By Fouad G. Major, Viorica N. Gheorghe, Günther Werth

This publication offers an advent and consultant to fashionable advances in charged particle (and antiparticle) confinement via electromagnetic fields. Confinement in numerous capture geometries, the impact of seize imperfections, classical and quantum mechanical description of the trapped particle movement, various tools of ion cooling to low temperatures, and non-neutral plasma homes (including Coulomb crystals) are the most matters. They shape the foundation of such functions of charged particle traps as high-resolution optical and microwave spectroscopy, mass spectrometry, atomic clocks, and, very likely, quantum computing.

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**Additional resources for Charged Particle Traps: Physics and Techniques of Charged Particle Field Confinement**

**Sample text**

The time averaged E (b) as a function of the trap potential parameter q, for a damping coeﬃcient γ/Ω = 10−7 corresponding to usual experimental conditions [65] where n is the ion density. 29) ωz = ωz (1 − ωp2 /3ωz2 )1/2 , and similarly for the radial frequency. In this approximation the shift is linear with the ion density. The maximum trapped ion density is given by ωp2 /ωz2 = 3 . 30) If we assume for example a potential depth of 10 eV, we obtain as limiting density nmax = 5 · 107 cm−3 . 31) where C is a normalization constant and kB the Boltzmann constant.

Experimental lines of instabilities in the ﬁrst region of stability of a real Paul trap taken with H+ 2 ions. 36), where Ω/2π is normalized to 1. 6 The Role of Collisions in a Paul Trap The presence of neutral background gas particles in a Paul trap, whether introduced intentionally or as inevitable residual gas in the vacuum system, will result in collisions between the ions and the background particles, that will abruptly change the stable orbits of the ions, and determine statistically the evolution of the mean energy and storage time of the ion population.

For the stability parameter β one obtains a continued fraction expression: βj2 = aj + fj (βj ) + fj (−βj ) , fj (βj ) = qj2 (2 + βj )2 − aj − qj2 (4+βj )2 −aj −··· . 8) For the coeﬃcients c2n which are the amplitudes of the Fourier components of the particle motion, we have the following recursion formula: c2n, j qj =− . 9) qj2 c2n∓2, j (2n + β )2 − a − j j (2n±2+βj )2 −aj −··· Examples of ion trajectories for diﬀerent values of the stability parameters are shown in Fig. 6. Further examples and trajectories in the x–z-plane as well as phase space trajectories are given in Appendix B.