H=18 mm O A. R=22 mm

Transcription

1 Geometrical acceptance in LHC Verion. J.B. Jeanneret and R.Otojic LHC Project Note 111 September 1997 Keyword: aperture, injection, optic, collimation, croing angle Summary The geometrical acceptance of LHC Verion. i preented for the regular arc and the machine inertion. The acceptance and beam eparation in the low- triplet are determined for variou croing condition at injection. 1 Introduction The algorithm ued to compute the geometrical acceptance of the LHC regular cell have been expanded to allow element by element evaluation of the acceptance in the complete LHC ring. The trajectory of the beam relative to the magnet axi i now taken exactly into account, allowing the analyi of the croing beam in the experimental inertion, a well a optimiing the acceptance in the eparation dipole. In the injection inertion, beide the acceptance for the circulating beam, the acceptance for the injected and mikicked beam i calculated. Finally, to complete the procedure, a imple databae containing the mechanical and alignment tolerance, and the geometrical denition of the vacuum chamber aociated with magnet clae ha been developed. The procedure i applied to the calculation of the geometrical acceptance of the Verion. of the LHC ring at injection, and attention i drawn to poible bottleneck. The beam eparation and the geometrical acceptance of the low- triplet i preented for variou croing condition at injection. Finally, on the bai of the nominal colliion parameter, a thicker cold bore of the low- triplet in the high luminoity inertion i propoed. The cold bore add to the protection of the triplet without limiting the acceptance of the inertion. 2 Denition and computational method We give here a ummary of the denition and of the computational method for determining the geometrical acceptance preented in detail in [1]. Normalied tranvere pace coordinate are ued, dened by: n x = x n y = y (1) k x k y 1

2 n y n a n r n 1 n a n x Figure 1: The geometrical edge of the econdary halo a given by the cleaning ytem. For the ratio of primary and econdary aperture of n2 =n 1 =7=6, the parameter of the econdary halo are nr =n 1 =1:4 and na =n 1 =1:22. For the nominal primary aperture of =7:, nr =9:8 and na =8:. where: x, y are the tranvere coordinate, k i the quare root of the -beating factor, and x;y the r.m. beam ize. The primary collimator of the machine are at the ditance n 1 in the n x n y plane, and dene the primary aperture, Figure 1. The econdary collimator are at n 2, retracted by a factor n 2 =n 1 = 7=6. For thee parameter of the cleaning ytem it ha been hown that the econdary halo i dened by n r =n 1 = 1:4 and n a =n 1 = 1:22, o that for the primary aperture of n 1 =7:, n r =9:8 and n a =8: [2]. The minimum required primary aperture i n min 1 =: (2) However, to allow for an operational margin, the primary aperture of the LHC i pecied a [1, 3]: n pec 1 =7: (3) Thi value of n 1 i the criterion for the geometrical acceptance of the ring. Since the machine i cold almot everywhere, the econdary halo ecaping the collimation ytem could induce a quench at a location where the n 1 () < n pec 1. The geometrical edge of the econdary halo coincide quite well with a detailed imulation of the econdary halo generated by the collimation ytem. The Verion. of the collimation ytem, located in IR7, i now quite well dened, and will be reported in the near future. The geometrical acceptance in any part of the ring i calculated on the bai of the larget econdary halo that can be incribed in the vacuum chamber, taking into account the diplacement of the beam at a particular point, Figure 2. The maximum beam diplacement i given a a linear um: x;y () =CO peak x;y +[ mech x;y ()+x;y()] al + k D x;y () p +[d ep x;y()+d inj y ()+d axi x ()] (4) where CO peak i the peak cloed orbit excurion, and mech and al aggregate mechanical and alignment tolerance of the vacuum chamber. The diperion term contain the linear term and 2

