# Presentation: 797323

## The Fermilab Accelerator Complex

- 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....

## Intro To Accelerator Physics

- All Classical (Relativistic) E&M
- good reference is “An Introduction to the Physics of High Energy Accelerators” by D. Edwards and M. Syphers
- Hamiltonian of a charged particle in EM field
- Small angle approximation around CENTRAL ORBIT
- 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
- Equation of Motion:
- C is circumference of accelerator -- Periodicity!

## Intro To Accelerator Physics

- Restoring force *k(s)*   is dependent on location
- Dipoles
- Quadrupoles
- Drifts
- 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 upstreamused for extraction/injection/cooling/IP position

## 4 Bumps to Control Position and Angle 

## Beam Size

- 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+s2/*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

## Longitudinal Effects

- 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

## Frequency Domain

- Frequency Spectrum
- Time Domain:  (t+nT0)  at pickup
- Frequency Domain:harmonics of revolution frequency f0 = 1/T0
- Accumulator:T0~1.6 sec (1e10 pbar = 1 mA)f0 (core) 628888 Hz
- 127th Harmonic ~79 MHz

## Luminosity Distribution

- Simplifying Assumptions:
- Transverse planes have same lattice functions
- p and pbar beams have same emittance
- p = pbar = 
- *z* = √(p2 + pbar2)
- Not simply Gaussian in longitudinal or transverse planes
- Transverse size grows with longitudinal position!

## FNAL Accelerators Proton Chain

- 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)

## 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

## FNAL Accelerators:Making Pbars

- 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

## 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

## FNAL Accelerators:Pbar Chain

- 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

## Coming Attraction

- 14 December 2000
- Antiprotons:  Stochastic Cooling
- Paul Derwent
- FNAL BD/Pbar