Larmor frequency

The Larmor frequency, named after Joseph Larmor, is the frequency at which the magnetic moment of a charged particle, such as an electron, proton, or nucleus, precesses around an external magnetic field. This phenomenon is fundamental in many areas of physics, including nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

In the context of MRI (Magnetic Resonance Imaging), the Larmor frequency is crucial because it determines the resonance frequency of the hydrogen nuclei (protons) in the human body when subjected to a magnetic field. The Larmor frequency in MRI is given by the formula:

Example Calculation

Let’s calculate the Larmor frequency for a typical MRI magnetic field strength of (teslas):

Significance in MRI

Image Formation: The Larmor frequency is used to tune the RF (radiofrequency) pulses that excite the protons in the body. These RF pulses need to be at the same frequency as the Larmor frequency to effectively cause the protons to resonate.

Signal Detection: After excitation, the precession of the protons at the Larmor frequency generates a signal that can be detected and used to create images. The frequency of this signal is directly related to the Larmor frequency.

Magnetic Field Strength Variations: Different MRI machines use different magnetic field strengths (commonly 1.5 T, 3 T, etc.), which correspond to different Larmor frequencies. For instance, at 3 T, the Larmor frequency would be $42.58 MHz/T \times 3 T = 127.74 MHz$ .