Emittance Dilution In Electron/Positron Damping Rings David Rubin (for Jeremy Perrin, Mike Ehrlichman, Sumner Hearth, Stephen Poprocki, Jim Crittenden, and Suntao Wang)
Outline CESR Test Accelerator Single Particle Emittance Current dependent effects Intra-beam scattering Emittance growth from transverse wakefields Electron cloud induced emittance growth Summary/Conclusions January 4, 216 University of Chicago 2
January 4, 216 CESR Test Accelerator R&D University of Chicago 3 Cornell Electron/Positron Storage Ring (CESR) 768 m circumference Energy reach: 1.8 GeV < E < 6 GeV CESR operates at 5.3 GeV for CHESS (Cornell High Energy Synchrotron Source) Horizontal emittance ε x ~ 1 nm 2.1 GeV as CesrTA (CESR Test Accelerator) Horizontal emittance ε x ~ 2.5 nm
Manipulate/control beams ~ 3 magnets Dipoles - Steer Quadrupoles - Focus Sextupoles -Compensate energy spread Skew quadrupoles - Compensate coupling Wigglers - Vary radiation damping Pulsed magnets drive oscillations 4 SRF Accelerating cavities focusing and vary bunch length Monitor beams 1 Beam position montors X-ray and visible synchrotron light beam size monitors Tune tracker Current monitors Bunch length measurement Spectral measurement Storage Ring - CESR Monitor beam environment Retarding field analyzers, shielded pickups, resonant microwave detection > electron cloud Residual gas analyzers Pressure gauges Thermometry Control System Modeling codes Lattice design and correction Orbit,coupling,beta closed bumps Tracking simulations January 4, 216 University of Chicago 4
Laboratory CESR, reconfigured as CesrTA is a laboratory for investigating the physics of low emittance charged particle beams Intra-beam scattering Fast ion effect Single particle emittance Emittance tuning Wakefields and impedances Particle beam optics Electron cloud growth and mitigation Electron cloud beam dynamics January 4, 216 University of Chicago 5
Emittance Emittance ε x ~ σ x σ x (product of size and divergence) σ x σ x' = q hx 2 ihp x 2 i + hxp x i 2 Two broad categories of effects contribute to emittance of a stored electron (or positron beam) Single particle effects volume of a single particle in phase space on multiple turns Collective effects that depend on the number and density of particles in a bunch. January 4, 216 University of Chicago 6
January 4, 216 University of Chicago 7 Single Particle Emittance Outline
Damping Ring In the rest frame of a bunch - h~pi = Kinetic energy of the particles corresponds to a temperature, and we can assign an equivalent temperature to motion in each of x,y and z Hot bunches are injected into a damping ring, and cold bunches extracted i.e. - ILC damping ring reduces emittance of positron bunch by 6 orders of magnitude at a repetition rate of 5 Hz January 4, 216 University of Chicago 8
Closed Orbit January 4, 216 University of Chicago 9 Phase space coordinates are mapped through a single turn 1 x Bp x C @ y A p y start Full Turn(!) 1 x Bp x C @ y A p y For particles with coordinates on the closed orbit 1 x Bp x C @ y A p y start = 1 x Bp x C @ y A p y end end
Closed orbit January 4, 216 University of Chicago 1 Simple closed orbit in uniform vertical B-field closed orbit If the initial coordinates are displaced from the closed orbit the trajectory will oscillate about it. x(s) =a p (s) cos( (s) ) (s = C) =2 Q The area in phase space mapped out in subsequent turns is the single particle emittance
Closed Orbit January 4, 216 University of Chicago 11 The closed orbit is generally not a simple circle Two beam operation for CHESS Electrostatic separators differentially kick electrons and positrons generating distinct closed orbits Positron Transfer Electron Transfer Electrons Positrons Xray Source Feedback Kicker Separator IP_L
