An ion trap consists of electrodes and in some cases magnets to produce a combination of electric and/or magnetic fields to hold charged particles: the ions, which may be atoms, molecules, or large particles such as dust. Atomic and molecular ion traps have a number of applications in physics and chemistry such as precision mass spectrometry, improved atomic frequency standards, and quantum computing. In comparison to neutral atom traps, ion traps have deeper trapping potentials (up to several electronvolts) that do not depend on the internal electronic structure of the trapped ions. The two most popular ion traps are the Penning trap, which forms a potential via a combination of static electric and magnetic fields, and the Paul trap which uses static and oscillating electric fields.

Penning traps can be used for precise magnetic measurements in spectroscopy. Studies of quantum state manipulation most often use the Paul trap. This may lead to a trapped ion quantum computer and has already been used to create the world's most accurate atomic clocks. Electron guns (a device emitting high-speed electrons, used in CRTs) can use an ion trap to prevent degradation of the cathode by positive ions.

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. A scheme for confining charged particles in three dimensions without the use of magnetic fields was developed by W. Paul 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.

Any charged particle, such as an ion, feels a force from an electric or magnetic field. Ion traps work by using this force to confine ions in a small, isolated volume of space so that they can be studied or manipulated. Although any static (constant in time) electromagnetic field produces a force on an ion, it is not possible to confine an ion using only a static electric field. This is a consequence of Earnshaw's theorem. However, physicists have various ways of working around this theorem by using combinations of static magnetic and electric fields (as in a Penning trap) or by an oscillating electric field and a static electric field (Paul trap). Ion motion and confinement in the trap is generally divided into axial and radial components, which are typically addressed separately by different fields. In both Paul and Penning traps, axial ion motion is confined by a static electric field. Paul traps use an oscillating electric field to confine the ion radially and Penning traps generate radial confinement with a static magnetic field.

A Paul trap is a quadrupole ion trap that 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. The invention of the quadrupole ion trap itself is attributed to Wolfgang Paul, hence its name, who shared the Nobel Prize in Physics in 1989 for this work. One realization consists of two hyperbolic metal electrodes with their foci facing each other and a hyperbolic ring electrode halfway between the other two electrodes. Ions are trapped in the space between these three electrodes by the oscillating and static electric fields. Often the trap has four parallel electrodes along the ${\displaystyle z}$-axis that are positioned at the corners of a square in the ${\displaystyle xy}$-plane. The pairs of electrodes diagonally opposite each other are connected and an a.c. voltage ${\displaystyle V=V_{0}\cos(\Omega t)}$ is applied. Using Maxwell's equations, the electric field produced by this potential is electric field ${\displaystyle \mathbf {E} =\mathbf {E} _{0}\sin(\Omega t)}$. Applying Newton's second law to an ion of charge ${\displaystyle e}$ and mass ${\displaystyle M}$ in this alternating electric field, we can find the force on the ion using ${\displaystyle \mathbf {F} =e\mathbf {E} }$. We wind up with

Assuming that the ion has zero initial velocity, two successive integrations give the velocity and displacement as

where ${\displaystyle \mathbf {r} _{0}}$ is a constant of integration. Thus, the ion oscillates with angular frequency ${\displaystyle \Omega }$ and amplitude proportional to the electric field strength and is confined radially.