The LHC Accelerator and some of its Challenges

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The LHC Accelerator and (some of) its Challenges Rüdiger Schmidt - CERN AAPT Baltimore

The LHC Accelerator and (some of) its Challenges Rüdiger Schmidt - CERN AAPT Baltimore January 2008 The LHC and the relativistic hammer thrower Acceleration and Deflection High intensity beams at very high energy The LHC accelerator complex Operation und Machine Protection R. Schmidt - AAPT 2008 Status and Outlook 1

CERN: leading European institute for Particle Physics, started 1954 with 2600 staff and 6800

CERN: leading European institute for Particle Physics, started 1954 with 2600 staff and 6800 users Close to Geneva across the French-Swiss border 20 member states, ~7 observers (e. g. USA), many others participating LEP / LHC The U. S. LHC Accelerator Research Program (LARP) is a collaboration of BNL, FNAL, LBNL, and SLAC, working with CERN to address a variety of issues. R. Schmidt - AAPT 2008 2

LHC: Energy and Luminosity l Particle physics requires an accelerator colliding beams with a

LHC: Energy and Luminosity l Particle physics requires an accelerator colliding beams with a centre-of-mass energy substantially exceeding 1 Te. V l To observe rare events, the luminosity should be in the order of 1034 [cm-2 s-1] (challenge for the LHC accelerator) l Event rate: l Nuclear and particle physics require heavy ion collisions in the LHC (quark-gluon plasma. . ) R. Schmidt - AAPT 2008 3

LEP e+e. CERN (1989 -2000) 104 Ge. V/c Tunnel with a Circumference of 26.

LEP e+e. CERN (1989 -2000) 104 Ge. V/c Tunnel with a Circumference of 26. 8 km LHC proton beams colliding in 4 points at 7 Te. V/c Ion collisions also planned accelerator complex Switzerland Lake Geneva LHC Accelerator (about 100 m underground) LHCb CMS CERN Prevessin site ALICE SPS accelerator ATLAS France CERN Main site R. Schmidt - AAPT 2008 4

LHC: From first ideas to realisation 1982 : First studies for the LHC project

LHC: From first ideas to realisation 1982 : First studies for the LHC project 1983 : Z 0 detected at SPS proton antiproton collider 1985 : Nobel Price for S. van der Meer and C. Rubbia 1989 : Start of LEP operation (Z-factory) 1994 : Approval of the LHC by the CERN Council 1996 : Final decision to start the LHC construction 1996 : LEP operation at 100 Ge. V (W-factory) 2000 : End of LEP operation and removal of LEP equipment 2003 : Start of the LHC installation 2005 : Start of hardware commissioning 2007 : Installation of superconducting magnets finished 2008 : Beam commissioning and first collisions planned R. Schmidt - AAPT 2008 5

The LHC: just another collider? Name TEVATRON Fermilab Illinois USA Start Particles Max proton

The LHC: just another collider? Name TEVATRON Fermilab Illinois USA Start Particles Max proton energy [Ge. V] 1983 p-pbar 980 Length B Field Stored beam [m] [Tesla] energy [MJoule] 6300 4. 5 1. 6 for protons HERA DESY 1992 p – e+ Hamburg p – e. Germany 920 6300 5. 5 2. 7 for protons RHIC Brookhaven Long Island USA LHC CERN Geneva Switzerland 2000 Ion-Ion p-p 250 3834 4. 3 0. 9 per proton beam 2008 Ion-Ion p-p 7000 26800 8. 3 362 per proton beam R. Schmidt - AAPT 2008 6

To accelerate protons to 7 Te. V … Acceleration of the protons in an

To accelerate protons to 7 Te. V … Acceleration of the protons in an electrical field with 7000 Billion Volt……. But: § no constant electrical field above some Million Volt (break down) § no time dependent electrical field above some 10 Million Volt Proton travel around the circular accelerator with the speed of light and are accelerated by ~1 Million Volt per turn R. Schmidt - AAPT 2008 7

…. and to keep them on the circle The relativistic hammer thrower Very strong

…. and to keep them on the circle The relativistic hammer thrower Very strong magnetic field • Magnets deflect protons and keep them on a circle • Electrical field accelerates proton and magnetic field increases R. Schmidt - AAPT 2008 8

Lorentz force on a charged particle: acceleration The force on a charged particle is

