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Intermediate Accelerator Physics and Beam Measurements Jan 18 – Jan 22, 2010 at San Francisco, CA

Intermediate Accelerator Physics and Beam Measurements Jan 18 – Jan 22, 2010 at San Francisco, CA. instructors: Michiko Minty (BNL) and Frank Zimmermann (CERN) this is a 1 week course consisting of daily lectures daily homework computer labs

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Intermediate Accelerator Physics and Beam Measurements Jan 18 – Jan 22, 2010 at San Francisco, CA

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  1. Intermediate Accelerator Physics and Beam Measurements Jan 18 – Jan 22, 2010 at San Francisco, CA instructors: Michiko Minty (BNL) and Frank Zimmermann (CERN) this is a 1 week course consisting of daily lectures daily homework computer labs final exam (open book / open notes) the course may be audited or taken for credit (decision by end of Tuesday) 2 UC Santa Cruz quarter units of credit are granted* for this course grading will be based as follows: homework (50%) computer lab (20%) final exam (30%)

  2. Course outline: Mon Beam Diagnostics Transverse Optics Measurement and Correction Transverse Optics Measurement and Correction, continued Orbit Measurement and Correction Computer Lab Longitudinal Optics Measurement and Correction Longitudinal Beam Manipulation Computer Lab Injection and Extraction Beam Polarization Computer Lab Contingency (and/or special topic) Final Exam Tues Wed Thur Fri

  3. a few comments concerning the book “Measurement and Control of Charged Particle Beams”: attempt to organize in a coherent way the multitude of measurement techniques presented in many conference proceedings and lab internal notes provide (easy-to-access) references focus on “bridging the gap” between theory used and experimental results provide wherever appropriate real data from existing accelerators include exercises (many from real-life experiences) and solutions

  4. Diagnostics I Introduction Beam Current Beam Position Summary Introduction Transverse Beam Emittance Longitudinal Beam Emittance Summary Diagnostics I Diagnostics II

  5. Introduction Accelerator performance depends critically on the ability to carefully measure and control the properties of the accelerated particle beams In fact, it is not uncommon, that beam diagnostics are modified or added after an accelerator has been commissioned This reflects in part the increasingly difficult demands for high beam currents, smaller beam emittances, and the tighter tolerances place on these parameters (e.g. position stability) in modern accelerators A good understanding of diagnostics (in present and future accelerators) is therefore essential for achieving the required performance A beam diagnostic consists of the measurement device associated electronics and processing hardware high-level applications focus of lectures on diagnostics subject of many recent publications and internal reports (often application specific) remainder of course

  6. Fields of a relativistic particle induced wall current iw(t) has opposite sign of beam current ib(t): ib(t)=-iw(t) Lorentz-contracted “pancake” Detection of charged particle beams – beam detectors: iw is a current source with infinite output impedance, iw will flow through any impedance placed in its path many “classical” beam detectors consist of a modification of the walls through which the currents will flow Sensitivity of beam detectors: (in ) = ratio of signal size developed V() to the wall current Iw() beam charge: (in /m) = ratio of signal size developed /dipole mode of the distribution, given by D()=Iw() z, where z = x (horizontal) or z = y (vertical) beam position:

  7. Beam Current – the Faraday Cup (1) thick (e.g. ~0.4 m copper for 1 GeV electrons) or series of thick (e.g. for cooling) charge collecting recepticles Principle: beam deposits (usually) all energy into the cup (invasive) charge converted to a corresponding current voltage across resistor proportional to instantaneous current absorbed In practice: termination usually into 50 ; positive bias to cup to retain e- produced by secondary emission; bandwidth-limited (~1 GHz) due to capacitance to ground cylindrically symmetric blocks of lead (~35 rad lengths) carbon and iron (for suppression of em showers generated by the lead) bias voltage (~many 100 Volts) for suppression of secondary electrons cross-sectional view of the FC of the KEKB injector linac (courtesy T. Suwada, 2003)

  8. Beam Current – the Faraday Cup (2) photo of FC used in the BNL tandem-to-downstream transfer lines “Beam instrumentation for the BNL Heavy Ion Transfer Line”, R.L. Witkover et al, 1987 PAC http://www.n-t-g.de/beam_diagnostic_Seite_2.htm

  9. Beam Current – Current Transformers (1) Consider a magnetic ring surrounding the beam, from Ampere’s law: if r0 (ring radius) >> thickness of the toroid, Add an N-turn coil – an emf is induced which acts to oppose B: Load the circuit with an impedance; from Lenz’s law, iR=ib/N: Principle: the combination of core, coil, and R produce a current transformer such that iR (the current through the resistor) is a scaled replica of ib. This can be viewed across R as a voltage.

