1. Paul Derwent 30 Nov 00 1 The Fermilab Accelerator Complex o Series of presentations  Overview of FNAL Accelerator Complex  Antiprotons: Stochastic Cooling  Antiprotons: Shots and Shot preparation  Main Injector: Preparing Beam for Pbar and Tevatron  Tevatron: From 150 to 980 and collisions To increase local knowledge among CDF members of what is going on over there in the Main Control Room….

2. Paul Derwent 30 Nov 00 2 Intro To Accelerator Physics o All Classical (Relativistic) E&M  good reference is “An Introduction to the Physics of High Energy Accelerators” by D. Edwards and M. Syphers o Hamiltonian of a charged particle in EM field o Small angle approximation around CENTRAL ORBIT o Set of Conjugate variables:  x, x’ horizontal displacement and angle  y, y’ vertical displacement and angle  E, s energy and longitudinal position »s =  ct sometimes use t instead o Equation of Motion:  C is circumference of accelerator -- Periodicity!

3. Paul Derwent 30 Nov 00 3 Intro To Accelerator Physics o Restoring force k(s) is dependent on location  Dipoles  Quadrupoles  Drifts o General Solution:   s) is solution to a messy 2nd order Differential Equation  Beam size depends on Amplitude of oscillation and value of  (s)  Can change Position by changing angle 90  upstream used for extraction/injection/cooling/IP position

4. Paul Derwent 30 Nov 00 4 4 Bumps to Control Position and Angle

5. Paul Derwent 30 Nov 00 5 Beam Size o Relate the INVARIANT EMITTANCE (phase space area) to physical size  Gaussian Beams  95% (Fermi Standard) »  2 =  / 6   Include relativistic contraction (beams gets smaller as they are accelerated!)  At B0:  (s) =  * (1+s 2 /  *2 )  For 20  mm mr beams at IP   = (20  x10 -6 m r  m / 6    x 10 -5 m = 35  m  Convolute p and pbar  m

6. Paul Derwent 30 Nov 00 6 Longitudinal Effects o Longitudinal Acceleration  Time Varying Fields to get net acceleration  Synchronous PHASE and Particle »Path Length can depend on ENERGY »Revolution Frequency can depend on ENERGY  Expressed via Phase Slip Factor    t transition energy »Accelerating phase needs to change by 180° as cross transition

7. Paul Derwent 30 Nov 00 7 Frequency Domain o Frequency Spectrum  Time Domain:  (t+nT 0 ) at pickup  Frequency Domain: harmonics of revolution frequency f 0 = 1/T 0  Accumulator: T 0 ~1.6  sec (1e10 pbar = 1 mA) f 0 (core) 628888 Hz 127th Harmonic ~79 MHz

8. Paul Derwent 30 Nov 00 8 Luminosity Distribution o Simplifying Assumptions:  Transverse planes have same lattice functions  p and pbar beams have same emittance  p =  pbar =   z = √(  p 2 +  pbar 2 )  Not simply Gaussian in longitudinal or transverse planes  Transverse size grows with longitudinal position!

9. Paul Derwent 30 Nov 00 9 FNAL Accelerators Proton Chain o Protons for Collisions:  H - Source »Plasma Ion Source »Cockroft-Walton 18 KeV to 750 KeV  Linac »750 KeV to 400 MeV H - ions  Booster »400 MeV H - ions to 8 GeV protons Multiple injection into same phase space Stripping Foil to convert H - to proton »RF 37 MHz to 53 MHz »84 RF Buckets »Bunch: 1 RF Bucket »Turn: 1 Filling of 84 bunches with H - ions ~10 turns, ~5 bunches -- remaining protons sent to Booster abort »Batch: transfer of beam to MI »15 Hz cycle (RLC resonant circuit)

10. Paul Derwent 30 Nov 00 10 FNAL Accelerators: Proton Chain  Main Injector »8 GeV protons to 150 GeV protons »2 second cycle »RF 52.8 MHz to 53.1 MHz »588 RF Buckets 7x Booster Circumference 7 Booster batches would fill every bucket »Coalescing of 5 bunches into 1 bunch at 150 GeV  Tevatron »150 GeV protons to 980 GeV protons »RF 53.1 MHz (doesn’t change much!!!) »1113 RF Buckets (18.8 nsec spacing) 13.25x Booster Circumference »36 transfers from MI »Injected on Helical orbit, ß * = 1.7 m »Low ß squeeze (ß * = 0.35 m) »Bring beams to collision

11. Paul Derwent 30 Nov 00 11 FNAL Accelerators: Making Pbars o From protons to pbars  H - source  Linac  Booster »~9 Turns, 84 buckets »Goal: 5e12 to MI  Main Injector »From 8 GeV to 120 GeV »1.5 second cycle »Bunch Rotation »Extraction to Pbar target »Goal: 4.5e12 on target  Pbar target and collection »Ni target »Lithium Collection Lens »Transfer Line: Select 8 GeV pbars, 4% momentum acceptance

12. Paul Derwent 30 Nov 00 12 FNAL Accelerators: Making Pbars  Debuncher »8 GeV pbars, 4% momentum spread, 250π mm mr emittance »90 buckets (note: only 84 come in!) »RF 53.1 MHz (matched to MI at 120 GeV) »Debunch »Stochastic cooling in transverse and longitudinal planes »Goal: 9e7 pbars per cycle  Accumulator »8 GeV pbars, 0.05% momentum spread, 80π mm mr emittance »84 Buckets »RF 52.8 MHz »RF and stochastic stacking »>100e10 pbars »Goals: 18.5 pbars/1e6 protons on target 20e10 pbars/hour

13. Paul Derwent 30 Nov 00 13 FNAL Accelerators: Pbar Chain o Pbars to Collisions:  Accumulator »‘Select’ fraction of stack into 4 RF Buckets »Put 52.8 MHz on top (7 - 11 RF Buckets per group)  Main Injector »8 GeV pbars to 150 GeV pbars »Coalescing of 7-11 RF buckets into 1 bunch »Transfer of 4 bunches to Tevatron  Tevatron »150 GeV pbars to 980 GeV pbars »9 transfers from MI (4 per transfer -> 36 bunches) »Injected on Helical orbit, ß * = 1.7 m »Low ß squeeze (ß * = 0.35 m) »Bring beams to collision

14. Paul Derwent 30 Nov 00 14 Coming Attraction o 14 December 2000 Antiprotons: Stochastic Cooling Paul Derwent FNAL BD/Pbar