Minutes of the 15th LHC Insertions Upgrade Working Group held on 28 May 2008
Present: R. Assmann, O. Brüning, F. Cerutti, S. Fartoukh, P. Fessia, M.
Giovannozzi, J. Kerby, N. Kos, D. Nisbet, R. Ostojic, H. Prin, R. Thomas,
Excused: J.P. Koutchouk
Invited: M. Aiba, A. Mereghetti,
A. Morita, Y.-P. Sun, S. Feher
1. News and approval of the minutes of the last meeting
The minutes of the last meeting are approved with the correction of a typo noted by N. Kos and P. Lebrun.
2. Optics challenges and solutions for Phase-I (S. Fartoukh, ppt slides)
2a. Part I: objectives, optics and aperture.
Stephane started his presentation by recalling the objective of Phase-I which is an increase of the peak LHC luminosity by a factor of 2. The main ingredients of the upgrade are the reduction of b* to 25 cm and an increase of the nominal bunch intensity up 1.4 1011 p/bunch. A fortiori, this will allow operation of the LHC in nominal conditions with a very comfortable margin, notably in terms of the triplet aperture.
The goal of the optics studies is to reach the above targets with a sufficient aperture (n1=7), and, if possible, with some additional aperture margin in the triplet and D1 (n1=8-9). These aperture requirements must be fulfilled within a certain momentum range (ideally up to 1.5 per-mil, corresponding to the opening of the momentum collimator at 7 TeV for abort gap cleaning) in the presence of huge chromatic aberrations induced by the small b*, in particular the off-momentum beta-beating and the spurious horizontal and vertical dispersion generated by the crossing scheme in IR1 and IR5. The chromatic aberrations must also be minimized in the collimation insertions IR3 and IR7 in order to preserve the hierarchy of the primary and secondary collimators (n1 & n2) and of the tertiary absorbers (n3) in these insertions (see minutes of the LIUWG#4 for more details). A larger beam clearance would also be preferable in the LSS magnets (estimated at n1=9-10 as compared to the present n1=12-15), so as to avoid additional protection or collimation devices in this area (the estimate is based on the present TCT, which is needed to protect the triplet although it satisfies the standard aperture specification of n1=7).
Assuming a standard race-track shape of the beam-screen, aligned to the vertical and horizontal beam crossing planes of IR1 and IR5, the minimum aperture of the new triplet compatible with n1=7 and b* =25 cm is 110 (+e) mm. The aperture of the LSS can only be preserved (n1>9-10) by a substantial reduction of the co-focal length P of the triplet. This length is defined as the distance between the triplet exit and the position of the waist of the beta-function (in a given plane) assuming that there are no MS or DS quadrupoles in between (see slides for more details). The lower the P, the larger will be the mechanical acceptance in the LSS, in particular in the D2, Q4 & Q5 magnets. For a given gradient of the triplet quadrupoles, this length hardly changes for low values of b* (up to ~ 1m) but is very sensitive to the detailed layout of the triplet itself (i.e. interconnect distance, magnet lengths). In order words, this distance can be tuned to any value (e.g. down to P=L* in an extreme case) by careful design of the triplet layout or by using the trims foreseen for the triplet quadrupoles.
On the other hand, the dispersion suppressor and the matching section in their present layout may not be suitable for a small value of P. First indications in this sense are apparent for a 110 mm-136 T/m triplet (where the Q4/Q5 strength is reduced to 5-10 T/m and the Q7 strength is close to max. gradient of 200 T/m, see case Ib). Low-P optics is even harder or even impossible to obtain if the triplet gradient is reduced (see case IIb and III for a 120 mm-126 T/m and 130 mm-112 T/m triplet). However, displacement of the LSS magnets towards the arc (Q4, and eventually Q5, moved by ~ 10 m, comparable to the increase in length of the triplet) restores the matching of low-P optics with the MS and DS (as seen from a favorable LSS quadrupole strength, optical functions in the DS, and intersection between injection and collision tunability diagram). The latter are indicators of a smooth squeeze sequence (at constant phase advance over the IR), and of a solid robustness of the overall insertion to small changes in the triplet design, or errors in the longitudinal positions of the low-b quadrupoles. As a result, a reduction of P by a factor of 2, from 1 km in the nominal LHC to about 450 m, and the displacement of D2/Q4 and/or Q5 (e.g. by 16m and 10.5 m, respectively, in the case of 120 mm-126 T/m low-b quadrupoles) lead to a full preservation the IR matchability and to a further improvement of the mechanical acceptance of the LSS. The serious aperture restrictions (n1<7) in the LSS discovered a few months ago (see presentations given at the LIUWG#2 & LIUWG#3) are not only fully solved, but the target of n1=9-10 can also be reached. Furthermore, if so needed for collimation, the LSS aperture could almost be equal to the nominal value if the beam-screens in D2, Q4 and Q5 are reoriented, without any implication on the IR aperture at injection (for b* < 14 m limited by the Q6 aperture @ 450 GeV).
