Streamer discharge

Last updated October 28, 2024

Video clip of streamers from a Tesla coil. The electrostatic repulsion of ions, ionic recombination, and air convection currents due to heating tend to break up ionized regions, so streamers have a short lifetime. TeslaCoilSparks.gif — Video clip of streamers from a Tesla coil. The electrostatic repulsion of ions, ionic recombination, and air convection currents due to heating tend to break up ionized regions, so streamers have a short lifetime.

In electromagnetism, a streamer discharge, also known as filamentary discharge, is a type of transient electric discharge which forms at the surface of a conductive electrode carrying a high voltage in an insulating medium such as air. Streamers are luminous writhing branching sparks, plasma channels composed of ionized air molecules, which repeatedly strike out from the electrode into the air.

Like the related corona discharges and brush discharges, a streamer discharge represents a region around a high voltage conductor where the air has suffered electrical breakdown and become conductive (ionized), so electric charge is leaking off the electrode into the air, but the opposite polarity electrode is not close enough to create an electric arc between the two electrodes. It occurs when the electric field at the surface of a conductor exceeds the dielectric strength of air, around 30 kilovolts per centimeter. When the electric field created by the applied voltage reaches this threshold, accelerated electrons strike air molecules with enough energy to knock other electrons off them, ionizing them, and the freed electrons go on to strike more molecules in a chain reaction. These electron avalanches (Townsend discharges) create ionized, electrically conductive regions in the air near the electrode. The space charge created by the electron avalanches gives rise to an additional electric field, causing the ionized region to grow at its ends, forming a finger-like discharge called a streamer.

Streamers are transient (exist only for a short time) and filamentary, which makes them different from corona discharges. They are used in applications such as ozone production, air purification or plasma medicine.^{[ citation needed ]} If a streamer reaches the opposite polarity conductor it creates an ionized conductive path through which a large current can flow, releasing a large amount of heat, resulting in an electric arc; this is the process through which lightning leaders create a path for lightning bolts. Streamers can also be observed as sprites in the upper atmosphere. Due to the low pressure, sprites are much larger than streamers at ground pressure, see the similarity laws below.

Large Tesla coil producing 3.5 meter (10 foot) streamer arcs, indicating a potential of millions of volts. Teslacoil.jpg — Large Tesla coil producing 3.5 meter (10 foot) streamer arcs, indicating a potential of millions of volts.

Simulation of a positive streamer discharge. Shown from left to right are: the electric field, electron density, charge density and the light emission.

History

The theory of streamer discharges was preceded by John Sealy Townsend's discharge theory ^[1] from around 1900. However, it became clear that this theory was sometimes inconsistent with observations. This was especially true for discharges that were longer or at higher pressure. In 1939, Loeb^[2]^[3] and Raether ^[4] independently described a new type of discharge, based on their experimental observations. Shortly thereafter, in 1940, Meek presented the theory of spark discharge,^[5] which quantitatively explained the formation of a self-propagating streamer. This new theory of streamer discharges successfully explained the experimental observations.

Applications

Streamers are used in applications such as ozone generation, air purification and plasma-assisted combustion. An important property is that the plasma they generate is strongly non-equilibrium: the electrons have much higher energies than the ions. Therefore, chemical reactions can be triggered in a gas without heating it. This is important for plasma medicine, where "plasma bullets", or guided streamers,^[6] can be used for wound treatment,^[7] although this is still experimental.

Streamer physics

Streamers can emerge when a strong electric field is applied to an insulating material, typically a gas. Streamers can only form in areas where the electric field exceeds the dielectric strength (breakdown field, disruptive field) of the medium. For air at atmospheric pressure, this is roughly 30 kV per centimeter. The electric field accelerates the few electrons and ions that are always present in air, due to natural processes such as cosmic rays, radioactive decay, or photoionization. Ions are much heavier, so they move very slowly compared to electrons. As the electrons move through the medium, they collide with the neutral molecules or atoms. Important collisions are:

Elastic collisions, which change the direction of motion of the electrons.
Excitations, where the neutral particle is excited, and the electron loses the corresponding energy.
Impact ionization, where the neutral particle becomes ionized, with the incident electron losing the energy.
Attachment, where the electron attaches to the neutral to form a negative ion.

