Paul Derwent 18-Oct-15 1 Stochastic Cooling in the Fermilab AntiProton Source Paul Derwent Beams Division/Pbar/CDF Sunday, October 18, 2015

Paul Derwent 18-Oct-15 2 Stochastic Cooling Main Entry: sto·chas·tic Pronunciation: st&-'kas-tik, stO- Function: adjective Etymology: Greek stochastikos skillful in aiming, from stochazesthai to aim at, guess at, from stochos target, aim, guess -- more at STING Date: : RANDOM; specifically : involving a random variable 2 : involving chance or probability : PROBABILISTIC <a stochastic model of radiation-induced mutation> - sto·chas·ti·cal·ly /-ti-k(&-)lE/ adverb Main Entry: 2 cool Date: before 12th century intransitive senses 1 : to become cool : lose heat or warmth <placed the pie in the window to cool> -- sometimes used with off or down 2 : to lose ardor or passion transitive senses 1 : to make cool : impart a feeling of coolness to -- often used with off or down 2 a : to moderate the heat, excitement, or force of : CALM b : to slow or lessen the growth or activity of -- usually used with off or down <wants to cool off the economy without freezing it -- Newsweek> - cool it : to calm down : go easy <the word went out to the young to cool it -- W. M. Young> - cool one's heels : to wait or be kept waiting for a long time especially from or as if from disdain or discourtesy From Webster’s Collegiate Dictionary

Paul Derwent 18-Oct-15 3 Why an Antiproton source? o p pbar physics with one ring  Dense, intense beams for high luminosity

Paul Derwent 18-Oct-15 4 Luminosity History Collider Run I It’s all in the pbars!

Paul Derwent 18-Oct-15 5 Making Anti-protons o 120 GeV protons off metal target o Collect some fraction of anti-protons which are created  Within collection lens aperture  Momentum ~8 GeV (±2%)

Paul Derwent 18-Oct-15 6 Why an Anti-proton source? ~11,000 cycles Store and cool in the process! o Collect ~2 x pbars/proton on target  ~5e12 protons on target  ~1e8 pbars per cycle  0.67 Hz  Large Energy Spread & Emittance o Run II Goals  36 bunches of 3 x pbars  Small energy spread  Small transverse dimensions

Paul Derwent 18-Oct-15 7 Pbar Longitudinal Distribution

Paul Derwent 18-Oct-15 8 Overview Information o Frequency Spectrum  Time Domain:  (t+nT 0 ) at pickup  Frequency Domain: harmonics of revolution frequency f 0 = 1/T 0  Accumulator: T 0 ~1.6  sec (1e10 pbar = 1 mA) f 0 (core) Hz 127th Harmonic ~79 MHz

Paul Derwent 18-Oct-15 9 Idea Behind Stochastic Cooling o Phase Space Compression: Dynamic Aperture: Area where particles can orbit Liouville’s Theorem * : Local Phase Space Density for conservative system is conserved *J. Liouville, “Sur la Théorie de la Variation des Constantes arbitraires”, Journal de Mathematiques Pures et Appliquées”, p. 342, 3 (1838) WANT TO INCREASE PHASE SPACE DENSITY! x x’ x

Paul Derwent 18-Oct Idea Behind Stochastic Cooling o Principle of Stochastic cooling  Applied to horizontal  tron oscillation o A little more difficult in practice. o Used in Debuncher and Accumulator to cool horizontal, vertical, and momentum distributions  COOLING? Temperature ~ minimize transverse KE minimize  E longitudinally Kicker Particle Trajectory

Paul Derwent 18-Oct Why more difficult in practice? o Standard Debuncher Operation:  10 8 particles, ~uniformly distributed  Central revolution frequency Hz »Resolve seconds to see individual particles! »100 THz antennas = 3 µm!  pickups, kickers, electronics in this frequency 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

Paul Derwent 18-Oct Simple Betatron Cooling With correction ~ g, where g is related to gain of system  New position: x - g o Emittance Reduction: RMS of kth particle

Paul Derwent 18-Oct Stochastic Nature? o Result depends upon independence of the measured centroid in each sample  In case where have no frequency spread in beam, cannot cool with this technique!  Some number of turns M to completely generate independent sample o But…  Where is randomization occurring? »WANT: kicker to pickup GOOD MIXING »ALSO HAVE: pickup to kicker BAD MIXING

Paul Derwent 18-Oct Cooling Time o Electronic Noise:  Random correction applied to each sample  More likely to heat than cool  Noise/Signal Ratio U  High Bandwidth  Low Noise  Optimum Gain (in correction g) goes down as N goes up!