  10. Beam Current – Current Transformers (2) with Rh = reluctance of magnetic path sensitivity: cutoff frequency, L, is small if L~N2 is large trade-off between bandwidth and signal amplitude detected voltage: if N is large, the voltage detected is small

  11. Beam Current – Current Transformers (3) A iron B Mu-metal C copper D “Supermalloy” (distributed by BF1 Electronique, France) with ~ 8104 E electron shield F ceramic gap shielding schematic of the toroidal transformer for the TESLA Test facility (courtesy, M. Jablonka, 2003) (based on design of K. Unser for the LEP bunch-by-bunch monitor at CERN) linacs: resolution of 3106 storage rings: resolution of 10 nA rms details: www.bergoz.com (one of many) current trans- formers available from Bergoz Precision Instru- ments (courtesy J. Bergoz, 2003)

  12. Beam Current – Current Transformers (4) recent developments of toroids for TTF II (DESY) 2 iron halves 50 output impedance ferrite ring calibration windings (25 ns , 100 mV / dvsn) bronze pick-ups ferrite rings (for suppression of high frequency resonance) (courtesy D. Noelle, L. Schreiter, and M. Wendt, 2003)

  13. Beam Current – Current Transformers (5) http://www.agsrhichome.bnl.gov/RHIC /Instrumentation/Systems/DCCT “Overview of RHIC Beam Instrumentation and First Experience from Operations”, P. Cameron et al, DIPAC 2001

  14. Beam Current – Current Transformers (6) “Diagnostics and Feedback system update for NSLS-II Storage Ring”, Om Singh and Igor Pinayev (2007)

  15. Beam Current – Current Transformers (7) Bergoz tests of a their wide-band “in flange” current transformer S21 measurement showing frequency-independent response up to very high frequency http://www.bergoz.com/products/In-Flange.CT/In-flange-downloads/files/TN_FCT_04-08r1.pdf output input Bench-test with 50 Ω source and output impedance Beam-test with infinite source and 50 Ω output impedance

  16. Beam Current – Wall Gap / Current Monitor (1) principle: remove a portion of the vacuum chamber and replace it with some resistive material of impedance Z detection of voltage across the impedance gives a direct measurement of beam current since V= iw(t) Z = -ib(t) Z (susceptible to em pickup and to ground loops) add high-inductance metal shield add ferrite to increase L add ceramic breaks add resistors (across which V is to be measured) alternate topology - one of the resistors has been replaced by the inner con- ductor of a coaxial line

  17. Beam Current – WCM (2) sensitivity: circuit model using parallel RLC circuit: high frequency response is determined by C: (C =1/RC) low frequency response determined by L: (L =R/L) intermediate regime:R/L <  < 1/RC – for high bandwidth, L should be large and C should be small remark: this simplified model does not take into account the fact that the shield may act as a resonant cavity

  18. Beam Current – WCM (3) RHIC design based on prototype WCM shown below by R.C. Webber. “The RHIC [WCM] system”, P. Cameron, et al, PAC (1999) resistors ceramic gap ferrite “An Improved Resistive Wall Monitor”, B. Fellenz And Jim Crisp, BIW (1998) for the FNAL main injector “Longitudinal Emittance: An Introduction to the Concept and Survey of Measurement Techniques Including Design of a Wall Current Monitor”, R.C. Webber (FNAL, 1990) available at: http://www.agsrhichome.bnl.gov/RHIC/Instrumentation/Systems/WCM /WCM%20Shafer%20BIW%201989%2085_1.pdf

  19. Beam Current – WCM (4) RHIC 01/16/10; ~ 100 ns bunch spacing peak detector  bunch intensity (near) real-time fitting  bunch lengths

