16.4 Field instrument: The flux-gate magnetometer

There are two classes of instruments to measure the ambient magnetic field: scalar and vector magnetometers. While nuclear precession and optical pumping magnetometers are the most common scalar magnetometers used on board s/c (see Pfaff et al.

, 1998b for related material), the flux-gate magnetometer is, with no doubt, the mostly used one to perform vector measurements of the ambient magnetic field. In this section, we will briefly describe only this last instrument just for those who are not familiar at all with this kind of measurements in space.

The working principle of this magnetometer is based on the phenomenon of magnetic hysteresis. The primary element (see Figure 106 ) is made of two bars of high magnetic permeability material. A magnetizing coil is spooled around the two bars in an opposite sense so that the magnetic field created along the two bars will have opposite polarities but the same intensity. A secondary coil wound around both bars will detect an induced electric potential only in the presence of an external magnetic field.

Figure 106:

Outline of a flux-gate magnetometer. The driving oscillator makes an electric current, at frequency $f$ , circulate along the coil. This coil is such to induce along the two bars a magnetic field with the same intensity but opposite direction so that the resulting magnetic field is zero. The presence of an external magnetic field breaks this symmetry and the resulting field $/= 0$ will induce an electric potential in the secondary coil, proportional to the intensity of the component of the ambient field along the two bars.

The field amplitude $BB$ produced by the magnetizing field $H$ is such that the material periodically saturates during its hysteresis cycle as shown in Figure 107

Figure 107:

Left panel: This figure refers to any of the two sensitive elements of the magnetometer. The thick black line indicates the magnetic hysteresis curve, the dotted green line indicates the magnetizing field $H$ , and the thin blue line represents the magnetic field $B$ produced by $H$ in each bar. The thin blue line periodically reaches saturation producing a saturated magnetic field B. The trace of $B$ results to be symmetric around the zero line. Right panel: magnetic fields $B1$ and $B2$ produced in the two bars, as a function of time. Since $B1$ and $B2$ have the same amplitude but out of phase by $180o$ , they cancel each other.

In absence of an external magnetic field, the magnetic field $B 1$ and $B 2$ produced in the two bars will be exactly the same but out of phase by $o 180$ since the two coils are spooled in an opposite sense. As a consequence, the resulting total magnetic field would be $0$ as shown in Figure 107

. In these conditions no electric potential would be induced on the secondary coil because the magnetic flux $P$ through the secondary is zero.

On the contrary, in case of an ambient field $HA /= 0$ , its component parallel to the axis of the bar is such to break the symmetry of the resulting $B$ (see Figure 108 ). $HA$ represents an offset that would add up to the magnetizing field $H$ , so that the resulting field $B$ would not saturate in a symmetric way with respect to the zero line. Obviously, the other sensitive element would experience a specular effect and the resulting field $B = B + B 1 2$ would not be zero, as shown in Figure 108 .

Figure 108:

Left panel: the net effect of an ambient field $HA$ is that of introducing an offset which will break the symmetry of $B$ with respect to the zero line. This figure has to be compared with Figure 107

when no ambient field is present. The upper side of the $B$ curve saturates more than the lower side. An opposite situation would be shown by the second element. Right panel: trace of the resulting magnetic field $B = B1 + B2$ . The asymmetry introduced by $HA$ is such that the resulting field $B$ is different from zero.

In these conditions the resulting field $B$ , fluctuating at frequency $f$ , would induce an electric potential $V = - dP/dt$ , where $P$ is the magnetic flux of $B$ through the secondary coil.

Figure 109:

Time derivative of the curve $B = B1 + B2$ shown in Figure 108

assuming the magnetic flux is referred to a unitary surface.

At this point, the detector would measure this voltage which would result proportional to the component of the ambient field $HA$ along the axis of the two bars. To have a complete measurement of the vector magnetic field $B$ it will be sufficient to mount three elements on board the spacecraft, like the one shown in Figure 106

, mutually orthogonal, in order to measure all the three Cartesian components.