3 y D H=18 mm B C y O A R=22 mm x x Figure 2: Fit of the larget econdary halo in the vacuum chamber with the beam diplaced by x;y with repect to the ideal centre of the chamber. a correction due to paraitic coupling: v ut D x;y () =D linear x;y () x;y ()+k D D QF () QF;x Here, k D i the coupling coecient, and D QF i the peak linear diperion in the arc (2.1 m in the focuing quadrupole). The diplacement due to the diperion i proportional to the momentum oet p (dierent for injection and colliion energie), and i corrected for -beating. In the croing point the beam travel in a common beam tube and are eparated to avoid paraitic colliion and collective beam-beam eect. The eparation i generated by kicker located on either ide of the croing point. The eparation i dened by the croing angle and the tranvere eparation of the beam at the interaction point. For a given et of croing parameter, the orbit i diplaced with repect to the ring axi by d ep, not only in the common part of the ring (from D1R-D1L), but alo within all element which are located between the eparation kicker. In the machine ection common to the circulating and injected beam, i.e. between Q and D2 in IR2 and IR8, the diplacement d inj decribe the eect of the injection kicker MKI. Beide the cae where the beam i injected onto the circulating orbit, two other poibilitie, related to MKI malfunction, are conidered: an injected beam which i not diverted onto the circulating orbit, and a circulating beam which i accidentally mikicked out of the ring. Since MKI act in the vertical plane, d inj ha a vertical component only. Finally, in the dipole eparator in the inertion (D1-D2 and D3-D4 pair), the magnet axi doe not necearily coincide with the ring axi, and the ideal orbit i diplaced by d axi. Thi value may be modied by electing the eparation of the two aperture o a to improve the geometrical acceptance of the eparator (particularly ueful for D3-D4 in IR4, and for D2 in IR2/8). Depending on the location in the ring, e.g. in the arc cell or traight ection without croing, ome or all of the d term may be identical to zero. 3

4 Table 1: Coecient entering the calculation of beam diplacement x;y Coecient Name Value Peak Cloe orbit excurion COx;y peak 4. mm Beta beating (root) k 1.1 Relative paraitic diperion k D.273 Momentum oet,injection p 3 Momentum oet,colliion p 2 4 The diplacement x;y are calculated with PERL cript under UNIX. The linear optical function and eparation are retrieved by running MAD uing the LHC V. databae, and are calculated exactly inide the magnet, with a tep of one metre. The additional parameter entering the calculation for Verion. of LHC are given in Table 1. For each location, the larget econdary halo which t inide the vacuum chamber of a given magnet cla i calculated. Thi in turn give the equivalent primary collimator aperture n 1, which erve a the denition of the local acceptance. The reult are preented a table and gure, and are compared with the required global acceptance of n pec 1 = 7. The mechanical and alignment tolerance for magnet clae preently ued in LHC Verion. are tored in a PERL module a a imple databae, and are given in Table 2. The databae alo contain the denition of the vacuum chamber geometry and magnet axi oet relative to the average ring axe. It can be eaily extended for new propertie and magnet clae. 4

5 Table 2: Databae of aperture parameter for the LHC magnet clae. The databae contain mechanical and alignment tolerance, axi oet relative to the average ring axi, and the vacuum chamber type, decribed by it hape and dimenion. Decription Cla x mech x al y mech y al Axi Vacuum name [mm] [mm] [mm] [mm] [mm] chamber Main dipole MB r22-v18 Warm eparator D1 MBXW r6-v27. Cold eparator D1 MBS r37 Separator D2 (IR1) MBT r37 Separator D2 (IR2) MBT r37 Separator IR4 D4B MBR4B r34-v3 Separator IR4 D4A MBR4A r34-v3 Separator IR4 D3B MBR3B r34-v3 Separator IR4 D3A MBR3A r34-v3 Warm eparator IR3 MBW r31.-v23 Warm eparator IR7 MBW r31.-v23 Main quad MQ r22-v18 Main quad (no creen) MQ NOBS r2 Wide aper. quad MQY r31. Low- quad (IR2) MQX r31. Low- quad (IR1, Q1) MQX r23 Low- quad (IR1, Q2) MQX r3 Low- quad (IR1, Q3) MQX r3 Warm quad MQW hyp-r2.-h24 Injection kicker MKI r19 Injection eptum MSI r2 Dump kicker MKD r29 Dump eptum MSD r23 Orbit corrector MCBY r33. TAS aborber ABS r17

