Magnetization

From a practical point of view, we need only concern ourselves with the "net magnetization vector," M (Fig. 5-1), which is the vector sum of all the individual spins (small arrows) aligned parallel to the main magnetic field, B0. At equilibrium, M is steady along the axis of B0 (conventionally the "z" axis) and experiences no tendency to rotate off axis; i.e., there is no twisting effect or "torque." This is because the main field and the magnetization vector are parallel; in order for there to be a torque, the magnetization must be at least partially perpendicular to the main field. So, when aligned along z, the magnetization is essentially static and does not generate a detectable signal in the presence of the static external field. In order to be detectable, the magnetization must have a net component which lies within the transverse (x-y) plane. If rotated away from z, the magnetization will experience a torque, proportional to its component in the x-y plane, and will precess coherently about B0 and be detectable in the x-y plane by a suitable probe. The Larmor frequency is the resonant frequency with which the spins rotate in the presence of a magnetic field; it is specific for each nuclear species and, for any given nucleus, it increases proportionately with the strength of the applied external magnetic field. At 1.5 Tesla, the Larmor frequency for hydrogen nuclei (protons) is approximately 63.75 megahertz (MHz); at 3.0 Tesla, it is approximately 127.8 MHz. Recall that a changing magnetic field always implies a changing electric field, and vice versa. The changing electric field constitutes a sinusoidally alternating voltage in the transverse plane, and this is detectable by a probe. How might M be rotated partially or fully into the transverse plane? The rotation of the magnetization vector, M, is accomplished by the magnetic field of an RF pulse, generally designated the B1 field. Recall that radio waves are part of the spectrum of electromagnetic radiation, and that all electromagnetic waves are composed of electric and magnetic fields perpendicular to each other, and oscillating sinusoidally at a specific frequency. The magnetic field of the RF wave, B1, can be thought of as adding to the main field, B0, but in a perpendicular direction. Now we have M and B1 perpendicular to each other, so B1 exerts a torque on M. The direction of the torque is at all times perpendicular both to B1 and M, and is defined by a "vector product" as detailed below (don't worry if you're not familiar with the vector product).