ACCELERATORS

1. ACCELERATORS

2. Topics • types of accelerators • relativistic effects • Fermilab accelerators • Fermilab proton-antiproton collider • beam cooling • summary

3. Luminosity and cross section • Luminosity is a measure of the beam intensity (particles per area per second) ( L~1031/cm2/s ) • “integrated luminosity” is a measure of the amount of data collected (e.g. ~100 pb-1) • cross section s is measure of effective interaction area, proportional to the probability that a given process will occur. • 1 barn = 10-24cm2 • 1 pb = 10-12b = 10-36cm2 = 10-40m2 • interaction rate:

4. _ How to make qq collisions _ • Quarks are not found free in nature! • But (anti)quarks are elements of (anti)protons. • So, if we collide protons and anti-protons we should get some qq collisions. • Proton structure functions give the probability that a single quark (or gluon) carries a fraction x of the proton momentum (which is 980 GeV/c at the Tevatron) _ -

5. ACCELERATORS • are devices to increase the energy of charged particles; • use magnetic fields to shape (focus and bend) the trajectory of the particles; • use electric fields for acceleration. • types of accelerators: • electrostatic (DC) accelerators • Cockcroft-Walton accelerator (protons up to 2 MeV) • Van de Graaff accelerator (protons up to 10 MeV) • Tandem Van de Graaff accelerator (protons up to 20 MeV) • resonance accelerators • cyclotron (protons up to 25 MeV) • linear accelerators • electron linac: 100 MeV to 50 GeV • proton linac: up to 70 MeV • synchronous accelerators • synchrocyclotron (protons up to 750 MeV) • proton synchrotron (protons up to 900 GeV) • electron synchrotron (electrons from 50 MeV to 90 GeV) • storage ring accelerators (colliders)

6. electrostatic accelerators: generate high voltage between two electrodes charged particles move in electric field, energy gain = charge times voltage drop; Cockcroft-Walton and Van de Graaff accelerators differ in method to achieve high voltage. ACCELERATORS, cont’d

7. Cockcroft-Walton generator • C-W generator uses diodes and capacitors in a rectifier and voltage-multiplier circuit

8. Van de Graaff accelerator • use powersupply to deposit charges on belt; pick charges off at other end of belt and deposit on “terminal” • now rubber belt replaced by “pellet” chain – “pelletron”

9. Van de Graaff accelerator -- 2 • tandem – VdG: use potential difference twice, with change of charges in the middle (strip off electrons)

10. Proton Linac • proton linac (drift tube accelerator): • cylindrical metal tubes (drift tubes) along axis of large vacuum tank • successive drift tubes connected to opposite terminals of AC voltage source • no electric field inside drift tube  while in drift tube, protons move with constant velocity • AC frequency such that protons always find accelerating field when reaching gap between drift tubes • length of drift tubes increases to keep drift time constant • for very high velocities, drift tubes nearly of same length (nearly no velocity increase when approaching speed of light)

11. CYCLOTRON • cyclotron • consists of two hollow metal chambers called (“dees” for their shape, with open sides which are parallel, slightly apart from each other (“gap”) • dees connected to AC voltage source - always one dee positive when other negative  electric field in gap between dees, but no electric field inside the dees; • source of protons in center, everything in vacuum chamber; • whole apparatus in magnetic field perpendicular to plane of dees; • frequency of AC voltage such that particles always accelerated when reaching the gap between the dees; • in magnetic field, particles are deflected: p = qBRp = momentum, q = charge, B = magnetic field strength, R = radius of curvature • radius of path increases as momentum of proton increases time for passage always the same as long as momentum proportional to velocity; this is not true when velocity becomes too big (relativistic effects)

12. Cyclotron

13. Accelerators: “relativistic effects” • “relativistic effects” • special relativity tells us that certain approximations made in Newtonian mechanics break down at very high speeds; • relation between momentum and velocity in “old” (Newtonian) mechanics: p = m v relativistically this becomes p = mv, with  = 1/1 - (v/c)2m = “rest mass”, i.e. mass is replaced by rest mass times  - “relativistic growth of mass” • factor  often called “Lorentz factor”; ubiquitous in relations from special relativity; energy: E = mc2 • acceleration in a cyclotron is possible as long as relativistic effects are negligibly small, i.e. only for small speeds, where momentum is still proportional to speed; at higher speeds, particles not in resonance with accelerating frequency; for acceleration, need to change magnetic field B or accelerating frequency f or both; ________

14. more types of Accelerators • electron linac • electrons reach nearly speed of light at small energies (at 2 MeV, electrons have 98% of speed of light); no drift tubes; use travelling e.m. wave inside resonant cavities for acceleration. • synchrocyclotron: • B kept constant, f decreases; • synchrotron : • B increases during acceleration, f fixed (electron synchrotron) or varied (proton synchrotron); radius of orbit fixed.

