By F. G. Major;Viorica N. Gheorghe;G????nther Werth
This ebook presents an creation and consultant to trendy advances in charged particle (and antiparticle) confinement through electromagnetic fields. Confinement in several capture geometries, the effect of seize imperfections, classical and quantum mechanical description of the trapped particle movement, assorted equipment of ion cooling to low temperatures, and non-neutral plasma houses (including Coulomb crystals) are the most topics. They shape the root of such functions of charged particle traps as high-resolution optical and microwave spectroscopy, mass spectrometry, atomic clocks, and, in all probability, quantum computing.
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Additional info for Charged Particle Traps: Physics and Techniques of Charged Particle Field Confinement (Springer Series on Atomic, Optical, and Plasma Physics)
4. The stability domains for the ideal Paul trap. Light grey: z-direction; dark grey: r-direction curves an , bn in the a–q-plane, forming the boundaries separating stable from unstable regions (Fig. 3). 6) for n ≥ 0. The values of a and q for which the solutions are stable simultaneously for the axial and radial directions, an obvious requirement for three-dimensional conﬁnement, are found by using the relationship az = −2ar , qz = 2qr to make a composite plot of the boundaries of stability for both directions on the same set of axes (Fig.
15. 2 . Copyright (2003) by the American Physical Society obtained by a statistical model using similar density distributions  and graphically represented in Fig. 15. The shift averaged over the total cloud would be experimentally observed. The axial resonance, taken with high resolution, exhibits two components : the center-of-mass frequency (collective Fig. 16. Axial resonance of a stored ion cloud showing excitation of the centerof-mass (collective) and individual (noncollective) ion oscillations for ﬁve diﬀerent excitation voltages.
We present a general eﬀective potential approach to the quantum motion of charged particles in rapidly oscillating ﬁelds. 82) ∂t 2M where V is a time-periodic function of period T = 2π/Ω and V = 0. Here denotes the time-average over a period. 7 Quantum Dynamics in Paul Traps 47 where W is a function of r and t such that ∂W = V, ∂t W =0. 85) 1 i i 2 ∆W + (∇W ) . 86) We deﬁne the time-independent eﬀective potential by V eﬀ = S . Then 2 V eﬀ = (∇W ) . 87) is equivalent to the classical result of .