  20. Beam Current – BPM Sum signals U U ~ up D ~ down L ~ left R ~right L R D (figure, courtesy M. Wendt, 2003) beam “position” VR-VL (horizontal) VU-VD (vertical) beam intensity VR+VL, VU+VD, VR+VL+VU+VD normalized (intensity-independent) beam position = “position” intensity Remarks:1) as we will see, higher-order nonlinearities must occassionally be taken into account 2) in circular e+/- accelerators, assembly is often tilted by 45 degrees

  21. Beam Position – Capacitive Monitors (1) (capacitive monitors offer better noise immunity since not only the wall current, but also PS and/or vacuum pump returns and leakage current, for example, may flow directly through the resistance of the WGM) principle: vacuum chamber and electrode act as a capacitor of capacitance, Ce, so the voltage generated on the electrode is V=Q/Ce with Q = iwt = iw L/c where L is the electrode length and c = 3  108 m/s long versus short bunches: since the capacitance Ce scales with electrode length L, for a fixed L, the out- put signal is determined by the input impedance R and the bunch length  (bunch long compared to electrode lengthL) the electrode becomes fully charged during bunch passage signal output is differentiated signal usually coupled out using coax attached to electrode for c for c output voltage rises rapidly and is followed by extended negative tail (since dc component of signal is zero) induced voltage usually detected directly through a high impedance amplifier

  22. Beam Position – Capacitive Monitors (2) (r0,0) • position information: • replace cylinder by curved electrodes (usually 2 • or 4) symmetrically placed with azimuth +/- • (usually small to avoid reflections between the • edges and the output coupling) example – capactive split plate: surface charge density  due to a unit line charge collinear to electrodes at (r0,0) integrate over area of electrode the current on a single electrode depends on the detector geometry via the radius a and the angle subtended by the electrode; e.g. if the signal from a single electrode is input into a frequency analyzer, higher harmonics arise due to these nonlinearities voltage across impedance R sensitivity the voltage and sensitivity are large if the azimuthal coverage is large or the radius a is small; e.g. =30deg, R = 50 , a = 2.5 cm  S = 2 /mm

  23. Beam Position – Capacitive Monitors (3) example – capactive split cylinder: charge in each detector half is found by integrating the surface charge density: (can be shown) detected voltage sensitivity the capacitive split cylinder is a linear detector; there are no geometry -dependent higher order contributions to the position sensitivity.

  24. Beam Position – Capacitive Monitors (4) BNL Booster andBooster – to – AGS transfer line side-view end-view http://www.agsrhic home.bnl.gov/RHIC/ Instrumentation /Systems/BPM/ InjectionBPMmaps/ InjectionBPMfit.html figures from “Design and Testing of the AGS Booster BPM Detector”, R. Thomas et al, PAC (1991) See also “The AGS Booster [BPM] System” and “Design of the AGS Booster [BPM] Electronics, D.J. Ciardullo et al, PAC (1991)

  25. Beam Position – Button Monitors (1) Buttons are used frequently in synchrotron light sources are a variant of the capacitive monitor (2), however terminated into a characteristic impedance (usually by a coax cable with impedance 50 ). The response obtained must take into account the signal propagation (like for transmission line detectors, next slide) button electrode for use between the undulators of the TTF II SASE FEL (courtesy D. Noelle and M. Wendt, 2003) cross-sectional view of the button BPM assembly used in the DORIS synchrotron light facility design reflects geometrical constraints imposed by vacuum chamber geometry note: monitor has inherent nonlinearities (courtesy O. Kaul, 2003)

  26. Beam Position – Button Monitors (2) Four wide band button pickups (two horizontal and two vertical in each ring) “Analysis of Intensity Instability Threshold at Transition in RHIC”, W. Fischer et al, EPAC (2008) “Electron Cloud and Single-Bunch Instabilities in [RHIC]”, J. Wei et al, HB2006 (2006)

  27. Beam Position – Stripline / Transmission Line Detectors (1) principle: electrode (spanning some azimuth ) acts as an inner conductor of a coaxial line; shield acts as the grounded outer conductor  signal propagation must be carefully considered unterminated transmission line R1 Z0 transmission line terminated (rhs) to a matched impedance ZL R1 R2 reminder: characteristic impedance Z0 terminated in a resistor R 0 if R=Z0 -1if R=0 >0 if R>Z0 <0 if R<Z0 R-Z0  = reflection coefficient = = R+Z0  = 1-  = transmission coefficient

