Outline Some Traditional Methods of Measuring Emittance Emittance Dependence on Envelope Mode Frequency Experimental Excitation of Envelope Resonances at the University of Maryland Electron Ring UMER ID: 1043592
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1. Will Stem3-19-2015Resonant Excitation of Envelope Modes as an Emittance Diagnostic in High-Intensity Circular Accelerators
2. OutlineSome Traditional Methods of Measuring EmittanceEmittance Dependence on Envelope Mode FrequencyExperimental Excitation of Envelope Resonances at the University of Maryland Electron Ring (UMER)Using Simulations to Infer Emittance from Experimental MeasurementsApplication to Other High-Intensity Circular Accelerators
3. Measuring EmittanceUli Raich. USPAS Lecture Notes, http://uspas.fnal.gov/materials/09UNM/Emittance.pdfWire ScannersPepperpotsQuad Scans
4. My IdeaNew method of measuring emittanceSensitiveNon-invasiveWorks for high-intensity beams in circular acceleratorsNow: brief introduction to envelope modes
5. Beam Envelope in the Smooth Approximation Described by the rms Envelope Equations:For simplicity, approximate A-G lattice by an average focusing forcematched envelope (smooth)singleparticletrajectory
6. “1-D” Simple Harmonic Motion Envelope Modes Equations of Motion:Mode Coordinates:Y “Breathing”“Quadrupole”Perturbations to the matched envelope solutions of the rms Envelope Equations drive envelope mode oscillationsY
7. Space-Charge EffectsPhase advance can be used as a measure of space-charge intensitymatched envelope (smooth)Undepressed Single Particle Trajectory ~ s0Space-Charge Depressed Single Particle Trajectory ~ s So in this case, normalized phase advance is
8. Breathing ModeQuadrupole ModeEnvelope Modes in the Smooth ApproximationMode scaling as a function of space-charge (normalized phase advance)Type equation here. Quad Mode Frequencies
9. Beam Energy: 10 keV 11.52 m CircumferenceCirculation Time: 197 nsBunch Length: 100 ns72 Quadrupole Focusing Magnets14 Beam Diagnostic Ring Chambers (RCs) University of Maryland Electron Ring (UMER)Robust, scalable research facility for intense-beam experiments
10. Tunable UMERAperture wheel Tunes Beam Current/ IntensityMask SettingExpected Quad Mode Frequency0.6 mA65.5 MHz6 mA48.1 MHz21 mA36.9 MHz40 mA33.7 MHz21 mA6 mA
11. Experimental OutlineMaster Control for Time Delay~Do this for a range of emittances (Bias Voltages)Excite quadrupole mode with RF-driven electric quadrupole at RC9RF-Driven QuadrupoleKO PulserFast Phosphor Screen3 ns res.Image beam using KO technique with gated PIMAX camera and 3ns-resolution fast phosphor screen at RC8
12. Apparatus – QuadrupoleI designed it in SolidworksI built it in the Machine ShopI simulated it with Maxwell 3D and Poisson SuperfishI simulated fringe field particle tracing in MatlabMeasurementSimulation
13. Apparatus – RF BoxI designed, built, and soldered the RF boxThe quadrupole acts as a capacitor in the RF circuitSimplified Circuit DiagramL2L1RF AntennaCVARCoupling LoopTrim CapacitorVacuum Feedthrough to Quad
14. Reminder – Goal of ExperimentFind the RF driving frequencies at which envelope resonances occurCompare results with simulationInfer Emittance
15. Consider a periodically driven 1-D SHO (Reductionist Toy Model)w0 is the natural (resonant) frequency of the oscillator (env. mode)wk is the RF driving frequency of the quadrupoleA0 is the amplitude of the rf quadrupolen is the number of interactions with the quadrupole (or turn)T is the period between interactions (197 ns)
16. Analytic Solution Three Frequency System …Steady State Structure … Resonance Conditions
17. Resonance Lines (Dispersion Relation)=37 MHz
18. What Frequencies Do Resonances Occur?f0 = 37 MHz 20th Turn
19. Agreement in Simulation and Experiment5th Turn**50 μm per pixel A-G env. solver
20. Resonance Frequencies vs EmittanceBreathing ModeQuadrupole Mode* 30 mm-mrad
21. Resonance Frequencies vs Emittance * 30 mm-mrad
22. Agreement in Simulation and Experiment5th Turn**50 μm per pixel ~9% Adjustment in Emittance!
23. Emittance vs. Bias Voltage…Working on reducing error!* 30 mm-mrad
24. Undepressed Single Particle FrequencySingle Particle Frequency in Core½ Breathing Mode Frequency½ Quadrupole Mode FrequencyCoreX(s)x(s)Measuring Frequency by Beam HaloResonance Conditions for Halo Growth
25. ConclusionsEnvelope mode frequencies can be used as a sensitive, non-invasive emittance diagnostic in high-intensity ringsMeasurements of multi-turn envelope excitations shows good agreement with simulationImprovements can be made by applying more kicks before measurement (and before space-charge bunch-end erosion)Halo formation can be used as a diagnostic in rings with longer beam lifetime
26. AcknowledgementsAdvisor: Tim KoethUMER Group: Brian Beaudoin, Irv Haber, Kiersten Ruisard, Rami Kishek, Santiago Bernal, Dave Sutter, Eric MontgomeryMisc. Advice and Consultations: Steve Lund, Luke Johnson, Aram Vartanyan
27. ReferencesWeiming Guo and S. Y. Lee, Quadrupole-mode transfer function and nonlinear Mathieu instability, Phys. Review E, Vol. 65, 066505.M. Bai, Non-Destructive Beam Measurements, Proc. of EPAC 2004, Lucerne, Switzerland.S.M. Lund and B. Bukh, Stability Properties of the Transverse Envelope Equations Describing Intense Ion Beam Transport, PRST-AB 7, 024801 (2004)M. Reiser, Theory and Design of Charged Particle Beams (2nd Edition, Wiley-VCH, 2008).
28. Resonant Growth
29. Amplitude Dependence Chosen Kick Amplitude for Simulations
30. Mid-DriftXrmsYrmsEnvelope SimulationsPhase Scan @ 36.89 MHz
31. Experimental Phase ScanPhase Scan @ 37 MHzPhase (Nearly 3 Periods)Normalized Beam SizeXrmsYrms**X,Y not 180 degree out of phase due to skew?
32. PIC Code HaloBeam with no haloBeam with haloWARP PIC simulations of experiment