The Magnetic Compensation Scheme of the FCC-ee Detectors
TTHE MAGNETIC COMPENSATION SCHEME OF THE FCC-eeDETECTORS
M. Koratzinos, MIT and CERN and K. Oide, KEK and CERN
Abstract
A crucial part of the design of an FCC-ee detector is theminimisation of the disruption of the beam due to thepresence of a large and powerful detector magnet. Indeed,the emittance blow-up of the few meters around theinteraction point (IP) at lower energies is comparable to theemittance introduced by the rest of the 100 km ring. Verticalemittance is the single most important factor in achievinghigh performance (luminosity, in this case) in a modern π + π β storage ring such as the FCC-ee. The design adoptedis the simplest possible arrangement that can neverthelessdeliver high performance: two additional coils per IP side.The performance achieved is such that vertical emittanceblow-up will not be a limiting performance factor even inthe case of a ring with four experiments, and even in themost demanding energy regime, that of the Z running(about 45 GeV beam energy). INTRODUCTION
The FCC project, as a first step, aims to deliver a high-luminosity π + π β storage ring in a range of energies from45 to 182.5 GeV per beam (FCC-ee) [1] [2]. It incorporatesa βcrab waistβ scheme to maximize luminosity at allenergies [3] [4]. This necessitates a crossing angle betweenthe electron and positron beams, which is Β±15 mrad in thehorizontal plane. The detector solenoid envisaged is a large2 T coil. No magnetic elements can be present in the regionapproximately Β±1.2 m from the interaction point (IP), toleave space for the particle tracking detectors and theluminosity counter.Therefore, beam electrons experience the full strength ofthe detector magnetic field close to the IP. The resultingvertical kick needs to be reversed and this is performed inthe immediate vicinity. This vertical bump, however, leadsto vertical dispersion and an inevitable increase of thevertical emittance of the storage ring, which we here try tominimize. The effect is most important at the Z energies.The vertical emittance budget [1] varies between 1 pm (Zenergies) and 2.9 pm (top energies).Moreover, the very low vertical π½ β of the machinenecessitates that the final focusing quadrupoles have adistance from the IP ( πΏ β ) of 2.2 m and therefore are insidethe main detector solenoid. The final focus quadrupolesshould reside in a region with very low residual magneticfield: the equivalent roll of the quad due to the overlappingsolenoid should be much smaller than the value assumedfor quad misalignment (0.1 mrad), leading to β« π΅ π§ ππ βͺ . . β2 ππ , which corresponds to a vertical emittanceblow up of 0.05 pm (The effect increases quadratically withthe residual field).Another obvious requirement is that any magneticelements should not be in the way of physics sub-detectors, and therefore are made as compact as possible, which inturn increases fringe fields and, therefore, dispersion. Inorder not to compromise the physics goals of theexperiment, the area allowed for magnetic elements isinside a 100mrad cone at the IP along the median path ofelectrons and positrons (defined as the Z axis, the directionof the experiment solenoid field). THE REQUIREMENTS
We here summarise the list of requirements for thecompensation scheme:1. All elements within a 100mrad cone2. Vertical emittance blow-up (cumulative for all IPs)less than 1 pm.3. The integral β« π΅ π§ ππ should vanishβ¦4. and so should the integral β« π΅ π₯ ππ , so that any verticaldispersion would not leak to the rest of the ring.5. β« π΅ π§ ππ in the vicinity of final focus quads should bemuch less than β2 ππ .All the above (conflicting) requirements are satisfied withthe design presented here. This work follows frompreviously presented work in the subject [5] [6], optimised,simplified and improved. Figure 1 : The design of the compensation scheme, orthographicthree-quarter view. Visible elements are: The IP (magenta), thebeam pipe (yellow), the luminosity counter (pink), thecompensating solenoid (blue), the screening solenoid (red). Thefinal focus quadrupoles QC1L1 can be seen in green. Thedetector solenoid has been omitted for clarity.
