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Langmuir probe
The above charging process is also the basic mechanism of an instrument
designed to measure plasma parameters and called a Langmuir probe. The
Langmuir's probe is a conductor for which the potential with respect to
a ground (in general the whole satellite) and the collected current can
be monitored.
In density mesearement mode, the potential
is fixed and the current
I
is measured. The plasma parameters can
be retrieved if a theoretical model of
I
is available. In principle,
a model of
I
must be determined by expressing each component of
the current using the distribution function at the surface of the object,

(2)

where
J is the current densities at the object surface.
q is the charge of the particle.
u is the speed of the particle.
n is the normal to the surface.
f is the distribution function.
is the electric potential.
In general the determination of
requires to solve the VlasovPoisson system of equation,



(3)




(4)

where
E is the electric field.
B is the magnetic field.
m is the mass of the particle.
Fortunately, there are several possible simplifications of the problem
leading to more tractable equations. For instance, it can be shown that
in the case of a system with spherical symmetry and a radius much smaller
than the plasma DebyeLength,
,
the current due to attracted Maxwellian species can be written (MottSmith
and Langmuir 1926),

(5)

where
r_{p} is the radius of the probe.
n_{e} is the electronic density.
T_{e} is the electronic temperature.
is the potential of the probe.
Next:
Influence
of the geomagnetic
Up:
General
problem of plasmabody
Previous:
Charging
phenomenon
19991010
