Tools of Particle Physics I Accelerators

Transcription

1 Tools of Particle Physics I Accelerators W.S. Graves July, 2011 MIT W.S. Graves July, 2011

2 1.Introduction to Accelerator Physics 2.Three Big Machines Large Hadron Collider (LHC) International Linear Collider (ILC) Muon Collider Outline 3.Future Laser/Plasma Accelerators W.S. Graves July, 2011

3 Motion in Electric and Magnetic Fields Governed by Lorentz force E 2 p E 2 de dt c m0c 2 dp c p dt 2 qc p E de dt qc E dp dt E v B p E Acceleration along a uniform electric field (B=0) 2 q E v B A magnetic field does not alter a particle s energy. Only an electric field can do this. x z vt ee t 2m0 2 parabolic path for v c Courtesy of C. Prior, RAL

4 Behaviour under constant B-field, E=0 Motion in a uniform, constant magnetic field Constant energy with spiralling along a uniform magnetic field m v 0 ( a) ( b) 2 qvb m0 v qb v qb m 0 p qb qbc E 2 v Courtesy of C. Prior, RAL

5 Methods of Acceleration: Linear Simplest example is a vacuum chamber with one or more DC accelerating structures with the E-field aligned in the direction of motion. Limited to a few MeV To achieve energies higher than the highest voltage in the system, the E-fields are alternating at RF cavities. Avoids expensive magnets No loss of energy from synchrotron radiation But requires many structures Large energy increase requires a long accelerator SLAC linear accelerator SNS Linac, Oak Ridge Courtesy of C. Prior, RAL

6 Methods of Acceleration: Circular p qb f n qbc E 2 Synchrotron Principle of frequency modulation but in addition variation in v time of B-field to match increase in energy and keep revolution radius constant. Magnetic field produced by several bending magnets (dipoles), increases linearly with momentum. For q=e and high energies: p E. Bρ so E[GeV] 0.3 B[T] [m] per unit charge e ce Practical limitations for magnetic fields => high energies only at large radius e.g. LHC E = 8 TeV, B = 10 T, = 2.7 km Courtesy of C. Prior, RAL

7 Ring Concepts 2 R v 1 2 rf L c c L h p qb 2hc L Important concepts in rings: Revolution period Revolution (angular) frequency If several bunches in a machine, introduce RF cavities in straight sections with fields oscillating at a multiple h of the revolution frequency. h is the harmonic number. For synchrotrons, energy increase E when particles pass RF cavities can increase energy only so far as can increase B-field in dipoles to keep constant. B p q Courtesy of C. Prior, RAL

8 Effect on Particles of an RF Cavity Bunching Effect Cavity set up so that particle at the centre of bunch, called the synchronous particle, acquires just the right amount of energy. Particles see voltage V0 sin 2rf t V0 sin( t) In case of no acceleration, synchronous particle has s = 0 Particles arriving early see < s Particles arriving late see > s energy of those in advance is decreased relative to the synchronous particle and vice versa. To accelerate, make 0 < s < so that synchronous particle gains energy E qv sin 0 s Courtesy of C. Prior, RAL

9 Strong Focusing: Alternating Gradient Principle A sequence of focusing-defocusing fields provides a stronger net focusing force. Quadrupoles focus horizontally, defocus vertically or vice versa. Forces are linearly proportional to displacement from axis. A succession of opposed elements enable particles to follow stable trajectories, making small (betatron) oscillations about the design orbit. Technological limits on magnets are high. Courtesy of C. Prior, RAL

10 Focusing Elements SLAC quadrupole Sextupoles are used to correct longitudinal momentum errors. Courtesy of C. Prior, RAL

11 Transverse Phase Space Under linear forces, any particle moves on an ellipse in phase space (x,x ). x x Ellipse rotates in magnets and shears between magnets, but its area is preserved: Emittance x x General equation of ellipse is x 2 2,, are functions of distance (Twiss parameters), and is a constant. Area =. RMS emittance rms 2 xx x x 2 x 2 xx 2 (statistical definition) Courtesy of C. Prior, RAL

12 Electrons and Synchrotron Radiation Particles radiate when they are accelerated, so charged particles moving in dipole magnetic fields emit radiation (due to centrifugal acceleration) in the forward direction. After one turn of a circular accelerator, total energy lost by synchrotron radiation is E GeV m m p /m e = 1836 and m /m e = 207. For the same energy and radius, 18 m 0 E GeV GeV / c 2 4 E / E 10 E / E e p e Courtesy of C. Prior, RAL

13 Luminosity Measures interaction rate per unit cross section - an important concept for colliders. Area, A Simple model: Two cylindrical bunches of area A. Any particle in one bunch sees a fraction N /A of the other bunch. (=interaction cross section). Number of interactions between the two bunches is N 2 /A. Interaction rate is R = f N 2 /A, and Luminosity L f N A 2 CERN and Fermilab p-pbar colliders have L ~ cm -2 s -1. SSC was aiming for L ~ cm -2 s -1 Courtesy of C. Prior, RAL

