1. E. Todesco, Milano Bicocca January-February 2016 Unit 2 Magnets for circular accelerators: the interaction regions Ezio Todesco European Organization for Nuclear Research (CERN)

2. E. Todesco, Milano Bicocca January-February 2016 1. Equation for luminosity 2. Detector magnets 3. The interaction regions: low-beta magnet specifications How to squeeze the beam Gradient and aperture requirements for low-beta quadrupoles CONTENTS Unit 2 –2

3. E. Todesco, Milano Bicocca January-February 2016 1. LUMINOSITY After the energy, the luminosity is the other main characteristic of an accelerator Related to the quantity of collisions per second The property of the accelerator is the rate of collisions divided by the cross section: this is the luminosity L Expressed in cm -2 s -1 (CGS units) Luminosity multiplied by the cross section gives the rate of collisions Cross-sections usually given in barn 1 barn = 10 -28 m 2 = 10 -24 cm 2 Order of magnitudes for LHC Luminosity 10 34 cm -2 s -1 Cross-section 100 mbarn, 1 billion events per second Unit 2 –3 This is not a barn

4. E. Todesco, Milano Bicocca January-February 2016 1. LUMINOSITY Equation for the luminosity Accelerator features Energy of the machine 7 TeV Length of the machine 27 km Beam intensity features N b Number of particles per bunch 1.15  10 11 n b Number of bunches ~2808 Beam geometry features  n Size of the beam from injectors: 3.75 mm mrad  * Squeeze of the beam in IP (LHC optics): 55 cm F: geometry reduction factor: 0.84 Nominal luminosity: 10 34 cm -2 s -1 (considered very challenging in the 90’s, pushed up to compete with SSC) Unit 2 –4

5. E. Todesco, Milano Bicocca January-February 2016 1. LUMINOSITY Equation for the luminosity We will outline some of the luminosity limits Beam beam (limit on N b /  n ) Parasitic beam-beam and the crossing angle Electron cloud (limit on n b ) Squeeze (limit on  *  n ) Injectors (limit on N b, n b,  n ) Unit 2 –5

6. E. Todesco, Milano Bicocca January-February 2016 1. LUMINOSITY 1: the beam-beam limit (Coulomb) N b Number of particles per bunch  n transverse size of beam One cannot put too many particles in a “small space” (brightness) Otherwise the Coulomb interaction seen by a single particle when collides against the other bunch creates instabilities (tune-shift) This is an empirical limit, of the order of 0.01 Very low nonlinearities  larger limits LHC behaves better than expected – boost to 50 ns operation in RunI Unit 2 –6

7. E. Todesco, Milano Bicocca January-February 2016 1. LUMINOSITY 2: the parasitic beam-beam and crossing angle One has to open a crossing angle to avoid collisions inside the detector – this sets a limit to the increase for small  * Parasitic beam beam is the Coulomb interaction between non colliding bunches that are separated through the crossing angle Unit 2 –7 Layout around the detectors ATLAS and CMS in the LHC

8. E. Todesco, Milano Bicocca January-February 2016 1. LUMINOSITY 2: the parasitic beam-beam and crossing angle One has to open a crossing angle to avoid collisions inside the detector, but not at the centre – this sets a limit to the increase for small  * One can prove that in a free space beta function is quadratic in s, so beam size is shrinking linearly to the interaction point The non orthogonal collision gives a luminosity loss F F is the geometric reduction factor due to the crossing angle  Unit 2 –8  Detail of beam crossing in the detectors with non zero crossing angle

9. E. Todesco, Milano Bicocca January-February 2016 1. LUMINOSITY F is the geometric reduction factor due to the crossing angle The beam size is inverse proportional to  * Crossing angle has to be proportional to LHC example, crossing angle of 180  rad for a  * of 80 cm So for very small  * the geometric reduction factor compensates for the luminosity increase due to 1/  * Unit 2 –9

10. E. Todesco, Milano Bicocca January-February 2016 1. LUMINOSITY LHC case  *=55 cm, F=0.86 Unit 2 –10

11. E. Todesco, Milano Bicocca January-February 2016 1. LUMINOSITY 3: the electron cloud This is related to the extraction of electrons in the vacuum chamber from the beam A critical parameter is the spacing of the bunches: smaller spacing larger electron cloud – threshold effect So this effect pushes for 50 ns w.r.t. 25 ns Spacing (length)  spacing (time)  number of bunches n b 7.5 m  25 ns  3560 free bunches (2808 used) Mechanism of electron cloud formation [F. Ruggiero] Unit 2 –11