This analysis is performed for the immediate regionaround the IP of Β±3 m. THE COMPENSATION SCHEME
The beam-stay-clear area in the vicinity of theinteraction region is Β±12 mm. This allows for a compact beam pipe of 30mm in diameter.hysics reasons dictate the position of the luminosity counter : the overall rate of Bhabha events at the Z peak cannot be too much smaller than the Z to hadrons rate. This effectively fixes the position of the front face of the luminometer at a distance of 1076 mm from the IP (the depth of the calorimeter is 116 mm). This forces the first magnetic element of the compensation scheme to start at a distance of 1230 mm from the IP.The compensation scheme comprises two magnetic elements (solenoids) along the Z axis. The first is a compensating solenoid with a negative field compared to the detector solenoid field and the second is a screening solenoid , a longer coil that screens the final focus quadrupoles from the detector solenoid field. The presence of two elements makes it possible to minimize the β« π΅ π§ ππ and β« π΅ π§ ππ integrals at the same time.The detector solenoid is a cylinder with an inner radius of 376 cm and an outer radius of 382 cm. Its half-length is 400 cm. There is currently no end yoke design, so the field is not as uniform as with an iron return yoke (at 3 m from the IP the field has dropped to about 1.6T from 2T at the IP. This analysis will be updated when the detector magnet design is finalized, but the essence of the analysis and the results presented here will not change. The final focus quadrupoles start at a distance of 2.2 m from the IP.Since large fields are required, the coils mentioned in this work would all be superconducting. A thin, non-load-bearing cryostat is envisaged, as well as a strong load-bearing skeleton and the space is provided for. Figure 2 : The field profile seen by an electron from the IP up toa distance of 3 m (still inside the detector solenoid). During thefirst meter or so the electron sees the full detector solenoid field,then the field reverses, thanks to the compensating solenoid, andit finally approaches zero at the tip of the final focus quadrupoles(at 2.2m from the IP).B z varies between +2T and -2.9T (left scale,black) whereas B x between 210mT and -160 mT (right scale, red). The screening solenoid
The screening solenoid is a thin solenoid producing a field equal and opposite to the detector solenoid, that screens the final focus quadrupoles. It starts at 2000 mm from the IP and extends all the way to the endcap region of the detector, at 5.2 m from the IP. Its outer radius is 195mm and has 340 turns. The pitch varies from 7 to 13 mm. The conductor cross-section is 2 by 10 mm and the total current 9980 A, corresponding to a current density of 499 A/mm2. NbTi technology is adequate for this device. Its maximum standalone field is about -1.59T.
Figure 3 : Birdβs eye view of the right side of the compensationscheme. The longitudinal component of the magnetic field isshown in the region y=(-1,1 m) and z=(0,3 m) in the vicinity ofthe compensating solenoid (blue, -3
T), screening solenoid(green, 0
T), final focus quadrupoles (just visible in blue andyellow), all in the +2
T solenoidal field of the experiment(orange). The IP is at (0,0)
The compensating solenoid
The compensating solenoid sits in front of the screening solenoid, has a field higher than that of the detector solenoid, so that the magnetic field integral seen by the beam is zero. The length of this solenoid is 77 cm, its front face is at 1230 mm from the IP, its back face at 2000 mm, and its stand-alone strength is -4.77 T. It is tapered: its outer diameter at the front tip is 118 mm and at the back tip 195 mm. This leaves space for a thin cryostat of 5 mm depth up to the allowed 100 mrad cone. The coil has 162 turns and the pitch varies between 2.5mm and 6 mm. The conductor is assumed to be 2 by 10 mm and the total current is 19880 A corresponding to 994 Amm -2 . This current density is beyond the capability of NbTi conductors, so HTS should be used. To be able to use NbTi conductor, the conductor cross-section area should increase by 50%, which is a minor modification. The different elements of the design can be seen in Figure 1 . In
Figure the field components in the x (horizontal), and z (longitudinal) direction along the electron path are shown . Figure 3 shows the map of the longitudinal component of the magnetic field.
