Post on 31-Dec-2015
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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
Paul Derwent2 Oct 982
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( )
Paul Derwent2 Oct 983
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
Paul Derwent2 Oct 987
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)
Paul Derwent2 Oct 988
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 )[ ]
Paul Derwent2 Oct 989
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
Paul Derwent2 Oct 9810
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
Paul Derwent2 Oct 9811
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
Paul Derwent2 Oct 9812
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
Paul Derwent2 Oct 9813
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)
Paul Derwent2 Oct 9815
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’
Paul Derwent2 Oct 9816
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
Paul Derwent2 Oct 9817
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
Paul Derwent2 Oct 9818
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[ ]( )
Paul Derwent2 Oct 9819
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
⎛
⎝ ⎜
⎞
⎠ ⎟
Paul Derwent2 Oct 9820
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
Paul Derwent2 Oct 9822
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
Paul Derwent2 Oct 9824Beam Pickups
At A:
Current induced by voltage across junction splits in two, 1/2 goes out, 1/2 travels with image current
AI
Paul Derwent2 Oct 9825Beam 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
Paul Derwent2 Oct 9826Beam 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
I =Ibeamπ
tan− sinhπd
x+w2
⎛ ⎝
⎞ ⎠
⎛ ⎝
⎞ ⎠
⎡ ⎣ ⎢
⎤ ⎦ ⎥−tan− sinh
πd
x−w2
⎛ ⎝
⎞ ⎠
⎛ ⎝
⎞ ⎠
⎡ ⎣ ⎢
⎤ ⎦ ⎥
⎧ ⎨ ⎩
⎫ ⎬ ⎭
≈Ibeamπ
exp−πxd
⎛ ⎝
⎞ ⎠ for largex
Paul Derwent2 Oct 9827Beam Pickups
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
Paul Derwent2 Oct 9830
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
Paul Derwent2 Oct 9831
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
Paul Derwent2 Oct 9832
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
Paul Derwent2 Oct 9835
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
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
Paul Derwent2 Oct 9837
AntiProton Source
Shorter Cycle Time in Main Injector Target Station Upgrades Debuncher Cooling Upgrades Accumulator Cooling Upgrades
GOAL: >20 mA/hour