16. Fermilab aerial view

17. Fermilab accelerator chain: 0 to 400 MeV Plasma ion source: H- ions, 18keV Cockroft-Walton H- ions, 18keV to 750keV Linac : H- ions, 750keV to 400 MeV

18. The Cockcroft-Walton pre-accelerator provides the first stage of acceleration; hydrogen gas is ionized to create negative ions, each consisting of two electrons and one proton. ions are accelerated by a positive voltage and reach an energy of 750,000 electron volts (750 keV). (about 30 times the energy of the electron beam in a television's picture tube.) FNAL Cockcroft-Walton acc.

19. Next, the negative hydrogen ions enter a linear accelerator, approximately 500 feet long. Oscillating electric fields accelerate the negative hydrogen ions to 400 million electron volts (400 MeV). Before entering the third stage, the ions pass through a carbon foil, which removes the electrons, leaving only the positively charged protons. FNAL Linac

20. Fermilab Linac

21. Fermilab accelerator chain: 400 MeV to 980 GeV Booster: H- ions, stripped to p 400 MeV to 8 GeV Main Injector: Protons, 8GeV to 150GeV TeVatron Protons and Antiprotons 150GeV to 980GeV

22. Main Injector and recycler • recycler: • antiproton storage ring • fixed momentum (8.9 GeV/c), • permanent magnets • Main Injector: • proton synchrotron; cycle period 1.6-3 seconds; • delivers 120 GeV protons to pbar production target. • Also delivers beam to a number of fixed target experiments.

23. Fermilab TeVatron tunnel

24. when enough antiprotons: extract from accumulator or recycler transfer to Main Injector accelerate to 150 GeV transfer to Tevatron Antiproton manufacture • 120 GeV protons from Main Injector • extract, shoot on target (Ni) • collect with Lithium lens • select 8GeV antiprotons • transfer to debuncher • reduce beam spread by stochastic cooling • store in accumulator (“stacking”) • transfer to “recycler” when stack reaches 1012 pbars

25. Antiprotons -- target and collection • pbars from target have wide angular distribution; • Li lens focuses • bend magnet selects 8 GeV pbars • efficiency: 8 pbars per 1 M protons hitting target make it into accumulator

26. pbars from target are in “bunches” (small time spread), wide energy spread (4%); debuncher performs “bunch rotation” to swap large energy spread and small time spread into narrow energy spread and large time spread low momentum pbars have shorter path  arrive earlier at RF cavity  get stronger accelerating kick after sufficient turns, energy spread reduced Debuncher

27. Debuncher and accumulator debuncher accumulator

28. Accumulator • accumulates antiprotons • successive pulses of antiprotons from debuncher stacked over a day or so • momentum stacking: newly injected pbars are decelerated by RF cavity to edge of stack • stack tail cooling system sweeps beam deposited by RF towards core of the stack • additional core cooling systems keep antiprotons in core at desired energy and minimize beam size

29. Beam Cooling • Beam cooling: reduce size and energy spread of a particle beam circulating in a storage ring (without any accompanying beam loss) • motion of individual beam particles deviate from motion of beam center (ideal orbit) • transverse deviations in position and angle – “betatron oscillations” • longitudinal deviations due to energy (momentum) spread -- “synchrotron oscillations” • motions of particles with respect to beam center similar to random motion of particles in a gas • beam temperature = measure of average energy corresponding to these relative motions • “beam cooling” = reduction of these motions -- decrease of beam temperatures

30. x’ x x’ x Phase space Transverse Phase space • Phase Space = space defined by coordinates describing motion wrt beam center • Emittance = region of phase space where particles can orbit, also its size (phase space volume) • Liouville’s Theorem: phase space volume = constant (cannot be changed by conservative forces) • L.T. only for continous particle stream (liquid) – discrete particles  can swap particles and empty phase space – reduce area occupied by beam

