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FTICR Theory: A Brief Review


Motion of a charged particle in a magnetic field

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:

Lorentz's Equasion
(eq. 1)

The magnitude and direction of the force depend on the direction of the velocity as described using the vector cross product. An important characteristic of the magnetic force on a moving charged particle is that the force is always perpendicular to the velocity of the particle. The magnetic force does no work on the particle, so this force does not affect the kinetic energy of the particle. While the direction of the force changes, its magnitude remains constant.

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.

Lorentz Force
Figure 1: Illustration of the Lorentz force (F=qv xB) as it acts on a positive ion (left) and a negative ion (right), in the presence of a constant magnetic field [ B].

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

Newton's Second Law
(eq. 2)

where v/r represents the cyclotron frequency. The experimentally measured ion cyclotron frequency can thus be converted to an 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.

Cyclotron Orbit

Ions of two different m/q ratios excited on resonance for the same amount of time with the same excitation voltage. Ion [A] has the lower m/q ratio and thus has a higher cyclotron frequency. Ion [B] has the higher m/q ratio and thus a lower cyclotron frequency.


Ion cyclotron resonance phenomenon

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 an 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.

Ion cyclotron resonance phenomenon
Figure 3:

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 smaller inner orbit. 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 ion cyclotron resonance mass spectrometry because ions having a different cyclotron frequency are not accelerated.


Detection of image current

Detection

Illustration of how the image current is obtained. As the ion(s) in a circular orbit approach the top plate, electrons are attracted to this plate from ground. Then as the ion(s) circulate towards the bottom plate, the electrons travel back down to the bottom plate. This motion of electrons moving back and forth between the two plates produces a detectable current.

When the radio-frequency current 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 electrode 1, 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.


Fourier Transform Spectrometers

The decay over time of the image current resulting after applying a short radio-frequency sweep is transformed from the time domain into a frequency domain signal by a Fourier transform. Because the cyclotron frequency is related to m/q by

Lorentz's equasion

a spectrum as a 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.

The illustration below shows the basic steps involved in obtaining a mass spectrum using Fourier Transform Ion Cyclotron Resonance Mass Spectrometry

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