EuroCirCol European Circular Energy-Frontier Collider Study

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1 Grant Agreement No: EuroCirCol European Circular Energy-Frontier Collider Study Horizon 2020 Research and Innovation Framework Programme, Research and Innovation Action DELIVERABLE REPORT OVERVIEW OF ARC DESIGN OPTIONS Document identifier: Due date: End of Month 12 (June 1, 2016) Report release date: 28/05/2016 Work package: Lead beneficiary: Document status: WP2 (Arc lattice design) CEA RELEASED Abstract: This document describes the collider layouts to be taken into account for further detailed studies. The optimization of the arc cell lattice and the choice made on the dispersion suppressor are explained. The arc lattice is detailed with the procedures to tune the collider ring and to correct the chromaticity. The correction schemes of the orbit, of the dynamic aperture and of the spurious dispersion are detailed. Finally, the properties of the arc design at the injection energy are shown. Grant Agreement PUBLIC 1 / 24

2 Copyright notice: Copyright EuroCirCol Consortium, 2015 For more information on EuroCirCol, its partners and contributors please see The European Circular Energy-Frontier Collider Study (EuroCirCol) project has received funding from the European Union's Horizon 2020 research and innovation programme under grant No EuroCirCol began in June 2015 and will run for 4 years. The information herein only reflects the views of its authors and the European Commission is not responsible for any use that may be made of the information. Delivery Slip Name Partner Date Authored by Antoine Chancé CEA 09/05/16 Edited by Reviewed by Julie Hadre Johannes Gutleber Michael Benedikt Daniel Schulte CERN 25/05/16 CERN 23/05/16 Approved by EuroCirCol Coordination Committee 28/05/16 Grant Agreement PUBLIC 2 / 24

3 TABLE OF CONTENTS 1. LAYOUT OF THE COLLIDER RING PARAMETERS OF THE ARC CELL CELL LAYOUT PHASE ADVANCE OPTIMIZATION OF THE CELL LENGTH ARC DESIGN DISPERSION SUPPRESSOR COLLIDER TUNING TECHNICAL STRAIGHT SECTIONS SECOND ORDER OPTICS CORRECTION SCHEMES CLOSED ORBIT DIPOLE MULTIPOLE COMPONENT SPURIOUS DISPERSION INJECTION OPTICS SPECIFICITIES OF THE INJECTION OPTICS DYNAMIC APERTURE INJECTION ENERGY LIMITATIONS DESIGN OPTIONS CONCLUSIONS REFERENCES ANNEX GLOSSARY Grant Agreement PUBLIC 3 / 24

4 1. LAYOUT OF THE COLLIDER RING The current layout (see Figure 1) of the collider ring consists of a ring with 2 high-luminosity insertions and 2 low-luminosity insertions. Currently, only the first beam (H1) is considered and is assumed to run in the clockwise direction. The layout for the other, counter-rotating beam (H2) is exactly the same except that left and right are exchanged. Several collider lengths have been investigated: 3.5, 3.75, and 4.0 times the LHC length (respectively km, km, and km). The range of the possible length of the collider ring is set up by the dipole field for the lower limit and by the geological constraints for the upper limit [1]. The studies were jointly performed with FCC-ee to ensure the compatibility between both colliders [2]. The baseline circumference is 3.75 times the one of LHC, i.e km. This length was chosen as a good trade-off between the feasibility of the dipole field, the geological constraints and the total cost. The collider ring is made of 4 short arcs (SAR), 4 long arcs (LAR), 6 long straight sections (LSS) and 2 extended straight sections (ESS). The parameters of the ring are given in Table 1. Figure 1: Layout of the collider ring. The high luminosity interaction points (IPs) are located at PA and PG (in the named sections LSS- PA[PG]-EXP on the layout). The optics of these interaction regions is assumed to be antisymmetric and is presented in [3] for the former value of L * =36 m and in [4] for the current value of L * =45 m. In order to mitigate the beam-beam effects, the crossing angles in PA and PG are not in the same plane at the collision. The lower luminosity IPs are located at PF and PH (in the named sections LSS-PF[PH]-EXP). At the current state of the study, these insertions are made of FODO cells. Grant Agreement PUBLIC 4 / 24

