Editing Plasma diagnostics (section)

==Invasive probe methods==
===Ball-pen probe===
{{main|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.<ref>{{Cite journal|last1=Adámek|first1=J.|last2=Stöckel|first2=J.|last3=Hron|first3=M.|last4=Ryszawy|first4=J.|last5=Tichý|first5=M.|last6=Schrittwieser|first6=R.|last7=Ionită|first7=C.|last8=Balan|first8=P.|last9=Martines|first9=E.|date=2004|title=A novel approach to direct measurement of the plasma potential|journal=Czechoslovak Journal of Physics|language=en|volume=54|issue=S3|pages=C95–C99|doi=10.1007/BF03166386|issn=0011-4626|bibcode=2004CzJPS..54C..95A|s2cid=54869196}}</ref> The [[ball-pen probe]] balances the electron saturation current to the same magnitude as that of the ion saturation current. In this case, its [[Langmuir probe|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]].

===Faraday cup===
{{main|Faraday cup}}
The conventional [[Faraday cup]] is applied for measurements of ion (or electron) flows from plasma boundaries and for [[mass spectrometry]].

===Langmuir probe===
{{main|Langmuir probe}}
Measurements with electric probes, called [[Langmuir probe]]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 (electricity)|current]] versus [[voltage]] characteristics of a [[electrical network|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.

===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 (<math>\dot B</math>, read "B-dot") can be measured locally with a loop or coil of wire. Such coils exploit [[Faraday's law of induction|Faraday's law]], whereby a changing magnetic field induces an electric field.<ref>{{Cite journal|last1=Everson|first1=E. T.|last2=Pribyl|first2=P.|last3=Constantin|first3=C. G.|last4=Zylstra|first4=A.|last5=Schaeffer|first5=D.|last6=Kugland|first6=N. L.|last7=Niemann|first7=C.|date=2009|title=Design, construction, and calibration of a three-axis, high-frequency magnetic probe (B-dot probe) as a diagnostic for exploding plasmas|journal=Review of Scientific Instruments|language=en|volume=80|issue=11|pages=113505–113505–8|doi=10.1063/1.3246785|pmid=19947729|issn=0034-6748|bibcode=2009RScI...80k3505E}}</ref>  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.

===Energy analyzer===
An energy analyzer is a probe used to measure the energy distribution of the particles in a plasma. The charged particles are typically separated by their velocities from the electric and/or magnetic fields in the energy analyzer, and then discriminated by only allowing particles with the selected energy range to reach the detector.

Energy analyzers that use an electric field as the discriminator are also known as retarding field analyzers.<ref>{{Cite journal|last1=Pitts|first1=R. A.|last2=Chavan|first2=R.|last3=Davies|first3=S. J.|last4=Erents|first4=S. K.|last5=Kaveney|first5=G.|last6=Matthews|first6=G. F.|last7=Neill|first7=G.|last8=Vince|first8=J. E.|last9=Duran|first9=I.|date=2003|title=Retarding field energy analyzer for the JET plasma boundary|journal=Review of Scientific Instruments|volume=74|issue=11|pages=4644–4657|doi=10.1063/1.1619554|issn=0034-6748|bibcode=2003RScI...74.4644P|s2cid=31524396}}</ref><ref>{{Cite journal|last1=Stenzel|first1=R. L.|last2=Williams|first2=R.|last3=Agüero|first3=R.|last4=Kitazaki|first4=K.|last5=Ling|first5=A.|last6=McDonald|first6=T.|last7=Spitzer|first7=J.|date=1982|title=Novel directional ion energy analyzer|journal=Review of Scientific Instruments|volume=53|issue=7|pages=1027–1031|doi=10.1063/1.1137103|issn=0034-6748|bibcode=1982RScI...53.1027S}}</ref> It usually consists of a set of grids biased at different potentials to set up an electric field to repel particles lower than the desired amount of energy away from the detector. Analyzers with  cylindrical or conical face-field <ref>A. M. Ilyin (2003). "New class of electrostatic energy analyzers with a cylindrical face-field". Nuclear Instruments and Methods in Physics Research Section A. 500 (1–3): 62–67. Bibcode:2003NIMPA.500...62I. doi:10.1016/S0168-9002(03)00334-6.</ref> can be more effective in such measurements.

In contrast, energy analyzers that employ the use of a magnetic field as a discriminator are very similar to [[mass spectrometer]]s. Particles travel through a magnetic field in the probe and require a specific velocity in order to reach the detector. These were first developed in the 1960s,<ref>{{Cite journal|last1=Eubank|first1=H. P.|last2=Wilkerson|first2=T. D.|date=1963|title=Ion Energy Analyzer for Plasma Measurements|journal=Review of Scientific Instruments|volume=34|issue=1|pages=12–18|doi=10.1063/1.1718108|issn=0034-6748|bibcode=1963RScI...34...12E|doi-access=free}}</ref> and are typically built to measure ions. (The size of the device is on the order the particle's [[gyroradius]] because the discriminator intercepts the path of the gyrating particle.)

The energy of neutral particles can also be measured by an energy analyzer, but they first have to be ionized by an electron impact ionizer.

=== Proton radiography ===
Proton radiography uses a proton beam from a single source to interact with the magnetic field and/or the electric field in the plasma and the intensity profile of the beam is measured on a screen after the interaction. The magnetic and electric fields in the plasma deflect the beam's trajectory and the deflection causes modulation in the intensity profile. From the intensity profile, one can measure the integrated magnetic field and/or electric field.

=== 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 [[Maxwell's equations|Maxwellian]] equations leading to the [[Helmholtz equation]] for the magnetic field. The sheath model is based additionally on the [[Poisson equation]].