# Presentation: 274548

## Why an Antiproton source?

- p pbar physics with one ring
- Dense, intense beams for high luminosity
- Run II Goals
- 36 bunches of 3 x 1010 pbars
- Small energy spread
- Small transverse dimensions
- Collect ~1 x 10-5 pbars/proton on target
- MANY CYCLES
- Store and Accumulate
- Discuss today
- Accelerator Physics
- Pbar Production
- Pbar Collection
- Pbar Storage Rings
- Stochastic Cooling

## Some Necessary Accelerator Physics

- All Classical (Relativistic) E&M
- 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!

## Solutions to Equations of Motion

- Restoring force *k(s)*   is dependent on location
- Dipoles
- Quadrupoles
- Drifts
- General Solution:
- s) is solution to a messy 2nd order Diff Eqn
- 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

## 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

## 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

## Final Points

- 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) 628955 Hz
- 127th Harmonic ~79 MHz

## General Characteristics of Pbar Source

- 120 GeV Protons on Ni target
- Focus Negative Particles:  Lithium Lens
- Select 8 GeV with AP2 line
- Bend magnets along the line
- Inject into Debuncher
- , K, , etc. decay
- Decay products at different momenta and fall out
- Electrons radiate and fall out
- Left with stable negative particles at 8 GeV
- PBARs!
- RF Debunch
- Stochastically cool in H, V, p
- Inject into Accumulator
- Stochastically cool in H, V, p
- Accumulate a dense core
- Extract for use in collider
- Decelerate for use in fixed target (E835)

## Momentum Choices120 GeV

- Why 120 GeV protons?
- Phenomenological formula to describe pbar production
- From fits to available data in 1983
- Above 150 GeV, yield/time changes slowly
- Yield increases but have to include Main Ring Cycle time!
- 120 GeV Emax for extraction in medium straight section such as F17
- Operating cost increases as Energy increases

## Momentum Choices8 GeV

- Why 8 GeV pbars?
- Optimum production at 10 GeV
- >90% of optimum in range 7.5-13 GeV
- Main Ring injection (Booster Energy)
- 8 GeV
- Inject directly from Accumulator to Main Ring
- Booster p -> Main Ring -> Accumulator
- Momentum choices stay the same for Main Injector

## Target Station	

- 120 GeV protons on target
- Smaller spot size, larger acceptance
- Larger energy depositions
- Energy Deposition -> melting
- ~500 J/g -> T ~ 1700 K
- Shock Waves -> mechanical deformations
- Pressures ~ 5 GPa
- Sweeping system (in small circle) to go to smaller spot size and not destroy targets
- Lithium Lens for focussing

- 120 GeV

-  Proton Beam

- Nickel

- Target

- Lots of Particle

- Pions Kaons Protons

- Anti-Protons, etc

- Collection Lens

## Pbar Collection

- Lithium Lens
- Longitudinal Current (pulsed 650 kA)
- Develops Azimuthal Field
- Radial Focussing Force (H & V in same device!)
- 750 T/m field strength
- 1 cm aperture (60 mradian acceptance)
- AP2 4% momentum spread

## Pbar Storage Rings

- Two Storage Rings in Same Tunnel
- Debuncher
- Larger Radius
- ~few x 107 stored for cycle length
- 2.4 sec for MR, 1.5 sec for MI
- ~few x 10-7 torr
- RF Debunch beam
- Cool in H, V, p
- Accumulator
- ~1012 stored for hours to days
- ~few x 10-10 torr
- Stochastic stacking
- Cool in H, V, p
- Both Rings are ~triangular with six fold symmetry

## Debuncher Ring

- Main Purpose:
- “Debunch” RF Time Structure (84 buckets)RF locked to Main Injector
-  Rotation in Phase Space
-  E, t conjugate variables
- Initial large E (off target), small t (RF)
- 5 MV RF in ~1/4 turn down to ~100 kV
- Small E, large t
- Adiabatically turn off RF (~10 msec)
- Lots of time left (1.5 sec cycle)
- Cool in H, V, p

## Accumulator Ring

- Not possible to continually inject beam
- Violates Phase Space Conservation
- Need another method to accumulate beam
- Inject beam, move to different orbit (different place in phase space), stochastically stack
- RF Stack Injected beam
- Bunch with RF (2 buckets)
- Change RF frequency (but not B field)
- ENERGY CHANGE
- Decelerates ~ 30 MeV
- Stochastically cool beam to core
- Decelerates ~60 MeV

## Idea Behind Stochastic Cooling

- Phase Space compression			Dynamic Aperture: Area			where particles can orbit			Liouville’s Theorem:			Local Phase Space Density			for conservative system			is conserved			Continuous Media			Discrete Particles			Swap Particles and Empty			Area -- lessen physical			area occupied by beam

## Idea Behind Stochastic Cooling

- Principle of Stochastic cooling
- Applied to horizontal tron oscillation
- A little more difficult in practice.
- Used in Debuncher and Accumulator to cool horizontal, vertical, and momentum distributions
- COOLING?  Temperature ~ <Kinetic Energy>minimize transverse KE minimize E longitudinally

## Stochastic Coolingin the Pbar Source

- Standard Debuncher operation:
- 108 pbars, uniformly distributed
- ~600 kHz revolution frequency
- To individually sample particles
- Resolve 10-14 seconds...100 GHz bandwidth
- Don’t have good pickups, kickers, amplifiers in the 100 GHz range
- Sample Ns particles -> Stochastic process
- Ns = N/2TW where T is revolution time and W bandwidth
- Measure <x> deviations for Ns particles
- Higher bandwidth the better the cooling

