f, s ref ) , (9)where P B,y,i ( f, s ref ) is the PSD of the magnetic field in the y -direction of the i th measure-ment made by the reference sensor at s ref and M is the number of measurements. This isshown, along with the standard deviation, in Fig. 7. f [Hz] − − − − − P B , y , r e f ( f ) [ n T H z ] (a) f [Hz] − − σ B , y , r e f ( f ) [ n T ] (b) Figure 7: (a) Stray field PSD P B,y, ref ( f ) vs frequency f and (b) standard deviation σ B,y, ref ( f )vs frequency f . Fig. 4 shows that the amplitude is approximately constant over the measured section.Therefore, a PSD measured at one location can be representative of the amplitude acrossthe entire section. The PSD shown in Fig. 7a will be used to characterise the PSD of strayfields. The standard deviation of the stray field is approximately 35 nT.
The stray field model should reproduce the correlation shown in Fig. 6b. There are threedifferent regions in Fig. 6b: • Frequencies below 10 Hz, which are highly correlated over the 40 m section. • Frequencies between 10 Hz and 400 Hz, which are correlated over length scales of10 m. • Frequencies above 400 Hz, which are uncorrelated.The PSD in Fig. 7 characterises the power distribution over different frequencies. Tocalculate a two-dimensional PSD, the power in each frequency must be distributed over9ifferent wavenumbers. The distribution over wavenumbers determines the spatial corre-lation of the stray field. If there are many modes of differing wavenumber, their superposi-tion leads to an uncorrelated stray field. Whereas if the modes have similar wavenumbers,the stray field is highly correlated.Simultaneous measurements at many locations are required to determine the wavenum-ber spectrum. However, only a maximum of four sensors was available for measurements.This is not enough to parameterise a wavenumber spectrum from measurements.A particular functional form for the wavenumber spectrum must be assumed. Wepropose a Gaussian function for simplicity and because its width is determined by asingle parameter. The power density of a mode with frequency f i and wavenumber k j isgiven by P B ( f i , k j ) = P B ( f i ) (cid:114) πα exp (cid:18) − k j α (cid:19) , (10)where P B ( f i ) the power density of frequency mode i and α is half the width of the dis-tribution. The factor (cid:112) / ( πα ) was introduced to ensure that the two-dimensional PSDcorrectly recovers the one-dimensional PSD P B ( f ) after integrating over all wavenumbers, P B ( f ) = (cid:90) ∞ P B ( f, k ) d k. (11)The width α is parameterised from measurements to produce a desired spatial corre-lation. A small value for α produces a stray field which is correlated over large distances,whereas a large value for α produces a stray field which is only correlated over shortdistances. The following widths were found to reproduce the correlation measured in theLHC tunnel, [10] α = . π for f ≤
10 Hz , . π for 10 Hz < f ≤
400 Hz , . π for f >
400 Hz . (12) The stray field is simulated as a grid of zero length dipoles, which is inserted into thelattice. The purpose of the generator is to calculate the kick applied by each dipole. Adipole spacing of 1 m was used in the simulation. With this dipole spacing, only wave-lengths of λ min > k max = 2 π/λ min = π .The stray field is modelled as a standing wave. The stray field at location s and time t is given by B ( s, t ) = (cid:88) i (cid:88) j a ij cos( k j s + θ j ) cos(2 πf i t + φ ij ) , (13)where a ij is the amplitude determined by the two-dimensional PSD (see Eq. (8)) and θ j and φ ij are uniformly distributed random numbers between 0 and 2 π . The computa-tional efficiency of calculating Eq. (13) can be improved by calculating a time-dependentamplitude, A ij ( t ) = a ij cos(2 πf i t + φ ij ) , (14)and calculating the stray field as B ( s, t ) = (cid:88) i (cid:88) j A ij ( t ) cos( k j s + θ j ) . (15)10his significantly reduces the computation time because A ij ( t ) only needs to be calculatedonce per time step. The stray field kick applied by each dipole is calculated using δ [ µ rad] = c [m/s] · B [nT] · L [m] E [GeV] × − , (16)where c is the speed of light, L is the dipole spacing and E is the beam energy.The generator was used to sample the stray field in a 40 m section of the beamline.Fig. 8 shows the PSD and correlation of the stray field from the generator. The generatoris able to qualitatively reproduce the features measured in the LHC tunnel (Figs. 4b and6b). f [Hz] s [ m ] − − − P B ( f , s ) [ n T H z ] (a) f [Hz] s [ m ] − . − . − . . . . . . C B ( f , s ) (b) Figure 8:
A sample from the generator of stray fields. (a) PSD P B ( f, s ) (RH scale) vs location s (LH scale) and frequency f and (b) correlation C B ( f, s ) (RH scale) vs location s (LH scale)and frequency f . The correlation was calculated with respect to the stray field at s = 30 m. The two-dimensional PSD model described in the previous section was used in integratedsimulations of CLIC at 380 GeV to evaluate the impact of stray fields on the luminosity.