5 The insertion sections and the RF cavities are located at PB and PL (LSS-PB-INJ and LSS-PL-RFS on the layout) for H1. The order is reverse for H2. As the beam separation must be enlarged to 420 mm for the RF cavities, a chicane is added at the entrance and at the exit of these sections. These sections are made of FODO cells. The cell length is enlarged to 300 m to enable the insertion of an injection septum [5]. The extraction and the betatron collimation are respectively located at PD[J] (ESS-PD-COL.EXT on the layout) for H1[H2] whereas the momentum collimation section is located in the other ESS at PJ[D]. The extraction [6], the betatron and momentum collimation sections [7] are scaled from the LHC with the factor k = 50/7 for the betatron functions and the distances. The factor k is derived from the ratio of the centre-of-mass energy at collision between the LHC and the collider ring. By multiplying all distances by this factor, we keep then the same gradient in the quadrupoles. The derivative of the dispersion is divided by this factor. The dispersion suppressors (DIS) are similar to the ones used in LHC. The choice of this configuration is explained in the sub-section 3.1. Special care has been taken to have a dispersion function lower than in the momentum collimation section in the DIS upstream in order not to spoil the collimator hierarchy. Parameter Table 1: Parameters of the collider ring Baseline Value Ultimate Unit c.m. Energy 100 TeV Circumference km LSS and ESS length 1.4 and 4.2 km SAR and LAR length 3.6 and 16 km β * m L * 45 m Normalized emittance (25 ns/5 ns spacing) 2.2/0.44 μm γtr Qx/Qy (collision) / Qx/Qy (injection) / Q x/ Q y 2/2 - Beam separation 250 mm Beam separation (RF) 420 mm Grant Agreement PUBLIC 5 / 24

6 2. PARAMETERS OF THE ARC CELL 2.1. CELL LAYOUT Contrary to the LHC, the synchrotron radiation of the protons is not negligible here [8]. An alternative to FODO cells is MBA cells [9] which are usual in synchrotron machines. The advantage of the MBA is to have smaller equilibrium emittances. The counterpart is stronger quadrupoles and less flexibility on the location of the magnets. The beam emittance will decrease while running, counterbalancing the emittance growth from beam-beam effects. Nevertheless, the aim is to optimize the average luminosity. A too large luminosity (coming from a too small emittance) will increase the beam burnoff in the experiment and thus decrease the beam lifetime. Therefore, having the smallest equilibrium emittance is not necessarily the best thing for the machine operation optimization. That is why the FODO lattice was chosen as the baseline for the arc cell. The layout or the half-fodo arc cell is shown in Figure 2. The cell is meter long. The cell optimization is detailed in the sub-section 2.3. Each dipole (with its spool pieces in blue) has its own cryostats drawn in yellow. The distance of 1.36 m is the minimum allowed spacing between two dipoles for the interconnections. Another cryostat contains the quadrupole (in green), the sextupole (in cyan), the BPM, the orbit corrector (in magenta), the trim quadrupole, and other multipole correctors. For mechanical reasons it is preferred that the dipole magnets are straight. The current lattice design approximates this with dipoles that follow the bending of the beam trajectory as in the LHC since the difference in impact on the beam is expected to be small. However, a full study remains to be performed. Figure 2: Layout of an arc half-cell. Grant Agreement PUBLIC 6 / 24

7 2.2. PHASE ADVANCE Currently, the phase advance is 90 in both planes. The optics functions of the arc cell as defined in Table 2 are shown in Figure 3. Such a phase advance is standard in colliders like the LHC [10]. The advantages of a phase advance of 90 are: A ratio β max/l cell near the minimum [11]. A small ratio D max/l cell. A good efficiency between the corrector and the BPM one cell downstream. A compensation of the sextupoles every other cell. A compatibility with more advanced scheme like the ATS [12]. The details of the optimization of the cell length are summarized in section 2.3. Table 2: Parameters of the arc FODO cell Parameter Value Unit Cell length m Cell phase advance H/V 90 deg Number of dipoles per cell 12 - Dipole magnetic length 14.3 m Dipole maximum field 15.9 T Quadrupole magnetic length 6.29 m Quadrupole maximum gradient 359 Sextupole magnetic length 0.5 m Sextupole maximum gradient Baseline/Ultimate T/m 8140/16030 T/m 2 Dipole-dipole spacing 1.36 m Quadrupole-dipole spacing >3.67 m Quadrupole-sextupole spacing 1.0 m Grant Agreement PUBLIC 7 / 24

8 Figure 3: Optics functions of the arc cell. An alternative to a phase advance of 90 degrees is 60 degrees. This phase advance is also standard and was used in LEP for example [13]. The advantages of a phase advance of 60 are: A smaller quadrupole gradient. A smaller sextupole gradient. A ratio β max/l cell near the minimum [11]. A compensation of the sextupoles every three cells. The drawbacks are an enlarged dispersion by a factor 1.8 (the dispersion maximum becomes 4.4 m against 2.4 m) and a less good efficiency of the correctors. A larger dispersion implies a decrease of the energy acceptance of the collider ring, which requires more care on the beam momentum cleaning. More studies are needed to adapt the ATS scheme to this phase advance. Grant Agreement PUBLIC 8 / 24