January 4, 216 University of Chicago 12 The closed orbit depends on the energy Dispersion On energy closed orbit High energy closed orbit Dispersion ~ = d~x d
Dispersion January 4, 216 University of Chicago 13 (s) The form of the dispersion is determined by the bending field and the quadrupole focusing η[cm] 3 2 1 6 384511-441 L L1 L3 L5 L Dispersion in CesrTA optics β y [m] 4 2 6 β x [m] 4 2 1 2 3 4 5 6 7 s[m]
January 4, 216 University of Chicago 14 Radiation excitation In the absence of any disturbance, a particle on the closed orbit will remain there and the single particle emittance is zero. Electrons emit photons due to synchrotron radiation with some probability distribution depending on energy and local B-field. Photons are emitted very nearly tangent to particle trajectory ~p ~p e To first order, only the energy of the electron is changed. The electron is abruptly displaced from the appropriate closed orbit by ~x = E E ~ The electron begins to oscillate about its new closed orbit
CESR parameters 5.3 GeV Beam energy ~ 8 photons are emitted/electron/turn corresponding to ~1 MeV Energy is restored by RF cavities p z = p z + qhv z i Radiation damping p z January 4, 216 University of Chicago 15 = (1 p z p z )
Equilibrium January 4, 216 University of Chicago 16 The radiation damping time corresponds to the number of turns to radiate all of the energy CESR at 5.3 GeV => 53 turns (~15 ms) Equilibrium of radiation excitation due to photon emission and radiation damping which depends on the average energy loss per turn => emittance Equilibrium horizontal emittance depends on 2 Beam energy (number and energy of radiated photons ~ ) Dispersion function Energy loss/turn
January 4, 216 CesrTA Low Emittance Optics University of Chicago 17 CesrTA 2.1 GeV Superconducting wigglers in zero dispersion straight increase radiation damping (X1) without adding to radiation excitation ε x ~ 2.5 nm η[cm] 3 2 1 384511-441 L L1 L3 L5 L 13cm β y [m] 6 4 2 7cm thick yoke plate flux return and support. Iron poles with superconduc ting coils 2cm 7.6cm β x [m] 6 4 2 1 2 3 4 5 6 7 s[m]
Vertical emittance January 4, 216 University of Chicago 18 In the horizontal plane, dispersion cannot be avoided. The particles have to go around in a circle. But not so the vertical. In a planar ring with magnets perfectly aligned, there are no vertical dipole kicks The vertical component of the closed orbit is independent of energy. Radiation of straight ahead photons contributes nothing to the emittance. Single particle vertical emittance is typically dominated by misalignments y
January 4, 216 University of Chicago 19 Photon emission is not precisely straight ahead Quantum Limit The small but nonzero transverse momentum of the photon recoils off of the particle. The theoretical minimum vertical emittance, the quantum limit, obtains when the vertical dispersion vanishes. In a couple of storage rings (considerably smaller than CESR), vertical emittance approaching the quantum limit has been achieved. In CesrTA, ε y ~ 1 15 pm (< 1% ε x ) The quantum limited vertical emittance <.1 pm θ~1/γ
January 4, 216 University of Chicago 2 Current Dependent Effects Intra-beam scattering (Mike Ehrlichman) Beam moving in z direction y z x p x p y p y p x Horizontal into longitudinal Intra-beam scattering can transfer horizontal momentum into vertical x z p z p x p x p z p z Exchange z momenta
IBS - 2.1 GeV January 4, 216 University of Chicago 21 Bands come from systematic uncertainty in measurement of zero-current vertical beam size Run ID Zero Current ε y (pm) ε x (nm) High Current (data) ε x (7.5 1 1 part) (nm) Low ε y 9.6 13.9 3.6 7.25 Med ε y 54.2 63.8 3.6 6.55 High ε y 163.6 179.9 3.5 5.18