Lorentz force on a charged particle: acceleration The force on a charged particle is proportional to the charge, the electric field, and the vector product of velocity and magnetic field: z s FE • Electric field about 10 MV E v x R. Schmidt - AAPT 2008 9

Lorentz force on a charged particle: acceleration and deflection The force on a charged

Lorentz force on a charged particle: acceleration and deflection The force on a charged particle is proportional to the charge, the electric field, and the vector product of velocity and magnetic field: z s B v FB x • • • Electric field about 10 MV Momentum 7000 Ge. V/c Radius 2805 m Magnetic field B = 8. 3 Tesla Superconducting magnets required operating at 1. 9 K • Deflecting magnetic fields for two beams in opposite directions R. Schmidt - AAPT 2008 10

A total number of 1232 dipole magnets, 15 m long, are required to close

A total number of 1232 dipole magnets, 15 m long, are required to close the 26800 m long circle R. Schmidt - AAPT 2008 11

LHC dipole magnet lowered into the tunnel First cryodipole lowered on 7 March 2005

LHC dipole magnet lowered into the tunnel First cryodipole lowered on 7 March 2005 Descent of the last magnet, 26 April 2007 R. Schmidt - AAPT 2008 12

Interconnecting two magnets out of 1700 R. Schmidt - AAPT 2008 13

Interconnecting two magnets out of 1700 R. Schmidt - AAPT 2008 13

Principle of LHC dipole magnets Proton beam 1 Proton beam 2 • • Two

Principle of LHC dipole magnets Proton beam 1 Proton beam 2 • • Two beam tubes Total current per aperture in one direction about 1 MA R. Schmidt - AAPT 2008 14

16 m. Bar cooling tube Ferromagnetic iron Nonmagnetic collars Superconducting coil Beam tubes (56

16 m. Bar cooling tube Ferromagnetic iron Nonmagnetic collars Superconducting coil Beam tubes (56 mm) Steelcylinder for pressurised helium Insulationvacuum Vacuumtank Support posts Dipole magnet cross section R. Schmidt - AAPT 2008 15

R. Schmidt - AAPT 2008 16

R. Schmidt - AAPT 2008 16

Operating temperature of Nb. Ti superconductors J [k. A/mm 2] The superconducting state only

Operating temperature of Nb. Ti superconductors J [k. A/mm 2] The superconducting state only occurs in a limited domain of temperature, magnetic field and transport current density Superconducting magnets produce high field with high current density Lowering the temperature enables better usage of the superconductor, by broadening its working range LHC dipole magnets operate in helium at a temperature of 1. 9 K T [K] B [T] Outside the domain the magnet quenches – m. J are sufficient to locally heat the superconductor R. Schmidt - AAPT 2008 17

RF cavities, four per beam with some 10 MVolt R. Schmidt - AAPT 2008

RF cavities, four per beam with some 10 MVolt R. Schmidt - AAPT 2008 18

High intensity beams at very high energy R. Schmidt - AAPT 2008 19

High intensity beams at very high energy R. Schmidt - AAPT 2008 19

Luminosity parameters Experiment ~40 m in straight section (not to scale) R. Schmidt -

Luminosity parameters Experiment ~40 m in straight section (not to scale) R. Schmidt - AAPT 2008 20

Beam beam interaction determines parameters Number of protons N per bunch limited to about

Beam beam interaction determines parameters Number of protons N per bunch limited to about 1011 f = 11246 Hz Beam size at IP σ = 16 m for = 0. 5 m (beam size in arc σ = ~0. 2 mm with one bunch Nb=1 with Nb = 2808 bunches (every 25 ns one bunch) L = 1034 [cm-2 s-1] => 362 MJoule per beam R. Schmidt - AAPT 2008 21

Challenges for LHC l l l High-field (8. 3 Tesla) superconducting magnets operating at

Challenges for LHC l l l High-field (8. 3 Tesla) superconducting magnets operating at 1. 9 K with 10 GJ stored energy in the magnets Beam-parameters pushed to the extreme Energy stored in the beam two orders of magnitude above other machines GJoule beams running through superconducting magnets that quench with m. Joule Complexity of the accelerator (likely to be the most complex scientific instrument ever constructed) with ~10000 magnets powered in ~1700 electrical circuits The energy stored in one LHC beam corresponds approximately to: 90 kg TNT 8 kg gasoline 15 kg chocolate R. Schmidt - AAPT 2008 22

