Langmuir Probe Theory

Since the early 1960’s, Langmuir probes have been used in ionospheric science investigations.  There are two types of Langmuir probe usages: swept bias (SBLP) and fixed bias (FBLP).  Swept bias Langmuir probes are useful for measuring electron temperature (T_e), electron and ion density (Ni, Ne), and relative spacecraft potential (Vs).  A collecting surface is extended from the investigating spacecraft into the nearby ambient plasma region.  This is typically accomplished using a boom mechanism.  When a negative voltage is applied to the collector surface, the positive ions in the plasma are attracted to it. This creates an “incoming” current from the plasma into the spacecraft.  Conversely, when a positive voltage is applied to the collector surface, electrons in the plasma are attracted to the surface.  Therefore an “outgoing” current flows from the spacecraft to the plasma.  In the case of a swept bias Langmuir probe, a volt-ampere curve is the resultant data to be analyzed.  The analysis of the curve yields the T_e, Ni, Ne, and Vs.  Figure 1 below represents a theoretical volt-ampere curve from a Langmuir probe sweep.

Figure 1: Theoretical transfer characteristic of a swept bias Langmuir probe (SBLP)

There are three important regions present in the volt-ampere curve: the ion saturation region, the electron retardation region, and the electron saturation region.  The amplitude of the electron current Ie is proportional to Ne, the amplitude of the ion current I_i is proportional to Ni, and the electron temperature, Te, determines the width of the electron retardation region for all probe geometries. There are two methods to extract the desired plasma parameters.  The reader is referred to Siegel 2002 [5] for more information regarding the orbital-motion-limited (OML) theory and child-langmuir theory for extracting Ne, Ni, and Te as that information is a bit cumbersome for the scope of this design document.

            For fixed bias Langmuir probe operation, the theory is much simpler.  Instead of sweeping the sensor head bias through the three regions of the above volt-ampere relationship, the bias is held fixed.  The result of this is a high-resolution relative measurement of the desired plasma parameters.  Which measurement is being made is determined by which region the probe bias is fixed in.