As demonstrated in Section 3.3.2, the SR are TM modes with a radial electric Er polarisation and
an azimuthal Hϕ polarisation. In ELF range, only vertical E and horizontal H are detected due to
the high conductivity of the ground [19]. Eris detected with vertical metallic ball capacitor antenna
mounted on top of a few metres long vertical mast. A full description and characterisation of the antenna are available in [13, 19]. For magnetic field detection, most commonly used horizontal H antennas which are search-coil and the fluxgate magnetometers. Both of these magnetometers are based on ferromagnetic3 material filled core that acts as a magnetic field concentrator, increasing the density of the magnetic field inside the coil, and therefore, increasing the sensitivity.
Introduction to Ferromagnetic Materials
Normal paramagnets are materials that are made up of tiny magnetised domains (comparable to tiny magnets) whose magnetic orientations are random in space, making the bulk appear as a non- magnetic material. However, when an external magnetic field is applied, the domains rearrange their magnetic moments in response to the applied field, and the material becomes magnetised. The rate of magnetisation is outcompeted by thermal agitation and it is very difficult to attain saturation
(total alignment of the moments of the tiny magnets); they require a very low temperature and a high intensity of applied magnetic field. On the other hand, ferromagnetic materials attain mag- netic saturation at ambient temperatures and ambient geomagnetic field strength. In some cases, they can display spontaneous magnetisation without any external magnetic field applied. Ferromag- netic materials are characterised by a critical temperature called Curie temperature beyond which ferromagnetism is destroyed and they behave as paramagnets4. Some examples of ferromagnetic materials are iron (Fe), cobalt (Co) and nickel (Ni ).
In the volume, the magnetic field induced M depends on the strength of the applied field H. By taking into account the statistical approach that describes the competition between the alignment of the tiny fields in the volume and thermal noise, the Langevin function [33] describes what happens when a gradually increasing field is applied to the ferromagnetic core.
Lf(x) = coth(x) − 1 x x = µ2H kBT , (5.8)
where, µ, kB and T are the permeability of the medium, Boltzmann’s constant and the absolute
temperature respectively. The overall magnetisation is the sum of magnetisation effect of all Nf
individual ferromagnetic domains
M = NfµLf(x). (5.9)
Here, two main possibilities arise
• When x 1, coth(x) 1/x: L(x) ≈ x
3, M is a linear function in terms of H. The effect of
thermal noise is greater than the alignment of moments. Hence, the magnetisation is directly proportional to the field applied, M = Nfµ3
3 kBT H . This is known as the Curie-Weiss law for
ferromagnetism.
• When x 1, coth(x) → 1: L(x) = 1, the effect of the magnetic field H is much greater than thermal noise. The alignment is total and the magnetisation is said to be saturated, Msat= Nfµ.
The evolution of Lf can be shown in Fig. 5.7. The optimal working range of the induction coil is
the linear response and the fluxgate in the saturation range.
5.5.1
Induction Coil Magnetometer
ICMs are vector magnetometers made of ferromagnetic filled cores wound with induction coils. Their working principle is based on Faraday’s law of induction by which the voltage induced in the core is proportional to the change in magnetic field in the coil as follows
V = −Seff
dB
dt, (5.10)
4In this section, we only consider the case where T > T Curie
(a)Magnetization curve x = µ2H/kBT (b) Magnetic saturation [105]
Figure 5.7: Magnetisation process of a ferroelectric material. Magnetic saturation is observed in the lower panel of (b). The upper panel of (b) shows a completely demagnetised system.
where Seffis a coefficient called the effective area of the coil. A feedback winding is also wired around
the core to flatten the frequency response of the magnetometer. The number of windings may vary, but they are usually more than 100,000 turns of wire. This allows an efficient voltage induction in the core of the antenna. Seff is therefore [106],
Seff= N πµeffm2b, (5.11)
where N is the number of windings, µeff the magnetic effective permeability dependent of the geo-
metry, mb the half-width (radius) of the ferromagnetic core.