6 3 Arc aperture at injection The geometrical acceptance of the regular cell i preented in Figure 3. A in other gure hown in later ection, the magnet layout i diplayed at the bottom of the gure. The cell hown in Figure 3 begin with a defocuing quadrupole QD16.R1, contain the focuing quadrupole QF17.R1 and two tring of three main dipole, and end with the trim quadrupole QT.QD18.R1 aociated with the defocuing quadrupole QD18.R1. The local geometrical acceptance i calculated inide each magnet a decribed above Figure 3: The geometrical aperture in the LHC cell. The element at the centre of the gure i the focuing quadrupole QF17.R1. The minimum acceptance occur in the main dipole on either ide of thi quadrupole, and for the preent table of tolerance i =:9. The geometrical acceptance of the regular cell hown in Figure 3 correpond to the et of parameter and tolerance given in Table 1 and 2. The geometrical acceptance of the cell i n 1 = :9, % below the pecication n 1 = 7:. Thi ituation wa dicued a year ago, and it wa decided [3] that the maximum diplacement x (); y () would be reduced from the preent value of 11 and 7 mm, by 1:4 mm in both plane, to meet the pecication of n 1 =7:. The improvement could be obtained by reviing 1. the thickne and mechanic of the cold bore 2. the thickne and the tolerance of the beam creen 3. the alignment tool and procedure 4. a reduction of the peak cloed orbit excurion The geometrical acceptance with thee modication i given in Figure 4. 6

7 Figure 4: The geometrical acceptance in the LHC cell with the diplacement x;y reduced by 1.4 mm. The minimum acceptance i =7:. 4 Straight ection without croing 4.1 Cleaning Inertion in IR3, IR7 The geometrical acceptance in the betatron cleaning inertion in IR7 i hown in Figure. It hould be noted that the large part of the inertion, tarting from D4L to D4R, contain only warm dipole and quadrupole (MBW and MQW). The mallet value of the acceptance i n 1 =6:73 and occur in Q6R. Although it i below the pecication of n 1 =7:, thi limitation i acceptable in a warm area, and would reult in a lightly larger lo rate if the collimator were not a coniderably deeper aperture limitation. The ituation in the momentum cleaning inertion in IR3, which ha identical layout and very imilar optic, i almot identical to that hown in Figure. 4.2 RF Inertion in IR4 The geometrical acceptance in the RF inertion in IR4 i well above the pecication, a hown in Figure 6. The acceptance of the eparator dipole D3 and D4 ha been maximized by the choice of the progreively larger axi eparation, and i above n 1 =8:even though the magnet are equipped with a beam creen. The minimum acceptance occur in QR and i n 1 =7:9. 7

8 Figure : The geometrical acceptance in the betatron cleaning inertion in IR7. The element limiting the aperture i a twin warm quadrupole Q6R where = 6: Figure 6: The geometrical aperture in the RF inertion in IR4. 8

9 Figure 7: The geometrical acceptance in IR6. The element limiting the acceptance are warm eptum MSD and the cold quadrupole Q6 and Q Dump Inertion in IR6 The geometrical acceptance in the dump inertion in IR6 i hown in Figure 7. Several dicult point may be noted. The minimum acceptance occur in the warm eptum MSD and i n 1 = :6 for a round vacuum chamber with a radiu of 23 mm. Several eriou limitation occur in the cold quadrupole, in Q6L where n 1 = 6:3, and imilarly in Q6R (n 1 = 6:4) and in Q7L (n 1 = 6:6). It mut be enviaged to either change the optic in order to reduce the -function by 2%, or to ue large aperture quadrupole and to modify the vacuum chamber in the MSD. 9

