doi:10.1016/S0168-9002(01)00899-3 
Copyright © 2002 Elsevier Science B.V. All rights reserved.
A new optimised quadrupole pick-up design using magnetic coupling
A. Jansson
, 
, a, b and D. J. Williamsa
a CERN, CH-1211 Geneva 23, Switzerland
b Manne Siegbahn Laboratory/Stockholm University, S-104 05 Stockholm, Sweden
Received 28 November 2000;
revised 16 February 2001;
accepted 3 March 2001
Available online 11 March 2002.
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Abstract
The idea of quadrupole pick-ups, sensitive to beam size, originated several decades back. Such pick-ups measure the quantity σx2−σy2, where σx and σy are the horizontal and vertical r.m.s. beam sizes. Thus, a quadrupole pick-up is a candidate for non-invasive study of processes such as coherent beam width oscillations due to injection mismatch. Up to now, quadrupole pick-ups have been produced essentially by enhancing the electronics of normal position pick-ups to produce the so-called quadrupole signal, with little or no effort being put into the design of the pick-up itself. In developing a quadrupole pick-up for the CERN PS, however, it has been found necessary to optimise the pick-up design. The result is a somewhat unconventional pick-up, where magnetic coupling is employed to suppress the otherwise very strong, and undesired, common mode-signal. In this paper, the basic design idea and the final optimised design are presented, together with simulations, test bench measurements and real beam data.
Author Keywords: Quadrupole pick-up; Magnetic coupling; Beam-size measurement
PACS classification codes: 41.85.Qg; 41.20.Gz; 41.75.−i; 29.20.Lq
Fig. 1. A typical position pick-up (electrostatic). The beam passes perpendicular to the plane of the drawing.
Fig. 2. Arrangement of antenna loops to couple with the radial component of the magnetic field. The arrow symbolises the beam.
Fig. 3. CAD drawing of the final pick-up design. The total length is 500 mm and the outer radius 300 mm.
Fig. 4. Schematic layout of one antenna loop, showing the transformer arrangement, the winding ratios and the position and value of the termination resistance.
Fig. 5. Measurement of transmission (forward scattering parameter s21) with a coaxial wire in the final pick-up. The two measurements are taken on different pick-up models, and show the effect of strip-line resonances in the antenna loops in the low frequency end, and cavity resonances at the high frequency end.
Fig. 6. Measurement of transmission with a coaxial wire in the final pick-up. The resonances present in Fig. 5 have been eliminated with the addition of resistive loop terminations and a 80 Ω coating on the inside of the ceramic. The response is now dominated by the wavy shape due to impedance mismatch at the signal entry and exit, and by losses in the wire at high frequencies.
Fig. 7. Simulated longitudinal impedance of the final pick-up.
Fig. 8. Measurement of the common-mode coupling (component independent of position) using a wire movable along the x-axis. Ideally, all signals should be zero. The common-mode rejection of the Σ signal is very good up to about 20 MHz, where the tail of the loop resonance begins. The other signal levels are affected by a small (less than 0.5 mm) offset between the electrical and geometrical centre (this is within the error of the absolute wire positioning accuracy). The rise of the Σ signal at low frequencies is an effect of the measurement instrument, that also influences the other measurements slightly.
Fig. 9. Measurement of the dipole mode coupling (component with linear dependence on position) using a wire movable along the x-axis. Note that the ΔH response is flat well above 20 MHz. The ΔV dependence on the horizontal position is due to a tilt of the order of 0.5° (within the alignment error margin). The small linear dependence of Ξ on position is due to the offset between the electrical and geometric centres. The dots are simulated values for ΔH.
Fig. 10. Measurement of the quadrupole mode coupling (component with quadratic dependence on position) using a wire movable along the x-axis. This is the coupling that is used to measure the quadrupole moment κ. Note that the Ξ response is flat well above 20 MHz. The dots are simulated values for Ξ.
Fig. 11. Measurement of the sextupole mode coupling (component with cubic dependence on position) using a wire movable along the x-axis. This coupling produces the lowest order non-linear dependence of Δ on beam position. The dots are simulated values for ΔH.
Fig. 12. Measurement of beam width oscillations after injection in the PS (quadrupole moment κ). The beam size oscillations were caused by dispersion mismatch in the horizontal plane, whereas the vertical beam size and the beam position was stable. To enable the comparison, the horizontal beam size measured with the SEM grid was squared and shifted by (estimated) to correct for the constant terms in κ. The dotted line is a sine curve fit to the first 6 turns.
Abstract
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