When the electric field approaches the breakdown field, the electrons gain enough energy between collisions to ionize the gas atoms, knocking an electron off the atom. At the breakdown field, there is a balance between the production of new electrons (due to impact ionization) and the loss of electrons (due to attachment). Above the breakdown field, the number of electrons starts to grow exponentially, and an electron avalanche (Townsend avalanche) forms.

The electron avalanches leave behind positive ions, so in time more and more space charge is building up. (Of course, the ions move away in time, but this a relatively slow process compared to the avalanche generation as ions are much heavier than electrons). Eventually, the electric field from all the space charge becomes comparable to the background electric field. This is sometimes referred to as the "avalanche to streamer transition". In some regions the total electric field will be smaller than before, but in other regions it will get larger, which is called electric field enhancement. New avalanches predominantly grow in the high-field regions, so a self-propagating structure can emerge: a streamer.

Positive and negative streamers

In direct current (DC) circuits, the streamers that form at electrodes with positive and negative voltages are different in appearance and form by different physics mechanisms.

Negative streamers propagate against the direction of the electric field, that is, in the same direction as the electrons drift velocity. Positive streamers propagate in the opposite direction. In both cases, the streamer channel is electrically neutral, and it is shielded by a thin space charge layer. This leads to an enhanced electric field at the end of the channel, the "head" of the streamer. Both positive and negative streamers grow by impact ionization in this high-field region, but the source of electrons is very different.

For negative streamers, free electrons are accelerated from the channel to the head region. However, for positive streamers, these free electrons have to come from farther away, as they accelerate into the streamer channel. Therefore, negative streamers grow in a more diffuse way than positive streamers. Because a diffuse streamer has less field enhancement, negative streamers require higher electric fields than positive streamers. In nature and in applications, positive streamers are therefore much more common.

As noted above, an important difference is also that positive streamers need a source of free electrons for their propagation. In many cases photoionization is believed to be this source.^[8] In nitrogen-oxygen gas mixtures with high oxygen concentrations, excited nitrogen emits UV photons which subsequently ionize oxygen.^[9] In pure nitrogen or in nitrogen with small oxygen admixtures, the dominant production mechanism of photons, however, is the Bremsstrahlung process.^[10]

Streamer velocity and other parameters

The electric streamer, strictly speaking, is an ionization front in the shape of a growing filament. One may identify, at least approximately, a set of parameters that characterizes this particularly shaped front, such as the velocity of its growth, the radius of the head etc, as well as physical laws (equations) that relate these parameters to each other. In one theory of electric streamers in air,^[11] the streamer "chooses" the maximum available velocity (with other parameters being uniquely determined by the said laws), similarly to how a linear instability, e.g., in a plasma, would "choose" the wavelength that gives the fastest growth. This approach gives good agreement with experimental data on positive streamer speeds and on the negative streamer threshold,^[12] as well as with the results from a simulation by directly solving hydrodynamic equations.^[11]

Similarity laws

Most processes in a streamer discharge are two-body processes, where an electron collides with a neutral molecule. An important example is impact ionization, where an electron ionizes a neutral molecule. Therefore, the mean free path is inversely proportional to the gas number density. If the electric field is changed linearly with the gas number density, then electrons gain on average the same energy between collisions. In other words, if the ratio between electric field $E$ and number density $N$ is constant, we expect similar dynamics. Typical lengths scale as $1/N$ , as they are related to the mean free path.

This also motivates the Townsend unit, which is a physical unit of the $E/N$ ratio.

Emission of run-away electrons and high-energy photons

It has been observed that discharges in laboratory experiments emit X-rays ^[13] and that lightning discharges emit X-rays and terrestrial gamma-ray flashes, bursts of photons with energies of up to 40 MeV.^[14] These photons are produced by runaway electrons, electrons which have overcome the friction force, through the Bremsstrahlung process.^[15] However, it has not been fully understood how electrons can gain such high energies in the first place since they constantly collide with air molecules and lose energy. A possible explanation is the acceleration of electrons in the enhanced electric fields of the streamer tips.^[16] However, it is uncertain whether this process can really explain a sufficiently high production rate.^[17] Recently, it has been proposed that ambient air is perturbed in the vicinity of streamer discharges and that this perturbation facilitates the acceleration of electrons into the run-away regime ^[18]^[19]

The relation between pressure waves and the production of X-rays in air discharges