The LHC accelerator complex R. Schmidt - AAPT 2008 23

The LHC accelerator complex R. Schmidt - AAPT 2008 23

LHC Layout eight arcs (sectors) eight long straight section (about 700 m long) Beam

LHC Layout eight arcs (sectors) eight long straight section (about 700 m long) Beam dump blocks IR 5: CMS IR 4: RF + Beam instrumentation IR 6: Beam extraction and dump IR 3: Momentum beam cleaning (warm) IR 7: Betatron beam cleaning (warm) IR 8: LHC-B IR 2: ALICE IR 1: ATLAS Injection R. Schmidt - AAPT 2008 24

LHC transfer lines and injections - overview TI 8 beam tests 23/24. 10. 04

LHC transfer lines and injections - overview TI 8 beam tests 23/24. 10. 04 6/7. 11. 04 • combined length 5. 6 km • over 700 magnets IR 8 TT 40 • ca. 2/3 of SPS TT 40 beam tests 8. 9. 03 LSS 4 TI 8 SPS 6911 m 450 Ge. V LHC IR 2 LSS 6 TI 2 beam test 28/29. 10. 07 TI 2 R. Schmidt - AAPT 2008 25

Transfer line TI 8 (MIBT magnet) R. Schmidt - AAPT 2008 26

Transfer line TI 8 (MIBT magnet) R. Schmidt - AAPT 2008 26

ATLAS Detector R. Schmidt - AAPT 2008 27

ATLAS Detector R. Schmidt - AAPT 2008 27

Collisions in multibunch operation QF QD Interaction point Experiment distance about 100 m •

Collisions in multibunch operation QF QD Interaction point Experiment distance about 100 m • • Focusing beam to a size of 16 m High gradient quadrupole magnet triplet with large aperture (US-JAPAN) Total crossing angle of 300 rad Beam size at interaction point 16 m, in arcs about 0. 3 mm R. Schmidt - AAPT 2008 28

One of the triplets at Point 5 (CMS) R. Schmidt - AAPT 2008 29

One of the triplets at Point 5 (CMS) R. Schmidt - AAPT 2008 29

Operation and machine protection R. Schmidt - AAPT 2008 30

Operation and machine protection R. Schmidt - AAPT 2008 30

LHC magnetic cycle - beam injection coast beam dump energy ramp coast 7 Te.

LHC magnetic cycle - beam injection coast beam dump energy ramp coast 7 Te. V start of the ramp injection phase 12 batches from the SPS (every 20 sec) one batch 216 / 288 bunches 450 Ge. V L. Bottura R. Schmidt - AAPT 2008 31

What happens in case the full LHC beam impact onto material? R. Schmidt -

What happens in case the full LHC beam impact onto material? R. Schmidt - AAPT 2008 32

Full LHC beam deflected into copper target 2808 bunches Copper target 2 m Energy

Full LHC beam deflected into copper target 2808 bunches Copper target 2 m Energy density [Ge. V/cm 3] on target axis vaporisation melting Beam could tunnel for ~30 m into target Target length [cm] N. Tahir (GSI) et al. R. Schmidt - AAPT 2008 33

SPS experiment: Beam damage at 450 Ge. V Controlled SPS experiment l l 8

SPS experiment: Beam damage at 450 Ge. V Controlled SPS experiment l l 8 1012 protons clear damage beam size σx/y = 1. 1 mm/0. 6 mm above damage limit l 2 1012 protons below damage limit 6 cm 2 1012 4 1012 8 1012 6 1012 25 cm 0. 1 % of the full LHC beam energy 10 times the cross section R. Schmidt - AAPT 2008 34

The only component that can stand a loss of the full beam is the

The only component that can stand a loss of the full beam is the beam dump block all other components would be damaged beam absorber (graphite) about 8 m max 800 0 C about 35 cm concrete shielding R. Schmidt - AAPT 2008 35

Beam Cleaning System • Beam cleaning (collimation) system capture particles that would be lost