ANALYSIS AND MINIMIZATION
All magnetic design was performed using the
Field suite of programs [7]. The vertical emittance blow-up was calculated analytically using the equations described in [6] in an excel sheet. This allowed for rapid progress and convergence of the minimization process, which was done to a large extend empirically. The sizes of the coils were iven and what was minimized was the pitch of the coils along their length and the current in the conductor. Only after the best configuration was identified were the exact field maps transferred to the SAD suite of programs, where the exact value of the emittance blow-up was calculated. Some important optics functions can be seen in
Figure 4 . Figure 4 : Optics functions in the area +-2m from the IP. Fromtop to bottom: longitudinal magnetic field, closed orbit deviationfrom the tilted straight line going through the IP, verticaldispersion, vertical momentum dispersion, β π¦ (verticalemittance generation function). The emittance blow up of the optimized setup was 0.24 pm at a beam energy of 45.6 GeV. (The simplified excel analysis gave an emittance blow-up of 0.27 pm)Integral fields are: β« π΅ π₯ ππ = 2.4 Γ 10 β5 ππ , β« π΅ π§ ππ = β2 ππ and in the vicinity of the final focus quadrupole (QC1L1, from 2.2 to 3.6 m from the IP) β« π΅ π§ ππ = 6.2 Γ 10 β3 ππ . . . The relatively large β« π΅ π§ ππ value is due to the uncertainty in the design of the end yoke of the detector magnet; when this is finalized, the compensation can be tuned to keep this value arbitrarily small. VARIATION WITH ENERGY AND DETECTOR MAGNETIC FIELD
The vertical emittance blow-up is a strong function of beam energy, βπ π¦ β πΈ ππππβ3 therefore going from the Z to W running (45 to 80 GeV) the problem reduces by a factor 5.6. Emittance blow-up is also a strong function of detector solenoid field βπ π¦ β π΅ πππ‘πππ‘ππ5 therefore if the detector field is increased from 2T to 3T, the emittance blow-up is a factor of 7.6 larger. MISALIGNMENT
The above analysis is with perfect alignment. Out of possible misalignments the most dangerous is a (horizontal) tilt of the detector solenoid with respect to the rest of the system (beam, screening and compensating solenoids- which is relatively easy to align as the beam position monitors and the two solenoids of the are in close proximity). Any horizontal tilt of the detector solenoid will generate a horizontal magnetic field component and a vertical orbit distortion and dispersion over the whole ring. For a 1mrad tilt of the detector solenoid the corresponding uncorrected distortion is unacceptably large. However, a correction on orbit/dispersion/coupling (no the assumption that we can measure them) using dipoles and skew quadruples on a few sextupoles around the IP, gives an acceptable orbit/dispersion, with the resulting vertical emittance at 0.288 pm (20% larger than the perfectly aligned case).In the actual machine, the measurement of dispersion and coupling at the IP will be difficult, however we can perform the following: Any tilt of the compensation solenoid with respect to the detector solenoid gives rise to a sizable torque on the compensation solenoid (400Nm per mrad, see
Figure ). Equipping the compensating solenoid with strain sensors can ensure alignment to 50 ΞΌ rad, an operation that can be performed at the beginning of every data-taking period. Figure 5 : Torque on the compensation solenoid as a function ofrelative horizontal tilt to the detector solenoid. The screeningsolenoid is switched off.
CONCLUSIONS
We have designed an efficient and high-performance compensation scheme with two magnetic elements per IP side. We have demonstrated that the very stringent and conflicting requirements are met with this elegant design. The vertical emittance blow up from two IPs is 0.24 pm at the Z energies, compared to the emittance budget of 1 pm. Therefore, the presence of detector solenoids will not impair the performance of the FCC-ee collider, even with existence of 4 IPs.
REFERENCES [1] The FCC collaboration, A. Abada et al., βFCC-ee: TheLepton Collider : Future Circular Collider ConceptualDesign Report Volume 2,β
Eur. Phys .J. ST 228(2019) 2, 261-623. [2] The FCC Collaboration, A. Abada et al., βFCCPhysics Opportunities : Future Circular Collideronceptual Design Report Volume 1,β
Eur. Phys. J.C 79 (2019) 6, 474. [3] P. Raimondi, D. N. Shatilov and M. Zobov, βBeam-Beam Issues for Colliding Schemes with LargePiwinski Angle and Crabbed Waist,β LNF-07/003(IR), arXiv:physics/0702033 [physics.acc-ph] , 2007.[4] A. Bogomyagkov et al., βBeam-beam effectsinvestigation and parameters optimization for acircular e+e β collider at very high energies,β Phys.Rev. ST Accel. Beams 17, 041004 ,
IPAC 2016 , Busan, Korea,THOPOR023.[6] M. Koratzinos et al., βProgress in the FCC-eeInteraction Region Magnet Design,β in proceedings ofIPAC2017proceedings ofIPAC2017