1. Paul Derwent 14 Dec 00 1 Stochastic Cooling Paul Derwent 14 Dec 00 http://cosmo.fnal.gov/organizationalchart/derwent/cdf_accelerator.htm

2. Paul Derwent 14 Dec 00 2 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 x x’ x

3. Paul Derwent 14 Dec 00 3 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 ~ minimize transverse KE minimize  E longitudinally Kicker Particle Trajectory

4. Paul Derwent 14 Dec 00 4 Stochastic Cooling in the Pbar Source  Standard Debuncher operation:  10 8 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 N s particles -> Stochastic process »N s = N / 2TW where T is revolution time and W bandwidth »Measure deviations for N s particles  Higher bandwidth the better the cooling

5. Paul Derwent 14 Dec 00 5 Betatron Cooling With correction ~ g, where g is gain of system  New position: x - g  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

6. Paul Derwent 14 Dec 00 6 Momentum Cooling  Momentum Cooling explained in context of Fokker Planck Equation  Case 1: Flux = 0 Restoring Force  (E-E 0 ) Diffusion = D 0  Cooling of momentum distribution (as in Debuncher)  ‘Small’ group with E i -E 0 >> D 0  Forced into main distribution  MOMENTUM STACKING

7. Paul Derwent 14 Dec 00 7 Stochastic Stacking Gaussian Distribution  CORE  Injected Beam (tail)  Stacked  E0E0 ‘Stacked’ C(E) D(E)

8. Paul Derwent 14 Dec 00 8 Pbar Storage Rings  Two Storage Rings in Same Tunnel  Debuncher »Larger Radius »~few x 10 7 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 »~10 12 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

9. Paul Derwent 14 Dec 00 9 Debuncher Ring  ßtron cooling in both horizontal and vertical planes  Momentum cooling using notch filters to define gain shape  4-8 GHz using slot coupled wave guides in multiple bands  All pickups at 10 K for signal/noise purposes

10. Paul Derwent 14 Dec 00 10 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 Injected Pulse Core Stacktail Frequency (~Energy) Power (dB)

11. Paul Derwent 14 Dec 00 11 Stochastic Stacking  Simon van Der Meer solution:  Constant Flux:  Solution:  Exponential Density Distribution generated by Exponential Gain Distribution  Max Flux = (W 2 |  |E d )/(f 0 p ln(2)) Gain Energy Density Energy Stacktail Core Stacktail Core Using log scales on vertical axis

12. Paul Derwent 14 Dec 00 12 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

13. Paul Derwent 14 Dec 00 13 Beam Pickups Pickup disrupts image currents, inducing a voltage signal 3D Loops Planar Loops

14. Paul Derwent 14 Dec 00 14 Beam Pickups  At A: Current induced by voltage across junction splits in two, 1/2 goes out, 1/2 travels with image current A I

15. Paul Derwent 14 Dec 00 15 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

16. Paul Derwent 14 Dec 00 16 Beam Pickups  Current intercepted by pickup:  Use method of images  In areas of momentum dispersion D  Placement of pickups to give proper gain distribution +w/2-w/2 y x xx d Current Distribution

17. Paul Derwent 14 Dec 00 17 Accumulator Pickups  Placement, number of pickups, amplification are used to build gain shape Stacktail Core = A - B Energy Gain Energy Stacktail Core

18. Paul Derwent 14 Dec 00 18 AntiProton Source  Shorter Cycle Time in Main Injector  Target Station Upgrades  Debuncher Cooling Upgrades  Accumulator Cooling Upgrades  GOAL: >20 mA/hour