INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 953–959 PII: S0953-4075(03)56539-7 Self-bunching induced by negative effective mass instability in an electrostatic ion beam trap D Strasser, O Heber, S Goldberg and D Zajfman Department of Particle Physics, Weizmann Institute of Science, Rehovot, 76100, Israel Received 22 November 2002, in final form 8 January 2003 Published 24 February 2003 Online at stacks.iop.org/JPhysB/36/953 Abstract We demonstrate that the synchronization effect, which has been observed when a bunch of ions oscillates between two mirrors in an electrostatic ion beam trap, can be explained as a negative effective mass instability. We derive simple necessary conditions for the existence of a regime in which this dispersionless behaviour occurs and demonstrate that, in this regime, the ion trap can be used as a high resolution mass spectrometer. (Some figures in this article are in colour only in the electronic version) 1. Introduction In a recent experiment, Pedersen et al [1, 2] demonstrated that, when a bunch of interacting (charged) particles oscillates between two electrostatic mirrors, its size can be kept constant, in spite of the fact that not all the ions have the same velocity, not all of them move on the same trajectory and the Coulomb repulsion between them is non-negligible. This counter-intuitive effect, which was called motion synchronization by Pedersen et al [1, 2], but which we term self-bunching in this work, was tentatively explained as due to the interaction between the particles and some kinematical effects due to the special geometry of the trap. In a typical experiment, an ion bunch, with kinetic energy of the order of several kiloelectronvolts, made of singly charged ions, is injected into an electrostatic ion beam trap [3–5]. The trap is made of two identical electrostatic mirrors composed of several cylindrically symmetric electrodes. The potential of each of these electrodes can be changed independently, so that various trapping potentials are possible. The distance between the innermost grounded electrodes of each mirror is 227 mm, so that the region between the mirrors is practically field-free. The number of ions in a bunch varies between 10 4 and 10 6 , corresponding to typical densities of between 5 × 10 3 and 5 × 10 5 cm −3 . The typical oscillation time of the ions in the trap is a few microseconds. The bunch size and intensity is detected via a capacitive pickup electrode which produces a signal whose width is proportional to the bunch length. When such a bunch is introduced into the trap, its bunch length usually increases rapidly, because of the reasons mentioned above, and reaches the trap size in a few hundred oscillations. However, under certain conditions which are related to the specific shape of the electrical 0953-4075/03/050953+07$30.00 © 2003 IOP Publishing Ltd Printed in the UK 953