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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 Vlasov-Poisson 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 Debye-Length,
, the current due to attracted Maxwellian species can be written (Mott-Smith and Langmuir 1926),

 (5)

where

                rp is the radius of the probe.
ne is the electronic density.
Te is the electronic temperature.
is the potential of the probe.

Next:Influence of the geomagnetic Up:General problem of plasma-body Previous:Charging phenomenon

1999-10-10