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Astron. Astrophys. 354, 321-327 (2000)

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2. Basic equations

We consider particles with charge q and mass m moving in a magnetized medium. A magnetic field is carried by a flow with velocity varying in height with the form [FORMULA] where [FORMULA] and the magnetic field has the form [FORMULA] as is illustrated in Fig. 1.

[FIGURE] Fig. 1. Basic configuration of the magnetic field and velocity shear

We consider that the flow is collisionless, and that particles move exclusively as a result of the Lorentz force; in such a way that the equation of motion for these particles can be written in the form:

[EQUATION]

where [FORMULA] is the convective electric field felt in a frame at rest with respect to obstacle and is given by.

[EQUATION]

The components of the equation of motion are given by

[EQUATION]

[EQUATION]

[EQUATION]

in which

[EQUATION]

and,

[EQUATION]

We note that as opposed to the standard cyclotron frequency the components, [FORMULA] and [FORMULA] depend on the magnetic field direction and on the sign of the charge. We restrict our analysis to constant velocity shears. This is consistent with the observations of bulk velocity of solar wind protons in the vecinity of comets Giacobini-Zinner (Bame et al. 1986), Halley (Goldstein et al. 1986) and planet Venus (Romanov et al. 1979) as discussed in Perez-de-Tejada (Perez-de-Tejada 1989, 1994) so, Eq. (5) can be rewritten as:

[EQUATION]

which renders the system of equations linear with constant coefficients, and thus allows us and exact solution.

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© European Southern Observatory (ESO) 2000

Online publication: January 31, 2000
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