Beam Cleaning System • Beam cleaning (collimation) system capture particles that would be lost in superconducting magnets and induce quenches and damage • More than 100 collimators jaws needed for the LHC beam • Most collimators made of carbon to survive severe beam impact! • Collimators must be precisely aligned (< 0. 1 mm) to guarantee a high efficiency above 99. 9% at nominal intensities. Protection devices Primary collimator Secondary collimators Tertiaryhadronic Triplet showers Experiment collimators magnets Absorbers Tertiary halo Primary halo particle Beam Secondary halo It’s not easy to stop 7 Te. V protons !! + hadronic showers R. Schmidt - AAPT 2008 36

RF contacts for guiding image currents Beam spot ~2 mm Carbon jaw 1. 2

RF contacts for guiding image currents Beam spot ~2 mm Carbon jaw 1. 2 m long R. Schmidt - AAPT 2008 37

Status and Outlook R. Schmidt - AAPT 2008 38

Status and Outlook R. Schmidt - AAPT 2008 38

Status summary l l l Installation and magnet interconnections finished Cryogenics • Nearly finished

Status summary l l l Installation and magnet interconnections finished Cryogenics • Nearly finished and operational (e. g. cryoplants) Powering system: commissioning on the way • Power converters commissioning on short circuits in tunnel finished Magnet powering tests started in two sectors l l • Other systems (RF, Beam injection and extraction, Beam instrumentation, Collimation, Interlocks, Controls) Injector complex and transfer lines ready In May / June ready for first beam Some months later first luminosity operation… …. . if there are no problems that require partial warm-up R. Schmidt - AAPT 2008 39

Magnet temperature in one 3 km long sector Two-In-One superconducting magnets inside 1. 9

Magnet temperature in one 3 km long sector Two-In-One superconducting magnets inside 1. 9 K system R. Schmidt - AAPT 2008 40

Ramping the dipole magnets to a current for 5 Te. V High current power

Ramping the dipole magnets to a current for 5 Te. V High current power converters controlling the current with an unprecedented accuracy of 1 ppm 8000 A Dipole magnet current 4000 A 12 hours R. Schmidt - AAPT 2008 41

Current leads with High Temperature Superconductors at an industrial scalce Feedboxes (‘DFB’) : transition

Current leads with High Temperature Superconductors at an industrial scalce Feedboxes (‘DFB’) : transition from copper cable to super-conductor Water cooled Cu cables R. Schmidt - AAPT 2008 42 42

DFB with ~17 out of 1600 HTS current leads R. Schmidt - AAPT 2008

DFB with ~17 out of 1600 HTS current leads R. Schmidt - AAPT 2008 43

Cold compressors of LHC 1. 8 K units to provide helium at 1. 9

Cold compressors of LHC 1. 8 K units to provide helium at 1. 9 K Axial-centrifugal impeller Air Liquide & IHI-Linde 1 st stage cartridge 4 stages R. Schmidt - AAPT 2008 44

First collimator in the tunnel Vacuum tank with two jaws installed Designed for maximum

First collimator in the tunnel Vacuum tank with two jaws installed Designed for maximum robustness: Advanced Carbon Composite material for the jaws with water cooling! R. Assmann et al R. Schmidt - AAPT 2008 45

Always smooth progress? No …. . this is unrealistic l l l The LHC

Always smooth progress? No …. . this is unrealistic l l l The LHC is a machine with unprecedented complexity The technology is pushed to its limits The LHC is a ONE-OFF machine The LHC was constructed during a period when CERN had to substantially reduce the personel Problems came up and were solved / are being solved, such as dipole magnets, cryogenics distribution line, collimators, inner triplet, RF fingers (Pi. MS), He level gauges, …. In my view what makes such project a success: not absence of problems, but because problems are detected and adressed with competent and dedicated staff and collaborators that master all different technologies R. Schmidt - AAPT 2008 46

Conclusions l The LHC is a global project with the world-wide highenergy physics community

Conclusions l The LHC is a global project with the world-wide highenergy physics community devoted to its progress and results l As a project, it is much more complex and diversified than the SPS or LEP or any other large accelerator project constructed to date Machine Advisory Committee, chaired by Prof. M. Tigner, March 2002 l l No one has any doubt that it will be a great challenge for both machine to reach design luminosity and for the detectors to swallow it However, we have a competent and experienced team, and 30 years of accumulated knowledge from previous CERN projects has been put into the LHC design L. Evans (LHC Project Leader) R. Schmidt - AAPT 2008 47