In this work, we combine the Ring to Main Linac (RTML), Main Linac (ML) and BeamDelivery System (BDS) of CLIC into a single tracking simulation, referred to as an ‘inte-grated simulation’. This is necessary because stray fields can be correlated over the entirelength of the machine. Therefore, the entire machine must be simulated to evaluate theirfull effect.The particle tracking code PLACET [27] was used to track the electron and positronbeams. A full simulation of the collision, including beam-beam effects [5] was performedwith GUINEA-PIG [28] to estimate the luminosity.11 .2 Mitigation of Stray Fields
The impact of a mitigation system can be described using a transfer function T ( f ),which acts on the two-dimensional PSD of stray fields P B ( f, k ) to give an effective two-dimensional PSD, P B, eff ( f, k ) = | T ( f ) | P B ( f, k ) , (17)which is used to generate the stray field. Here, the mitigation system only impacts thetemporal variation of the stray field, i.e. all wavenumbers are affected in the same way.Therefore, Eq. (17) is true for mitigation systems that act equally across the accelerator.In the following sections we look at the impact of two mitigations systems: a beam-based feedback system and a mu-metal shield. The aim of the beam-based feedback system is to correct the beam offset along theaccelerator. This is achieved by measuring the offset of a pulse using beam positionmonitors and applying a correctional kick to the following pulse using magnets. Thetransfer function for the CLIC feedback system is shown in Fig. 9 [10]. The feedbacksystem is effective at suppressing low frequency noise, below 1 Hz, but amplifies noisein the frequency range 4-25 Hz. The repetition frequency of the beam is 50 Hz, whichcorresponds to a Nyquist frequency of 25 Hz. Therefore, noise above 25 Hz is aliased tolower frequencies.This feedback system was optimised to minimise the luminosity loss from groundmotion [10, 11]. The same feedback system was used in stray field simulations to ensurethat the proposed mitigation strategy is consistent for the combined effects of groundmotion and stray fields. f [Hz] . . . . . . . . T ( f ) Figure 9:
Transfer function of the beam-based feedback system T ( f ) vs frequency f . Another approach to mitigate stray fields is to prevent them from reaching the beam. Thiscan be achieved by surrounding the beam pipe with a magnetic shield. The tolerancesfor magnetic field ripples are larger than the tolerances for stray fields [10]. Therefore,12he magnetic shield does not need to run through the aperture of magnets, shielding thedrifts is sufficient.Ferromagnetic materials with a large magnetic permeability are commonly used toshield magnetic fields. Mu-metal offers one of the highest permeabilities. The use ofmu-metal to shield magnetic fields in linear colliders is discussed in [10].A methodology for calculating the transfer function of a cylindrical magnetic shield isoutlined in [29]. The transfer function for a cylindrical mu-metal shield with a thicknessof 1 mm and inner radius of 1 cm is shown in Fig. 10. A relative permeability of 50,000was used for this calculation, which is a reasonable estimate for the permeability withvery low amplitude external magnetic fields [10]. The mu-metal shield is very effective atmitigation. f [Hz] − − − − T ( f ) Figure 10:
Transfer function of a mu-metal cylinder with 1 mm thickness and inner radius of1 cm T ( f ) vs frequency f . Stray field simulations in [10, 13] identified particular sections of CLIC, which aresensitive to stray fields. The most sensitive regions are the Vertical Transfer and LongTransfer Line in the RTML and the Energy Collimation Section and Final-Focus Systemin the BDS. It is possible to devise an effective mitigation strategy by just shielding thesesections. The ML is the least sensitive section and benefits from shielding from the copperaccelerating cavities.