Pressure and shock waves released by electric discharges are capable of perturbing the air in their vicinity up to 80%.^[20]^[21] This, however, has immediate consequences on the motion and properties of secondary streamer discharges in perturbed air: Depending on the direction (relative to the ambient electric field), air perturbations change the discharge velocities, facilitate branching or trigger the spontaneous initiation of a counter discharge.^[22] Recent simulations have shown that such perturbations are even capable to facilitate the production of X-rays (with energies of several tens of keV) from such streamer discharges, which are produced by run-away electrons through the Bremsstrahlung process.^[23]

Related Research Articles

The Geiger–Müller tube or G–M tube is the sensing element of the Geiger counter instrument used for the detection of ionizing radiation. It is named after Hans Geiger, who invented the principle in 1908, and Walther Müller, who collaborated with Geiger in developing the technique further in 1928 to produce a practical tube that could detect a number of different radiation types.

<span class="mw-page-title-main">Cold cathode</span> Type of electrode and part of cold cathode fluorescent lamp.

A cold cathode is a cathode that is not electrically heated by a filament. A cathode may be considered "cold" if it emits more electrons than can be supplied by thermionic emission alone. It is used in gas-discharge lamps, such as neon lamps, discharge tubes, and some types of vacuum tube. The other type of cathode is a hot cathode, which is heated by electric current passing through a filament. A cold cathode does not necessarily operate at a low temperature: it is often heated to its operating temperature by other methods, such as the current passing from the cathode into the gas.

A corona discharge is an electrical discharge caused by the ionization of a fluid such as air surrounding a conductor carrying a high voltage. It represents a local region where the air has undergone electrical breakdown and become conductive, allowing charge to continuously leak off the conductor into the air. A corona discharge occurs at locations where the strength of the electric field around a conductor exceeds the dielectric strength of the air. It is often seen as a bluish glow in the air adjacent to pointed metal conductors carrying high voltages, and emits light by the same mechanism as a gas discharge lamp (Chemiluminescence). Corona discharges can also happen in weather, such as thunderstorms, where objects like ship masts or airplane wings have a charge significantly different from the air around them.

An ion source is a device that creates atomic and molecular ions. Ion sources are used to form ions for mass spectrometers, optical emission spectrometers, particle accelerators, ion implanters and ion engines.

<span class="mw-page-title-main">Flashtube</span> Incoherent light source

A flashtube (flashlamp) produces an electrostatic discharge with an extremely intense, incoherent, full-spectrum white light for a very short time. A flashtube is a glass tube with an electrode at each end and is filled with a gas that, when triggered, ionizes and conducts a high-voltage pulse to make light. Flashtubes are used most in photography; they also are used in science, medicine, industry, and entertainment.

Paschen's law is an equation that gives the breakdown voltage, that is, the voltage necessary to start a discharge or electric arc, between two electrodes in a gas as a function of pressure and gap length. It is named after Friedrich Paschen who discovered it empirically in 1889.

A glow discharge is a plasma formed by the passage of electric current through a gas. It is often created by applying a voltage between two electrodes in a glass tube containing a low-pressure gas. When the voltage exceeds a value called the striking voltage, the gas ionization becomes self-sustaining, and the tube glows with a colored light. The color depends on the gas used.

An electric arc is an electrical breakdown of a gas that produces a prolonged electrical discharge. The current through a normally nonconductive medium such as air produces a plasma, which may produce visible light. An arc discharge is initiated either by thermionic emission or by field emission. After initiation, the arc relies on thermionic emission of electrons from the electrodes supporting the arc. An arc discharge is characterized by a lower voltage than a glow discharge. An archaic term is voltaic arc, as used in the phrase "voltaic arc lamp".

A Crookes tube is an early experimental electrical discharge tube, with partial vacuum, invented by English physicist William Crookes and others around 1869–1875, in which cathode rays, streams of electrons, were discovered.

A nitrogen laser is a gas laser operating in the ultraviolet range using molecular nitrogen as its gain medium, pumped by an electrical discharge.

An electron avalanche is a process in which a number of free electrons in a transmission medium are subjected to strong acceleration by an electric field and subsequently collide with other atoms of the medium, thereby ionizing them. This releases additional electrons which accelerate and collide with further atoms, releasing more electrons—a chain reaction. In a gas, this causes the affected region to become an electrically conductive plasma.

