A Langmuir probe, named after Nobel Prize winning physicist Irving Langmuir, is used to determine the electron temperature, electron density, and electric potential of a plasma. It works by inserting one or more electrodes into a plasma, with an constant of time-varying electric potential between them or between them and the surrounding vessel. The measured currents and potentials in this system allow the determination of the physical properties of the plasma.

Single probe

A single probe consists of a one electrode biased with a voltage ramp relative to the vessel. The current as a function of voltage is measured to produce an I-V characteristic. The voltage at which the current is zero is known as the floating potential. When the voltage is sufficiently negative relative to the floating potential, essentially no electrons will be able to reach the probe. The current collected then is known as the ion saturation current because it is due solely to ions and is nearly independent of the applied voltage. (For some geometries the ion current may rise with the applied voltage, but only with a small power of the voltage.) As the voltage is made more positive, electrons with sufficient energy will overcome the potential barrier and reach the probe. If the electrons have a Maxwell-Boltzmann distribution, that is, the number of electrons with energy E is proportional to exp(-E/k_BT_e), then the electron current will rise exponentially with the voltage. The slope of a log-linear plot of the electron current gives the electron temperature. The electron density can be found using the Bohm criterion, which states that the ion saturation current density is equal to the electron (charge) density times the speed of sound sqrt(k_BT_e/m_e). The plasma potential or space potential is approximately (k_BT_e/q_e)*ln(m_i/m_e) more positive than the floating potential.

In some situations a more detailed analysis can yield information on the, ion density (ni), the ion temperature, or the electron energy distribution function (EEDF) or f(e).

Double probe

An electrode can be biased relative to a second electrode, rather than to the vessel. The theory is similar to that of a single probe, except that the current is limited to the ion saturation current for both positive and negative voltages. The advantage is that the current is always in the exponential region, regardless of the potential.

Triple probe

Another useful configuration is two electrodes biased with a fixed voltage and a third which is floating. The current is the ion saturation current and the potential difference between the positive and the floating electrodes is proportional to the temperature.

Practical considerations

For laboratory and technical plasmas, the electrodes are most commonly tungsten wires several thousandths of an inch thick. For fusion plasmas, graphite electrodes with dimensions from 1 to 10 mm are usually used. The electrode surface exposed to the plasma must be defined, e.g. by insulating all but the tip of a wire electrode.

A Langmuir probe can be purchased off the shelf for on the order of 15,000 U.S. Dollars, or they can be built by an experienced researcher and/or technician. When working at frequencies under 100 MHz, it is advisable to use blocking filters, and take necessary grounding precautions.