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Why an Antiproton source?

Why an Antiproton source?. p pbar physics with one ring Dense, intense beams for high luminosity Run II Goals 36 bunches of 3 x 10 10 pbars Small energy spread Small transverse dimensions Collect ~1 x 10 -5 pbars/proton on target MANY CYCLES Store and Accumulate Discuss today

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Why an Antiproton source?

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  1. 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 Storage Rings • Stochastic Cooling

  2. 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 = bct sometimes use t instead • Equation of Motion: • C is circumference of accelerator -- Periodicity!

  3. 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

  4. 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*(1+s2/b*2) • 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

  5. 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

  6. 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

  7. 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

  8. E t E t 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

  9. Power (dB) Core Stacktail Frequency (~Energy) Injected Pulse 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

  10. x’ x x’ x 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

  11. Particle Trajectory Kicker 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 ~ <Kinetic Energy>minimize transverse KE minimize DE longitudinally

  12. 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 THz bandwidth • Don’t have good pickups, kickers, amplifiers in the 100 THz 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

  13. 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

  14. Momentum Cooling • Momentum Cooling explained in context of Fokker Planck Equation • Case 1: Flux = 0 Restoring Force a(E-E0) Diffusion = D0 • Cooling of momentum distribution (as in debuncher) • ‘Small’ group with Ei-E0 >> D0 • Forced into main distribution • MOMENTUM STACKING

  15. y ‘Stacked’ E0 Stochastic Stacking Gaussian Distribution • CORE • Injected Beam (tail) • Stacked

  16. Upgrades for Run II • 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

  17. Beam Direction Slot Coupled Waveguides Output Port Output Termination Output Port Output Termination • Slot Coupled Waveguide an electromagnetic whistle • Narrow Band (~0.5 GHz), High Sensitivity • Cover 4 bands (2 GHz bandwidth)

  18. Debuncher Upgrade • Slot Coupled Waveguide • Narrow Band (~0.5 GHz), High Sensitivity • Cover 4 bands (2 GHz bandwidth)

  19. Debuncher Upgrade • Slow Wave Structure: size, spacing, and number of slots determines sensitivity and bandwidth

  20. Debuncher Upgrades • 4 Kicker bands • 8 Pickup bands

  21. Debuncher Momentum Cooling Blue Trace: Debuncher Momentum Cooling Off Orange Trace: Debuncher Momentum Cooling On Beam on Accumulator Injection Orbit

  22. Debuncher Signal to Noise • For Horizontal Band 1 • Signal to Noise for 1e7 particles (expect 8e7 during Run II) • Room Temperature (red), He Temperature (blue/purple)

  23. Gain Density Stacktail Core Stacktail Core Energy Energy Stochastic Stacking • Simon van Der Meer solution: • Constant Flux: • Solution: • Exponential Density Distribution generated by Exponential Gain Distribution Using log scales on vertical axis

  24. 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, 2-4,4-8 GHz) • Output is combined using binary combiner boards to make a phased antenna array

  25. Planar Loops 3D Loops Beam Pickups Pickup disrupts image currents, inducing a voltage signal

  26. I A Beam Pickups • At A:Current induced by voltage across junction splits in two, 1/2 goes out, 1/2 travels with image current

  27. Beam Pickups • At B:Current splits in two paths, now with OPPOSITE sign • Into load resistor ~ 0 current • Two current pulses out signal line I B DT = L/bc

  28. 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

  29. Accumulator Pickups • Placement, number of pickups, amplification are used to build gain shape Core = A - B Stacktail Energy Gain Core Stacktail Energy

  30. Accumulator 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

  31. Why change h? f/f = p/p = h/DDx/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

  32. Accumulator Stacktail Performance with Protons • Inject 8 GeV protons • ‘Stacking’ rate ~ 13 mA/hour!

  33. 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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