9 2.3. OPTIMIZATION OF THE CELL LENGTH The cost of the arcs is driven by the dipole and more precisely by the peak field in the dipoles. That is why the cell length was calculated to maximize the filling ratio of the collider. A python script was written, which generates a list of sequences of the collider ring from a variation range for the arc cell length and from a list of parameters [14]: The collider ring length. The length of the insertions LSS and ESS. The dipole magnetic length. The minimum quadrupole magnetic length. The spacing dipole-dipole. The minimum spacing quadrupole-dipole. The minimum magnetic quadrupole length. The dispersion suppressor type. The variation range for the cell length is from 200 to 250 m. The magnetic field versus the arc cell length is plotted in Figure 4 for a collider length of km. Several dipole magnetic lengths were considered from 14 m to 15 m. The upper limit is given by the transportation limitations of the cryostat. A minimum is reached for a cell length of 210 m to 220 m according to the dipole length. The dipole length is fixed to 14.3 m, which is the same as the LHC dipole length. The optimum length is then m. It is worth notifying that there is a dipole field minimum every m of cell length, when a dipole is added or removed in the half-cell. Therefore, there are alternatives for the cell length like 182 m, 245 m, or 276 m. The value of 182 m is excluded because the needed gradients are above the upper limit of 370 T/m. Longer cells enable to reduce at once the integrated gradient (and thus their length) and the total number of arc quadrupoles. The filling ratio decreases thus a little. However, betatron functions and dispersion proportionally increase with the arc cell length. That means that the beam stay clear will decrease at the injection. The dispersion in the momentum collimation insertion must increase too to keep the collimator hierarchy: the dispersion in the DIS downstream must be lower than in this section. The larger dispersion with 60 (or longer cells) reduces the energy acceptance of the arcs. Longer FODO cells are still an alternative to be studied. A cell length of m and phase advances of 90 are a good compromise between energy acceptance, feasible quadrupole gradients and filling factor. Figure 4: Variation of the dipole field with the cell length in the case of a kilometer-long collider ring and a LHC-like dispersion suppressor. Grant Agreement PUBLIC 9 / 24

10 3. ARC DESIGN 3.1. DISPERSION SUPPRESSOR The baseline dispersion suppressor is of the same type as the one used in the LHC. A specific dipole is used in the dispersion suppressor to scale from LHC. This dipole is shorter (13.5 m long) than the ones used in the arc cells. A layout of the dispersion suppressor is given in Figure 5. The quadrupoles of the dispersion suppressor are varied to match with the insertions. Other alternatives to the LHC-like dispersion suppressors were investigated [14] [15]. The other schemes use three FODO cells with variables quadrupole gradients to match with the insertions. The dipole field in the DIS was scaled from the arc dipoles by a factor from 0.5 (half-bend dispersion DIS) to 1 (full-bend DIS). A layout of the full-bend dispersion suppressor is shown in Figure 6. The conclusions of this study are that the half-bend DIS is not enough compact: the minimum dipole field is 16.3 T. The full-bend DIS is the most compact with a required dipole field of 15.7 T. The drawbacks of the full-bend DIS are stronger quadrupoles and less flexibility compared to the LHC-like DIS. That is why the baseline DIS is the LHC-like one. Nevertheless, a collimator may be inserted in the DIS downstream to the collimation section to protect the arcs from the debris. Such a requirement may change the layout of the DIS downstream to ESS- PD[J]-EXT. The full-bend DIS cannot be used in this case because of the lack of space for a collimator. Figure 5: Layout of the LHC-like dispersion suppressor. Figure 6: Layout of the full-bend dispersion suppressor COLLIDER TUNING The optics of the different main insertions and of the whole ring are given in Figure 7 for LSS-PA[G]- EXP, Figure 8 for LSS-PF[H]-EXP, Figure 9 for LSS-PB-INJ, Figure 10 for ESS-PD-EXT, Figure 11 for ESS-PJ-EXT, and Figure 12 for the whole ring for the baseline parameters given in Table 1. Currently, there is no constraint on the phase advance between the different IPs. In the future, the tuning scheme of the collider may change accordingly. The phase advance in the FODO cells is exactly 90 in the SAR whereas it is 90 +εx,y in the LAR. The value of εx,y is currently adjusted to tune the whole ring at the injection and at the collision. Because of the large number of FODO cells in the LAR, the value of εx,y stays small. Grant Agreement PUBLIC 10 / 24

