Burnod, L

Jeanneret, J B

Trenkler, T

CERN Document Server

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH CERN - SL DIVISION SL/Note 93-45 (EA) THE OPTICS AND LAYOUT OF THE CLEANING INSERTION OF LHC FOR A BETATRON-MOMENTUM COLLIMATION SYSTEM T. Trenkler, L. Burned, J.B. Jeanneret ABSTRACT We present a possible layout with corresponding optics for the central part of the cleaning insertion of LHC. We summarize constraints defined elsewhere [1,2,3] leading to a good collimation system for combined betatron-momentum collimation. These constraints link a possible layout to its optics in a unique way if one demands in addition that the twiss parameters at the entrance of the central part (downstream end of Q1) excluding dispersion are comparable to those of the pink book optics. Thus we hope that it should be possible to match this optics to the arcs. (SL I EA I Notes. '93) Geneva, Switzerland 11May,1993 - 1 -1. INTRODUCTION We discuss the impact of a combined betatron and momentum collimation system for the LHC on the layout and optics of its cleaning insertion. This is done by stating constraints defined by an efficient collimation system. We show how these constraints link a possible layout in a unique way to an optics of the central part of the cleaning insertion of the LHC. A possible solution for a layout and corresponding optics is presented. It remains to match this optics to the arcs. 2. BETATRON COLLIMATION The need of a two stage collimation system in coast at h\gh energy with a primary collimator located at a distance of 6cr from the beam axis and secondary collimators further retracted is discussed in detail by the authors of [l]. At injection,the primary colimator shall be placed between 6cr and 7cr to accomodate for injection errors. However, after damping of the injection oscillations ( a gain of approximately 2cr in transverse amplitude) a distance of Scr will be chosen, necessary during the process of elimination of the RF-uncaptured particles [4]. Obviously, the potential fluctuations around the optimal values of the numerous injection parameters makes it necessary to also use the secondary collimators during the whole of the injection process. We assume that a retraction of lcr is realistic thus positioning the secondary collimators at a distance of 7cr from the beam axis at high energy. As also shown in [1] they must longitudinally be placed at phase advances of 30° and 150° with respect to the primary collimator if one considers only one dimensional motion. Two dimensional betatron collimation requires two changes [2]: • Circular collimators being approximated by a set of planar jaws mounted as an octagon. • An additional secondary collimator at 90° phase advance mainly to trap particles scattered into the plane orthogonal to their plane of motion. 3. MOMENTUM COLLIMATION Particles with a too big momentum deviation from the nominal momentum might be lost somewhere in the machine where dispersion is high. The mechanism of momentum losses and a detailed quantification of them is given in [5]. To run the machine safely these particles must be intercepted by the primary collimator before touching the vacuum tube. - 2 -Thus we need a certain value of dispersion at the primary collimator. We fix its value in the following way: A particle with zero transverse emittance touches the primary collimator when the condition (1) holds, where nl is the distance of the primary collimator from the beam axis measured in units of cr. As collimators will be placed on both sides of the beam we do not have to care about signs in equation (1) and assume that all values are positive. To insure that this particle will not be lost earlier in the arcs at locations of maximum dispersion one has to demand ~p - Dmax <A Pi where Dmax is the maximum Dispersion and A the aperture at its location. Extracting ~p/p I 1 from (1) yields (2) (3) Due to synchrotron motion particles on stable trajectories will move inside the bucket. Such particles should not be intercepted by the primary collimator. Assume a particle with ~p/p=~p/p I buck being the half bucket height and betatron amplitude of ncr. The condition for not touching the primary collimator is: (4) If one allows the collimator to cut at approximately n = nl-1 conditions (3) and (4) yield: (5) The limits for Dl defined in (5) must be evaluated at the extreme energies, i.e. top- and injection energies, to cover the whole energy range. We use the values: - 3 -Dmax = 2m, A= 15.3mm = (20mm aperture - 4.7mm errors of any kind), En= 3.75mm mrad; In section 5 we show that ~l = 200m is a realistic value for ~ at the primary collimator. • injection (450GeV) =>al= l.25mm, nl = 5, ~p/p I buck= 1.3· 10-3 (5) => 0.82m < Dl < 0.96m (5.1) • top energy (7.3TeV) =>al= 0.3lmm, nl = 6, ~p/p I buck= 3.6· 10-4 (5) => 0.24m < Dl < 0.86m (5.2) As for beam cleaning it is very desirable to work with the same optics over the whole energy (5.1) and (5.2) determine the narrow interval 0.82m < 01 < 0.86m (6) allowed for the value of dispersion. • • One must stress that a certain degree of violation of (6) is no problem. The probability that zero emitance particles will reach the aperture in the arcs is very small as non-linearities of any kind will always increase the transverse emitance when ~p/p is large as discussed in [5]. Fixing n of (4) to nl-1 was somewhat arbitrary. We could have chosen n = nl-1.5. Then 0.82m < Dl < l .3m, (6.1) leaving quite a comfortable margin. 