Calculation of the Signal Voltage Induced in a Toroidal Proton-Precession Magnetometer Sensor

The signal EMF induced as a function of time in a proton-precession magnetometer sensor of toroidal shape with an elliptical cross-sectional area is calculated in terms of the magnetic properties of the sensor fluid, polarizing current, orientation of the sensor with respect to the direction of the ambient magnetic field, and geometric proportions of the sensor. It is assumed that the sensor is in a uniform ambient magnetic field; the polarizing current is reduced to zero in a time that is short compared to the period of the Larmor precession of the nuclear magnetic moments in the sensor fluid; the nuclear magnetic moments do not interact; and no significant current flows in the sensor winding during the relaxation process in which the EMF is measured. In the specific case that the sensor winding fills the toroid window and that the polarizing supply is a constant voltage source, the calculations permit a simple comparison of variously proportioned sensors in terms of the signal EMF amplitude.