A capacitively coupled plasma (CCP) is one of the most common types of industrial plasma sources. It essentially consists of two metal electrodes separated by a small distance, placed in a reactor. The gas pressure in the reactor can be lower than atmosphere or it can be atmospheric.

Neutral-beam injection (NBI) is one method used to heat plasma inside a fusion device consisting in a beam of high-energy neutral particles that can enter the magnetic confinement field. When these neutral particles are ionized by collision with the plasma particles, they are kept in the plasma by the confining magnetic field and can transfer most of their energy by further collisions with the plasma. By tangential injection in the torus, neutral beams also provide momentum to the plasma and current drive, one essential feature for long pulses of burning plasmas. Neutral-beam injection is a flexible and reliable technique, which has been the main heating system on a large variety of fusion devices. To date, all NBI systems were based on positive precursor ion beams. In the 1990s there has been impressive progress in negative ion sources and accelerators with the construction of multi-megawatt negative-ion-based NBI systems at LHD (H⁰, 180 keV) and JT-60U (D⁰, 500 keV). The NBI designed for ITER is a substantial challenge (D⁰, 1 MeV, 40 A) and a prototype is being constructed to optimize its performance in view of the ITER future operations. Other ways to heat plasma for nuclear fusion include RF heating, electron cyclotron resonance heating (ECRH), ion cyclotron resonance heating (ICRH), and lower hybrid resonance heating (LH).

In electromagnetism, the Townsend discharge or Townsend avalanche is an ionisation process for gases where free electrons are accelerated by an electric field, collide with gas molecules, and consequently free additional electrons. Those electrons are in turn accelerated and free additional electrons. The result is an avalanche multiplication that permits significantly increased electrical conduction through the gas. The discharge requires a source of free electrons and a significant electric field; without both, the phenomenon does not occur.

<span class="mw-page-title-main">Brush discharge</span> Ionization of air characterized as writhing streamers and sparks

A brush discharge is an electrical disruptive discharge similar to a corona discharge that takes place at an electrode with a high voltage applied to it, embedded in a nonconducting fluid, usually air. It is characterized by numerous luminous writhing sparks, plasma streamers composed of ionized air molecules, which repeatedly strike out from the electrode into the air, often with a crackling sound. The streamers spread out in a fan shape, giving it the appearance of a "brush".

Plasma activation is a method of surface modification employing plasma processing, which improves surface adhesion properties of many materials including metals, glass, ceramics, a broad range of polymers and textiles and even natural materials such as wood and seeds. Plasma functionalization also refers to the introduction of functional groups on the surface of exposed materials. It is widely used in industrial processes to prepare surfaces for bonding, gluing, coating and painting. Plasma processing achieves this effect through a combination of reduction of metal oxides, ultra-fine surface cleaning from organic contaminants, modification of the surface topography and deposition of functional chemical groups. Importantly, the plasma activation can be performed at atmospheric pressure using air or typical industrial gases including hydrogen, nitrogen and oxygen. Thus, the surface functionalization is achieved without expensive vacuum equipment or wet chemistry, which positively affects its costs, safety and environmental impact. Fast processing speeds further facilitate numerous industrial applications.

In mass spectrometry, direct analysis in real time (DART) is an ion source that produces electronically or vibronically excited-state species from gases such as helium, argon, or nitrogen that ionize atmospheric molecules or dopant molecules. The ions generated from atmospheric or dopant molecules undergo ion-molecule reactions with the sample molecules to produce analyte ions. Analytes with low ionization energy may be ionized directly. The DART ionization process can produce positive or negative ions depending on the potential applied to the exit electrode.

Plasma-enhanced chemical vapor deposition (PECVD) is a chemical vapor deposition process used to deposit thin films from a gas state (vapor) to a solid state on a substrate. Chemical reactions are involved in the process, which occur after creation of a plasma of the reacting gases. The plasma is generally created by radio frequency (RF) alternating current (AC) frequency or direct current (DC) discharge between two electrodes, the space between which is filled with the reacting gases.

An ion is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by convention. The net charge of an ion is not zero because its total number of electrons is unequal to its total number of protons.

<span class="mw-page-title-main">Plasma (physics)</span> State of matter

Plasma is one of four fundamental states of matter characterized by the presence of a significant portion of charged particles in any combination of ions or electrons. It is the most abundant form of ordinary matter in the universe, mostly in stars, but also dominating the rarefied intracluster medium and intergalactic medium. Plasma can be artificially generated, for example, by heating a neutral gas or subjecting it to a strong electromagnetic field.

