D2SET - Langmuir probe

- Introduction
- General problem of plasma-body interactions
- Space plasma environment
- Charging phenomenon
Langmuir probe
- Influence of the geomagnetic field, special case of the polar orbits

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Langmuir probe

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

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.

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In density mesearement mode, the potential $\Phi_p$ 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,

$\begin{displaymath}J = q \int \int \int \mathbf{u}\cdot\mathbf{n} f(\phi,\mathbf{u})\cdotd^3u\end{displaymath}$

(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 $f(\phi,\mathbf{u})$ requires to solve the Vlasov-Poisson system of equation,

$\displaystyle \nabla^2 \phi = 4 \pi q (n_e+n_s - n_i)$			(3)
$\displaystyle \partial_t f+ \mathbf{u} \cdot \partial_{\mathbf{r}} f+ \frac{q......}(\mathbf{E} + \mathbf{u} \wedge \mathbf{B})\cdot \partial_{\mathbf{u}} f = 0$			(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,
$\lambda_D = \left(\frac{\epsilon_0 k_B T_e}{n_e e^2}\right)^{\frac{1}{2}}$ , the current due to attracted Maxwellian species can be written (Mott-Smith and Langmuir 1926),

$\begin{displaymath}I = 2 \pi r_p^2 n_e q \sqrt{\frac{k_BT_e}{2\pi m}}( 1 + \frac{q\phi_p}{k_BT_e})\end{displaymath}$

(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 plasma-body Previous: Charging phenomenon

1999-10-10

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