Finally, in all cases discussed, the normalized aperture of the TAN is found to be the bottleneck [for the nominal LHC, the tightest aperture is in the triplet (n1=7), then in the TAN (n1=12) followed by D2 and the other matching section quadrupoles (n1=12-15)]. In the worst case, the 26 mm radial aperture of the TAN results in a normalized aperture which is even smaller than the secondary collimator (for n2=7). As a consequence, if the TAN vacuum chamber is not changed, any gain in aperture in the triplet or in the LSS (for example with a 120 mm or 130 mm triplet, low-P optics, Q4/Q5 displacement or even increase of b*) will be of minimal or no use to the primary beam (for instance to open the collimator beyond their present setting n1/2=6/7 in case of intensity limitations due to impedance related reasons).
The presentation raised a number of questions and comments:
O. Bruning asked what would be the difference in the LSS matching if the triplet were non-symmetric. Stephane responded that the non-symmetric triplet does not change the matching conditions, but has a possible advantage of reducing the length of the triplet and the peak value of the beta function. He estimates these gains to be of the order of 5%, e.g. in the case of the so-called low-beta-max optics but with the worrying draw-back that the normalized Q1 aperture (with liner) will be below n1=7.
E. Todesco asked about the possibility of using quadrupoles with less than 120 T/m. Stephane responded that gradients lower than 120 T/m inevitably lead to modifications in the LSS, in particular in moving Q4 towards the arc, since the problem of aperture cannot be solved otherwise. The required displacement of Q4 is proportional to the increase in length of the triplet and is defined within a few meters. The displacement of Q5 is also necessary, but is much more relaxed. In addition, increasing the strength of Q6 may be necessary.
R. Assmann commented that the goal of achieving the aperture margin in the LSS similar to the nominal LHC (n1~12 ) may be relaxed by assuming from the start that additional protection elements will be installed.
R. Ostojic commented that the changes in the LSS have to follow certain priorities (for example: any change of Q7 and additional quadrupoles are excluded; change in operating temperature of the LSS magnets is very difficult; displacement of Q6 towards the arc is very difficult, its movement towards the IP is possible; displacements of Q4-D2 and Q5 and additional collimators can be envisaged but need detailed integration studies). Then, O. Brüning and Stephane further insisted on the fact that neither Q7 nor Q6 are concerned in the present proposals.
2b. Part II: chromatic aberrations and strategies of correction.
In the second part of his talk, Stephane reported on the very large chromatic aberrations induced by the small b*, the long-standing problem of off-momentum beta-beating and the spurious dispersion induced by the crossing scheme (in particular in the vertical plane), which affect the non-linear chromaticity (Q'', Q'''), the off-momentum aperture of the triplet, but also and mainly the collimation inefficiency of IR3 and IR7. For example, in some cases, the second order chromaticity induced by the triplet can reach 60'000 and can change the sign of the off-momentum chromaticity Q'(d) for momentum deviations as small as a few 10-5 (therefore risking a strong head-tail instability during off-momentum beam measurement in pre-collision). Even with a dedicated phasing between IR1 and IR5 (e.g. p/2 between IR1 and IR5 which kills Q'' and the first chromatic derivative of the beta-function in the half of the ring containing IR7), the third order chromaticity can reach more than 100'000'000 units, inducing a substantial tune ripple in the bunch and displacing the off-momentum tunes very close to the third order resonance for d=0.5 - 1 ×10-3. Assuming that the phase between IR1 and IR5 is chosen such to minimize the off-momentum beta-beating in the triplet and in the betatron cleaning insertion IR7, the chromatic variations of the beta-functions are maximized in IR3 and can be as large as 300% for a momentum deviation of ±1.5 10-3 (corresponding the opening of the momentum collimator jaws). Also, while the first chromatic derivative of the b-function is minimized in the triplets and in IR7, the second and higher order effects can partially spoil the compensation achieved.
