By Fouad G. Major, Viorica N. Gheorghe, Günther Werth
This e-book offers an creation and consultant to fashionable advances in charged particle (and antiparticle) confinement via electromagnetic fields. Confinement in numerous seize geometries, the impression 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 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, possibly, quantum computing.
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Additional resources for Charged Particle Traps: Physics and Techniques of Charged Particle Field Confinement
5 Instabilities in an Imperfect Paul Trap 35 Fig. 18. Theoretical lines of instabilities in the ﬁrst region of stability of the Paul trap for perturbations of order n = 3 to n = 8 obtain long storage times at high amplitudes of the trapping voltage (for a given frequency). In fact, the most stable conditions are obtained for small q values near the a = 0-axis; here the instability condition on the frequencies is met only for a very high resonance order n which would occur only if the ﬁeld was highly imperfect, with the multipole expansion signiﬁcant to very high orders.
53) Thus we obtain a complete set of orthonormal solutions ψn , n = 0, 1, . 42), and ϕn is the normalized Hermite function. 46), we can write w = v exp(iβτ ), where v is a π-periodic function of τ and the characteristic exponent is given by π β= 1 dτ . 54) 0 The quasienergy functions can be rewritten √ ψn (q, τ ) = δ ρ √ 1/2 ϕn δ 1 q exp −i n + ρ 2 and ψn (q, τ + π) = exp −iπβ n + 1 2 βτ exp ψn (q, τ ) . 56) Thus the functions ψn have the scaled quasienergies εn = (n + 1/2) β, and the quasienergy spectrum is discrete.
25. 5. 3 Eﬀective Potentials The ﬁrst quantum-mechanical treatment of the time-dependent trapping potential was given by Cook, Shankland, and Wells in . 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 ) .
Charged Particle Traps: Physics and Techniques of Charged Particle Field Confinement by Fouad G. Major, Viorica N. Gheorghe, Günther Werth