Why an Antiproton source?

Paul Derwent2 Oct 981

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!

H = r p−e r A( )2c2 +m2c4 +eV

d2 x

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


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

x s( )=A s( )cosφ s( ) +δ( )

φ s( )=ds s( )∫

Tune =φ C( )2π

= ds s( )0

C

∫

Paul Derwent2 Oct 984Beam 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

2 = −εβ

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

Paul Derwent2 Oct 985Longitudinal 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

=1

γ t2 −

1

γ 2

Δf

f= −η

ΔE

E

Paul Derwent2 Oct 986Final Points

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) 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

π, 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 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

E

abs

⎛

⎝ ⎜

⎞

⎠ ⎟ ddp ⎛

⎝ ⎜

⎞

⎠ ⎟ = 0.06 −xr( )8 (exp−pt

2 )[ ] ×

+24s−2 (exp8xr )[ ] × a (expbpt2 ) (exp−cxr )[ ]


Momentum Choices8 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 ProtonsAnti-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

E

t

E

t

Paul Derwent2 Oct 9814Accumulator 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

Injected Pulse

Core

Stacktail

Frequency(~Energy)

Power(dB)


Idea Behind Stochastic Cooling

Phase Space compressionDynamic Aperture: Areawhere particles can orbit

Liouville’s Theorem:Local Phase Space

Densityfor conservative systemis conserved

Continuous MediaDiscrete Particles

Swap Particles and Empty

Area -- lessen physicalarea occupied by beam

x

x’

x

x’


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

Kicker

Particle Trajectory


Stochastic Coolingin 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

xk −g⟨x⟩( )2 =xk2 −2gxk + g2 ⟨x⟩2

⟨x⟩ = Ns

xi =Ns

xk +Nsi

∑ xii≠k∑

Average over all particles and do lots of algebra

d⟨x⟩2

dn=−2g⟨x2 ⟩

Ns+ g2

Ns⟨x2 ⟩, where n is 'sample'

⇒ Cooling Timeτ=2W

N2g−g2( )

⇒ Cooling Time 1

τ=

2W

N2g − g2 M +U[ ]( )


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

∂ψ∂t

= −∂

∂EC E( )ψ − D E( )

∂ψ

∂E ⎛ ⎝

⎞ ⎠

where ψ = density function ∂N

∂EC E( ) is energy gain function

D E( ) represent diffusion terms (noise, mixing, feedback)

ψ =ψ 0 exp−α E −E0( )

2

2D0

⎛

⎝ ⎜

⎞

⎠ ⎟


Stochastic Stacking

Gaussian Distribution CORE

Injected Beam (tail) Stacked

E0

‘Stacked’

Paul Derwent2 Oct 9821Stochastic Stacking

Simon van Der Meer solution: Constant Flux:

Solution:

Exponential Density Distribution generated by Exponential Gain Distribution

∂ψ∂t

= constant

∂ψ∂E

=ψ

Ed, where Ed characteristic of design

ψ =ψ 0 expE − Ei( )

Ed

⎡

⎣ ⎢ ⎤

⎦ ⎥

Gain

Energy

Density

Energy

StacktailCore

Stacktail

Core

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

Paul Derwent2 Oct 9823Beam Pickups

Pickup disrupts image currents, inducing a voltage signal

3D Loops Planar Loops


At A:

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

AI


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


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

I =Ibeamπ

tan− sinhπd

x+w2

⎛ ⎝

⎞ ⎠

⎛ ⎝

⎞ ⎠

⎡ ⎣ ⎢

⎤ ⎦ ⎥−tan− sinh

πd

x−w2

⎛ ⎝

⎞ ⎠

⎛ ⎝

⎞ ⎠

⎡ ⎣ ⎢

⎤ ⎦ ⎥

⎧ ⎨ ⎩

⎫ ⎬ ⎭

≈Ibeamπ

exp−πxd

⎛ ⎝

⎞ ⎠ for largex


Prototype Measurements:

Use Network Analyzer

Pickup Comparisons

10

100

1000

10000

100000

800 820 840 860 880 900 920 940

Frev (628xxx Hz)

Magnitude (normalized to

1 mA peak current)

#1 arb units

#3 arb units

#2 arb units

#4 arb units

Model Response

Pickup

NA

Kicker

Beam

Paul Derwent2 Oct 9828Accumulator Pickups

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

StacktailCore = A - B

Energy

Gain

Energy

StacktailCore

Paul Derwent2 Oct 9829Accumulator

Not quite as simple: -Real part of gain cools beam

frequency depends on momentumf/f = -p/p (higher f at lower p)

Position depends on momentumx = Dp/p

Particles at different positions have different flight times

Cooling system delay constant

» OUT OF PHASE WITH COOLING SYSTEM AS MOMENTUM CHANGES


105

106

107

108

109

1010

1011

1012

-100-50050

Leg 1Leg 2CoreTotal

Abs(Real)

Energy

0

60

120

180

240

300

360

-100-50050

Leg 1Leg 2CoreTotal

Phase (degrees)

Energy


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

Paul Derwent2 Oct 9833Debuncher Upgrade

Slot Coupled Waveguide

Narrow Band (~0.5 GHz), High Sensitivity Cover 4 bands (2 GHz bandwidth)

Paul Derwent2 Oct 9834Debuncher 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

Paul Derwent2 Oct 9836Why change ?

f/f = p/p = Dx/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


f ~ 508000 Hz


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

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Why an Antiproton source?

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