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

This e-book offers an creation and advisor to trendy advances in charged particle (and antiparticle) confinement by means of electromagnetic fields. Confinement in several catch geometries, the impact of seize imperfections, classical and quantum mechanical description of the trapped particle movement, diverse 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, most likely, quantum computing.

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

**Sample text**

In order to derive a more quantitative description of the ion motion in a Paul trap in the presence of a background of very light particles, the eﬀect of the collisions can be modeled as a viscous damping force proportional to the ion velocity, thus F = −Dv. If we deﬁne a damping constant as b = D/M Ω, then the equation of motion of an ion in a Paul trap reads d2 u du + 2b + (au − 2qu cos 2τ )u = 0 . 38) The transformation u = w exp(−bτ ) leads to the equation d2 w/dτ 2 + (a − b2 − 2q cos 2τ )w = 0 .

13) [63, 64]. The intensity of ﬂuorescence light emitted from the ions Fig. 13. Vertical and horizontal laser scan through the ion trap. Experimental points ﬁtted Gaussian [64] 30 2 The Paul Trap after laser excitation is proportional to the ion number inside the laser beam proﬁle. From the width of the distribution a value for the mean kinetic energy of the cloud can be derived. When no particular damping mechanism is ¯ = (1/10) QD. applied one ﬁnds experimentally to a good approximation E The fact that the density distribution can be well described by a Gaussian, which implies a Maxwellian velocity distribution, justiﬁes the idea that a temperature can be ascribed to the ion cloud.

Similarly we ﬁnd zero radial potential depth at the βr = 0 line. 18)). 9)), resulting in increasing ion loss for higher q, in a trap of a given size. 4 Real Paul Traps 27 Fig. 11. Optimum trapping conditions. (a) Computed lines of equal ion density within the stability diagram. 02 (Fig. 11a). This is conﬁrmed experimentally by systematic variation of the trapping parameters and measurement of the relative trapped ion number by laser induced ﬂuorescence (Fig. 11b). 4 Real Paul Traps A single ion in a perfect quadrupole potential does not describe a real experimental situation.