Acknowledgement The LHC accelerator is being realised by CERN in collaboration with institutes from

Acknowledgement The LHC accelerator is being realised by CERN in collaboration with institutes from many countries over a period of more than 20 years Main contribution come from USA (via LARP) and from other countries (Japan, Russia, India, Canada, special contributions from France and Switzerland) Industry plays a major role in the construction of the LHC see also P. Limons (FERMILAB) LHC talk tomorrow Thanks for the material from: R. Assmann, R. Bailey, F. Bordry, L. Bottura, L. Bruno, L. Evans, B. Goddard, M. Gyr, Ph. Lebrun R. Schmidt - AAPT 2008 48

Reserve Slides R. Schmidt - AAPT 2008 49

Reserve Slides R. Schmidt - AAPT 2008 49

Particle acceleration: RF cavity with electric field orthogonal 2 a z LHC RF frequency

Particle acceleration: RF cavity with electric field orthogonal 2 a z LHC RF frequency 400 MHz Revolution frequency 11246 Hz g R. Schmidt - AAPT 2008 50

Schematic layout of beam dump system in IR 6 Septum magnet deflecting the extracted

Schematic layout of beam dump system in IR 6 Septum magnet deflecting the extracted beam Beam 1 Q 5 L H-V kicker for painting the beam Beam Dump Block Q 4 L about 700 m Fast kicker magnet Q 4 R about 500 m Q 5 R Beam 2 R. Schmidt - AAPT 2008 51

Beam losses into material l l Proton losses lead to particle cascades in materials

Beam losses into material l l Proton losses lead to particle cascades in materials The energy deposition leads to a temperature increase For the maximum energy deposition as a function of material there is no straightforward expression Programs such as FLUKA are being used for the calculation of the energy deposition Magnets could quench…. . • beam lost - re-establish condition will take hours The material could be damaged…. . • melting • losing their performance (mechanical strength) Repair could take several weeks R. Schmidt - AAPT 2008 52

Operational margin of a superconducting magnet Applied Magnetic Applied magnetic. Field field [T] Bc

Operational margin of a superconducting magnet Applied Magnetic Applied magnetic. Field field [T] Bc critical field Bc quench with fast loss of ~5 · 106 protons This is about 1000 times more critical than for TEVATRON, HERA, RHIC 8. 3 T QUENCH Tc critical Tc temperature quench with fast loss of ~5 · 109 protons 0. 54 T 1. 9 K Temperature [K] R. Schmidt - AAPT 2008 9 K 53

Quench - transition from superconducting state to normalconducting state Quenches are initiated by an

Quench - transition from superconducting state to normalconducting state Quenches are initiated by an energy in the order of m. J (corresponds to the energy of 1000 protons at 7 Te. V) l Movement of the superconductor by several m (friction and heat dissipation) l Beam losses l Failure in cooling To limit the temperature increase after a quench (in 1 s to 5000 K) l The quench has to be detected l The energy is distributed in the magnet by force-quenching the coils using quench heaters l The magnet current has to be switched off within << 1 second R. Schmidt - AAPT 2008 54

Current tracking between three main circuits 2 ppm Courtesy F. Bordry R. Schmidt -

Current tracking between three main circuits 2 ppm Courtesy F. Bordry R. Schmidt - AAPT 2008 55

R. Schmidt - AAPT 2008 56

R. Schmidt - AAPT 2008 56

Beam lifetime with nominal intensity at 7 Te. V Beam lifetime Beam power into

Beam lifetime with nominal intensity at 7 Te. V Beam lifetime Beam power into equipment (1 beam) Comments 100 h 1 k. W Healthy operation 10 h 10 k. W Operation acceptable, collimation must absorb large fraction of beam energy (approximately beam losses = cryogenic cooling power at 1. 9 K) 0. 2 h 500 k. W Operation only possibly for short time, collimators must be very efficient 1 min 6 MW Equipment or operation failure operation not possible - beam must be dumped << 1 min > 6 MW Beam must be dumped VERY FAST Failures will be a part of the regular operation and MUST be anticipated R. Schmidt - AAPT 2008 57

