An ion trap consists of electrodes that produce electric fields to trap ions (charged particles), which may be atoms, molecules, or large particles such as dust. Ion traps have a number of applications including mass spectrometry, atomic frequency standards, and quantum computing. In comparison to neutral atom traps, ion traps have deeper trapping potentials (up to several electronvolts) that are agnostic to the internal structure of the ions. The two most popular ion traps are the Paul trap which uses static and oscillating electric fields and the Penning trap, which uses a static electric field and static magnetic field. Paul traps are used in trapped ion quantum computers and realizing atomic clocks, including the most precise instrument humankind has ever made. Penning traps are powerful tools for mass spectrometry and measuring magnetic dipole moments.
History The physical principles of ion traps were first explored by F. M. Penning, who observed that electrons released by the cathode of an ionization vacuum gauge follow a long cycloidal path to the anode in the presence of a sufficiently strong magnetic field. Later Wolfgang Paul developed a method to trap ions without magnetic fields that was based on his work with quadrupole mass spectrometers. Ion traps were used in television receivers prior to the introduction of aluminized CRT faces around 1958, to protect the phosphor screen from ions. The ion trap must be delicately adjusted for maximum brightness.
Theory
A trap requires confining forces in all three spatial directions. Electric and magnetic fields exert forces on ions, called the Lorentz force. Due to Earnshaw's theorem it is not possible to confine an ion using only static electric fields. However, a static magnetic and electric field (a Penning trap), or the combination of an oscillating electric field with a static electric field (a Paul trap), can trap ions. The confining fields and the resulting motion of ions in a trap are generally decomposed into one axial and two radial components with respect to the trap geometry. In both Paul and Penning traps, a static electric field provides the axial confinement. Paul traps confine the ion radially with an oscillating electric field whereas Penning traps use a static magnetic field.
Paul trap A Paul trap (also known as a quadrupole ion trap) uses static direct current (DC) and radio frequency (RF) oscillating electric fields to trap ions. Paul traps are commonly used as components of mass spectrometers. Wolfgang Paul invented the Paul trap, hence its name. For this work he shared the 1989 Nobel Prize in Physics.
The RF field generates an average radial confining force with an oscillating quadrupole potential. The confining and anti-confining directions of the potential are switched faster than the particle's escape time. Since the field affects the acceleration, the position lags behind (by approximately 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. The quadrupole is the simplest electric field geometry used in such traps, though more complicated geometries are possible and used in specialized devices. The electric fields are generated from electric potentials on metal electrodes. A pure quadrupole is created from hyperbolic electrodes, though cylindrical electrodes are often used for ease of fabrication. Microfabricated chip traps exist where the electrodes lie in a plane with the trapping region above the plane. There are two main classes of traps, depending on whether the oscillating field provides confinement in three or two dimensions. In the two-dimension case (a so-called "linear RF trap"), confinement in the third direction is provided by static electric fields.
A typical trap configuration has four parallel electrodes along the z {\displaystyle z} -axis that are positioned at the corners of a square in the x y {\displaystyle xy} -plane. Diagonally opposite electrodes are connected and a voltage V = V 0 cos ( Ω t ) {\displaystyle V=V_{0}\cos(\Omega t)} is applied. The electric field produced by this potential is E = E 0 sin ( Ω t ) {\displaystyle \mathbf {E} =\mathbf {E} _{0}\sin(\Omega t)} . The force on an ion of charge e {\displaystyle e} is F = e E {\displaystyle \mathbf {F} =e\mathbf {E} } which with ion mass M {\displaystyle M} leads to the radial equation of motion
M r ¨ = e E 0 sin ( Ω t ) {\displaystyle M\mathbf {\ddot {r}} =e\mathbf {E} _{0}\sin(\Omega t)\!} . If the ion is initially at rest, two successive integrations give the velocity and displacement as
r ˙ = e E 0 M Ω cos ( Ω t ) {\displaystyle \mathbf {\dot {r}} ={\frac {e\mathbf {E} _{0}}{M\Omega }}\cos(\Omega t)\!} ,
… excerpt ends here. Continue reading the full article.
