What happens to the processional frequency when a gradient magnetic field is applied?

When a gradient magnetic field is applied, the processional frequency of magnetic moments, particularly those of protons in a magnetic resonance imaging (MRI) context, is altered. The processional frequency, also known as the Larmor frequency, is dependent on the strength of the magnetic field in which the spins are located. In a uniform magnetic field, the frequency is determined by the gyromagnetic ratio of the nuclei (such as protons) and the strength of that static magnetic field.

When a gradient magnetic field is applied, the magnetic field strength varies linearly across space. This variation causes nearby protons to experience different magnetic field strengths, leading to variations in their resonance frequencies. As a result, the processional frequency increases in regions where the magnetic field strength increases due to the gradient. Therefore, the presence of the gradient introduces a frequency shift that is dependent on the position within the gradient field.

This is critical in MRI as it allows for spatial encoding of the MR signal, which means that the position of each signal can be determined based on its frequency. Thus, applying a gradient magnetic field increases the processional frequencies of protons in regions where the field is stronger, which enhances the ability to localize signals and acquire images with detailed spatial resolution