11 Other alternatives to tune the collider are to tune the phase advance of the insertions LSS-PB[L]-INJ or of ESS-PD[J]-EXT. Tuning the collider with the DIS seems to be difficult because of the large number of constraints in this section. Figure 7: The optics functions of LSS-PA-EXP (corresponds also to LSS-PG-EXP). Figure 8: The optics functions of LSS-PF-EXP (corresponds also to LSS-PH-EXP). Figure 9: The optics functions of LSS-PB-INJ (corresponds to LSS-PL-INJ). Figure 10: The optics functions of ESS-PD-COL. Figure 11: The optics functions of ESS-PJ-COL. Figure 12: The optics functions of the whole FCC ring. Grant Agreement PUBLIC 11 / 24

12 3.3. TECHNICAL STRAIGHT SECTIONS A dipole is removed at the middle of the LAR to save some space for the technical straight sections (TSS). To cancel the dispersion wave generated by this missing dipole, another dipole is removed downstream at the phase advance of about 180 degrees (two FODO cells far away). The field increase in the other dipoles is only 0.02 T. Since the phase advance is not exactly 90, there is a residual dispersion beating which is cancelled in the DIS downstream. The advantage of this solution is to keep the same dispersion maximum. Indeed, the dispersion wave is cancelled a half-period after creation: the dispersion wave amplitude is thus always negative. The drawback of this method is to work only if the phase advance between the two missing dipoles is 180, which fixes the phase advance in the LAR cells. An alternative is to cancel the dispersion wave in the DIS downstream. In this case, we are not dependent on the phase advance in the LAR but the dispersion maximum in the LAR increases by more than 15%. The optics functions in the LAR with one missing dipole and two missing dipoles are respectively shown in Figure 13 and Figure 14. If the phase advance in the LAR FODO cells is frozen at 90, the solution with two missing dipoles is preferred. Figure 13: Optics functions in LAR with 1 missing dipole. Figure 14: Optics functions in LAR with 2 missing dipoles. Grant Agreement PUBLIC 12 / 24

13 3.4. SECOND ORDER OPTICS In the current design, the chromaticity is corrected by two sextupole families distributed in the SAR and LAR. First attempts were done to test the layout compatibility with more advanced schemes like ATS [16]. The horizontal/vertical phase advance between PA and PG was firstly tuned to 90 degrees/270 degrees modulo 360 degrees. The obtained Montague functions are shown in Figure 15. They are similar to the ones obtained in LHC. In a second step, four sextupole families were used (two strong sextupole families and two weak sextupole families) and positioned at the right phase advance from PA and PG as explained in [12]. The obtained Montague functions are then shown in Figure 16. This first attempt shows that the ATS is compatible with the collider ring layout. Nevertheless, at this state of the study, this scheme is not chosen as the priority because of the needed fine tuning between the different insertions. When the layout of the collider ring and the first order optics are frozen, more advanced schemes like ATS will be then investigated in details. Figure 15: Montague functions in the collider ring (2 sextupole families). Figure 16: Montague functions in the collider ring (presqueze of the ATS scheme). Grant Agreement PUBLIC 13 / 24

14 4. CORRECTION SCHEMES 4.1. CLOSED ORBIT There are several error contributions that can affect the closed orbit of the particles in the arcs of the collider ring [17]: Quadrupole alignment errors. Dipole field errors (random b1). Quadrupole roll angle errors. Dipole roll angle errors. BPM readout errors. Incoming beam errors. Currently, only the first two contributions are studied and are considered as static. In the baseline, next to each of the quadrupoles of the arcs and of the neighbouring DIS, there are a BPM and a meter-long orbit corrector made with Nb-Ti technology (as well as a sextupole), both located after the quadrupole. Figure 17 shows the structure around an arc quadrupole unit. An alternative is to use the LHC scheme with the BPM located before the quadrupole. The BPM is after the sextupole in the baseline to reduce the closed orbit in the sextupole and thus the beta-beating. Some studies are necessary to compare the baseline with the LHC scheme. Figure 17: Structure of a quadrupole unit in the arc sections, with from left to right, the quadrupole itself (QP), a BPM, a sextupole (SX), and an orbit corrector (COR). The current correction scheme is to use all BPMs and all correctors. The corrector polarity is the same as the one of the neighbouring quadrupole. Each BPM is measuring the beam position in the plane in which the neighbouring quadrupole is focusing. This scheme means that a residual orbit measured by a BPM will be corrected by an orbit corrector placed in the second next quadrupole (located at a phase advance of 90 degrees downstream). With this scheme the horizontal and vertical orbit corrections are made with a separate set of BPMs and correctors. The orbit correction optimization is performed with the MAD-X code [18]. The alignment error is defined only for the arc quadrupoles. The field error is defined for all dipoles present in arcs and in DIS sections. Only one error contribution is varied once, the other error contribution being fixed to 0.35 mm and to 0.1 % for the quadrupole alignment error and the dipole field error, respectively [17]. Those values are currently considered as reference tolerance values and lead to integrated strengths for the orbit correctors below 4 Tm, which is compatible with having them built with the Nb-Ti technology. The sensitivity of the maximum residual orbit in the arcs with the quadrupole misalignement and the dipole field error is respectively shown in Figure 18 and Figure 19. Grant Agreement PUBLIC 14 / 24