2.3 GeV Results (V15) January 4, 216 University of Chicago 22 Run ID Input Parameters ε y (pm) ε x (nm) Result at high current ε x (7.5 1 1 ) (nm) Low ε y 4.9 8.1 5.7 1.4 High ε y 52.3 61.8 5.7 7.62
Intra-Beam Scattering January 4, 216 University of Chicago 23 The direct transfer of momentum from horizontal to vertical by IBS is small Dominant contribution to IBS emittance growth is due to exchange of longitudinal momentum coupled with dispersion IBS effects are most evident in the horizontal dimension And small in the vertical since v h The amount of the blow-up can be controlled by varying the vertical emittance, and thus the particle density. Coupling [%] Vertical dispersion[cm] 384511-45 2 1 C 12-1 -2 1 2 3 4 5 6 7 4 2 η y -2-4 1 2 3 4 5 6 7 s[m] Closed vertical dispersion/coupling bump through wigglers generate vertical emittance without introducing global coupling
Wakefield induced emittance growth January 4, 216 University of Chicago 24 Vertical Beam Size (µm) 38 36 34 32 3 28 26 b) Model (with tail-cut) Data 2 4 6 8 1 12 14 (N/bunch) 1 1 Puzzle Abrupt change in slope of vertical beam vs current at ~6 X1 1 particles Observed to depend on synchrotron tune and vertical betatron tune The phenomenon is not intra-beam scattering (positive curvature) Observed with both electron and positron beams
Current Dependent Effects Transverse Wakefields (Jeremy Perrin, Stephen Poprocki) January 4, 216 University of Chicago 25
January 4, 216 University of Chicago 26 Wake Formalism Two particles, drive (a) and witness (b), travel through some vacuum chamber geometry. Wake is time-integrated force on witness particle Longitudinal and transverse components Depends on, the delay of the witness relative to the drive Depends on transverse displacement of drive and witness particle
January 4, 216 University of Chicago Wakefields 27 Expand vertical wake about the transverse coordinates Wake Formalism Vertical Monopole Wake Vertical Dipole and Quadrupole Wakes (Cause tune shifts, etc.) Transverse monopole wakes only occur in the absence of top-down symmetry Or if the beam is displaced in a symmetric structure
Asymmetric Wake Scrapers can be inserted to within 3.5 mm of chamber axis With both scrapers inserted we observe current dependent tune shift, but no blow up. A single scraper causes significant increase in vertical beam size Motivation: Asymmetric Vacuum Chamber Measurements December 214 Scrapers out Bottom scraper Both scrapers January 4, 216 University of Chicago 28
January 4, 216 University of Chicago Off Center beam 29 Recent Measurements (April 215) April 215 Measure current dependence of vertical size as a function of displacement in a narrow gap (undulator) chamber (4.5 mm aperture) Displacement generates an effective monopole wake Resonance f y nf s = f s = 22.65 khz
January 4, 216 Simulation of Wakefield Effect University of Chicago 3 Plan A Compute single particle wake (already difficult) Track a distribution of macro-particles Each particle generates a wake that kicks all of the trailing macro-particles Statistical noise dominates effect we are looking for unless the number of macro-particles is impractically large
January 4, 216 Simulation of Wakefield Effect University of Chicago 31 Plan B Note that transverse monopole wakes depend only on longitudinal structure of bunch, but do not influence longitudinal structure of bunch. W y ba (,, ) Therefore, the longitudinal dependence of the wake kick will not vary turn-to-turn. Represent the wake as a single element that applies vertical kick with longitudinal (temporal) dependence 1 x p x y Bp y C @ z A Narrow gap chamber wake