4. COMBINED BETATRON-MOMENTUM COLLIMATION The average particle will have a certain excursion due to betatron motion and due to dispersion at the location of the primary collimator. If it touches the primary collimator without doing an inelastic interaction it will be scattered out again with a certain angle b' added to its divergence. The purpose of the secondary collimators is to trap such particles. As for the betatronic case [1] one can give a formula for the angle b'min defined such that all particles receiving a kick b' with bigger absolute value than the one of - 4 -b'min will be intercepted by a secondary collimator located at a phase advance ~µwhile all other particles will pass this collimator. (7) Formula (7) derived in [3] contains the twiss parameters at the location of the primary (index=l) and at the location of the secondary collimators (index=2) and the distance of them to the beam axis measured in units of a (nl,n2), while it is completely independent of the optics which lies between the collimators. How to define the optimum collimation system by making I b'min I as small as possible for all ~p/p is described in dt.~tail in [3]. The resulting conditions on the optics of the collimation system are quite complicated (formula (28) of [3]). Relaxing a bit on the efficiency one can define much simpler conditions, by making b'min (instead of its derivative with respect to the phase advance) independent of ~p/p. From (7) we get the condition (8) which has also been mentioned in [3]. One obtains small I b'min I in the whole range of ~p/p by choosing the optimum phase advances for the betatronic case (30°, 90° and 150°). Thus we obtain a collimation system which has equal efficiencies for every ~p/p and which is optimised for the betatronic case. How far (8) may be violated to still garantee a good collimation system will be discussed in a different note. - 5 -5. LAYOUT AND OPTICS 02 02 02 02 C2 ~-~\jf=30° __J ~---- ~\jf=90° ----Pi - -02 02 02 02 i..-.-------- ~\jf=l50° ---------~ 118.99m Fig. 1 Schematic layout for the central part of the collimation system of LHC Fig. 1 shows a possible layout for the central part of the collimation system. This layout and the corresponding optics (Table 1) are defined by the following constraints: a) The optics must be symmetric with respect to the IP as both beams need the same optical conditions. b) No super-conducting magnets are allowed to lie in this central region where one has to deal with high levels of energy deposition and radiation. c) A certain magnetic length of warm dipoles must lie downstream of the 150° collimators of each beam to sweep out secondary particles induced by inelastic interactions in the collimator jaws. We have chosen a magnet of approximately 1.8T and 6m length. Crude calculations indicate that this magnetic length will be of the right order of magnitude while a proof will only be given by quite detailed studies. - 6 -d) The recombination magnets D2 must separate the beams horizontally to the arc value of 180mm. This requirement defines the need of 5 elements of D2 as defined inc) on each side of the IP. e) Due to the two dimensional concept of betatron collimation [2] the phase advances of 30° , 90° and 150° must lie at the same locations for both transverse planes and such that there is enough room to mount the collimators. An optics as simple as possible (no quadruples in the central collimation region) must thus have equal beta functions in both planes over the whole region. f) Due to several reasons one could tend to put the primary collimators between the super conducting Ql and the following element of the D2: 1) Due to the bigger distance it would be easier to establish the right phase advance between the primary and the 150° collimators. 