Here, the ferromagnetic core geometry is approximated by an ellipsoid with major and minor half- axes ma and mb respectively, with the condition ma mbso that µeff u µ [13, 106]. For a 1 m long, 5 cm wide core, when µ is increased up to 2000 or so, the sensitivity reaches magnetic saturation, limited by the geometry [13]. Here two challenges arise, either the ICM must be tens of metres long which is not very practical or its width should be reduced, which yet increases the possibility of saturation.
On the measuring site, inductance coils are very sensitive to vibrations and to variations of temper- ature and, therefore, need to be buried in dry sand to operate efficiently. As depicted in Fig. 5.8, the coils detect changes in magnetic field polarised along its axis, with the sensitivity in an angular pattern in a 8 lemniscate shape. The Hφ field is detected using two orthogonal horizontal induction
coils in respective directions South − N orth (SN) and W est − East (WE). Due to the transverse nature of the radiowaves, WE oriented coils detects waves that are travelling along the SN direction and vice versa. Because of their angular cross-section pattern, they need to be placed carefully apart from each or in a T letter configuration from each other to avoid interference.
Induction magnetometers come in a set of various designs, The best performing design used nowadays belongs to the British Geological Survey [30] and can sample from frequencies between 0.1 and
Figure 5.8: Depiction of an angular pattern for an inductance coil magnetometer measured for sym- metric and asymetric winding. In this case, sensitivity is maximum for waves that propagate along 90◦ and 270◦direction and zero for 0 and 180◦direction. Sensitivity also depends on the symmetry of the coil windings [13].
1000 Hz. The most commonly used ICM in for field detection were designed by Belyaev [107]5and
are used worldwide as ground magnetometers [13, 15, 19]. These types of magnetometers are used with the CARISMA network. Their bandwidth ranges from 0.001 − 30 Hz and their sensitivity is 20 mV/nT above 1 Hz, with a noise rejection ≤ 0.2 pT/√Hz [15].
5.5.2
Fluxgate Magnetometers (FGM)
FGMs are the most commonly used vector magnetometers for navigation applications and for Earth magnetometry 6 [21]. Their working principle relies on the magnetic saturation of a ferromagnetic
core. The different configurations of the cores are shown in Fig. 5.9. The design is made of two coils, a primary coil and the pick-up coil. The former excites the core with a strong alternating current that causes the core to reach saturation at each period and the latter is induced by a magnetic field gradient created in the material. The signals in the two coils are symmetrical as is shown in Fig 5.9b (left) and the output voltage of the fluxgate is zero as in Fig. 5.9d (left). However, when an external field is applied, the magnetic response between the two coils lose their symmetry because one coil saturates before the other (Fig. 5.9b (right)), then a harmonic voltage is developed at the terminal of the magnetometer (Fig. 5.9d (right).
For a double core magnetometer, a high sensitivity is achieved by a long ferromagnetic core with large number of secondary coils and a high-frequency of the exciting signal. Using coils n1= n2= 1000, a
frequency f = 10 kHz, on a double core 0.5 m long and an area of 2.5 mm2, a sensitivity of 10 µV/nT is achieved [108]. On the other hand, a ring core of 30 mm diameter, n1 = 150, n2 = 1100 shows
the best performance [109].
5LEMI-3 magnetometers of the Lviv Centre Institute for Space Research, Ukraine http://www.lemisensors.com 6Extensively used with the Intermagnet network
Figure 5.9: Designs of fluxgate magnetometers with different shapes of ferromagnetic cores (a) a double bar and (b) a ring core [14].
Figure 5.10: Fluxgate magnetometer working principle shown in two columns: At the left is the FGM working without any external field and the right, with the magnetic field applied. [15].
(a) range (b) sensitivity
Figure 5.11: Working range and sensitivity of different ELF magnetometers. Magnetoresistive (MR sensors) represented in (b) are not described in this work. [14]