14 Decision Tree for Future HEP Facilities 0.5 TeV e + e - 3 TeV e + e - Pierre Oddone 3-4 TeV + - W.S. Graves July, 2011

15 W.S. Graves July, 2011 HEP Facility Sizes

16 TI2 LHC accelerator complex 7 seconds from source to LHC Beam 1 Beam 2 TI8 LHC proton path The LHC needs most of the CERN accelerators LHC performance in LAL/Orsay

17 LHC layout and parameters 8 arcs (sectors), ~3 km each 8 long straight sections (700 m each) beams cross in 4 points RF 2-in-1 magnet design with separate vacuum chambers p-p collisions LHC performance in LAL/Orsay Nominal LHC parameters Beam energy (TeV) 7.0 No. of particles per bunch 1.15x10 11 No. of bunches per beam 2808 Stored beam energy (MJ) 362 Transverse emittance (μm) 3.75 Bunch length (cm) β * = 0.55 m (beam size =17 μm) - Crossing angle = 285 μrad -L = cm -2 s -1 17

18 The LHC Arcs

19 8.33 T nominal field A nominal current

20 W.S. Graves July, 2011

21 Incident of Sept. 19 th 2008 The final circuit commissioning was performed in the week following the startup with beam LHC performance in LAL/Orsay During the last commissioning step of the last main dipole circuit an electrical fault developed at ~5.2 TeV (8.7 ka) in the dipole bus bar (cable) at the interconnection between a quadrupole and a dipole magnet. Later correlated to quench due to a local R ~220 n nominal 0.35 n An electrical arc developed and punctured the helium enclosure. Around 400 MJ from a total of 600 MJ stored in the circuit were dissipated in the cold-mass and in electrical arcs. Large amounts of Helium were released into the insulating vacuum. The pressure wave due to Helium flow was the cause of most of the damage (collateral damage). 21

22 Magnet Interconnection Melted by arc Dipole busbar LHC performance in LAL/Orsay

23 Collateral damage Quadrupole-dipole interconnection Quadrupole support LHC performance in LAL/Orsay Main damage area covers ~ 700 metres. 39 out of 154 main dipoles, 14 out of 47 main quadrupoles from the sector had to be moved to the surface for repair (16) or replacement (37). Sooth clad beam vacuum chamber 23

24 International Linear Collider e + production e - e + damping rings e - transport line e + pre-acceleration target e - source + preacceleration undulator e + transport line 2-stage bunch compression e - main linac e + beam dump IP and 2 moveable detectors e + main linac e - beam dump 2-stage bunch compression W.S. Graves July, 2011

25 Why Superconducting RF Cavities? SC cavities offer a surface resistance six orders of magnitude lower than normal conductors high efficiency even when cooling is included low frequency, large aperture for smaller wake-field effects Relations for the surface fields to acclerating gradient: E peak /E acc = 2 -minimize this to reduce field emission B peak /E acc = 4 mt/(mv/m) -minimize to avoid quenches W.S. Graves July, 2011

26 Cavity Fabrication

27 W.S. Graves July, 2011 ILC RF unit at Fermilab

28 W.S. Graves July, 2011 Muon Collider

29 Muon Collider Schematic Proton source: Upgraded PROJECT X (4 MW, 2±1 ns long bunches) muons per year that fit within the acceptance of an accelerator s = 3 TeV Circumference = 4.5km L = cm -2 s -1 /bunch = 2x10 12 (p)/p = 0.1% * = 5mm Rep Rate = 12Hz W.S. Graves July, 2011 Courtesy of S. Geer, FNAL

30 Challenges Muons are born within a large phase space ( ) - To obtain luminosities O(10 34 ) cm -2 s -1, need to reduce initial phase space by O(10 6 ) Muons Decay ( 0 = 2s) - Everything must be done fast need ionization cooling - Must deal with decay electrons - Above ~3 TeV, must be careful about decay neutrinos! W.S. Graves July, 2011 Courtesy of S. Geer, FNAL

31 6D Cooling MC designs require the muon beam to be cooled by ~ O(10 6 ) in 6D Palmer Ionization cooling reduces transverse (4D) phase space. To also cool longitudinal phase space (6D) must mix degrees of freedom as the cooling proceeds s liq H Alexhin & Fernow This can be accomplished with solenoid coils arranged in a helix, or with solenoid coils tilted. W.S. Graves July, 2011 Courtesy of S. Geer, FNAL

32 Laser/Plasma Accelerators W.S. Graves July, 2011 Courtesy of W. Leemans, LBL

33 W.S. Graves July, 2011 Courtesy of W. Leemans, LBL

34 Thank you! Questions? W.S. Graves July, 2011