January 4, 216 Simulation of Wakefield Effect University of Chicago 32 Simulations failed to reproduce the observed emittance growth The wake couples longitudinal motion to vertical Perhaps the effect of the wake is to tilt the beam about a horizontal axis increasing the effective (observed) vertical size
January 4, 216 University of Chicago Scraper Wake Element 33 Consider the scraper wake Compute the wake due to the asymmetric scraper CUBIT: cubit.sandia.gov T3P: confluence.slac.stanford.edu/display/advcomp
January 4, 216 University of Chicago Wake Induced Crabbing 34 Tilt depends on the observation point y z tilt sin( v (s) z(s))
January 4, 216 University of Chicago Measurement of Tilt 35 scraper positrons Vary vertical phase advance from source of tilt (scraper) to beam size monitor to determine if observed increase is due to a tilt or emittance growth
January 4, 216 Create multiple lattice configurations University of Chicago 36 4 Bunch tilt 4 Bunch tilt mrad mrad -4-4 6 Projected vertical emittance 4 Projected vertical emittance pm 4 2 pm 2 Change in crabbing phase (degrees) Each of 12 lattices has same global tune but with varying vertical phase from scraper to beam size monitor Change in crabbing phase (degrees) These are the 5 that we tested
Baseline Lattice 45 4 Scrapers Out-Out In-In In-Out Phase + lattice 3 28 Scrapers Out-Out In-In In-Out Phase + lattice V size [µm] 35 H size [µm] 26 24 3 22 25 1 1.5 2 2.5 3 3.5 4 Current [ma] 2 1 1.5 2 2.5 3 3.5 4 Current [ma] Bunch Length [mm] 2 18 16 14 12 1 8 6 Scrapers Out-Out In-In In-Out Scrapers out out Bunch height, width and length vs current Scrapers inserted symmetrically Scrapers withdrawn symetrically One in and one out December 215 1 1.5 2 2.5 3 3.5 4 Current [ma] January 4, 216 University of Chicago 37
January 4, 216 Tilt vs Crabbing Phase & 36 deg University of Chicago 38 45 4 Scrapers Out-Out In-In In-Out Bunch height vs current Phase + lattice 3 28 Bunch width vs current Scrapers Out-Out In-In In-Out Phase + lattice V size [µm] 35 H size [µm] 26 24 3 22 25 1 1.5 2 2.5 3 3.5 4 Current [ma] 2 1 1.5 2 2.5 3 3.5 4 Current [ma] 45 4 Scrapers Out-Out In-In In-Out Phase -36 lattice 3 28 Scrapers Out-Out In-In In-Out Phase -36 lattice V size [µm] 35 H size [µm] 26 24 3 22 25 1 1.5 2 2.5 3 3.5 4 2 1 1.5 2 2.5 3 3.5 4 Current [ma] Current [ma]
Tilt vs Crabbing Phase, 54&72 deg 45 4 Bunch height vs current Scrapers Out-Out In-Out Phase -54 lattice 3 28 Bunch width vs current Scrapers Out-Out In-Out Phase -54 lattice V size [µm] 35 H size [µm] 26 24 3 22 25 1 1.5 2 2.5 3 3.5 4 Current [ma] 2 1 1.5 2 2.5 3 3.5 4 Current [ma] 45 4 Scrapers Out-Out In-In Phase -72 lattice 3 28 Scrapers Out-Out In-Out Phase -72 lattice V size [µm] 35 H size [µm] 26 24 3 22 25 1 1.5 2 2.5 3 3.5 4 2 1 1.5 2 2.5 3 3.5 4 Current [ma] Current [ma] January 4, 216 University of Chicago 39
Wake Induced Growth January 4, 216 University of Chicago 4 Monopole wake due to asymmetric structure tilts bunch in y-z plane Effect of wake on true emittance is small Current dependent increase in vertical size is almost entirely compensated by adjusting the crabbing phase The current dependent growth in horizontal size is indifferent However the coupling of transverse kick and longitudinal phase space coordinates effectively generates vertical dispersion, same as a vertical bend Simulations are underway to determine if our model includes the relevant physics and to make more quantitative comparison of theory and measurements Implications? Vacuum chamber design must preserve top down symmetry Misalignment of the beam in small aperture chambers can generate significant growth in vertical beam size Especially in ultra-low emittance rings with high bunch charge What about the anomalous emittance growth observed in the IBS measurements?
