Why an Antiproton source?

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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

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Some Necessary Accelerator Physics

• All Classical (Relativistic) EM
• 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 bct sometimes use t instead
• Equation of Motion
• C is circumference of accelerator -- Periodicity!
  

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Solutions to Equations of Motion

• Restoring force k(s) is dependent on location
• Dipoles
• Quadrupoles
• Drifts
• General Solution
• b(s) is solution to a messy 2nd order Diff Eqn
• Beam size depends on Amplitude of oscillation and
  value of b(s)
• Can change Position by changing angle 90?
  upstreamused for extraction/injection/cooling/IP
  position

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Beam Size

• Relate the INVARIANT EMITTANCE (phase space area)
  to physical size
• Gaussian Beams
• 95 (Fermi Standard)
• s2 eb / 6p
• Include relativistic contraction (beams gets
  smaller as they are accelerated!)
• At B0 b(s) b(1s2/b2)
• For 20p mm mr beams at IP
• s (20p x10-6 m r 0.35 m / 6pg)1/2 3.5 x
  10-5 m 35 mm

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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 h
• gt transition energy
• Accelerating phase needs to change by 180 as
  cross transition

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Final Points

• Frequency Spectrum
• Time Domain ???(tnT0) at pickup
• Frequency Domainharmonics of revolution
  frequency f0 1/T0
• AccumulatorT01.6 ?sec (1e10 pbar 1 mA)f0
  (core) 628955 Hz
• 127th Harmonic 79 MHz

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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
• p, K, m, 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)

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Momentum Choices120 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

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Momentum Choices8 GeV

• Why 8 GeV pbars?
• Optimum production at 10 GeV
• gt90 of optimum in range 7.5-13 GeV
• Main Ring injection (Booster Energy)
• 8 GeV
• Inject directly from Accumulator to Main Ring
• Booster p -gt Main Ring -gt Accumulator
• Momentum choices stay the same for Main Injector

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Target Station

• 120 GeV protons on target
• Smaller spot size, larger acceptance
• Larger energy depositions
• Energy Deposition -gt melting
• 500 J/g -gt T 1700 K
• Shock Waves -gt 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
Lots of Particle
Target
Pions Kaons Protons
Collection Lens
Anti-Protons, etc
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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

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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

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Debuncher Ring

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

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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

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Idea Behind Stochastic Cooling

• Phase Space compression Dynamic Aperture
  Area where particles can orbit Liouvilles
  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

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Idea Behind Stochastic Cooling

• Principle of Stochastic cooling
• Applied to horizontal btron oscillation
• A little more difficult in practice.
• Used in Debuncher and Accumulator to cool
  horizontal, vertical, and momentum distributions
• COOLING? Temperature ltKinetic Energygtminimize
  transverse KE minimize DE longitudinally

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Stochastic Coolingin the Pbar Source

• Standard Debuncher operation
• 108 pbars, uniformly distributed
• 600 kHz revolution frequency
• To individually sample particles
• Resolve 10-14 seconds100 GHz bandwidth
• Dont have good pickups, kickers, amplifiers in
  the 100 GHz range
• Sample Ns particles -gt Stochastic process
• Ns N/2TW where T is revolution time and W
  bandwidth
• Measure ltxgt deviations for Ns particles
• Higher bandwidth the better the cooling

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Betatron Cooling

• With correction gltxgt, where g is gain of system
• New position x - gltxgt
• 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

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Stochastic Stacking

• Momentum Stacking explained in context of Fokker
  Planck Equation
• Case 1 Flux 0 Restoring Force
  a(E-E0) Diffusion D0
• Small group with Ei-E0 gtgt D0
• Forced into main distribution
• MOMENTUM STACKING

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Stochastic Stacking

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

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Stochastic Stacking

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

Using log scales on vertical axis
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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

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Beam Pickups

• Pickup disrupts image currents, inducing a
  voltage signal

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Beam Pickups

• At ACurrent induced by voltage across
  junction splits in two, 1/2 goes out, 1/2 travels
  with image current

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Beam Pickups

• At BCurrent splits in two paths, now
  with OPPOSITE sign
• Into load resistor 0 current
• Two current pulses out signal line

I
B
DT L/bc
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Beam Pickups

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

w/2
-w/2
y
d
x
Dx
Current Distribution
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Beam Pickups

• Prototype Measurements
• Use Network Analyzer

NA
Pickup
Kicker
Beam
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Accumulator Pickups

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

Core A - B
Stacktail
Energy
Gain
Core
Stacktail
Energy
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Accumulator

• Not quite as simple
• -Real part of gain cools beam
• frequency depends on momentumDf/f -hDp/p
  (higher f at lower p)
• Position depends on momentumDx DDp/p
• Particles at different positions have different
  flight times
• Cooling system delay constant
• OUT OF PHASE WITH COOLING SYSTEM AS MOMENTUM
  CHANGES

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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

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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

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Debuncher Upgrade

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

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Debuncher Upgrade

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

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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 (h)
• 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

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Why change h?

• ?f/f ???p/p h/DDx/x
• Momentum Spread100 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 gt harmonic frequency!
• Frequency ? Energy Map no longer 1 ? 1

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AntiProton Source

• Shorter Cycle Time in Main Injector
• Target Station Upgrades
• Debuncher Cooling Upgrades
• Accumulator Cooling Upgrades
• GOAL gt20 mA/hour