15 The studies on the orbit correction are going on and additional error contributions like quadrupole roll angle, BPM readout error will be added in the near future. Currently, dedicated correction schemes of the beta-beating and dispersion beating are not investigated. Additional correctors will be inserted for this correction. The location and the strength of these correctors will be defined in the future. Figure 18: Sensitivity of the residual orbit to the quadrupole alignment error. Figure 19: Sensitivity of the residual orbit to the dipole field error DIPOLE MULTIPOLE COMPONENT The first estimate of the main dipole field quality was provided by the magnet group [19] and a preliminary analysis of its impact on the Dynamic Aperture (DA) was conducted at the baseline injection energy of 3.3 TeV and at collision energy. The same simulation procedure and inputs parameters (such as the fractional part of the tunes and momentum offset) of HL-LHC are used, and magnet misalignment is not considered in simulation [20] (see Table 3). Table 3: Multipoles used for the main dipole field quality. The values are in units of 10-4 at R ref=17 mm. Normal Systematic bns injection collision Uncertainty bnu Random bnr Skew Systematic ans injection collision Uncertainty anu Random anr Grant Agreement PUBLIC 15 / 24

16 The first tracking simulation effort was put on adapting the SixTrack code [21] to handle the number of elements in the collider ring. At the same time the analysis tool (called SixDesk Environment) required some modifications in order to take into account the 3 digits of the collider tunes, and MAD- X [18] scripts to generate the SixTrack inputs were developed. The optics configurations used in these simulations integrate the same arc cell design but different insertion region versions. In particular, two versions of the interaction region optics, using different L* and triplet design are integrated, called v2 [3] and v5 [4]. At collision, we use the ultimate β* of 0.3 m, while at injection a β* of 3.5 m or 4.6 m is used. Moreover, different momentum collimation sections were considered, as soon as they became available. At collision energy, the DA strongly reduces when the first estimate of the main dipole field quality is considered (below 10σ). In particular, the effect of the systematic b3 value is shown in Figure 20 (by comparing pink and grey dots). Given the maximum integrated strength reachable by the spool pieces (3 times the LHC ones) the maximum amount of b3 we can correct is about 6 units [22]. Moreover, in order to ensure that the arcs have a small impact on the DA at collision (which is already greatly reduced by the triplet imperfections [23] and beam-beam effects) it is important to fully correct the systematic component of b3 error. It has been agreed with the magnet group that a maximum value of 3 units is assigned as a target value for the systematic part of b3 at collision, allowing up to 7 units at injection [22]. Figure 20: Dynamic Aperture in number of beam RMS sizes versus the phase space angles at the energy of 50 TeV SPURIOUS DISPERSION While colliding, both beams cross with an angle which can reach values up to P Xing = ε N γβ n Xing where nxing is the half-crossing angle in sigmas. It is fixed to 7.6, corresponding to an angle of PXing=46.6 µrad for the baseline [4]. The orbit excursion in the triplet generates a residual dispersion, which must then be corrected. The studied correction scheme is similar to the one used for HL-LHC [12]: the entrance correctors and exit correctors of the SAR are switched on. The phase advance between the used correctors and PA[G] is near 90 modulo 90. The closed orbit in the SAR quadrupoles generates a dispersion wave which corrects the spurious dispersion. The angles in the correctors are then adjusted to cancel the dispersion at PB, PF, PH and PL. The β-beating is finally corrected in the DIS upstream of the left SAR and downstream of the right SAR around PA[G]. The chromaticity created by the closed orbit in the SAR is corrected by the sextupoles in the LAR. Before and after correction, we respectively obtain the closed orbit and the dispersion shown in Figure 21 and Figure 22 [24]. Grant Agreement PUBLIC 16 / 24