12. E. Todesco, Milano Bicocca January-February 2016 1. LUMINOSITY Electron cloud in the LHC has been observed where expected in RunI during 50 ns ramp up Was cured by scrubbing of surface with intense beam In runI we operated in a reliable way with 1300 bunches at 50 ns In LHC RunII we used 25 ns After initial run at 50 ns, scrubbing has just finished and ramp up of bunch number reached 2500 Scrubbing run effective, but many instabilities -50 ns looks much easier Reduction of beam losses during the scrubbing run [G. Rumolo, et al., LMC August 2015] Unit 2 –12

13. E. Todesco, Milano Bicocca January-February 2016 1. LUMINOSITY 4: optics: squeezing the beam Size of the beam in a magnetic lattice Luminosity is inverse prop to  and  * In the free path (no accelerator magnets) around the experiment, the  * has a nasty dependence with s distance to IP The limit to the squeeze is the magnet aperture Key word for reducing  *: not stronger magnets but larger Unit 2 –13

14. E. Todesco, Milano Bicocca January-February 2016 1. LUMINOSITY Optics: squeezing the beam Size of the beam in a magnetic lattice LHC was designed to reach  * = 50 cm with 70 mm aperture IR quads This aperture had no margin - when beam screen was added, one had to lower the target  * = 55 cm (and recover L=10 34 cm -2 s -1 by slightly increasing bunch intensity from 10 11 to 1.15  10 11 ) In RunI, less energy  larger beam  higher  * But lower emittance, so at the end we manage to run at 60 cm In RunII, we started at 80 cm 40 cm is the target for 2016 Unit 2 –14

15. E. Todesco, Milano Bicocca January-February 2016 1. LUMINOSITY The injector chain limits Emittance  n vs intensity N b This relation also depends on the bunch spacing n b 50 ns allow larger intensities and smaller emittances Pushing up these limits is the aim of the injector upgrade Limits imposed by the injectors to the LHC beam [R. Garoby, IPAC 2012] PSB space charge limit with Linac2 2012 PSB space charge limit with Linac2 nominal Unit 2 –15

16. E. Todesco, Milano Bicocca January-February 2016 1. LUMINOSITY In RunI, we reached at 4 TeV 70% of nominal luminosity at 50 ns operation In 2015, we reached at 6.5 TeV 20% of nominal luminosity at 50 ns operation We did not push more the number of bunches to go for 25 ns operation Today (August 25, 2015) we are in the middle of the ramp up of number of bunches at 25 ns operation, 10% of nominal reached For the moment, no bottlenecks in magnet operation due to 6.5 TeV Unit 2 –16

17. E. Todesco, Milano Bicocca January-February 2016 1. Equation for luminosity 2. Detector magnets 3. The interaction regions: low-beta magnet specifications How to squeeze the beam Gradient and aperture requirements for low-beta quadrupoles CONTENTS Unit 2 –17

18. E. Todesco, Milano Bicocca January-February 2016 E. Todesco - Superconducting magnets 18 2. THE INTERACTION REGIONS: DETECTORS The toroidal coils of ATLAS experiment The beam is small … why are detectors so large ?

19. E. Todesco, Milano Bicocca January-February 2016 E. Todesco - Superconducting magnets 19 2. THE INTERACTION REGIONS: DETECTORS Detector magnets provide a field to bend the particles generated by collisions (not the particles of the beam !) The measurement of the bending radius gives an estimate of the charge and energy of the particle Different lay-outs A solenoid providing a field parallel to the beam direction (example: LHC CMS, LEP ALEPH, Tevatron CDF) Field lines perpendicular to (x,y) A series of toroidal coils to provide a circular field around the beam (example: LHC ATLAS) Field lines of circular shape in the (x,y) plane Sketch of a detector based on a solenoid Sketch of the CMS detector in the LHC

20. E. Todesco, Milano Bicocca January-February 2016 E. Todesco - Superconducting magnets 20 2. THE INTERACTION REGIONS: DETECTORS The solenoid of CMS experiment

21. E. Todesco, Milano Bicocca January-February 2016 E. Todesco - Superconducting magnets 21 2. THE INTERACTION REGIONS: DETECTORS Detector transverse size The particle is bent with a curvature radius B is the field in the detector magnet R t is the transverse radius of the detector magnet The precision in the measurements is related to the parameter b A bit of trigonometry gives The magnetic field is limited by the technology If we double the energy of the machine, keeping the same magnetic field, we must make a 1.4 times larger detector …

22. E. Todesco, Milano Bicocca January-February 2016 E. Todesco - Superconducting magnets 22 2. THE INTERACTION REGIONS: DETECTORS Detector transverse size B is the field in the detector magnet R t is the transverse radius of the detector magnet The precision in the measurements is  1/ b Examples LEP ALEPH: E =100 GeV, B =1.5 T, R l =6.5 m, R t =2.65 m, b =16 mm that ’ s why we need sizes of meters and not centimeters ! The magnetic field is limited by technology But fields are not so high as for accelerator dipoles (4T instead of 8 T) Note that the precision with BR t 2 – better large than high field … Detector longitudinal size several issues are involved – not easy to give simple scaling laws