Ignoring the spatial variation, the transfer function can act on the one-dimensional PSD P B ( f ) to estimate the impact of a mitigation system at a single location. The one-dimensional PSD in Fig. 7 is used to characterise the PSD of stray fields at a singlelocation.Fig. 11 shows the effective PSD and standard deviation of stray fields including theimpact of different mitigation systems. The standard deviations are summarised in Ta-ble 2.Without mitigation, there is a large stray field of 35 nT. With a beam-based feedbacksystem, the effective stray field is 2.1 nT, which is still above the 0.1 nT level requiredfor CLIC. The mu-metal shield is the most effective mitigation system, which brings thestray field down to the level of 3 pT without the feedback system and 0.5 pT with thefeedback system. 13 f [Hz] − − − − − − P B , e ff ( f ) [ n T H z ] No MitigationWith FeedbackWith Mu-MetalWith Feedback and Mu-Metal (a) f [Hz] − − − − − σ B , e ff ( f ) [ n T ] No MitigationWith FeedbackWith Mu-MetalWith Feedback and Mu-Metal (b)
Figure 11: (a) Effective stray field PSD P B, eff ( f ) vs frequency f and (b) standard deviation σ B, eff ( f ) vs frequency f : without mitigation (blue); including a beam-based feedback system(orange); including a 1 mm mu-metal shield (green) and with the feedback system and mu-metalshield combined (red). Mitigation σ B, eff [nT] None 35Feedback System 2.1Mu-Metal Shield 3 . × − Feedback System 0 . × − + Mu-Metal ShieldTable 2: Standard deviation of the stray field σ B, eff with different mitigation techniques. Integrated simulations including stray fields were performed using nominal beam param-eters; additional details are provided in [10]. Table 3 shows the luminosity loss includinga beam-based feedback system and a 1 mm mu-metal shield in sensitive regions (VerticalTransfer, Long Transfer Line, Energy Collimation Section and Final-Focus System).Without mitigation, there is a significant luminosity loss of 43%. The beam-basedfeedback system alone is not enough to mitigate stray fields. A luminosity loss of 15%is expected if only the beam-based feedback system is used. With the mu-metal shieldonly, the luminosity loss is reduced to 2%. The combination of the beam-based feedbacksystem and mu-metal shield is an effective mitigation strategy for stray fields, reducingthe luminosity loss to 0.4%.
High-precision magnetic field measurements were performed in the LHC tunnel, whichcharacterised a realistic amplitude for stray fields in a live accelerator environment. Thesemeasurements were used to develop a two-dimensional PSD model, which could be usedto simulate stray fields in linear colliders.This model was used in integrated simulations of the 380 GeV stage of CLIC. The14 itigation ∆ L / L [%] None 43Feedback System 15Mu-Metal Shield 2.0Feedback System 0.4+ Mu-Metal ShieldTable 3: Relative luminosity loss ∆ L / L due to stray fields. L is the nominal luminosityof CLIC.simulations show CLIC is robust against the level of stray fields measured in the LHCtunnel provided a beam-based feedback system and mu-metal shield is used. Acknowledgements
We would like to thank our CERN colleagues Benoit Salvant and Daniel Noll for theirassistance in stray field measurements in the LHC tunnel.
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