Paul Derwent 18-Oct Momentum Cooling  Time evolution of the particle density function,  (E) = ∂N / ∂E  Fokker-Planck Equation -- c first used to describe Brownian motion o Two Pieces:  Coherent self force through pickup, amplifier, kicker »Directed motion of the particle  Random kicks from other particles and electronic noise »Diffusive flux from high density to low density

Paul Derwent 18-Oct Simple Example o Linear Restoring Force with Constant Diffusive Term (Electronic noise)  Gaussian Distribution o Inject at E> E 0  Coherent force dominates --- collected into core!  E0E0 ‘Stacked’ F(E) D(E) Simulation!

Paul Derwent 18-Oct Types of Momentum Cooling o Filter Cooling:  Use Momentum - Frequency map  Notch Filters for Gain Shaping »Debuncher »Recycler »Stack tail (as correction) Splitter Combiner Adjustable Delay Notch Filter

Paul Derwent 18-Oct Types of Momentum Cooling o Palmer Cooling  Use Momentum - Position Map in regions of Dispersion  Pickup Response vs Position to do Gain Shaping »Accumulator Core: Signal(A) - Signal(B) »Accumulator Stacktail (described in coming slides) AB Beam Distribution Top View

Paul Derwent 18-Oct Momentum Stacking Van der Meer’s solution: desire constant flux past energy point  static solution !

Paul Derwent 18-Oct Van der Meer’s Solution To build constant flux, build voltage profile which is exponential in shape and results in density distribution which is exponential in shape!

Paul Derwent 18-Oct  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

Paul Derwent 18-Oct Implementation in Accumulator o How do we build an exponential gain distribution? o 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

Paul Derwent 18-Oct Beam Pickups o At A: Current induced by voltage across junction splits in two, 1/2 goes out, 1/2 travels with image current A I

Paul Derwent 18-Oct Beam Pickups o 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 Derwent 18-Oct Current Intercepted by Pickup  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 Use Method of Images

Paul Derwent 18-Oct Accumulator Pickups  Placement  number of pickups  amplification  used to build gain shape  Also use Notch filters to zero signal at core Stacktail Core = A - B Energy Gain Energy Stacktail Core

Paul Derwent 18-Oct Accumulator Stacktail o Not quite as simple:  -Real part of gain cools beam  frequency depends  on momentum  f/f = -  p/p (higher f at lower p)  Position depends on momentum  x = D  p/p  Particles at different positions have different flight times  Cooling system delay constant »OUT OF PHASE WITH COOLING SYSTEM AS MOMENTUM CHANGES

Paul Derwent 18-Oct Accumulator Stacktail Use two sets of pickups at different Energies to create exponential Distribution with desired phase Characteristics Stacktail Design Goal For Run II E d ~ 7 MeV Flux ~ 35 mA/hour Show simulation!

Paul Derwent 18-Oct Performance Measurements o Fit to exponential in region of stacktail ( in these units) o Calculate Maximum Flux for fitted gain shape o Different beam currents o Independent of Stack Size o Max Flux ~30 mA/hour

Paul Derwent 18-Oct Performance Measurements EngineeringRun IiaBest Achieved Run Goal Protons on Target3.8e125e125e12 Cycle Time (sec) Production Efficiency (pbars/10 6 protons) Stacking Rate (1e10 per hour)  Stacking rate limited by input flux and cycle time »Which we limit because of core-stacktail coupling problems

Paul Derwent 18-Oct Performance Measurements o Best Performance:  39.9 mA in 4 hours o Restricted by core- stacktail couplings

Paul Derwent 18-Oct Stacktail - Core Coupling o Coupling in regions where frequency bands overlap  2-4 GHz ! much larger than previous overlap o Two phenomena  Coherent beam feedback »Stacktail kicks beam and coherent motion is seen at core  Misalignment gives transverse - longitudinal coupling »Try to correct with  kickers Pickup Kicker Beam Since beam does not decohere, Carry information back to pickup Feedback! Schottky Pickup Stacktail Core

Paul Derwent 18-Oct Stacktail Schottky Signals Core Freshly injected beam Later in cycle Stacktail Leg1

Paul Derwent 18-Oct Core 2-4 Schottky Signals Core Freshly injected beam Later in cycle Stacktail Leg1

Paul Derwent 18-Oct Pbar Longitudinal Distribution

Paul Derwent 18-Oct Antiprotons & the Collider o From the H - source, Linac, booster, Main Injector  120 GeV protons on the target o From the target:  8 GeV antiprotons through the Debuncher & Accumulator o Send them off to the Tevatron & D0 & CDF