An ion of charge q moving with velocity v in a static magnetic field B is subjected to a force F that is proportional to the magnitude of the charge and the speed of the particle:

(eq. 1)

In the special case where the velocity of a charged particle is perpendicular to a uniform magnetic field, as shown in Figure 1, the particle moves in a circular orbit. Note that ions with opposite charges rotate in opposite directions since changing the sign of q in equation 1, changes the sign and the direction of the magnetic force.

If we apply Newton's second law to the particle:

(eq. 2)

where v/r represents the cyclotron frequency. Therefore the experimentally measured ion cyclotron frequency can be converted to ionic mass-to-charge ratio. The frequency of the cyclotron gyration of an ion is inversely proportional to its mass-to-charge ratio (m/q) and directly proportional to the strength of the applied magnetic field. Ions with lower m/q have higher cyclotron frequencies.

Although ions in a static magnetic field move in cyclotron orbits, they will not generate any signal if placed between a pair of detection electrodes. In order to collect a signal, a packet of ions of a giver mass-to-charge ratio needs to be excited by applying an oscillating electrical field such as provided by a AC signal generator. If the frequency of the applied field is the same as the cyclotron frequency of the ions, the ions absorb energy thus increasing their velocity (and the orbital radius) but keeping a constant cyclotron frequency. Figure 3 illustrates this effect.

Ions characterized by a specific mass-to-charge ratio and affected by a magnetic field move at a given cyclotron frequency. Their original path is depicted by the inner solid circle. By applying a radio-frequency (rf) voltage at the same frequency as the cyclotron frequency, the ions absorb energy and are accelerated to larger orbit radius. When the rf signal is terminated, the accelerated ions continue to gyrate at a constant radius. This phenomenon provides the basis for mass spectrometry because ions having a different cyclotron frequency are not accelerated.

When the radio-frequency voltage is turned off, each packet of ions of a specific m/q induces an image current that is detected by a pair of electrodes in the analyzer cell. The electrodes are connected to ground through a resistor. When a packet of positive ions approaches electrode1, electrons through the external circuit are attracted from the ground and accumulate in electrode 1 causing a temporary current. As the ions continue to rotate and approach electrode 2, the electrons accumulate on electrode 2. The flow of electrons in the external circuit represents the image current. The amplitude of this current is proportional to the number of ions in the analyzer cell while its frequency is the same as the cyclotron frequency of the ions. A small ac voltage is generated across a resistor and this signal is amplified and detected.

The ions are therefore detected without ever colliding with the electrodes. This non-destructive detection scheme is unique to FTICR and allows for improved sensitivity and versatility compared to more traditional approaches that utilize destructive detection methods.

a spectrum as function of m or m/q can be obtained. Cyclotron frequencies can be measured with very high precision, leading to high accuracy mass measurements and ultra-high resolving power.