By Fouad G. Major, Viorica N. Gheorghe, Günther Werth
This ebook offers an creation and advisor to fashionable advances in charged particle (and antiparticle) confinement by means of electromagnetic fields. Confinement in several capture geometries, the impression of seize imperfections, classical and quantum mechanical description of the trapped particle movement, diversified tools of ion cooling to low temperatures, and non-neutral plasma houses (including Coulomb crystals) are the most matters. 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 likelihood, quantum computing.
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Additional info for Charged Particle Traps: Physics and Techniques of Charged Particle Field Confinement
24) and for the total energy of the charged particle we have H = Ek + Ep = 1 2 2 ω+ − R− ω− ) . 25) Note that the part of the total energy arising from the magnetron motion has a negative sign indicating that an increase in the magnetron radius leads to a decrease in the energy. 27) 1 2 2 − M ωz2 [R+ + R− + 2R+ R− cos(ω1 t + α+ − α− )] . 28) 2 2 ¯p = 1 M ωz2 (Rz2 − R+ E − R− ). 32) , Jz sin ϕz . 34), the Hamiltonian of the ideal Penning trap can be written as H = ω+ J+ − ω− J− + ωz Jz . 19). 2 Motional Spectrum in Penning Trap The motional spectrum of an ion in a Penning trap contains the fundamental frequencies ω+ , ω− , and ωz as shown in the solution of the equations of motion.
For rotational symmetry the odd coeﬃcients cn vanish. The terms beyond the quadrupole (c2 ) may be looked on as perturbing potentials, the lowest of which is the octupole (c4 ), followed by the dodecapole (c6 ); their dependence on (r, z) coordinates is given in App. 1. As a consequence of the presence of the higher order terms in the trapping potential, the motional eigenfrequencies are shifted with respect to the pure quadrupole ﬁeld, and moreover in an amplitude dependent way. These shifts are of particular importance in the case of Penning traps, which are used for very high resolution mass spectrometry.
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. The initial number of ions for the ﬁve diﬀerent curves is the same. The curves are vertically shifted for clarity of presentation .