10 High Luminoity Inertion.1 Injection A mentioned in ection 2, the beam cro in the four LHC experimental inertion, and are eparated in the common part of the ring. The eparation i dened in term of the croing angle and the tranvere eparation of the beam at the interaction point, and i generated by kicker located on either ide of the croing point. A long a the eparation kicker are beyond Q3, the diplacement in the inner triplet doe not depend on their exact location, and i to a large degree determined only by the croing angle. For the purpoe of the preent tudy the eparation kicker are aumed to be located next to Q4 and Q facing the IP, on both ide of the experimental inertion. Thi poition of the eparation kicker i the natural choice if independent control of the two beam i required, ince it limit to Q4 and D2 the region of the matching ection where the beam are diplaced. Moving the kicker cloer to the diperion uppreor would increae the number of magnet aected by diplaced orbit. However, in term of kicker force, thi cheme i far from optimal, ince it require kicker trength about two time higher than that of the MCBY corrector. Typical orbit diplacement in IR1 i hown for the injection optic in Figure 8. The parameter of the croing are: croing angle per beam 17 rad (full croing angle of 3 rad), 2. mm half beam eparation (full eparation between the two beam mm), and 9 deg. croing plane rotation angle (vertical croing). A can be een, the orbit i diplaced vertically by a much a 8 mm in Q4R, and horizontally by about 12 mm in D2R. 2 x_ep y_ep x_ep_tot y_ep_tot Separation [mm] [m] Figure 8: Beam trajectory in Ring 1 of IR1 correponding to the croing angle of 17 rad per beam, 2. mm half beam eparation at the IP, and croing plane rotation of 9 deg. The inertion i tuned to the injection of 18 m.

11 2 eparation in igma eparation in mm Separation [m] Figure 9: Phyical and normalized beam eparation (in mm and unit of, rep.) in IR1 region from D1R-D1L. (Vertical croing, 17 rad per beam, 2. mm half beam eparation at the IP). The inertion i tuned to the injection of 18 m. The eparation of the two beam in the common part of the inertion i hown for the above croing parameter in Figure 9. Alo hown i the normalized eparation n (), i.e. the phyical eparation normalized with repect to the larger of x or y. In thi particular cae, the 2. mm half beam eparation at the IP wa choen o that the minimum beam eparation n b occur inide the inner triplet, and i The dicontinuity of the normalized eparation in Q3 i due to the fact that x and y change magnitude, and the maximum of the two tranvere beam ize i ued for normalization. The geometrical acceptance in IR1 at injection i hown in Figure. The mallet value of the acceptance i n 1 =3: in Q4R (cold bore mm), which i clearly unacceptable, and reult from the combination of large vertical orbit diplacement and a y of 23 m in thi quadrupole. Elewhere in the matching ection the acceptance i above the pecication. The acceptance in Q4 i around n 1 =3: irrepective of the croing plane rotation angle, and could be improved either by reducing the injection (to 12 m a in IR2, ection 6), by diplacing the eparation kicker, or by introducing large aperture quadrupole at thi location. From Figure, the acceptance of the low- triplet i n 1 = 8:9. Thi reult aume reduced cold bore aperture of the low- quadrupole correponding, a explained in the next ection, to the requirement of radiation protection of the triplet in colliion. An intereting ituation occur in the front aborber TAS (hown in Figure 8- a the rt element of the triplet looking from the IP), whoe aperture ha been increaed from the \Yellow Book" value of 28 mm to 34 mm in order to improve it acceptance at injection to n 1 = 6:. In colliion, Figure 13, the aborber i not limiting the acceptance of the inner triplet. 11

