# Plasma diagnostics

Plasma diagnostics are a pool of methods, instruments, and experimental techniques used to measure properties of a plasma, such as plasma components' density, distribution function over energy (temperature), their spatial profiles and dynamics, which enable to derive plasma parameters.

## 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 or Vlasov 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.

## Ball-pen probe

A ball-pen probe is novel technique used to measure directly the plasma potential in magnetized plasmas. The probe was invented by Jiří Adámek in the Institute of Plasma Physics AS CR in 2004. The ball-pen probe balances the electron saturation current to the same magnitude as that of the ion saturation current. In this case, its floating potential becomes identical to the plasma potential. This goal is attained by a ceramic shield, which screens off an adjustable part of the electron current from the probe collector due to the much smaller gyro–radius of the electrons. The electron temperature is proportional to the difference of ball-pen probe(plasma potential) and Langmuir probe (floating potential) potential. Thus, the electron temperature can be obtained directly with high temporal resolution without additional power supply.

## Self Excited Electron Plasma Resonance Spectroscopy (SEERS)

Nonlinear effects like the I-V characteristic of the boundary sheath are utilized for Langmuir probe measurements but they are usually neglected for modelling of RF discharges due to their very inconvenient mathematical treatment. The Self Excited Electron Plasma Resonance Spectroscopy (SEERS) utilizes exactly these nonlinear effects and known resonance effects in RF discharges. The nonlinear elements, in particular the sheaths, provide harmonics in the discharge current and excite the plasma and the sheath at their series resonance characterized by the so-called geometric resonance frequency.

SEERS provides the spatially and reciprocally averaged electron plasma density and the effective electron collision rate. The electron collision rate reflects stochastic (pressure) heating and ohmic heating of the electrons.

The model for the plasma bulk is based on 2d-fluid model (zero and first order moments of Boltzmann equation) and the full set of the Maxwellian equations leading to the Helmholtz equation for the magnetic field. The sheath model is based additionally on the Poisson equation.

## 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.

## Faraday cup in plasma diagnostics

The conventional Faraday cup is applied for measurements of ion (or electron) flows from plasma boundaries and for mass spectrometry.

## 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 Lorentz 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.

### Spectral line ratios

The brightness of an Atomic spectral line emitted by atoms and ions in a gas (or plasma) can depend on the gas's temperature and pressure.

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

### Zeeman effect

The presence of a magnetic field splits the atomic energy levels due to the Zeeman effect. This leads to broadening or splitting of spectral lines. Analyzing these lines can, therefore, yield the magnetic field strength in the plasma.

## Active spectroscopy

Active spectroscopic methods stimulate the plasma atoms in some way and observe the result (emission of radiation, absorption of the stimulating light or others).

### Absorption spectroscopy

By shining through the plasma a laser with a wavelength, tuned to a certain transition of one of the species present in the plasma, the absorption profile of that transition could be obtained. This profile provides information not only for the plasma parameters, that could be obtained from the emission profile, but also for the line-integrated number density of the absorbing species.

### 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.

### Two-photon laser-induced fluorescence

The two-photon laser-induced fluorescence (TALIF) is a modification of the laser-induced fluorescence technique. In this approach the upper level is excited by absorbing two photons and registering the resulting emission from the excited state. The advantage of this approach is that the registered light from the fluorescence is with a different wavelength from the exciting laser beam, which leads to improved signal to noise ratio.

## 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 determined 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.

The Faraday effect will rotate the plane of polarization of a beam passing through a plasma with a magnetic field in the direction of the beam. This effect can be used as a diagnostic of the magnetic field, although the information is mixed with the density profile and is usually an integral value only.

## Neutron diagnostics

Fusion plasmas produces 3.5 MeV and 14 MeV neutrons. By measuring the neutron flux, plasma properties such as ion temperature and fusion power can be determined.