Plasma diagnostics
Encyclopedia
Plasma diagnostics are experimental techniques used to measure properties of a plasma
such as temperature
and density
.
s, 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.
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.
, 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.
.
, from which the ion temperature can be determined.
can be used to determine the local electric field.
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.
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 line
s
can provide very detailed information on temperature, density, and flows.
. 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.
, the phase shift will be proportional to the plasma density integrated along the path.
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.
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
such as temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
and density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
.
Langmuir probe
Measurements with electric probes, called Langmuir probeLangmuir probe
A Langmuir probe is a device named after Nobel Prize winning physicist Irving Langmuir, 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 a constant or time-varying electric potential...
s, are the oldest and most often used procedures for low-temperature plasmas. The method was developed by Irving Langmuir
Irving Langmuir
Irving Langmuir was an American chemist and physicist. His most noted publication was the famous 1919 article "The Arrangement of Electrons in Atoms and Molecules" in which, building on Gilbert N. Lewis's cubical atom theory and Walther Kossel's chemical bonding theory, he outlined his...
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
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
characteristics of a circuit
Electrical network
An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources and switches. An electrical circuit is a special type of network, one that has a closed loop giving a return path for the current...
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
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
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
Continuity equation
A continuity equation in physics is a differential equation that describes the transport of a conserved quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described...
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.
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 (, read "B-dot") can be measured locally with a loop or coil of wire. Such coils exploit Faraday's LawFaraday's law
Faraday's law may refer to the following:*Faraday's laws of electrolysis in chemistry*Faraday's law of induction, also known as Faraday-Lenz Law, in electromagnetism physics**The Maxwell–Faraday equation...
, 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
Ampère's law
In classical electromagnetism, Ampère's circuital law, discovered by André-Marie Ampère in 1826, relates the integrated magnetic field around a closed loop to the electric current passing through the loop...
, 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 effectDoppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...
.
Doppler broadening
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 broadeningDoppler broadening
In atomic physics, Doppler broadening is the broadening of spectral lines due to the Doppler effect caused by a distribution of velocities of atoms or molecules. Different velocities of the emitting particles result in different shifts, the cumulative effect of which is the line broadening.The...
, from which the ion temperature can be determined.
Stark effect
The splitting of some emission lines due to the Stark effectStark effect
The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to presence of an external static electric field. The amount of splitting and or shifting is called the Stark splitting or Stark shift. In general one distinguishes first- and second-order Stark effects...
can be used to determine the local electric field.
Stark broadening
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 forceLorentz force
In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:...
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
Stark effect
The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to presence of an external static electric field. The amount of splitting and or shifting is called the Stark splitting or Stark shift. In general one distinguishes first- and second-order Stark effects...
. 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 lineAtomic spectral line
In physics, atomic spectral lines are of two types:* An emission line is formed when an electron makes a transition from a particular discrete energy level of an atom, to a lower energy state, emitting a photon of a particular energy and wavelength...
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
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...
the temperature and density of plasmas which have helium present can be measured by taking ratios of the emission intensities of various Atomic spectral line
Atomic spectral line
In physics, atomic spectral lines are of two types:* An emission line is formed when an electron makes a transition from a particular discrete energy level of an atom, to a lower energy state, emitting a photon of a particular energy and wavelength...
s
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 fluorescenceLaser-induced fluorescence
Laser-induced fluorescence is a spectroscopic method used for studying structure of molecules, detection of selective species and flow visualization and measurements....
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 scatteringThomson scattering
Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism. It is just the low-energy limit of Compton scattering: the particle kinetic energy and photon frequency are the same before and after the scattering...
. The electron temperature can be determined very reliably from the Doppler broadening
Doppler broadening
In atomic physics, Doppler broadening is the broadening of spectral lines due to the Doppler effect caused by a distribution of velocities of atoms or molecules. Different velocities of the emitting particles result in different shifts, the cumulative effect of which is the line broadening.The...
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 interferometerInterferometry
Interferometry refers to a family of techniques in which electromagnetic waves are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy,...
, the phase shift will be proportional to the plasma density integrated along the path.
Faraday rotation
The Faraday effectFaraday effect
In physics, the Faraday effect or Faraday rotation is a Magneto-optical phenomenon, that is, an interaction between light and a magnetic field in a medium...
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.