Paul Derwent30 Nov 001

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….

Paul Derwent30 Nov 002

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!

H = r p−e r A( )2c2 +m2c4 +eV

d2 x

ds2 +k s( )x s( ) =0, wherek s+C( ) =k s( )

Paul Derwent30 Nov 003

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

x s( )=A s( )cosφ s( ) +δ( )

φ s( )=ds s( )∫

Tune =φ C( )2π

= ds s( )0

C

∫

Paul Derwent30 Nov 004

4 Bumps to Control Position and Angle

Angle Bump

Trim Magnets B0 Plane

Position Bump

Trim Magnets B0 Plane

x(s) =A β(s)cos(φ(s)+δ)

′ x (s) =A

β(s)sin(φ(s)+δ)+

Aα(s)β(s)

cos(φ(s)+δ)

φ(s) =1

β(s)ds∫

α(s)=−12

dβds

Paul Derwent30 Nov 005

Beam Size

Relate the INVARIANT EMITTANCE (phase space area) to physical size Gaussian Beams

95% (Fermi Standard)» 2 = / 6π

Include relativistic contraction (beams gets smaller as they are accelerated!)

At B0: (s) = *(1+s2/*2) For 20π mm mr beams at IP = (20π x10-6 m r 0 m / 6π2 x 10-5 m

= 35 m Convolute p and pbar 2m

2 = −εβ

2π ln 1− F( ), where F = fraction contained

Paul Derwent30 Nov 006

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

η =1

γt2 −

1γ2

Δff

=−ηΔpp

Paul Derwent30 Nov 007

Frequency Domain

Frequency Spectrum Time Domain: δ(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

Paul Derwent30 Nov 008

Luminosity Distribution

Simplifying Assumptions: Transverse planes have same lattice

functions p and pbar beams have same emittance

p = pbar =

z = √(p2 + pbar

2)

Not simply Gaussian in longitudinal or transverse planes

Transverse size grows with longitudinal position!

L =kexp(−

(z−z0)2

2σ z2 )

εβ*(1+z2

β*2)∫ dz

Paul Derwent30 Nov 009

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)

Paul Derwent30 Nov 0010

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

Paul Derwent30 Nov 0011

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

Paul Derwent30 Nov 0012

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

Paul Derwent30 Nov 0013

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

Paul Derwent30 Nov 0014

Coming Attraction

14 December 2000

Antiprotons: Stochastic Cooling

Paul Derwent

FNAL BD/Pbar