  28. Beam Position – Stripline / Transmission Line Detectors (2) equivalent circuit (approximation: velocity of iw = velocity of ib, approximately true in absence of dielectric and/or magnetic materials) (R1 = R2 = Z0) Consider a beam travelling from left to right. The voltage appearing across each resistor is evaluated by analyzing the current flow in each gap: voltage at R1: (+ higher-order terms) reflection initial (+ higher-order terms) beam delay transmission

  29. Beam Position – Stripline / Transmission Line Detectors (3) similarly, voltage at R2: transmission signal delay voltage on each resistor: beam delay reflection initial special cases: (i) R1=Z0, R2=0 (terminated to ground) (ii) R1=R2= ZL(matched line) (iii)R1=R2≠ ZL then solution as in (ii) to second order in 

  30. Beam Position – Stripline Monitors (4) again, sensitivity signal peaks at spacing between zeros sensitivity of a matched transmission line detector of length L=10 cm ( l=c/f ) the LEUTL at Argonne shorted S-band quarter-wave four-plate stripline BPM (courtesy R.M. Lill, 2003) specially designed to enhance port isolation (using a short tantalum ribbon to connect the stripline to the molybdenum feedthrough connector) and to reduce reflections L=28 mm (electrical length ~7% longer than theoretical quarter-wavelength), Z0=50 

  31. Beam Position – Stripline Monitors (5) 72 dual-plane BPMs in IRs 174 single-plane BPMs in arcs + 6 new BPMs per ring 324 detectors per ring figures from “RHIC Beam Position Monitor Assemblies”, P.R. Cameron et al, PAC (1993) see also “RHIC BPM System Modifications and Performance”, T. Satogata et al, PAC (2005)

  32. Beam Position – Cavity BPMs (1) principle: excitation of discrete modes (depending on bunch charge, position, and spectrum) in a resonant structure; detection of dipole mode signal proportional to bunch charge, qtransverse displacement, x theoretical treatment: based on solving Maxwell’s equations for a cylindrical waveguide with perpendicular plates on two ends motivation: high sensitivity (signal amplitude / m displacement) accuracy of absolute position, LCLS design report dipole mode cavity BPM consists of (usually) a cylindrically symmetric cavity, which is excited by an off-axis beam: reference: “Cavity BPMs”, R. Lorentz (BIW, Stanford, 1998) amplitude detected at position of antenna contains contributions from both modes  signal processing TM010, “common mode” (I) TM110, dipole mode of interest

  33. Beam Position – Cavity BPMs (2) pioneering experiments: 3 C-band cavity “RF” BPMs in series at the FFTB (SLAC) 25 nm position resolution at 1 nC bunch charge (courtesy, T. Shintake, 2003)

  34. Summary Detection of the wall current Iw allows for measurements of the beam intensity and position The detector sensitivities are given by for the beam intensity for the horizontal position with for the vertical position We reviewed basic beam diagnostics for measuring: the beam current – using Faraday cups, current transformers and BPM sum signals the beam position - using wall gap monitors - using capacitive monitors (including buttons) - using stripline / transmission line detectors - using resonant cavities We note that the equivalent circuit models presented were often simplistic. In practice these may be tailored given direct measurement or using computer models. Impedances in the electronics used to process the signals must also be taken into account as they often limit the bandwidth of the measurement. Nonetheless, the fundamental design features of the detectors presented were discussed (including variations in the designs) highlighting the importance of detector geometries and impedance matching as required for high sensitivity

  35. RHIC LF Schottky stub-tunes ¼-wave resonator frequency ~ 240 MHz (8.5 times rf frequency) Qloaded ~ 100 translatable “LARP Schottky Collaboration Proposal”, K. Vetter, LARP Danfords (2003) http://www.cadops.bnl.gov/RHIC/Instrumentation/schottky/docs “Resonant BPM for Continuous Tune Measurement In RHIC”, M. Kesselman et al, PAC (2001)

  36. RHIC HF Schottky frequencies: 2.071 GHz, df~4 MHz transverse 2.742 GHz, longitudinal Qloaded ~ 4700 translatable “Design of a Schottky Signal Detector for Use at [RHIC]”, W. Barry et al, EPAC (1998) http://www.cadops.bnl.gov/RHIC/Instrumentation/schottky/docs

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