The solution proposed consists in a clever use of the lattice sextupole families (2 per plane, per beam and per sector), both to compensate for the additional contribution of each triplet to the linear chromaticity (~-35 units per triplet for b*=25 cm) and to generate an off-momentum beta-beating wave which arrives with the right phase at the triplet itself. Due to strength limitations of the defocusing sextupole families SD (twice less efficient than the SFs due to a dispersions function of 1 m in the QDs compared to 2 m in the QFs), two sectors of sextupoles per triplet are needed to generate an off-momentum wave with a sufficient amplitude to counter-balance the off-momentum quadrupole kick induced by the triplet (one sector per triplet is sufficient for the nominal LHC). The main complexity is to re-phase IRs 2/4/6/8 such that the two sectors associated to each triplet (e.g. sector 34 and 45 for L5) combine in phase with the off-momentum b-beating wave that they generate. Furthermore, the overall wave must be phased to the correct value at the triplet by adjusting the arc cell phase advances of the two adjacent sectors, and of the left and right phase advances of the low-beta IR. Finally, the fractional part of the tune must be preserved by subtle detuning of the solution so obtained. As a result, the arc cell phase advances in all 8 LHC sectors and in all insertions have to be considerably modified.
Following these requirements, a new LHC phasing configuration has been proposed and a new overall LHC optics with a tune split of 3 has been re-matched (the tune split for the nominal LHC is 5). As a result, assuming that half of the 16 SD families per beam can be pushed up to the ultimate current of 600A, the off-momentum b-beating can be controlled within ±10% in a momentum range of ±1.5 10-3 both in IR3, IR7 and in LSS1/5 (i.e. including the triplets and the aperture critical magnets such as D2, Q4 and Q5). Also, the chromatic dependence of the betatron tunes can be made almost linear, easily controllable by the linear chromaticity of the machine. Finally, last but not least, while in the nominal LHC optics the correction of the vertical spurious dispersion is impossible, the proposed LHC phasing configuration now re-opens the possibility of this correction by vertical orbit bumps in the arcs. As a result, a substantial aperture margin (ranging between 3.5 and 5 mm) can be obtained in the triplet. Altogether, the aperture target defined above can be obtained over the full standard momentum window of 0.86 10-3 in collision, both in the LSS magnets and in the triplet, with a n1(d) of almost 9 in the case of 120 mm aperture triplets.
The different ingredients and new phasing concept proposed by Stephane solves all the optics issues of the Phase-I upgrade (except the TAN aperture, as described above). The overall scheme, however, is based on a new LHC injection optics with, in particular, a reduced phase split in the LHC arcs [also including a non-zero setting of the arc tune shift quadrupoles RQT, independent adjustment of the left/right phase advances of the low-b IR's and substantial modifications for the overall phase advances of IR4 and IR6 (see slides for more details)]. All these modifications have an impact on the mechanical aperture of the machine at injection (estimated reduction of 0.5 mm in the highest beta locations, which is not considered a major issue after having operated LHC for five years). The new injection optics requires full verification, in particular in terms of dynamic aperture at injection due to the reduction of the tune split by two units (taking into account the sorting of magnets at installation and their much better field quality than initially expected), but also in terms of collimation and machine protection (possibly unfortunate phase advances between distant objects in the LHC ring). If no difficulties are identified, this proposal would also be very beneficial for the performance of the nominal LHC (2 mm aperture, i.e. more than 1 sigma, margin in the present triplet by correcting the spurious dispersion and cancellation of the 30% off-momentum beta-beating in IR3 or IR7).
Finally, Stephane gave a non-exhaustive list of other studies which need to be launched (e.g. DA, beam-beam and collimation studies in collision) in order to converge quickly towards a robust and complete optics solution for the Phase-I upgrade of the LHC low-b insertions.
The presentation raised a number of questions and comments:
D. Nisbet asked why is it necessary to avoid zero-crossing of the SD families since the PC are designed to work in this regime. Stephane responded that the zero-crossing of SDs might lead to beam instabilities if the linear chromaticity cannot be controlled within 1 or 2 units during zero-crossing.
R. Ostojic asked what would be the procedure if the nominal LHC optics with a tune split of 5 was absolutely needed at injection. Stephane commented that in spite of the strict phase conditions for the new optics in all the LHC there are still possibilities to generate larger tune separations in each arc and hence create conditions similar to the nominal tune split.
E. Todesco asked what would be the changes in the proposed solutions if the LHC were operated at a different energy. Stephane responded that he expects the changes to come mostly from the beam size, but that this possibility needs to be examined in more detail.
The meeting congratulated Stephane on his presentation and on the originality of the solutions proposed, which have considerable potential for the nominal LHC and the upgrade.
3. A.O.B.
S. Fartoukh, R. Ostojic and H. Prin