End of data taking in normal operation: Beam Dump l l l l Luminosity

End of data taking in normal operation: Beam Dump l l l l Luminosity lifetime estimated to be approximately 10 h (after 10 hours only 1/3 of initial luminosity) Beam current somewhat reduced - but not much Energy per beam still about 200 -300 MJ Beams are extracted into beam dump blocks The only component that can stand a loss of the full beam is the beam dump block - all other components would be damaged At 7 Te. V, fast beam loss with an intensity of about 5% of one single “nominal bunch” could damage superconducting coils In case of failure: beam must go into beam dump block R. Schmidt - AAPT 2008 58

Density change in target after impact of 100 bunches copper solid state radial 100

Density change in target after impact of 100 bunches copper solid state radial 100 bunches – target density reduced to 10% Target radial coordinate [cm] • • Energy deposition calculations using FLUKA Numerical simulations of the hydrodynamic and thermodynamic response of the target with two. N. Tahir (GSI) et al. dimensional hydrodynamic computer code R. Schmidt - AAPT 2008 59

56. 0 mm +- 3 ~1. 3 mm Beam +/- 3 sigma Beam in

56. 0 mm +- 3 ~1. 3 mm Beam +/- 3 sigma Beam in vacuum chamber with beam screen at 7 Te. V R. Schmidt - AAPT 2008 60

56. 0 mm Collimators at 7 Te. V, squeezed optics 1 mm R. Assmanns

56. 0 mm Collimators at 7 Te. V, squeezed optics 1 mm R. Assmanns EURO +/- 8 sigma = 4. 0 mm Beam +/- 3 sigma Example: Setting of collimators at 7 Te. V - with luminosity optics Beam must always touch collimators first ! R. Schmidt - AAPT 2008 61

The LHC Phase 1 Collimator Vacuum tank with two jaws installed Designed for maximum

The LHC Phase 1 Collimator Vacuum tank with two jaws installed Designed for maximum robustness: Advanced Carbon Composite material for the jaws with water cooling! R. Assmann et al R. Schmidt - AAPT 2008 62

New approaches and novel technologies l l l l Two-In-One superconducting magnets inside 1.

New approaches and novel technologies l l l l Two-In-One superconducting magnets inside 1. 9 K system Compressors operating at cold to provide helium at 1. 9 K Beam screen inside vacuum chamber at higher temperature High Temperature Superconductors at an industrial scale, for current leads High current power converters and control of the current with an unprecedented accuracy of 1 ppm New devices and materials for absorbing the particles Overall consideration for machine protection: an accidental release of the energy can lead to massive damage R. Schmidt - AAPT 2008 63

Recalling LHC challenges and outlook l l l Enormous amount of equipment Complexity of

Recalling LHC challenges and outlook l l l Enormous amount of equipment Complexity of the LHC accelerator New challenges in accelerator physics with LHC beam parameters pushed to the extreme Fabrication of equipment Installation LHC “hardware” commissioning LHC Beam commissioning 1 2 3 4 5 6 7 8 9 10 11 12 2005 1 2 3 4 5 6 7 8 9 10 11 12 2006 1 2 3 4 5 6 7 8 9 10 11 12 2007 R. Schmidt - AAPT 2008 64

Repair of the inner triplett R. Schmidt - AAPT 2008 65

Repair of the inner triplett R. Schmidt - AAPT 2008 65

RF bellows in the 1700 interconnections R. Schmidt - AAPT 2008 66

RF bellows in the 1700 interconnections R. Schmidt - AAPT 2008 66

Arc plug-in module at warm temperature R. Schmidt - AAPT 2008 67

Arc plug-in module at warm temperature R. Schmidt - AAPT 2008 67

Arc plug-in module at working temperature R. Schmidt - AAPT 2008 68

Arc plug-in module at working temperature R. Schmidt - AAPT 2008 68

Solution is on the way… l l l Problem: fingers bend into beampipe obstructing

Solution is on the way… l l l Problem: fingers bend into beampipe obstructing the aperture Due to wrong angle of RF fingers PLUS size of the gap between the magnet apertures larger than nominal (still inside specification) Laboratory tests and finite element analysis confirm the two factors Only part of the interconnects is affected Complete survey of sector 78 using X-ray techniques Repair is not so difficult…once bad Pi. M identified l l A technique was developed for quickly checking at warm the LHC beam aperture Using air flow blowing a light ball equipped with a 40 MHz transmitter through the beam vacuum pipe, use BPMs to detect it as it passes R. Schmidt - AAPT 2008 69