Nuclear Spin and Behaviour in a Magnetic Field

Electromanetism tells us that a current carrying conductor e.g. a piece of wire, produces a magnetic field encircling it. When the wire is formed into a loop the field acts perpendicular to the surface area of the loop. Analogous to this concept is the field produced by negatively charged electrons orbitting the nucleus in an atom, or the spinning charge of the nucleus itself. This spinning momentum of nuclear charge ('the spin') produces a small magnetic field referred to as a magnetic moment. Under normal circumstances these moments have no fixed orientation so there is no overall magnetic field. However, when nuclei are placed in an external magnetic field, for example a patient placed in the MRI scanner, they begin to align in given directions dictated by the laws of quantum physics. It turns out that in the case of the hydrogen nucleus (a single proton with a spin quantum number, I = ½) that two discrete energy levels (2I +1) are created; a higher energy level where the magnetic moments are opposing the external magnetic field, and a lower energy level in which the nuclei are aligned with the magnetic field. It turns out that a tiny majority of spins are in the latter energy state thereby creating a net magnetisation in the direction of the main magnetic field. The population difference, and therefore the senstivity of the technique, can be altered by reducing the temperature or increasing the field, hence the need for a strong magnetic field, which for modern clinical scanners is between 0.5 and 3.0 Tesla. We refer to this field as B0 to distinguish it from a second field described later on. To put the magnitude of this field into context, 1 Tesla is equal to 10,000 Gauss and the Earth's magnetic field varies from between 0.3 - 0.7 Gauss. 

In terms of classical physics, when the spin is placed in a magnetic field it precesses about that field in a motion analogous to a spinning top. The frequency of precession is governed by the Larmor equation, w0 = gB0. The constant of proportionality in this equation is the magnetogyric ratio with every 'MR visible' nucleus having its own specific value. For the proton, in a field strength of 1.5 T, this frequency is about 63.8 MHz, which is in the radio-frequency (RF) range.