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 xx 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