17 The maximum closed orbit in the arcs reaches values up to 8.6 mm/10.9 mm in the horizontal/vertical plane. The maximum angle in the correctors is respectively 24.4/24.5µrad for a horizontal/vertical crossing angle. In the current state, these values are much too large and some solutions must be taken to mitigate these values. The length of the SAR could be enlarged to make the correction more efficient and thus to reduce the needed closed orbit in the SAR. The orbit bump amplitude is proportional to the length of the SAR. A maximum reduction of about 4-5 on the orbit bump can be obtained by inverting the SAR and the LAR in the layout. By this way, the maximum orbit bump becomes 2.4 mm in the arcs. Inverting LAR with SAR will have an impact on the injection transfer lines and the clustering with PF and PH will be lost. Anyways, the orbit bump is still too large and additional solutions must be undertaken to mitigate it. Applying the ATS scheme by using every other sextupole will be investigated in a future study. The experience with HL-LHC has shown that a reduction factor of 2 could be obtained with this scheme. Unfortunately, this gain is only enough if the LAR and SAR are inverted. Another alternative is to correct the horizontal spurious dispersion with the DIS neighbouring PA[G]. The needed gradients in the quadrupoles are likely to significantly increase and additional quadrupoles may be necessary to enable this correction scheme. More studies are necessary to validate or reject this alternative. The correction of the vertical spurious dispersion is more delicate because of the absence of vertical dipoles in the collider ring. There are three alternatives to handle the vertical spurious dispersion. The first solution is to have only horizontal crossing angles at both IPs. The advantage is to remove the issue of the vertical spurious dispersion. The bottleneck is the coherent beam-beam effects between both IPs, which requires special care to cure them. A second alternative is to use skew quadrupoles to correct the vertical dispersion like in SSC [25]. Further studies are necessary to calculate the needed gradients and to see if they are realistic. The other point is to find the right location of these skew quadrupoles and how to cancel the coupling introduced by them. The last possibility is to add a dedicated vertical dispersion matching section before the entrance of the arcs neighbouring PA[G]. The counterpart is additional elements and a serious amount of space for these insertions (and thus a reduced filling ratio). Figure 21: Closed orbit and dispersion in the collider ring before correction of the spurious dispersion in presence of the crossing scheme. Figure 22: Closed orbit and dispersion in the collider ring after correction of the spurious dispersion in presence of the crossing scheme. Grant Agreement PUBLIC 17 / 24

18 5. INJECTION OPTICS 5.1. SPECIFICITIES OF THE INJECTION OPTICS The optics of the arcs is not deeply changed while transiting from the injection optics to the collision optics. The main differences are: A different tune: / at injection against / at collision. A different β * at PA[G]. Several strength files of the interaction region were provided by WP3 for the injection regime. The current baseline values for β * are 4.6 m or 6.0 m. These lattices were matched to the SAR thanks to the DIS. Nevertheless, the change of the β * has a very local impact on the optics functions of the collider ring (typically in LSS-PA[G]-EXP and in the neighboring DIS). The sextupole strengths decrease too because of a reduced chromaticity contribution of the inner triplets. A different crossing scheme. At the injection, the separation scheme at the IPs is switched on. A larger RMS emittance (scaling with βγ). The main effect is that the beam stay clear is an issue in the arcs at the injection and may define the minimum injection energy we can afford (see subsection 5.3) DYNAMIC APERTURE At injection, without dipole imperfections the DA is above 80σ for each angle explored. As far as the main dipole field imperfections are considered in the tracking simulations the minimum DA reduces to 14 σ, which is above the target value of 12 σ as shown by the blue dots in Figure 23. The chosen working point and the first dipole field quality estimates are not critical in terms of DA at the injection energy of 3.3 TeV. Considering that the ratio of DA at two different energies is equal to the ratio of the corresponding γ, the lower limit for injection energy, as far as DA is concerned and with the present field quality table, is set to about 2.6 TeV. If the dipole field quality degrades due to persistent current at injection energy (up to 15 units of systematic b3), the minimum DA drops below the target value, as shown by the black dots in Figure 23, thus a local correction scheme is needed. We have considered spool piece correctors attached to the main dipoles, like in the LHC. The light blue dots in Figure 23 show that the 15 units of systematic b3 are fully corrected using spool pieces correctors placed at each dipole of the arcs, correcting each the average b3 of the 8 arcs. Furthermore, the corrector strength effectively used for the correction is about 15% of the maximum integrated strength that could be reached by current technology [7]. Finally, one unit of b5 reduces the average DA of about 3σ at 15, a similar impact is given by a difference of 1 in the horizontal phase advance of the long arc cell, as shown by comparing black dots and squares with grey dots in Figure 23. Moreover, after correcting b3 the minimum DA is already above the target value even with b5 errors. Therefore, decapole correctors do not seem to be required and no specification is given, at this stage of the design study. Grant Agreement PUBLIC 18 / 24

