RF MODULE

44 | CHAPTER 2: TUTORIAL MODELS
The conductivity of the Earth’s surface is of the magnitude of 0.01 S/m. The skin
depth, δ, is approximately:
For ω = 40 Hz, δ = 2 km, which is 50 times less than the height of the cavity. The
Earth surface can therefore be approximated as a perfect electric conductor:
Inside the cavity, the electric field E is described by the following equation:
The Schumann resonance frequencies for the Earth are nowadays measured at several
stations around the globe. The eigenmodes vary due to several different factors, such
as changes in the global climate and variations in the solar wind which affect the height
and conductivity profile of the cavity.
Modeling in COMSOL Multiphysics
In this model, the varying height of the cavity depending on day and night sides of the
Earth is modeled geometrically with two concentric spheres, the outer sphere having
a different center point than the inner. Let x be a point inside the cavity, r the radial
distance to the Earth’s center from x, R E the Earth radius, σ ion the conductivity at the
ionosphere boundary, and d the distance to the ionosphere boundary. The
conductivity profile is approximated with the following linear expression:
(2-1)
In COMSOL Multiphysics, the distance, d, to the boundary is available by defining a
boundary distance variable.
Table 2-2 presents the data used in the model.
TABLE 2-2: MODEL DATA
∇ µ r 1
δ =
-------------
2
µ 0ωσ ∇ × E = 0
2 εrc E
× ( – ∇ × E)
– k0 = 0
σion( r – RE) σ =
-------------------------------r+
d
PROPERTY VALUE
Earth radius 6371 km
Ionosphere height 100 km–300 km
Conductivity at inner D layer, σion 1·10 -8 S/m