Current Dependent Effects Electron Cloud (Stephen Poprocki, Sumner Hearth, Jim Crittenden) January 4, 216 University of Chicago 41
Electron cloud January 4, 216 University of Chicago 42
Electron Cloud Focusing January 4, 216 University of Chicago 43 What is the effect of the cloud on the beam?
Electron cloud tune shift Train witness Cloud density increases along a train of bunches The cloud electrons focus the traversing positron bunch, shifting the tune The differential focusing (tune shift) is our measure of the increasing cloud density along the train of bunches January 4, 216 University of Chicago 44
Electron cloud emitance growth January 4, 216 University of Chicago 45 Bunch size [µm] 16 14 12 1 8 6 Total Current [ma] 21.56 ma 21.31 ma 19.23 ma 1.93 ma 4 2 5 1 15 2 25 3 Bunch Number Threshold for emittance growth at bunch 13.
Model for emittance growth January 4, 216 University of Chicago 46 Physics models for electron cloud growth and beam dynamics Codes like ECLOUD (Rumolo and Zimmermann) and POSINST (Furman) with SYNRAD3D (Sagan) predict cloud distribution in reasonable agreement with direct measurements (RFA, resonant microwave, shielded pickups) and tune shifts Quantitative estimates of emittance growth are more elusive - CMAD (Pivi) and PHETS (Ohmi) are strong-strong simulations - Both electron cloud and positron bunch are represented as distributions of macro-particles that interact with each other - Limited to tracking through hundreds of turns - But damping times are 2, turns in CesrTA it is impractical to track long enough to equilibrate
Weak Strong Model The electron cloud is the strong beam Compute the cloud distribution using cloud growth codes (i.e. ECLOUD) Job 4136: Beampipe-averaged Cloud Density (1 12 m -3 ) Electron Density (1 12 m -3 ).6.5.4.3.2.1.9.8.7.6.5.4.3 The cloud is pinched by the passing bunch, the density increasing from head to tail.2 3 bunch train, 14ns spacing -1 1 2 3 4 5 6 Time (ns) January 4, 216 University of Chicago 47
January 4, 216 University of Chicago Electron cloud pinch 48 With ECLOUD we compute electron distribution in 11 time slices that extend the length of the bunch.2 Job 4136: Cloud charge snapshots (units are cm) -.2 -.2 -.1.1.2 15222 macroparticles, 2735682 e- at T=46.561 ns.2 -.2 -.2 -.1.1.2 983 macroparticles, 155688 e- at T=434.97 ns.2 -.2 -.2 -.1.1.2.2 1258 macroparticles, 16256958 e- at T=434.2 ns -.2 -.2 -.1.1.2 1261 macroparticles, 19941 e- at T=434.34 ns.2 -.2 -.2 -.1.1.2 14956 macroparticles, 2368338 e- at T=434.47 ns.2 -.2 -.2 -.1.1.2 16517 macroparticles, 536 e- at T=434.51 ns.35.2.3.25.2.15.1.5 -.2 -.2 -.1.1.2 9785 macroparticles, 1549688 e- at T=434.46 ns.2.2.175.15.125.1.75.5.25 -.2 -.2 -.1.1.2 9961 macroparticles, 1575234 e- at T=434.149 ns.2.25.2.15.1.5 -.2 -.2 -.1.1.2.5 1918 macroparticles, 17291198 e- at T=434.252 ns.2.4.3.2.1 -.2 -.2 -.1.1.2 13516 macroparticles, 21367112 e- at T=434.355 ns.45.2.4.35.3.25.2.15.1.5 -.2 -.2 -.1.1.2 15966 macroparticles, 25243816 e- at T=434.458 