19 Figure 23: Dynamic Aperture in number of beam RMS sizes versus the phase space angles at the energy of 3.3 TeV INJECTION ENERGY LIMITATIONS The injection energy was reviewed [26]. Two injection energies were retained as the most promising: 3.3 TeV with the LHC as an injector and 1.5 TeV with a new SPS (SPS magnets replaced by superconducting magnets). The beam size scales with the inverse of the square root of the energy. The calculations show that the minimum injection energy we can afford is 1.5 TeV with the current beam pipe size. Lower injection energy requires then a larger beam pipe (and thus more costly magnets). The current DA studies (given in the sub-section 5.2) show that the minimum we can afford is 2.6 TeV. Pushing to lower injection energy implies reducing the value of the beam stay clear we accept (and thus the safety margins). The other concern is the value of persistent currents in the magnets (and thus the multipole components) if the injection energy becomes too low. The behaviour of the multipole components may become very nonlinear with the magnetic field and it becomes difficult to predict the correction level we need in the spool pieces. That is why the baseline for the injection energy is 3.3 TeV. An alternative is 1.5 TeV but more studies (DA, impedance, electron-cloud, magnet field quality, ) are needed to exclude or keep this value. Grant Agreement PUBLIC 19 / 24

20 6. DESIGN OPTIONS The design baseline is: A layout of the collider ring as illustrated in Figure 1. The arc cell is a meter-long FODO cell with a phase advance of 90 in both planes. Experimental insertions: L * =45 m and β * =1.1 m (and β * =0.3 m for the ultimate set of parameters). Collimation sections: scaled from the LHC. Injection energy at 3.3 TeV and β * =4.6 m. The collider is tuned with the phase advances in the LAR. The chromaticity is corrected with two sextupole families. Spurious dispersion corrected with an orbit bump in the SAR neighboring the IPs. The alternatives, which are to be studied in parallel, are: Longer arc cells or a phase advance of 60 in both planes to reduce the needed quadrupole gradients and to increase (lightly) the filling ratio. But that implies a larger dispersion and thus a lower energy acceptance. Other values of L * like 36 m or 61 m and β * =1.1 m. These other versions will be provided by WP3 and integrated in the lattice for comparison tests (DA behavior, beam-beam effects, second order optics, ) with the baseline. Other versions of the insertions (SSC-like extraction section, FODO-based collimation sections ). These other versions have a small impact on the general behavior of the collider. Some specific modifications can be made to integrate them like a specific DIS downstream to the momentum collimation section. Nevertheless, the DA, the correction scheme or the magnet needs in the arcs should not dramatically change. That is why the arcs can be optimized in parallel of these insertions. New versions of these insertions will be integrated as soon as they become available. Injection energy at 1.5 TeV and other values of β *. The advantage of 1.5 TeV is to enable the use of normal conductions magnets in the injection transfer lines and to use the SPS (after replacing the normal conducting magnets by superconducting ones) as an injector to the collider ring. That has thus an interest for the cycling of the machine and for the cost operation [26]. Nevertheless, that implies larger beam sizes at the injection (and thus a smaller DA) and greater persistent current issues. Further studies are needed to keep or reject this option. The collider is tuned with the non-experimental insertions (LSS-PB-INJ and LSS-PL-RFS for instance). The advantage is to keep a phase advance of 90 in LAR and to keep the same quadrupole gradients in all arcs. Nevertheless, these insertions are shorter with less quadrupoles, which implies a good flexibility of these insertions. The chromaticity is corrected with more advanced scheme like ATS. The advantage is to make the matching of the Montague functions possible. The drawback is to give additional constraints on the lattice to tune the different IPs together. Alternative schemes to correct the spurious dispersion: other collider layout with longer SAR, correction with DIS, use of the ATS, skew quadrupoles for the vertical dispersion. Each alternative has limitations (see sub-section 4.3). It is likely to have to combine several schemes to be able to handle the large spurious dispersion generated by the crossing scheme. Grant Agreement PUBLIC 20 / 24

21 7. CONCLUSIONS A first order optics of the collider ring has been provided. The arcs are made of FODO cells with phase advances of 90 or of 60. The arc cell parameters were optimized to minimize the magnetic field in the dipoles. The need of a compact collider ring has driven the choice of the DIS too. The studies of the correction schemes of the orbit, of the multipole field errors and of the spurious dispersion have begun. They have shown that the spurious dispersion correction is recently an issue and must be solved to enable the collision regime with the ultimate parameters. The dynamic aperture was investigated at the collision and injection energies. Grant Agreement PUBLIC 21 / 24

