Editing Langmuir probe (section)

===Sheath expansion===

It is not enough to know the current ''density'' as a function of bias voltage since it is the ''absolute'' current which is measured. In an unmagnetized plasma, the current-collecting area is usually taken to be the exposed surface area of the electrode. In a magnetized plasma, the '''projected''' area is taken, that is, the area of the electrode as viewed along the magnetic field. If the electrode is not shadowed by a wall or other nearby object, then the area must be doubled to account for current coming along the field from both sides. If the electrode dimensions are not small in comparison to the Debye length, then the size of the electrode is effectively increased in all directions by the sheath thickness. In a magnetized plasma, the electrode is sometimes assumed to be increased in a similar way by the ion [[Larmor radius]].

The finite Larmor radius allows some ions to reach the electrode that would have otherwise gone past it. The details of the effect have not been calculated in a fully self-consistent way.

If we refer to the probe area including these effects as <math>A_{eff}</math> (which may be a function of the bias voltage) and make the assumptions
*<math>T_i=T_e</math>,
*<math>Z=1</math>
*<math>\gamma_i=3</math>, and
*<math>n_{e,sh}=0.5\,n_e</math>,
and ignore the effects of
*bulk resistivity, and
*electron saturation,
then the ''I-V'' characteristic becomes

<math> I = I_i^{max}(-1+e^{q_e(V_{pr}-V_{fl})/(k_BT_e)} )</math>,

where

<math> I_i^{max} = q_en_e\sqrt{k_BT_e/m_i}\,A_{eff} </math>.