Beam Instrumentation Introduction Beam Charge and Current Summary
Beam Instrumentation Introduction Beam Charge and Current Summary Instrumentation I Introduction Beam Position Summary Instrumentation II Introduction Instrumentation for Transverse Beam Parameters Summary Instrumentation III Instrumentation for Longitudinal Beam Parameters Selected Developments Summary Instrumentation IV
Beam Instrumentation II Introduction Beam Position Capacitive Pickups Button BPMs Striplines Cavity BPMs Summary
Beam Position U L D U ~ up D ~ down L ~ left R ~right R (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 e+/- accelerators, assembly is often tilted by 45 degrees
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 wall gap monitor) 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 output signal is determined by the input impedance R and the bunch length for c (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 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 ( c=1/RCe)
Beam Position – Capacitive Monitors (2) 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) (r 0, 0) example – capactive split plate: surface charge density due to a unit line charge collinear to electrodes at (r 0, 0) (from Poisson’s equation ) integrate over area of electrode the voltage 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. =30 deg, R = 50 , a = 2. 5 cm S = 2 /mm
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 L = total length of detector Z 0 = impedance of coaxial line sensitivity the capacitive split cylinder is a linear detector; there are no geometry - dependent higher order contributions to the position sensitivity.
Beam Position – Capacitive Monitors (4) BNL Booster and Booster – to – AGS transfer line side-view end-view http: //www. agsrhic home. bnl. gov/RHIC/ Instrumentation /Systems/BPM/ Injection. BPMmaps/ Injection. BPMfit. html split plate stripline 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)
Beam Position – Button Monitors Buttons are used frequently in synchrotron light sources are a variant of the capacitive monitor, 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 section) 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; monitor has inherent nonlinearities (courtesy O. Kaul, 2003) LHC 24 mm button electrode with curved surface
Beam Position – Stripline Monitors (1) “stripline” beam position monitor (BPM) v vacuum chamber
Beam Position – Stripline / Transmission Line Detectors (3) 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 terminated (rhs) to a matched impedance reminder: R 1 Z 0 ZL R 1 R 2 characteristic impedance Z 0 terminated in a resistor R = reflection coefficient = R-Z 0 R+Z 0 = = (1 - )1/2 = transmission coefficient 0 -1 >0 <0 if R=Z 0 if R=0 if R>Z 0 if R<Z 0
Beam Position – Stripline / Transmission Line Detectors (4) equivalent circuit (approximation: velocity of iw = velocity of ib, approximately true in absence of dielectric and/or magnetic materials) the voltage appearing across each resistor is evaluated by analyzing the current flow in each gap: voltage at R 1: initial beam delay reflection transmission
Beam Position – Stripline / Transmission Line Detectors (5) similarly, voltage at R 2: signal delay voltage on each resistor: transmission beam delay initial reflection special cases: (i) R 1=Z 0, R 2=0 (terminated to ground) (ii) R 1=R 2= ZL (matched line) (iii) R 1=R 2≠ ZL then solution as in (ii) to second order in
Beam Position – Stripline Monitors (6) again, sensitivity signal peaks at spacing between zeros sensitivity of a matched transmission line detector of length L=10 cm 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), Z 0=50
Beam Position – Stripline Monitors (7) 7 stripline monitors in the linac-to-Booster Transfer line Length chosen such that the first peak in the frequency response occurs at 402. 5 MHz – twice the linac bunching frequency (strong signal power nominally without rf interference) “Beam Position Monitoring in the AGS Linac to Booster Transfer Line”, T. J. Shea et al PAC (1991)
Beam Position – Stripline Monitors, Directional BPM (8) A closer look at how the current is generated / how the charges flow: Q Qimage = - Q + Q 1 Vlhs + Q 2 Vrhs (Relativistic) bunch of charge Q passes first gap from left to right. Image charge Qimage = - Q induced on upper surface of lower stripline (and lower surface of upper stripline) The charge/current flow is split depending on the values of the stripline and output impedances with Qimage=Q 1+Q 2 and net charge on left hand side is zero.
Beam Position – Stripline Monitors, Directional BPM (9) With equal impedances in stripline and output impedance: Q Qimage = - Q +Q/2 + Q /2 Vlhs Vrhs Net charge on left hand side: -Q+Q/2=0 Signal voltage Vlhs is a positive pulse (Q/2), dependent on bunch charge and proximity to stripline.
Beam Position – Stripline Monitors, Directional BPM (10) Back to general case (nonequal impedances), dynamics after bunch passage on rhs: Qimage = - Q + Q 1 Vlhs + Q 2 Q - Q 3 - Q 4 Vrhs Bunch then passes second gap from left to right. The image charge Qimage is split with no net charge on right hand side generated: Qimage = Q 3+Q 4. With equal impedances –Q = - Q/2. In this relativistic beam approximation, Q 2 and Q 4 arrive at the same time, therefore Vrhs=0. Meanwhile Q 3 propagates in the opposite direction and contributes a negative pulse at Vlhs.
Beam Position – Stripline Monitors, Directional BPM (11) Photo courtesy R. de Maria (2010)
Beam Position – Stripline Monitors, variants (12) From: Electron Beam Diagnostic System for the Japanese XFEL, SACLA IBIC 2012 H. Maesaka et al (Tsukuba, Japan)
Homework #5 At the Relativistic Heavy Ion Collider ~ 600 stripline BPMs (150/plane, two rings) are used to measure the orbits along the accelerator, examples are shown below. 4 km full scale The BPMs look like this: The stripline length is ~ 25 cm and one end of each stripline electrode is grounded. At 12 locations (on either side of each of the 6 interaction regions), the monitor detects beams travelling in opposite directions. The photograph shows such a measurement. (a) explain the polarities of the bipolar pulses (b) what is the distance of this BPM to the interaction point? (c) comment on the time separation between the peaks of the bipolar pulse
(d) comment on the time separation between the peaks of the bipolar pulse for this 1 m stripline (non-IR BPM)
Beam Position – Cavity BPMs (13) 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 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) TM 010, “common mode” ( I) TM 110, dipole mode of interest amplitude detected at position of antenna contains contributions from both modes signal processing
Beam Position – Cavity BPMs (14) -1/2 schematic of a “cold” cavity BPM tested at TTF I (Lorenz) Ttr (R/Q) Q 0, QL L r mn 0 x transit time factor geometrical property of cavity unloaded and loaded Q-factors cavity length cavity radius wavelength of mode of interest transverse displacement for the TTF cavity BPM: r = 115. 2 mm L = 52 mm V 110 out ~115 m. V/mm for 1 n. C pioneering experiments: 3 C-band cavity “RF” BPMs in series at the FFTB (SLAC) 25 nm position resolution at 1 n. C bunch charge (courtesy, T. Shintake, 2003)
Beam Position – Cavity BPMs (15) From: Electron Beam Diagnostic System for the Japanese XFEL, SACLA IBIC 2012 H. Maesaka et al (Tsukuba, Japan)
(Selected) classic references
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 charge and intensity with for the horizontal position for the vertical position We reviewed basic beam diagnostics for measuring the beam position - 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.
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, HB 2006 (2006)
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