22 8. REFERENCES [1] J. Osborne, 'FCC Civil Engineering', presented at the FCC week 2016, Rome, Italy, [2] K. Oide, 'FCC-ee Machine Layout and Beam Optics', presented at the FCC week 2016, Rome, Italy, [3] R. Martin, R. Tomás and B. Dalena, 'Interaction Region for a 100 TeV Proton-Proton Collider', in Proc. IPAC'15, Richmond, VA, USA, [4] A. S. Langner, 'Developments on IR baseline design', presented at the FCC week 2016, Rome, Italy, [5] W. Bartmann and others, 'Beam Transfer to the FCC-hh Collider from a 3.3 TeV Booster in the LHC Tunnel', in Proc. IPAC'15, Richmond, VA, USA, May 2015, [6] T. Kramer and others, 'Considerations for the Beam Dump System of a 100 TeV Centre-of-mass FCC hh Collider', in Proc. IPAC'15, Richmond, VA, USA, May 2015, [7] J. Molson, P. Bambade, S. Chance and A. Faus-Golfe, 'Simulation of the FCC-hh Collimation System', in Proc. IPAC'16, Busan, Korea, [8] D. Schulte, 'Preliminary collider baseline parameters', EuroCirCol-D1-1, [9] D. Einfeld, M. Plesko and J. Schaper, 'First multi-bend achromat lattice consideration', Journal of Synchrotron Radiation, vol. 21, no. Pt 5, pp , [10] O. Brüning and others, 'LHC Design Report', in Optics and Single Particle Dynamics, Geneva, CERN, [11] E. Keil, 'Lattices for Collider Storage Rings', in Handbook of accelerator physics and engineering, World Scientific, 2006, pp [12] S. Fartoukh, 'Achromatic telescopic squeezing scheme and application to the LHC and its luminosity upgrade', Phys. Rev. ST Accel. Beams, vol. 16, p , [13] J. A. Uythoven, 'A LEP (60,60) optics for energy calibration measurements', CERN-SL OP, CERN-SL OP, [14] A. Chance and others, 'First results for a FCC-hh ring optics design', Tech. Rep. CERN-ACC , CERN, Geneva, [15] B. Dalena and others, 'First Considerations on Beam Optics and Lattice', in Proc. IPAC'15, Richmond, VA, USA, May 2015, [16] B. Dalena, A. Chance and J. Payet, 'ATS compatibility: IR phase advanced constraints', 18 September [Online]. Available: [17] D. Boutin and others, 'Residual orbit correction studies for the FCC-hh', in Proc. IPAC'16, Busan, Korea, [18] 'MAD-X', [Online]. Available: [19] D. Tommasini, 'Baseline specifications and assumptions for accelerator magnet', EuroCirCol- P1-WP5-M5.2, Grant Agreement PUBLIC 22 / 24

23 [20] B. Dalena and others, "First evaluation of dynamic aperture at injection for FCC-hh," in Proc. IPAC'16, Busan, Korea, [21] "SixTrack website," [Online]. Available: cern.ch/sixtrack-ng. [22] E. Todesco and others, Field quality, correctors and filling factor in the arcs, presented at the FCC week 2016, Rome, Italy, [23] R. Martin, β* reach studies, presented at the FCC Week 2016, Rome, Italy, [24] A. Chance and others, "Status of the Beam Optics of the Future Hadron-Hadron Collider FCChh," in Proc. IPAC'16, Busan, Korea, [25] Y. Nosochlov and D. M. Ritson, "The provision of IP crossing angles for the SSC," in Proc. PAC-1993, Washington, DC, USA, [26] M. Benedikt and F. Zimmermann, Review of FCC-hh injection energy, presented at FCC week 2016, Rome, Italy, Grant Agreement PUBLIC 23 / 24

24 9. ANNEX GLOSSARY SI units and formatting according to standard ISO on quantities and units are used throughout this document where applicable. ATS BPM c.m. DA DIS ESS FCC FCC-ee FCC-hh FODO H1 H2 HL-LHC IP LHC LAR LSS MBA Nb3Sn Nb-Ti RF RMS σ SAR SR SSC TSS Achromatic Telescopic Squeezing Beam Position Monitor Centre of Mass Dynamic Aperture Dispersion suppressor Extended Straight Section Future Circular Collider Electron-positron Collider within the Future Circular Collider study Hadron Collider within the Future Circular Collider study Focusing and defocusing quadrupole lenses in alternating order Beam running in the clockwise direction in the collider ring Beam running in the anti-clockwise direction in the collider ring High Luminosity Large Hadron Collider Interaction Point Large Hadron Collider Long arc Long Straight Section Multi-Bend Achromat Niobium-tin, a metallic chemical compound, superconductor Niobium-titanium, a superconducting alloy Radio Frequency Root Mean Square RMS size Short arc Synchrotron Radiation Superconducting Super Collider Technical Straight Section Grant Agreement PUBLIC 24 / 24