Contents lists available at ScienceDirect Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima Analytical expression for position sensitivity of linear response beam position monitor having inter-electrode cross talk Mukesh Kumar a,b, ⁎ , A. Ojha a , A.D. Garg a , T.A. Puntambekar a , V.K. Senecha b,c a Beam Diagnostics Section, Indus Operations, Beam Dynamics & Diagnostics Division, Raja Ramanna Centre for Advanced Technology, Indore, 452013 MP, b Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400 094, India c Ion Source Lab., Proton Linac & Superconducting Cavities Division, Raja Ramanna Centre for Advanced Technology, Indore, 452013 MP, ARTICLE INFO Keywords: Shoe-box BPM Position sensitivity Inter electrode cross talk Capacitive coupling ABSTRACT According to the quasi electrostatic model of linear response capacitive beam position monitor (BPM), the position sensitivity of the device depends only on the aperture of the device and it is independent of processing frequency and load impedance. In practice, however, due to the inter-electrode capacitive coupling (cross talk), the actual position sensitivity of the device decreases with increasing frequency and load impedance. We have taken into account the inter-electrode capacitance to derive and propose a new analytical expression for the position sensitivity as a function of frequency and load impedance. The sensitivity of a linear response shoe-box type BPM has been obtained through simulation using CST Studio Suite to verify and confirm the validity of the new analytical equation. Good agreement between the simulation results and the new analytical expression suggest that this method can be exploited for proper designing of BPM. 1. Introduction Particle accelerators are the machines which accelerate charge particles for various applications in the field of material science, particle physics, medical science etc. In particle accelerators and associated transfer lines, the beam position of charge particles is an important beam parameter. Capacitive pick-ups are the most common non-destructive beam position monitors used in particle accelerators and transfer lines. A general capacitive BPM consists of four pick-up electrodes which are inserted in the beam pipe. Each electrode is electrically insulated from the beam pipe and has a certain capacitance which depends on its geometry and distance from the beam pipe. When beam passes through the BPM, the electric field associated with the beam induces electric charge on the electrodes. The time variation of the induced charge acts as an induced current and generates voltage signal across the load resistor connected between electrodes and the beam pipe. The position of the beam is obtained by comparing the voltages induced at different electrodes. A linear response capacitive BPM (like shoe-box BPM, Fig. 1) consists of two electrodes for a given transverse direction. The difference in voltage signals induced on opposite electrodes depends on the beam position. Therefore, the position of the beam is obtained by determining the difference in voltage signals (normalized with respect to the sum voltage signals) induced on right and left electrodes. For example, the horizontal position 'x' of the beam can be obtained by using Eq. (1). x S V V V V = 1 − + x R L R L (1) In Eq. (1), │V R │-│V L │ is the difference voltage, │V R │+│V L │is the sum voltage and S x is proportionality constant called position sensitivity. According to the quasi electrostatic model given by R.E. Shafer [1], the position sensitivity of linear response BPM is given by the inverse of half of the BPM's aperture. In practice, however, due to cross talk between pickup electrodes, the position sensitivity of linear response capacitive beam position monitor depends on frequency [2–6]. In most of the above references and other references mentioned therein, qualitative discussion on effect of cross talk on position (displacement) sensitivity has been presented but no proper mathematical model or expression is available to quantitatively explain the effect of cross talk on sensitivity. In this paper a mathematical expression has been derived based on equivalent circuit analysis method to explain the dependency of the position sensitivity of linear response capacitive beam position monitor on processing frequency and load impedance. In frequency domain, the http://dx.doi.org/10.1016/j.nima.2016.11.048 Received 10 August 2016; Received in revised form 11 November 2016; Accepted 21 November 2016 ⁎ Corresponding author at: Beam Diagnostics Section, Indus Operations, Beam Dynamics & Diagnostics Division, Raja Ramanna Centre for Advanced Technology, Indore, 452013 MP, India. E-mail address: mukeshk@rrcat.gov.in (M. Kumar). Nuclear Instruments and Methods in Physics Research A 844 (2017) 90–95 Available online 22 November 2016 0168-9002/ © 2016 Elsevier B.V. All rights reserved. MARK