23. E. Todesco, Milano Bicocca January-February 2016 1. Equation for luminosity 2. Detector magnets 3. The interaction regions: low-beta magnet specifications How to squeeze the beam Gradient and aperture requirements for low-beta quadrupoles CONTENTS Unit 2 –23

24. E. Todesco, Milano Bicocca January-February 2016 We are now in the straight sections of the machine There are no dipoles Only quadrupoles to keep the beam focused In the middle of the straight section one has a free space for the experiment, with the interaction point (IP) where beams collide Around the experiment the optics must keep two distinct aims Keep the beam focused Reduce the size of the beam in the interaction point (IP) to increase the rate of collisions (luminosity)  reduce  3. THE INTERACTION REGIONS: LOW-BETA MAGNET SPECIFICATIONS Unit 2 –24

25. E. Todesco, Milano Bicocca January-February 2016 A system of quadrupoles is used to reach a very low beta function, called  *, in the IP (LHC: 0.55 m instead of the 30-200 m in the arcs) Physical constraint: empty space around the IP – distance of the first magnet to the IP, called l *, (LHC: 23 m) – needed for the detectors ! 3. THE INTERACTION REGIONS: LOW-BETA MAGNET SPECIFICATIONS The lay-out of quadrupoles close to the interaction point in the LHC, and the beta functions Unit 2 –25

26. E. Todesco, Milano Bicocca January-February 2016 Drawback: beta function gets huge in the quadrupoles ! But this happens only in collision, where the beam is smaller In free space around IP ( s =0), one has At the entrance of the triplet one has And the beta function grows by a factor r within the triplet, depending on its length With approximately a =3.6 For instance in the LHC l t =25 m, l * =23 m,  m =4400 m, about 4.5 times larger than 3. THE INTERACTION REGIONS: LOW-BETA MAGNET SPECIFICATIONS Unit 2 –26

27. E. Todesco, Milano Bicocca January-February 2016 Second element: the integrated gradient of the triplet Triplet is like an optical system, where the strength is the inverse of the focal length One can take the focal length as the distance of the triplet midpoint to the IP Third element: magnet technology The quadrupole gradient over an aperture  is limited by the maximum field B m imposed by the technology About 2 T for resistive, 8 T for Nb-Ti, 12 T for Nb 3 Sn Longer triplet  smaller gradient  larger aperture But the longer triplet gives a larger beta function One can prove that the larger beta function is more than compensated by the larger aperture, and that for a given technology one can reach smaller and smaller  * by making the triplet longer and longer 3. THE INTERACTION REGIONS: LOW-BETA MAGNET SPECIFICATIONS Unit 2 –27

28. E. Todesco, Milano Bicocca January-February 2016 Example: the LHC interaction regions Baseline: Nb-Ti quadrupoles, 200 T/m, 70 mm aperture,  * =0.55 m First target: Nb 3 Sn quadrupoles, 200 T/m, 90 mm aperture,  * =0.25 m Present target: Nb 3 Sn quadrupoles, 132 T/m, 150 mm aperture,  * =0.15 m 3. THE INTERACTION REGIONS: LOW-BETA MAGNET SPECIFICATIONS LHC Nb-Ti triplet First LHC upgrade target HL LHC Nb 3 Sn triplet Unit 2 –28

29. E. Todesco, Milano Bicocca January-February 2016 We gave the principles of a synchrotron The problem is not only accelerating …but also keeping on a circle ! Magnets are needed for keeping particle on the orbit Arcs: dipoles for bending and quadrupoles for focusing How to determine apertures, fields and gradients Input: machine energy and beam emittance (injectors) Free parameter: cell length Output: dipole field, quadrupole gradient, magnet lengths and numbers (i.e. machine length, excluding IR regions) Interaction regions How to squeeze the beam size Determination of the aperture, gradient and length of the IR quads SUMMARY Unit 2 –29

30. E. Todesco, Milano Bicocca January-February 2016 During the next days: How these technological limits are determined ? What is the physics and the engineering behind? COMING SOON Unit 2 –30

31. E. Todesco, Milano Bicocca January-February 2016 Unit 5: Field harmonics – 5.31 QUESTIONS How to express the magnetic field shape and uniformity The magnetic field is a continuous, vectorial quantity Can we express it, and its shape, using a finite number of coefficients ? Yes: field harmonics But not everywhere … We are talking about electromagnets: What is the field we can get from a current line ? The Biot-Savart law ! What are the components of the magnetic field shape ? What are the beam dynamics requirements ? 41° 49’ 55” N – 88 ° 15’ 07” W 40° 53’ 02” N – 72 ° 52’ 32” W