By Dr. Fouad G. Major, Professor Dr. Viorica N. Gheorghe, Professor Dr. Günther Werth (auth.)
This booklet offers an creation and consultant to trendy advances in charged particle (and antiparticle) confinement through electromagnetic fields. Confinement in several capture geometries, the impression of capture imperfections, classical and quantum mechanical description of the trapped particle movement, varied equipment of ion cooling to low temperatures, and non-neutral plasma homes (including Coulomb crystals) are the most topics. They shape the foundation of such functions of charged particle traps as high-resolution optical and microwave spectroscopy, mass spectrometry, atomic clocks, and, in all likelihood, quantum computing.
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Extra info for Charged Particle Traps: Physics and Techniques of Charged Particle Field Confinement
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. 32) ωs = 2QV0 /M Ω(r02 + 2z02 ) , and Φsc (r) is the space charge potential that is itself determined by the density through the Poisson equation. 33) where R is the value of r at which the cloud density is reduced to 1/e of its center value, and can be roughly considered as the cloud radius.
39) This is again the Mathieu equation with the coeﬃcient a replaced by (a − b2 ); the solution would thus seem to be essentially the same as in the case of no damping. However, Hasegawa and Uehara  and also Nasse and 38 2 The Paul Trap Fig. 20. 10−4 Pa; (d) pHe = 10−3 Pa. The given value of the storage time T are deduced from the slopes of the second parts of the curves  Fig. 21. Stability diagram in the az –qz -plane. 3 Fig. 22. 09 (from left to right)  Foot  have shown that this is not the case; the exponential factor in the solution aﬀects its character.
The maximum resonance order corresponds to the order n of the perturbing potential in the series expansion, whose magnitude is determined by the shape of the imperfections actually present in the trap. The instabilities should occur along certain lines within the stability diagram, as graphically represented in Fig. 18 for the lowest orders. If we take an octupole perturbation (n = 4) as an example, there are lines of instabilities arising from this contribution deﬁned by: 4βz = 2, 3βz +βr = 2, 2βz +2βr = 2, βz + 3βr = 2, 4βr = 2.