Schottky signals for longitudinal and transverse bunched-beam diagnostics

Abstract

Following a brief historical overview on the origin and the evolution of Schottky noise we discuss applications in the field of beam diagnostics in particle accelerators. A very important aspect of Schottky diagnostics is the fact that it is a non perturbing method. Essentially statistics based, it permits to extract beam relevant information from rms (root mean square) noise related to the movement of the individual particles. This is also the basis for stochastic cooling. Schottky diagnostics permits one to extract a considerable number of important beam parameters such as the revolution frequency, momentum spread, incoherent tune, chromaticity and emittance. INTRODUCTION In the year 1918 the German physicist Walter Schottky (* 23 July 1886 in Zurich) published a paper describing the mechanism of spontaneous current fluctuations in different conductors. This is the origin of the term Schottky noise. The term Schottky noise refers both to thermal noise in resistors and noise in charged particle beams. Additional important contributions from Walter Schottky are the Schottky diode, Schottky defects (in semiconductors) and the Schottky equation (Langmiur – Schottky equation for space charge). In 1915 Schottky invented the tetrode and in 1918 he pioneered the superhet concept. In 1928 the thermal noise in resistors was first measured by J.B Johnson (Bell Labs) and he discussed his findings with Harry Nyquist who worked at the same laboratory. This is the origin of the term Johnson-Nyquist noise which is more frequently used in the English literature when referring to thermal noise. An important milestone in accelerator technology was the invention of the stochastic cooling concept in 1968 by Simon van der Meer (Nobel price shared with Carlo Rubbia in 1984). Clear Schottky noise signals from a strong coasting (unbunched) beam of protons were observed in 1972 in the CERN–ISR (Intersecting Storage Rings) followed in the same year by the first publication of the cooling idea by Simon van der Meer [1]. In 1975 schemes for pbar accumulation were developed and tested experimentally with protons in 1976 (ICE = Initial Cooling Experiment). Over the following years a rapid worldwide evolution of beam diagnostics with Schottky noise took place, both for bunched and unbunched beams. Nowadays Schottky diagnostics is a vital element in nearly all large circular machines operating with hadrons and also to a certain extent for electron rings and even linacs. The information extracted this way allow continuous monitoring of important beam parameters and the control of a number of related machine settings. SHOT NOISE IN A VACUUM DIODE Consider a simple vacuum diode (fig 1) where a small number of electrons pass from a heated cathode to the anode [2]. Fig. 1 a: Vacuum diode with two electrodes (from [2] ) Fig. 1 b: Anode current related to individual electrons When a single electron is emitted from the cathode and starts moving to the anode (due to the acceleration voltage U0) an approximately linear increase of current at the anode is measured. This is due to the dD/dt (D = dielectric displacement) related displacement current which continues as a conducting current when the electron approaches the flat anode. Each of these saw tooth like signals (fig 1b) has a length τ which is the travel time of the electron from the cathode to the anode. As the individual electrons are emitted in a random manner, those saw tooth like signals occur as a non periodic time function. This is very similar to the time function of acoustic noise originating from little grains falling on a metal plate and is the origin of the term “shot noise”. If we assume this diode to be working in the saturated regime (i.e. the anode voltage is high enough that all emitted electrons are accelerated to the anode and there is no space charge cloud near the cathode) then, after some d i(t)