The Paul trap is designed to create a saddle-shaped field to trap a charged ion, but with a quadrupole, this saddle-shaped electric field cannot be rotated about an ion in the centre. It can only 'flap' the field up and down. For this reason, the motions of a single ion in the trap are described by Mathieu equations , which can only be solved numerically by computer simulations.
The intuitive explanation and lowest order approximation is the same as strong focusing in accelerator physics.
Since the field affects the acceleration, the position lags behind to lowest order by half a period. So the particles are at defocused positions when the field is focusing and vice versa. Being farther from center, they experience a stronger field when the field is focusing than when it is defocusing. Ions in a quadrupole field experience restoring forces that drive them back toward the center of the trap. The motion of the ions in the field is described by solutions to the Mathieu equation.
By using the chain rule , it can be shown that. By Newton's laws of motion , the above equation represents the force on the ion.
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This equation can be exactly solved using the Floquet theorem or the standard techniques of multiple scale analysis. The forces in each dimension are not coupled, thus the force acting on an ion in, for example, the x dimension is. The boundaries of the shaded regions in the figure are the boundaries of stability in the two directions also known as boundaries of bands.
The domain of overlap of the two regions is the trapping domain.
The linear ion trap uses a set of quadrupole rods to confine ions radially and a static electrical potential on-end electrodes to confine the ions axially. This constraint is additionally present in the machining requirements of the 3D trap. Ion traps with a cylindrical rather than a hyperbolic ring electrode      have been developed and microfabricated in arrays to develop miniature mass spectrometers for chemical detection in medical diagnosis and other fields.
Viorica N. Gheorghe (Author of Charged Particle Traps II)
Quadrupole traps can also be "unfolded" to create the same effect using a set of planar electrodes. A combined radio frequency trap is a combination of a Paul ion trap and a Penning trap. But in certain applications like antihydrogen production it is important to confine two species of charged particles of widely varying masses.
To achieve this objective, a uniform magnetic field is added in the axial direction of the quadrupole ion trap.
From Wikipedia, the free encyclopedia. Not to be confused with Quadrupole mass analyzer. This section needs expansion. You can help by adding to it. May Paul and H. Bibcode : RvMP Seidelin; et al.
Charged Particle Traps II: Applications
Bibcode : PhRvL.. Kelley; J. Syka; W. Reynolds; J. Todd 7 September Elsevier Science B. Journal of Mass Spectrometry. Bibcode : JMSp Mass Spectrometry Reviews. Bibcode : MSRv International Journal of Mass Spectrometry. Bibcode : IJMSp. Senko; John E. Syka June Journal of the American Society for Mass Spectrometry.
Download Charged Particle Traps II: Applications (Springer Series on Atomic Optical and Plasma
Rapid Communications in Mass Spectrometry. Review of Scientific Instruments. Bibcode : RScI Physical Review Letters. Applied Physics Letters. AIP Publishing. Bibcode : ApPhL. Walz; S. Ross; C. Zimmermann; L. Viorica N.
Major, F. Fouad G. Edition 1st ed. Medium [electronic resource] Content Types text Carrier Types online resource Physical Description 1 online resource x, p. Series Springer series on atomic, optical, and plasma physics, ; 54 Springer series on atomic, optical, and plasma physics ; Electromagnetic fields.
Plasma confinement. Trapped ions. Plasma Ionized gases Physical measurements. Nuclear engineering. Nuclear Engineering. Atomic, Molecular, Optical and Plasma Physics. Plasma Physics. Measurement Science and Instrumentation. Nuclear Energy. In recent years, applications of far reaching importance have emerged ranging from the ultra-precise mass determinations of elementary particles and their antiparticles and short-lived isotopes, to high-resolution Zeeman spectroscopy on multiply-charged ions, to microwave and optical spectroscopy, some involving "forbidden" transitions from metastable states of such high resolution that optical frequency standards are realized by locking lasers to them.
Further the potential application of trapped ions to quantum computing is explored, based on the extraordinary quantum state coherence made possible by the particle isolation. Consideration is given to the Paul and Penning traps as potential quantum information processors. Mass Spectrometry in Paul Traps 3. Microwave Spectroscopy 5.
Optical Spectroscopy 6. Quantum Effects in Charged Particle Traps 8. Quantum Computing with Trapped Charged Particles. Notes Description based upon print version of record. Includes bibliographical references and index. Also available in print. Electronic reproduction.