ns.3.25.2.15.1.5.225.2.175.15.125.1.75.5.25.225.2.175.15.125.1.75.5.25.4.35.3.25.2.15.1.5.7.6.5.4.3.2.1.4.35.3.25.2.15.1.5.5.25 46.561 ns 434.97 ns 434.2 ns 434.47 ns Job 4136: Fits to cloud charge Y distribution 132.7 / 57 P1.1275 P2 -.1477E-2 P3.7977E-1 P4.381 86.83 / 57 P1.1942E-1 P2 -.3222E-2 P3.1E+ P4.249 16.8 / 57 P1.2178 P2.363E-4 P3.9616E-2 P4.25 263.9 / 57 P1.5665 P2.5373E-3 P3.4892E-1 P4.269 434.46 ns 434.149 ns 434.252 ns 434.458 ns 91.42 / 57 P1.1995E-1 P2.1239E-2 P3.1E+ P4.2393 -.2 -.1.1.2 -.2 -.1.1.2.2 97.69 / 57 P1.227E-1 P2 -.1255E-1 P3.6123E-1 P4.2465 135.6 / 57 P1.541 P2.5515E-3 P3.1169E-1 P4.2424 218.7 / 57 P1.5111 P2 -.183E-2 P3.8467E-1 P4.1412 -.2 -.1.1.2 -.2 -.1 19.3 / 57 Y(mm).1.2.5 434.51 ns P1.3249 P2 -.1214E-2.1 P3 P4.2282 -.2 -.1.1.2 Y(mm).2.2 -.2 -.1.1.2 -.2 -.1.1.2.4.2 -.2 -.1.1.2 -.2 1 136.1 / 57 1 -.1.1.2 213.7 / 57 434.34 ns 434.355 ns P1.6414 P1.6392 P2 -.499E-3 P2 -.5563E-4.3111E-1 P3.194E-1 P3.5.5 P4.2313 P4.2197.5 -.2 -.1.1.2 -.2 -.1.1.2.5.25.5 The distribution is ~ Gaussian with varying width and amplitude 15/12/13 11.24
Strong Beam The Cloud January 4, 216 University of Chicago 49 Model the cloud as strong beam with Gaussian charge distribution The parameters of the Gaussian depend on the longitudinal coordinate (x, y, t) =A x (t)a y (t)e Compute A x (t i ),A y (t i ), x(t i ), y(t i ) x 2 y 2 x(t) 2 y (t) 2 with ECLOUD Particles at the head of the positron bunch experience a relatively weak kick Particles near the tail get a much stronger kick Does this representation of the positron bunch / electron cloud interaction predict emittance growth?
January 4, 216 University of Chicago 5 Charge [1 Charge [1 Charge [1 Charge [1 6 e ] Charge [1 Charge [1 6 e ] 6 2 41.5 1 2.5 4 13.5 8 3 2.5 6 2 41.5 1 2.5 448.1 42.1 448.2 42.2 Time [ns] [ns] Bunch 45, 37, Total Cloud x x y y Charge [1 Charge [1 Charge [1 Charge [1 6 e ] Charge [1 Charge [1 6 e ] 6 2 1.5 4 1 2.5 4 3.5 1 8 3 2.5 6 2 1.5 4 1 2.5 448.1 42.1 448.2 42.2 Time [ns] Electron cloud is represented in the tracking Bunch code 37, 33, Total Cloud as a time dependent Bunch 37, 33, Cloud 4 4 Bg 13.5 x x 3.5 1 x beam-beam y y kick 8 3 8 3 y 2.5 2.5 6 11 time slices 2 6 2 41.5 Each slice the kick from 1.5 4 a Gaussian 1 1 2 2.5 charge distribution.5 Charge 448.1 54.1 distribution 448.2 is computed by Time [ns] [ns] ECLOUD for a witness bunch in slot 31 448.1 54.1 448.2 Time [ns] Bunch 45, 37, Cloud Bg x y An electron cloud element is place in each dipole in the CesrTA lattice Positron bunch represented as a 616.154.1 616.2 distribution Time of [ns] [ns] macro-particles 616.1 54.1 616.2 Time [ns] Bunch 45, Cloud Bunch 45, Bg 4 3.5 x 1 x Tracking 3 simulation y includes all magnets y in 8 2.5 the storage ring lattice, (dipoles, 2 6 quad, 1.5 sextupoles, wigglers) and 4radiation 1 2 excitation.5 and damping 616.1 616.2 616.1 616.2 Time [ns] Time [ns] Charge [1 6 e ] Track positrons for several damping times Charge [1 6 e ] Charge [1 Charge [1 6 e ] Charge [1 6 e ] 6 4 2 1 8 6 4 2 1 8 6 4 2 448.1 448.2 Time [ns] Bunch 37, Bg x y 54.1 Time [ns] Bunch 45, Bg x y 616.1 616.2 Time [ns] Simulation We find Significant emittance growth at nominal ecloud charge density Cloud density threshold for emittance growth ~ half nominal No growth at 1% nominal density
