The ellipsoid of alinement and its precessional motion in magnetic resonance

A surface of the second degree is constructed from the five components of the second rank tensor which describes the alinement of a spin-assembly undergoing magnetic resonance. The functions which characterize alinement are given a simple geometric interpretation in terms of radii vectores of this ellipsoid. The time-dependence of the different resonance functions at frequencies 0, ω and 2 ω is easily understood in terms of the rotation of the ellipsoid. In the absence of an r.f. field, and with pumping and relaxation processes only, the ellipsoid is uniaxial with its axes in the direction of the static field ( Z axis). With a weak r.f. field the shape of the ellipsoid is unchanged, but it is tilted and precesses round the Z axis at the frequency of the driving field. With stronger r.f. fields the shape of the ellipsoid changes, but at resonance one of the principal axes is always in the direction of the r.f. field and the length of this axis is independent of the field strength. At resonance also, the tilt increases to a limiting value of 1/4π with increasing r.f. field strength and the lengths of the axes in the plane perpendicular to the r.f. field tend to equality.