31. Beam cooling -- 2 • beam cooling beats constraints of Liouville theorem (phase space volume is constant) because phase space volume is not reduced, only occupancy (distribution of particles) within phase space volume is changed • Cooling is, by definition, not a conservative process. The cooling electronics act on the beam through a feedback loop to alter the beam's momentum or transverse oscillations. • Two types of beam cooling have been demonstrated and used at various laboratories: electron cooling which was pioneered by G. I. Budker, et. al., at Novosibirsk, and stochastic cooling, developed by Simon van der Meer of CERN.

32. Stochastic cooling -- 1 • Stochastic cooling: • pick-up electrode detects excursions of a particle from its central orbit • sends signal to a “kicker” downstream • kicker applies a correction field to reduce this amplitude. Short cut, (n+¼)

33. The cooling process can be looked atas a competition between two terms: (a) the coherent term which is generated by the single particle, (b) the incoherent term which results from disturbances to the single particle. (a)=linear with gain (b)=quadratic by suitable choice of gain, overall cooling can be achieved Stochastic cooling - 2

34. Stochastic Cooling - 3 • Particle beams are not just a single particle, but rather, a distribution of particles around the circumference of the storage ring. Each particle oscillates with a unique amplitude and random initial phase. The cooling system acts on a sample of particles within the beam rather than on a single particle. • Since stochasticcooling systems cannot resolve the motion of asingle antiproton, only a phenomenon called mixingmakes cooling possible. Mixing arises because particles with differentmomenta take different times to travel around thering, and get spread out over the beam. After afew turns around the ring, the noiseaverages to zero for accumulatingantiprotons.

35. Stochastic Cooling in the Pbar Source • Standard Debuncher operation: • 108 pbars, uniformly distributed • ~600 kHz revolution frequency • To individually sample particles • to resolve 10-14 seconds, would need 100 THz bandwidth • Don’t have good pickups, kickers, amplifiers in the 100 THz range • Sample Ns particles -> Stochastic process • Ns = N/2TW where T is revolution time and W bandwidth • Measure <x> deviations for Ns particles • The higher the bandwidth the better the cooling

36. Betatron Cooling • With correction ~ g<x>, where g is gain of system • New position: x - g<x> • Emittance Reduction: RMS of kth particle(W = bandwidth and N = number of circulating particles), • Must also consider noise (characterized by U = Noise/Signal) • Mixing: • Randomization effects M = number of turns to completely randomize sample • Net cooling effect if g sufficiently small

37. Momentum cooling • Momentum cooling systems reduce the longitudinal energyspread of a beam by accelerating or decelerating particles in the beam distribution towards a central momentum. • The sum signal is used for longitudinal cooling and the difference for betatron cooling.

38. AntiProton Source

39. Electron cooling • invented by G.I. Budker (INP, Novosibirsk) in 1966 as a way to increase luminosity of p-p and p-pbar colliders. • first tested in 1974 with 68 MeVprotons in the NAP-M ring at INP. • cooling of ion beams by a co-moving low emittance electron beam is a well-established technique forenergies up to hundreds of MeV per nucleon • at higher energy, expect slower cooling, but may still give enhancement in the performance of high energy colliders as well. • is now used for cooling of 8 GeV antiprotons in the Fermilab recycler ring • GSIproject for cooling antiprotons

40. How does electron cooling work? • velocity of electrons made equal to velocity of ions (antiprotons) • ions undergo Coulomb scattering in the “electron gas” and lose energy which is transferred from the ions to the co-streaming electrons until thermal equilibrium is attained

41. electron collector electron gun high voltage platform electron beam magnetic field ion beam Electron cooling

42. Summary • many different types of accelerators have been developed for nuclear and particle physics research • different acceleration techniques suitable for different particles and energy regimes • most accelerators in large research laboratories use several of these techniques in a chain of accelerators • beam cooling has become important tool in improving beam quality and luminosity • active research going on to develop new accelerating techniques for future applications • many types of accelerators have found applications in fields other than nuclear and particle physics (e.g. medicine, ion implantation for electronics chips, condensed matter research, biology,….)