PROBLEMS OF GEOCOSMOS

Proceedings of the 7th International Conference "Problems of Geocosmos" (St. Petersburg, Russia, 26-30 May 2008)
Figure 1. Fragment of the Bow Shock (BS), of the Transition
Layer (TL) or magnetosheath, magnetopause (MP). Location of
the orthogonal coordinate system with the origin in the Earth’s
center (axis x is directed towards the sun, axis y is directed
from dawn to dusk and axis z is directed towards the
geographic north) and location of auxiliary coordinate system
(r, φ, ψ) and local coordinate system (l, n, τ).
The bow shock front will be approximated by a paraboloid of rotation with a focus at the Earth's center (fig.
1). The front equation has the form:
r = yg/(1+ cos φ) = yg/2cos(φ/2) (2)
where φ is the angle between the X axis directed toward the Sun and the radius vector r, and yg is the
distance from the origin along the Y axis to the intersection with the surface of a paraboloid. Any section a
paraboloid of rotation by the M plane passing the X axis will be parabola. Let us introduce an auxiliary
coordinate system l, τ, n. In this system n will be the normal to the parabola at a certain point and will lie in
our plane, l will be the tangent at the same point and will also lie in the M plane, and τ will complete this
system to the orthogonal coordinate system. The surface currents have been written in these coordinates. It is
evident that: div J = -jn. From this it follows that
jln = -c[B0τcos 3 (φ/2) ∂σ/∂φ]/2πyg (3)
where В0τ is the IMF tangential component. In the equatorial plane, this is simply Вz, σ(φ)=В1τ/B0τ,, i.e.,
σ(φ)is equal to the ratio of the strength of the magnetic field tangential components before and behind the
bow shock front. The dependence of this quantity on coordinates was studied in [Ponomarev et al., 2006 a,
b]. With increasing distance from the bow point, the coefficient σ(φ) decreases (tending to unity at infinity),
and this means that the current could become divergent and that the current component normal to the front
appears, which will close outside the front, e.g., through the body of the magnetosphere or within the
magnetosheath. Such a situation is actually observed. This problem was considered in detail in [Ponomarev
et al., 2006 a, b] and includes many interesting details, but we are interested in the conceptual aspect. Let us
consider the situation in more detail but in a simplified case. It is clear that the current direction depends on
the sign of the tangential component. For the current flowing along the front in the equatorial plane, IMF Bz
is the tangential component. At Bz < 0, the dawn-dusk current will correspond to the current closing through
the magnetosphere. Since the magnetic field together with plasma will sweep over the bow shock front, the
electric field (which can be easily estimated) will appear in the front coordinate system. The electric field
component directed along the E1 front is defined as:
El = VnB0τ/c (4)
Taking into account that the element of length of the parabola is dl= yg/2cos 3 (φ/2)dφ, and dФg/dl = -El, Vn =
V0 cos(φ/2) and B0τ are independent of φ, we find the bow shock front potential: Фg= -(V0B0τ/c) tg(φ/2)⋅yg ,
(5). It has been demonstrated [Ponomarev et al., 2006 a, b] that the corresponding electric field is always
directed against the current so that the bow shock front is the generator of electric power. Almost a half of
the SW kinetic energy is transformed into this power; consequently, the problems of energetic character do
not arise in this case. Ponomarev et al. [Ponomarev et al., 2006 a, b] considered the problem of the
magnetopause potential and find the explicit expression for this potential: Фm = (a/b)⋅Φg , (6), where a is an
almost constant quantity. It is evident that Фg changes its sign at a change of the B0τ sign. The electric
current depends on the Bz sign and is directed from dawn to dusk only at Bz < 0. However, this current
cannot change its direction in the body of the magnetosphere since the plasma pressure gradients remained
unchanged, corresponding to the previous current direction. Consequently, the external current really does
not fall into the magnetosphere at Bz > 0. The previous internal current, which will be always spent on the
maintenance of ionospheric processes and will gradually decay, will continue circulating in the
magnetosphere. Thus, the magnetosphere becomes energetically isolated at Bz > 0. We used the expression
for Фm(φ) as a boundary condition for solving the boundary-value problem of finding the potential within the
magnetosphere. Ponomarev et al. [Ponomarev et al., 2006 a, b] obtained the known expressions for this
potential.
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