12 Figure : The geometrical acceptance in IR1 for injection optic. (Vertical croing, 17 rad per beam, 2. mm half beam eparation at the IP). Figure 11: The minimum beam eparation nb and the geometrical acceptance in the IR1 low- triplet at injection a function of the croing angle. (Vertical croing, 2. mm half beam eparation at the IP). 12

13 In order to determine the range of croing angle available at injection, the geometrical acceptance of the low- quadrupole in IR1 i plotted in Figure 11 a function of the croing angle. Alo hown in thi gure i the minimum beam eparation n b in the inner triplet. With repect to the pecication of n 1 = 7:, the maximum croing angle in IR1 i very cloe to rad. The correponding value of the minimum beam eparation i n b = 16:6. On the other hand, in order for n b to be larger than, a croing angle greater than 26 rad i required. Baed on thee criteria, the allowed range of croing angle in IR1 extend from 26 to rad..2 Colliion The nominal in the high luminoity inertion at colliion i. m, and the beam collide with a croing angle of rad per beam. Obviouly, the acceptance limit in IR1 occur in the low- triplet, where the function reache 4 m. The beam eparation in the common part of the inertion i hown in Figure 12, and the geometrical acceptance in the inertion in Figure eparation in igma eparation in mm Separation [m] Figure 12: Beam eparation in IR1 from D1R-D1L for beam colliding in the vertical plane with an angle of rad per beam. The colliion i. m. In view of improving the protection of the triplet againt high econdary beam ux, the cold bore aperture aumed in thee calculation ha been reduced from the nominal value of 63 mm to 46 mm for Q1, and to 6 mm for Q2 and Q3 (MQX1, MQX2 and MQX3 in Table 2). A a reult, the geometrical acceptance of Q1-Q3 in colliion ha become almot identical in all magnet, but reduced with repect to the maximal acceptance of the 7 mm low- quadrupole. It i neverthele ucient for the nominal colliion parameter ince n 1 = 8:. 13

14 Calculation of the energy depoition in the quadrupole coil auming thee value of the cold bore aperture [4], indicate that the peak azimuthal energy denity in the quadrupole i within the required afety margin, even though the aperture of the front aborber ha been increaed to 34 mm, a neceary for injection in IR Figure 13: The geometrical acceptance in IR1 for colliion optic. (Vertical croing, rad per beam). The colliion i. m. The geometrical acceptance of the inner triplet and the minimum beam eparation are hown a function of the croing angle in Figure 14. With repect to the acceptance pecication of n 1 = 7:, the maximum allowed croing angle in colliion i 3 rad. For thee condition, the beam eparation inide the triplet i n b =7.2, and increae to 8.4 for a croing angle of 3 rad, for which the acceptance of the triplet i till acceptable. If the eparation of the colliding beam in the triplet would need to be till larger, the iue of the thickne of the cold bore wall would need to be reviewed. 14

15 Figure 14: The minimum beam eparation nb and the geometrical acceptance in the low- triplet of IR1 at colliion a function of the croing angle. 6 Experimental Inertion Combined with Injection The LHC injection inertion in IR2 and IR8 feature imilar layout of the inner triplet a in IR1. The matching ection, however, i modied due to the preence of injection element. In particular, the injection kicker MKI i located in between Q4 and Q quadrupole, which implie that both magnet mut have wider aperture than elewhere. For thi reaon, 7 mm aperture quadrupole are foreeen, but the acceptance of thee quadrupole may not be ucient if the croing orbit i not cloed before Q. Therefore, we conider the ame layout of the eparation kicker a in IR1, i.e. a et of horizontal/vertical kicker next to Q4 and Q. In addition, the preence of the injection kicker cloe to the eparation dipole D2 require that the acceptance of the Q4-D2 aembly be conidered alo for the cae of eventual kicker mire. Two ituation are identied: a) premature ring of the kicker which deviate the circulating orbit (tandard econdary halo of Figure 1) out of the ring, and b) abence of kicker action on the injected beam (round beam halo) which may crape the neighbouring element. The beam eparation in the common part of IR2 i hown in Figure for the injection optic ( =12 m), and for the following et of croing parameter: croing angle 17 rad per beam, 2 mm half beam eparation, and vertical croing plane. With repect to beam eparation in IR1, Figure 9, it can be oberved that the optical function, and therefore beam eparation, are not ymmetric around the IP. Thi i due to the fact that the requirement of round beam at the IP ha been relaxed in order to maximize the phae advance between the kicker and the injection dump TDI. A a conequence, the minimum beam eparation n b =8.7 occur in the inner triplet on the injection ide, and i ubtantially le than what could be expected on the bai of a relatively large injection of 12 m. Similarly, the low- quadrupole on the MKI

