APS/ Stability of ion confinement for a novel mass spectrometer of infinite mass range Alexandre Vallette, ∗ C. I. Szabo, † and P. Indelicato ‡ Laboratoire Kastler Brossel, ´ Ecole Normale Sup´ erieure, CNRS, Universit´ e Pierre et Marie Curie – Paris 6, Case 74; 4, place Jussieu, 75252 Paris CEDEX 05, France (Dated: October 24, 2012) We study the ions dynamics inside an Electrostatic Ion Beam Trap (EIBT) and show that the stability of the trapping is ruled by a Hill’s equation. This unexpectedly demonstrates that an EIBT, in the reference frame of the ions works very similar to a quadrupole trap. The parallelism between these two kinds of traps is illustrated by comparing experimental and theoretical stability diagrams of the EIBT. The main difference with quadrupole traps is that the stability depends only on the ratio of the acceleration and trapping electrostatic potentials, not on the mass nor the charge of the ions. All kinds of ions can be trapped simultaneously and since parametric resonances are proportional to the square root of the charge/mass ratio the EIBT can be used as a mass spectrometer of infinite mass range. PACS numbers: 07.75.+h,37.10.Ty,82.80.Ms Electrostatic Ion Beam Traps [1] are taking an impor- tant place in between very low-energy charged-particles storage devices, such as quadrupole and Penning traps [2] and high energy storage rings [3]. With the Cone- Trap [4], electrostatic rings [5] and the Mini-Ring [6], they form a new family of traps operating at energies of a few keV. They are used for atomic and molecular metastable-states studies, molecular fragmentation and photodissociation (see, e.g., [7] for a review). Beyond pro- viding trapping of energetic particles in a well defined di- rection, these traps have many interesting features : they are small, relatively inexpensive, easy to setup and ope- rate and have a field-free region where ions move freely and where measurements can easily be performed. They can even be used as Time Of Flight (TOF) mass spec- trometers [8] or cooled at cryogenic temperatures [9]. Despite these interesting features, all the published theoretical models describing EIBT are based on one di- mensional approximations, neglecting the radial motion. This leads to inaccurate predictions of the trap stabi- lity and operating domain, and restricts their flexibility, as finding reasonable working points requires lengthy and tedious experimental exploration. This may partly be ex- plained by the lack of an analytical formula for the elec- trostatic potential inside these traps leading to the di- lemma of choosing between a simplistic analytical model and a heavy numerical treatment unsuited to explore the huge space of parameters. Usual beam simulation codes fail to produce good results as the numerical inaccuracies at the ion turning points lead to energy non conservation reaching a few 100 eV over a few tens of oscillations. Here we solve the problem, using methods developed for radio-frequency quadrupole traps. We show that the ra- dial dynamic is ruled by a Hill’s equation, a particular case of the Mathieu equation that describes quadrupole traps. This model yields accurate predictions of the ions motion in the trap and of the stability region. The design and operation of the EIBT has been des- Vz V4 V3 V1 V2 ion bunch Excitation signal Faraday cup Figure 1. (Color online) Overview of the experimental se- tup. Five potentials are applied to the electrodes (striped rec- tangles with Vi ), the others are grounded. The resulting elec- trostatic field is represented by contour lines. The injection of the ion bunch (orange) is performed when all the electrodes on one side of the trap are grounded. The potentials are rai- sed before the bunch has time to come back so that the ions go back and forth between the two stacks of electrodes. The faraday cup (green) is linked to an oscilloscope via a charge amplifier. A sinusoidal voltage can be applied to a central electrode via a signal generator. cribed previously in detail [1] and a schematic drawing of the ion trap is shown in Fig. 1. The trap consists of two sets of coaxial cylindrical electrodes roughly equi- valent to two spherical mirrors, the electrostatic analog of a Fabry-Perot interferometer. The configuration of the trap is defined by the potentials of five of these electrodes {V 1 ,V 2 ,V 3 ,V 4 ,V z } on both ends of the trap, the others being grounded. The length of the trap is 422 mm and the inner radius of the electrodes varies from 8 mm to 13 mm. An oscillating potential V ex sin(ω ex t) can be applied to a hollow electrode located at the center of the trap, in order to destabilize ion trajectories as we will see in the sequel. Both V ex (a few volts) and ω ex (a few MHz) are hal-00589631, version 2 - 16 May 2013