Penning trap
Penning traps are devices for the storage of charged particles using a constant static magnetic field and a  spatially inhomogeneous static electric field.  This kind of trap is particularly well suited to precision measurements of properties of ions and stable subatomic particles which have electric charge. Recently this trap has been used in the physical realization of quantum computation and quantum information processing as well.  Currently Penning traps are used in many laboratories worldwide, for example at CERN it is used to store antiprotons. The Penning Trap was named after F. M. Penning(1894-1953) by Hans Georg Dehmelt who built the first trap. Dehmelt got inspiration from the vacuum gauge built by F. M. Penning where a current through a discharge tube in a magnetic field is proportional to the pressure.  Citation from H. Dehmelts autobiography: "I began to focus on the magnetron/Penning discharge geometry, which, in the Penning ion gauge, had caught my interest already at Gottingen and at Duke. In their 1955 cyclotron resonance work on photoelectrons in vacuum Franken and Liebes had reported undesirable frequency shifts caused by accidental electron trapping. Their analysis made me realize that in a pure electric quadrupole field the shift would not depend on the location of the electron in the trap. This is an important advantage over many other traps that I decided to exploit. A magnetron trap of this type had been briefly discussed in J.R. Pierce's 1949 book, and I developed a simple description of the axial, magnetron, and cyclotron motions of an electron in it. With the help of the expert glassblower of the Department, Jake Jonson, I built my first high vacuum magnetron trap in 1959 and was soon able to trap electrons for about 10 sec and to detect axial, magnetron and cyclotron resonances. "
H. Dehmelt shared the Nobel Prize in Physics in 1989 for the development of the ion trap technique.

# How it works
Penning traps use a strong homogeneous axial magnetic field to confine particles radially and a quadrupole electric field to confine the particles axially.  The static electric potential can be generated using a set of three electrodes: a ring and two endcaps. In an ideal Penning trap the ring and endcaps are hyperboloids of revolution. For trapping of positive (negative) ions, the endcap electrodes are kept at a positive (negative) potential relative to the ring. This potential produces a saddle point in the centre of the trap, which traps ions along the axial direction. The electric field causes ions to oscillate (harmonically in the case of an ideal Penning trap) along the trap axis. The magnetic field in combination with the electric field causes charged particles to move in the radial plane with a motion which traces out an epitrochoid.
The orbital motion of ions in the radial plane is composed of two modes at frequencies which are called the magnetron \omega_{-}and the modified cyclotron \omega_{+} frequencies. These motions are similar to the deferent and epicycle, respectively, of the Ptolemaic model of the solar system.
The sum of these two frequencies is the cyclotron frequency, which depends only on the ratio of electric charge to mass and on the strength of the magnetic field. This frequency can be measured very accurately and can be used to measure the masses of charged particles. Many of the highest-precision mass measurements (masses of the electron, proton, 2H, 20Ne and 28Si) come from Penning traps.
Buffer gas cooling, resistive cooling, and laser cooling are techniques to remove energy from ions in a Penning trap.  
Buffer gas cooling relies on collisions between the ions and neutral gas molecules that bring the ion energy closer the energy of the gas molecules. 
In resistive cooling, moving image charges in the electrodes are made to do work through an external resistor, effectively removing energy from the ions. 
Laser cooling can be used to remove energy from some kinds of ions in Penning traps.  This technique requires ions with an appropriate electronic structure.
Radiative cooling is the process by which the ions lose energy by creating electromagnetic waves by virtue of their acceleration in the magnetic field.  This process dominates the cooling of electrons in Penning traps, but is very small and usually negligible for heavier particles.
Using the Penning trap can have advantages over the radio frequency
trap (Paul trap). Firstly, in the Penning trap only static fields are applied and
therefore there is no micro-motion and resultant heating of the ion due to the
dynamic fields. Also, the Penning trap can be made larger whilst maintaining strong
trapping. The trapped ion can then be held further away from the electrode
surfaces. Interaction with patch potentials on the electrode surfaces can be responsible
for heating and decoherence effects and these effects scale as a high power
-f the inverse distance between the ion and the electrode.

# Fourier transform mass spectrometry
Fourier transform ion cyclotron resonance mass spectrometry (also known as Fourier transform mass spectrometry), is a type of  mass spectrometry used for determining the mass-to-charge ratio (m/z) of ions based on the cyclotron frequency of the ions in a fixed magnetic field. The ions are trapped in a Penning trap where they are excited to a larger cyclotron radius by an oscillating electric field perpendicular to the magnetic field. The excitation also results in the ions moving in phase (in a packet). The signal is detected as an image current on a pair of plates which the packet of ions passes close to as they cyclotron. The resulting signal is called a free induction decay (fid), transient or interferogram that consists of a superposition of sine waves. The useful signal is extracted from this data by performing a Fourier transform to give a mass spectrum.