16 2 eparation in igma eparation in mm Separation [m] Figure : Beam eparation in IR2 from D1R-D1L. (Vertical croing, 17 rad per beam, 2 mm half beam eparation at the IP). The inertion i tuned to an injection of 12 m ide determine the geometrical acceptance of the triplet, a can be een in Figure 16, where the geometrical acceptance of IR2 i hown at injection. The geometrical acceptance in IR2 for the circulating beam, Figure 16, atie the peci- cation everywhere. The minimum occur in Q4R, n 1 =7., in marked contrat to IR1, which ha an identical eparation kicker layout. The dierence can be traced to the lower, which reult in maller orbit diplacement in the Q4-D2 ection for equal croing parameter, and to the lower -function in the matching ection, which in IR2 are below m in both plane. The acceptance of MSI i n 1 =7.26, and of MKI n 1 =7.22 for the tolerance and vacuum chamber parameter of Table 2. The minimum beam eparation and the geometrical acceptance of the inner triplet in IR2 are hown a function of the croing angle in Figure 17. A mentioned above, due to the aymmetric -function the dierence between the acceptance and beam eparation in the left and right triplet i of the order of one igma. A a conequence, in order to have n b =, a croing angle of 4 rad i required, while the acceptance of the inner triplet (injection ide) fulll the n 1 =7 pecication at 44 rad. The range of allowed croing angle in IR2 i therefore ubtantially maller than in IR1, largely due to the aymmetric optical function in the inner triplet. The geometrical acceptance for the two cae of kicker miring mentioned above are hown in Figure 18 and 19. In Figure 18, the injected round beam i aumed to pa through QL and MKI, and to continue without deviation through Q4L and D2L. Note alo the poition of the eparation kicker MCBY, located next to QL and Q4L, with a lightly larger aperture of 72 mm. The minimum acceptance for the round injected beam i 6.8 at the Q end of 16

17 Figure 16: The geometrical acceptance for the circulating beam in IR2 at injection. (Vertical croing plane, 17 rad per beam, half beam eparation at the IP of 2 mm.) Figure 17: The minimum beam eparation nb and the geometrical acceptance in IR2 the low- triplet at injection a function of the croing angle. (Vertical croing, 2 mm half beam eparation at the IP. 17

18 Figure 18: The geometrical acceptance in IR2 from Q-D2 for the cae of injected beam (round beam halo). (Vertical croing plane, 17 rad per beam, half beam eparation at the IP of 2 mm.) MKI. The acceptance for the mikicked circulating beam, Figure 19, i maller in all magnet and i minimum at the IP end of MKI, n 1 =4., while it i 7.2 in Q4L and 7.3 in D2L. Thi ituation indicate that it would be highly adviable to cloe the orbit before the kicker, ince in that cae the acceptance of the MKI would atify the pecication for all three ituation. The vertical croing (-9 deg. rotation angle) aumed in the previou gure give the larget acceptance in IR2 for all cae conidered. Thi i a conequence of the vertical injection plane, with a negative MKI kick. For croing plane rotation larger than -9 deg., the acceptance in the Q4L and D2L (and even more o in the MKI) i reduced coniderably both for the injected and mikicked beam, a hown in Figure 2, where the acceptance in Q4L, which i lightly maller than in D2L, i hown. Beide the rotation angle, the poition of the beam at the IP (above or below the croing plane, a indicated by 2 mm half beam eparation) play a very important role. For the croing angle of 3 rad, and the aumed poition of the eparation kicker, the horizontal croing in IR2 i not feaible becaue of very low acceptance in the Q4L and D2L, both for injected and mikicked beam. In LHC Verion., IR2 i tuned in colliion to a high- optic with a of 2 m. The peak value of the -function do not occur in the inner triplet, but rather in Q, where they are around 37 m. The geometrical acceptance of the inertion i hown for colliion croing angle of 2 rad in Figure 21. The minimum n 1 i 8.64 in the MKI. The acceptance of the triplet in the low- optic will be tudied when it become available. 18