3 Bunch train Bunch size [µm] 16 14 12 1 8 6 4 Total Current [ma] 21.56 ma 21.31 ma 19.23 ma 1.93 ma Vertical emittance increases with cloud density with threshold at bunch 13 Tuneshift increases ~ linearly with cloud density 2 5 1 15 2 25 3 Bunch Number vertical tune.64.62.6.598.7ma/bunch 14W 15W 16W 17W 18W 2151217.596 January 4, 216.594 5 1 15 2 25 3 University of Chicago bunch 51
January 4, 216 Witness bunch measuements University of Chicago 52 Generate a cloud with a long train Explore dependence on cloud density by varying delay of witness with respect to train Measure dependence on bunch charge for fixed density by varying charge in witness bunch
Witness Bunch Measurements Bunch Size [µm] 16 14 12 1 8 6 4 Witness Bunch Current [ma] 1..75.5.25 Witness bunches trailing a 3 bunch train (.7mA/bunch) (1mA = 1.6 X 1 1 positrons) 2 3 32 34 36 38 4 42 Bunch Number Vertical emittance growth increases with: Density of the cloud (bunch number) Witness bunch charge (pinch effect) Vertical tune shift increases with cloud density ~ Decreases with pinch vertical tune.6.598.596.594.592.59 1 ma.75 ma.5 ma.25 ma January 4, 216.588 3 35 4 45 5 55 6 bunch University of Chicago 53
Horizontal emittance growth 42 4 train.25ma.5ma.75ma 1.mA 38 Sigma x (um) 36 34 32 3 28 1 2 3 4 5 6 Bunch number Horizontal emittance increases with Cloud density (proximity to train) Tune shift increases with cloud, Decreases with pinch horizontal tune.59.585.58.575.57 1 ma.75 ma.5 ma.25 ma January 4, 216.565 3 35 4 45 5 55 6 University of Chicago bunch 54
Electron Cloud Summary January 4, 216 University of Chicago 55 Goal: Model that quantitatively predicts vertical and horizontal emittance growth and tune shifts due to the cloud We measure Q x, Q y, x, y All three quantities depend on average cloud density, which we control via the train length, bunch current and delay of the witness with respect to the train pinch, independently controlled via the witness bunch current The weak-strong model has promise. We plan to further develop the model and compare predictions with measurements
Sources of Emittance Growth Summary January 4, 216 University of Chicago 56 Single particle emittance (well understood) Correct or compensate sources of vertical dispersion Intra-beam scattering (theory and measurements in good agreement) Minimize dispersion Wakefields (developing the fixed wakefield model) Symmetrize vacuum chambers Minimize transverse impedance of chambers Center beam Electron cloud(developing weak-strong model) Mitigate cloud growth Explore bunch spacing
Speculation January 4, 216 University of Chicago 57 Can we learn to exploit collective effects? Shape the vacuum chamber better focus or stabilize the beam? Taylor the electron cloud to compensate intra-beam scattering? Depends on developing predictive models