## Betatron Cooling

- With correction ~ g<x>, where g is gain of system
- New position:   x - g<x>
- Emittance Reduction:  RMS of kth particle
- Add noise (characterized by U = Noise/Signal)
- Add MIXING
- Randomization effects M = number of turns to completely randomize sample

## Stochastic Stacking

- Momentum Stacking explained in context of Fokker Planck Equation
- Case 1:  Flux = 0  Restoring Force (E-E0)			Diffusion = D0
- ‘Small’ group with Ei-E0 >> D0
- Forced into main distribution
- MOMENTUM STACKING

## Stochastic Stacking

- Gaussian Distribution
- CORE
- Injected Beam (tail)
- Stacked

## Stochastic Stacking

- Simon van Der Meer solution:
- Constant Flux:
- Solution:
- Exponential Density Distribution generated by Exponential Gain Distribution

- Using log scales on vertical axis

## Implementation in Accumulator

- Stacktail and Core systems
- How do we build an exponential gain distribution?
- Beam Pickups:
- Charged Particles:  E & B fields generate image currents in beam pipe
- Pickup disrupts image currents, inducing a voltage signal
- Octave Bandwidth (1-2, 2-4 GHz)
- Output is combined using binary combiner boards to make a phased antenna array

## Beam Pickups

- Pickup disrupts image currents, inducing a voltage signal

## Beam Pickups

- At A:Current induced by voltage across junction splits in two, 1/2 goes out, 1/2 travels with image current

## Beam Pickups

- At B:Current splits in two paths, now with OPPOSITE sign
- Into load resistor ~ 0 current
- Two current pulses out signal line

- B

- I

- T = L/c

## Beam Pickups

- Current intercepted by pickup:
- Use method of images
- Placement of pickups to give proper gain distribution

- +w/2

- -w/2

- y

- x

- x

- d

- Current Distribution

## Beam Pickups

- Prototype Measurements:
- Use Network Analyzer

- Pickup

- NA

- Kicker

- Beam

## Accumulator Pickups

- Placement, number of pickups, amplification are used to build gain shape

- Stacktail

- Core = A - B

- Energy

- Gain

- Energy

- Stacktail

- Core

## Accumulator 

- Not quite as simple:
- -Real part of gain cools beam
- frequency dependson momentumf/f = -p/p  (higher f at lower p)
- Position depends on momentumx = Dp/p
- Particles at different positions have different flight times
- Cooling system delay constant
**OUT OF PHASE WITH COOLING SYSTEM AS MOMENTUM CHANGES**

## Stochastic Cooling

- Tevatron 1:  Run I
- Debuncher:  2-4 GHz
- Accumulator:
- Stacktail:  1-2 GHz
- Core: 2-4 GHz and 4-8 GHz
- Fermi III:  Run II
- Debuncher:  4-8 GHz
- Accumulator:
- Stacktail:  2-4 GHz
- Core: 2-4 GHz and 4-8 GHz

## Upgrades for Run II

- Target Station:
- Beam Sweeping System
- Magnets and pulsed power supplies
- Transfer Lines
- Aperture improvements and beam line model
- Debuncher
- All stochastic cooling systems
- Larger bandwidth (4-8 GHz vs. 2-4 GHz)
- All new electronics and  signal transmission
- Lower Noise (Liquid Helium vs. Liquid Nitrogen)
- Different Technology
- Slot coupled waveguides vs. Octave bandwidth pickups
- Remove H & V trim magnets to make room for cooling tanks
- Move quadrupoles for use in steering
- Adjust quad positions in D-to-A line to make room for cooling tanks

## Debuncher Upgrade

- Slot Coupled Waveguide
- Narrow Band (~0.5 GHz), High Sensitivity
- Cover 4 bands (2 GHz bandwidth)

## Debuncher Upgrade

- Slow Wave Structure:  size, spacing, and number of slots determines sensitivity and bandwidth

## Upgrades for Run II

- Accumulator
- Stacktail Stochastic Cooling Systems
- Larger Bandwidth (2-4 GHz vs. 1-2 GHz)
- New technologies for signal combination
- Recycled (from Debuncher) and new Electronics to cover larger bandwidth
- Lattice changes
- Halve phase slip factor ()
- Driven by Stacktail upgrade
- Keep dispersion, phase advance (pickup to kicker) injection and extraction regions, tunes, aperture, chromaticity ~ the same
- Requires construction 4 new quadrupoles (strength vs. current characteristics)
- Reworking of power supplies

## Why change ?

- f/f = p/p = Dx/x
- Momentum Spread~100 MeV
- Frequency Spread ~ 160 Hz
- fcentral ~ 628900 Hz
- f /f ~	2.5e-4
- Stacktail assumes position(energy) frequency relation in design
- 1 GHz ~ 1590 Harmonic
- 		 f ~ 254000 Hz
- 2 GHz ~ 3180 Harmonic
- 		 f ~ 508000 Hz
- 3 GHz ~ 4770 Harmonic
- 		 f ~ 763000 Hz
- Frequency Spread > harmonic frequency!
- Frequency  Energy Map no longer 1  1

## AntiProton Source 

- Shorter Cycle Time in Main Injector
- Target Station Upgrades
- Debuncher Cooling Upgrades
- Accumulator Cooling Upgrades
- GOAL:  >20 mA/hour