19 Figure 19: The geometrical acceptance in IR2 from MKI-D2L for the cae of mikicked circulating beam. (Vertical croing plane, 17 rad per beam, half beam eparation at the IP of 2 mm.) The minimim acceptence (=6.7) occur in the IP ide of MKI. Figure 2: The geometrical acceptance in Q4L of IP2 a function of croing plane rotation for the injected and mikicked beam and half beam eparation of 2 mm at the IP. (Croing angle 17 rad per beam). 19

20 Figure 21: The geometrical acceptance in IR2 for colliion optic. (Vertical croing, rad per beam). The colliion i 2 m. 7 Concluion In thi report, we have preented the geometrical acceptance in LHC Verion.. The algorithm previouly ued to compute the geometrical acceptance of the LHC arc have been improved, and extended to treat all the magnet in the ring. The previouly noted acceptance limitation in the LHC arc remain in Verion., and the improvement in the tolerance budget and reduction of the peak cloed orbit error have already been identied a poible remedie. In the machine inertion, eriou dicultie are encountered in the dump inertion in IR6, where both the extraction kicker and the cold quadrupole have unacceptably mall acceptance. In the cleaning inertion, the acceptance of the warm magnet i lightly below the pecication, but neverthele acceptable. The acceptance in the RF inertion i very comfortable, well above the ret of the ring. A tudy of the croing beam in the low- triplet in the experimental inertion indicate that there exit a range of croing angle at injection which atie both the beam eparation requirement and the pecication for the geometrical acceptance in the common ection of the machine. The range i from 26 rad to rad in IR1, and from 4 rad to 44 rad in IR2, reduced by the fact that in the injection inertion the -function are aymmetric around the IP. In IR1, it i propoed that the cold bore aperture of the low- quadrupole i reduced by 3 mm with repect to the tandard cold bore (63 mm) of a 7 mm low- quadrupole in order to improve the inner triplet protection, while preerving it acceptance within pecication. The range of croing angle at colliion i then from 2 rad to 3 rad. In the injection inertion, the acceptance of the matching ection need to be determined alo in cae of injection kicker failure. It ha been hown that a uitable olution in IR2 exit 2

21 in cae of a vertical croing plane. For other croing plane rotation, the acceptance i reduced either for the injected beam or for the mikicked circulating beam, and i unacceptably low for le than 4 degree. No attempt ha been made to optimie the parameter of the eparation kicker. We have noted, however, that the range of croing parameter that are compatible with the acceptance of the experimental inertion depend trongly on the injection optic and the exact poition of the kicker, and require extenive tudie if full exibility i required. Acknowledgement We thank O.Bruening, W.Chou, J.Mile, N. Mokhov, J.P.Koutchouk and E.Weie for their collaboration. Reference [1] J.B. Jeanneret and T.Rielada, LHC project note 66, September [2] D. Kaltchev et al., PAC'97 Vancouver and LHC Project Report, to be iued. [3] Minute of the 9th meeting of the Parameter & Layout Committee, P.Lefevre, revied verion, 4th September [4] N. Mokhov, private communication, July