2) One could make use of the biggest value of the beta function of the whole region to create bigger impact parameters on the primary jaws. Contradictory to these facts matching work shows that relation (8) may not be satisfied by choosing this configuration, while the symmetric approach of Fig. 1 allows to implement (8) in a very convenient way. Choosing a value for 13· at the IP in addition to the constraints defined above yields a unique solution and defines in addition the total length of the central part of the cleaning insertion. g) The beta functions at the entrance of Ql (as seen from the IP) shall not exceed a certain value, such that the maximum value of beta in the inner triplet does not exceed 630m (a value discussed in the pink book). This condition can be fulfilled by choosing a solution for which beta and alpha at the entrance of Ql are comparable to the values of the pink book optics. This condition fixes a maximum for 13· of about 13.Sm. Table 1 gives values of an optics with 13*=13.4m, D1=0.9m and the values of dispersion at the secondary collimators perfectly well matched to condition (8). It remains to further match this optics to the arcs. - 7 -NAME s ~x ax Ox D'x µx ~z az µz Dx[m] [m] [m] [1] [m] [1] [ ·1 [m] [1] [1 equ. (8) EX Ql 0.00 277.5 4.440 1.04 -0.0151 -2.307 277.5 4.440 -2.307 1.25 266.6 4.347 1.02 -0.0151 -2.044 266.6 4.347 -2.044 DI- 7.4 215.9 3.888 0.93 -0.0155 -0.575 215.9 3.888 -0.575 I a 9.48 200.0 3.732 0.90 -0.0155 0.000 200.0 3.732 0.000 0.90 11.57 184.8 3.577 0.87 -0.0155 0.621 184.8 3.577 0.621 DI- 17.72 143.6 3.118 0.77 -0.0160 2.785 143.6 3.118 2.785 18.52 138.7 3.058 0.76 -0.0160 3.110 138.7 3.058 3.110 DI- 24.67 103.9 2.599 0.66 -0.0164 6.046 103.9 2.599 6.046 25.47 99.8 2.539 0.64 -0.0164 6.496 99.8 2.539 6.496 DI- 31.62 71.4 2.080 0.54 -0.0169 10.675 71.4 2.080 10.675 32.42 68.l 2.020 0.53 -0.0169 11.333 68.l 2.020 11.333 DI- 38.57 46.1 1.562 0.42 -0.0173 17.636 46.1 1.562 17.636 I c30· 46.09 26.8 1.000 0.29 -0.0173 30.003 26.8 1.000 30.003 0.29 IP 59.49 13.4 0.000 0.06 -0.0173 75.000 13.4 0.000 75.000 I c90· 63.09 14.4 -0.268 0.00 -0.0173 90.000 14.4 -0.268 90.000 0.00 80.42 46.l -1.562 -0.30 -0.0173 132.369 46.1 -1.562 132.369 DI+ 86.57 68.1 -2.021 -0.41 -0.0169 138.671 68.1 -2.021 138.671 87.37 71.4 -2.080 -0.42 -0.0169 139.328 71.4 -2.080 139.328 DI+ 93.52 99.8 -2.539 -0.52 -0.0164 143.506 99.8 -2.539 143.506 94.32 103.9 -2.599 -0.54 -0.0164 143.956 103.9 -2.599 143.956 DI+ 100.47 138.7 -3.058 -0.64 -0.0160 146.893 138.7 -3.058 146.893 101.27 143.7 -3.118 -0.65 -0.0160 147.217 143.7 -3.118 147.217 DI+ 107.42 184.8 -3.577 -0.75 -0.0155 149.380 184.8 -3.577 149.380 I c150· 109.50 200.0 -3.732 -0.78 -0.0155 150.000 200.0 -3.732 150.000 111.59 216.0 -3.888 -0.81 -0.0155 150.576 216.0 -3.888 150.576 DI+ 117.74 266.6 -4.347 -0.91 -0.0151 152.045 266.6 -4.347 152.045 BEGQl 118.99 277.6 -4.440 -0.93 -0.0151 152.308 277.6 -4.440 152.308 Table 1: Optics corresponding to layout of Fig. 1 It is quite astonishing but satisfactory that condition (8) holds at the locations of all 3 secondary collimators while there is only one degree of freedom for matching (for example D'x at the primary collimator). The corresponding matching has also been done for the limiting values of D1 being of practical interest i.e. the limits of equ. (6.1) leading as well to satisfactory results. Although the situation is slightly different for a negative sign of D1 (due to the field of the recombination magnets) condition (8) can be fulfilled as well in this case. Thus we are convinced that (8) can be satisfied for a range of D1 being much larger than the one of practical interest at all secondary collimators. -0.78 - 8 -6. CONCLUSIONS We give a possible layout with corresponding optics for the central region of the cleaning insertion of the LHC. Further we give the constraints defined by an efficient collimation system linking a possible layout to an optics in a unique way. We further discuss, that momentum collimation does not allow layouts with primary and 150°- collimators positioned asymmetrically with respect to the IP. 7. ACKNOWLEDGEMENTS The authors had the benefit of discussions with. Y. Baconnier encouraging them to study the case of injection more precisely. 8. REFERENCES [1] L.Burnod,J.B.Jeanneret, Beam losses and collimation in the LHC: A quantitative approach, CERN SL/91-39 (EA) and LHC Note 167 [2] T.Trenkler, The Optimum Set of Circular Collimators for Global Two Stage Betatron Collimation Compared to Realistic Systems, CERN SL/93-10 (EA) and LHC Note 217 [3] T.Trenkler, The Optimum Phase Advance in a Two-Stage Collimator, CERN SL/92-50 (EA) [4] J.B. Jeanneret, Momentum losses in LHC: The special case of RF uncaptured protons at injection,CERN /SL/ Note 92-56 (EA) [S] J.B.Jeanneret, Momentum Losses and Momentum Collimation in LHC, a first Approach, CERN SL/92-44 (EA) and LHC Note 211 

The optics and layout of the cleaning insertion of LHC for a betatron-momentum collimation system

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