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# Plasma diagnostics

Plasma diagnostics are experimental techniques used to measure properties of a plasma such as temperature and density.

## Langmuir probe

Measurements with electric probes, called Langmuir probes, are the oldest and most often used procedures for low-temperature plasmas. The method was developed by Irving Langmuir and his co-workers in the 1920s, and has since been further developed in order to extend its applicability to more general conditions than those presumed by Langmuir. Langmuir probe measurements are based on the estimation of current versus voltage characteristics of a circuit consisting of two metallic electrodes that are both immersed in the plasma under study. Two cases are of interest: (a) The surface areas of the two electrodes differ by several orders of magnitude. This is known as the single-probe method. (b) The surface areas are very small in comparison with the dimensions of the vessel containing the plasma and approximately equal to each other. This is the double-probe method.

Conventional Langmuir probe theory assumes collisionless movement of charge carriers in the space charge sheath around the probe. Further it is assumed that the sheath boundary is well-defined and that beyond this boundary the plasma is completely undisturbed by the presence of the probe. This means that the electric field caused by the difference between the potential of the probe and the plasma potential at the place where the probe is located is limited to the volume inside the probe sheath boundary.

The general theoretical description of a Langmuir probe measurement requires the simultaneous solution of the Poisson equation, the collision-free Boltzmann equation, and the continuity equation with regard to the boundary condition at the probe surface and requiring that, at large distances from the probe, the solution approaches that expected in an undisturbed plasma.

## Magnetic (B-dot) Probe

If the magnetic field in the plasma is not stationary, either because the plasma as a whole is transient or because the fields are periodic (radio-frequency heating), the rate of change of the magnetic field with time ($\dot B$, read "B-dot") can be measured locally with a loop or coil of wire. Such coils exploit Faraday's Law, whereby a changing magnetic field induces an electric field. The induced voltage can be measured and recorded with common instruments.

Also, by Ampere's Law, the magnetic field is proportional to the currents that produce it, so the measured magnetic field gives information about the currents flowing in the plasma. Both currents and magnetic fields are important in understanding fundamental plasma physics.

## Passive spectroscopy

Passive spectroscopic methods simply observe the radiation emitted by the plasma.

### Doppler shift

If the plasma (or one ionic component of the plasma) is flowing in the direction of the line of sight to the observer, emission lines will be seen at a different frequency due to the Doppler effect.

The thermal motion of ions will result in a shift of emission lines up or down, depending on whether the ion is moving toward or away from the observer. The magnitude of the shift is proportional to the velocity along the line of sight. The net effect is a characteristic broadening of spectral lines, known as Doppler broadening, from which the ion temperature can be determined.

### Stark effect

The splitting of some emission lines due to the Stark effect can be used to determine the local electric field.

Even if the macroscopic electric field is zero, any single ion will experience an electric field due to the neighboring charged particles in the plasma. This results in a broadening of some lines that can be used to determine the density of the plasma.

### Motional Stark effect

If an atom is moving in a magnetic field, the Lorenz force will act in opposite directions on the nucleus and the electrons, just as an electric field does. In the frame of reference of the atom, there is an electric field, even if there is none in the laboratory frame. Consequently, certain lines will be split by the Stark effect. With an appropriate choice of beam species and velocity and of geometry, this effect can be used to determine the magnetic field in the plasma.

### Helium Line Ratios

The brightness of an Atomic spectral line emitted by atoms in a gas (or plasma) can be proportional to the gas's temperature, pressure or a weighted sum of both.

Due to the completeness and accuracy of collisional radiative models for helium the temperature and density of plasmas which have helium present can be measured by taking ratios of the emission intensities of various Atomic spectral lines

## Active spectroscopy

Active spectroscopic methods stimulate the plasma atoms in some way and observe the resulting emission of radiation.

### Laser-induced fluorescence

If the plasma is not fully ionized but contains ions that fluoresce, laser-induced fluorescence can provide very detailed information on temperature, density, and flows.

## Optical effects from free electrons

The optical diagnostics above measure line radiation from atoms. Alternatively, the effects of free charges on electromagnetic radiation can be used as a diagnostic.

### Thomson scattering

Scattering of laser light from the electrons in a plasma is known as Thomson scattering. The electron temperature can be determined very reliably from the Doppler broadening of the laser line. The electron density can be dtermined from the intensity of the scattered light, but a careful absolute calibration is required. Although Thomson scattering is dominated by scattering from electrons, since the electrons interact with the ions, in some circumstances information on the ion temperature can also be extracted.

### Interferometry

If a plasma is placed in one arm of an interferometer, the phase shift will be proportional to the plasma density integrated along the path.