References

↑ Townsend, J. S. (1900). "The Conductivity produced in Gases by the Motion of Negatively–charged Ions". Nature. 62 (1606): 340–341. Bibcode:1900Natur..62..340T. doi:10.1038/062340b0. ISSN 0028-0836. S2CID 4007488.
↑ Leonard Benedict Loeb (1939). Fundamental processes of electrical discharge in gases. J. Wiley & Sons, inc. Retrieved 22 August 2012.
↑ Loeb, Leonard B.; Kip, Arthur F. (1939). "Electrical Discharges in Air at Atmospheric Pressure The Nature of the Positive and Negative Point-to-Plane Coronas and the Mechanism of Spark Propagation". Journal of Applied Physics. 10 (3): 142. Bibcode:1939JAP....10..142L. doi:10.1063/1.1707290. ISSN 0021-8979.
↑ Raether, H. (1939). "Die Entwicklung der Elektronenlawine in den Funkenkanal". Zeitschrift für Physik. 112 (7–8): 464–489. Bibcode:1939ZPhy..112..464R. doi:10.1007/BF01340229. ISSN 1434-6001. S2CID 124856050.
↑ Meek, J. (1940). "A Theory of Spark Discharge". Physical Review. 57 (8): 722–728. Bibcode:1940PhRv...57..722M. doi:10.1103/PhysRev.57.722. ISSN 0031-899X.
↑ Lu, X., Naidis, G., Laroussi, M., and Ostrikov, K. (2014) Guided Ionization Waves: Theory and Experiments. Physics Reports, Vol. 540, 123166.
↑ Laroussi, M.(2009) Low Temperature Plasmas for Medicine. IEEE Trans. Plasma Sci., Vol. 37, 714.
↑ Nijdam, S; van de Wetering, F M J H; Blanc, R; van Veldhuizen, E M; Ebert, U (2010). "Probing photo-ionization: experiments on positive streamers in pure gases and mixtures". Journal of Physics D: Applied Physics. 43 (14): 145204. arXiv: 0912.0894 . Bibcode:2010JPhD...43n5204N. doi:10.1088/0022-3727/43/14/145204. ISSN 0022-3727. S2CID 44203888.
↑ Wormeester, G; Pancheshnyi, S; Luque, A; Nijdam, S; Ebert, U (2010). "Probing photo-ionization: simulations of positive streamers in varying N₂:O₂-mixtures". J. Phys. D: Appl. Phys. 43 (50): 505201. arXiv: 1008.3309 . Bibcode:2010JPhD...43X5201W. doi:10.1088/0022-3727/43/50/505201. S2CID 56165202.
↑ Köhn, C; Chanrion, O; Neubert, T (2017). "The influence of bremsstrahlung on electric discharge streamers in N₂, O₂ gas mixtures". Plasma Sources Sci. Technol. 26 (1): 015006. Bibcode:2017PSST...26a5006K. doi: 10.1088/0963-0252/26/1/015006 .
1 2 Lehtinen, Nikolai; Marskar, Robert (2021). "What Determines the Parameters of a Propagating Streamer: A Comparison of Outputs of the Streamer Parameter Model and of Hydrodynamic Simulations". Atmosphere. 12 (12): 1664. doi: 10.3390/atmos12121664 . hdl: 11250/2977612 .
↑ Lehtinen, Nikolai (2021). "Physics and Mathematics of Electric Streamers". Radiophys Quantum El. 64: 11–25. doi:10.1007/s11141-021-10108-5.
↑ Kochkin, P., Köhn, C., Ebert, U., van Deursen, L. Analyzing x-ray emissions from meter-scale negative discharges in ambient air. Plasma Sour. Sci. Technol. (2016), vol. 25, 044002
↑ Köhn, C., Ebert, U. Calculation of beams of positrons, neutrons, and protons associated with terrestrial gamma ray flashes. J. Geophys. Res. Atmos. (2015), vol. 120, pp. 1620-1635
↑ Köhn, C., Ebert, U. Angular distribution of Bremsstrahlung photons and of positrons for calculations of terrestrial gamma-ray flashes and positron beams. Atmos. Res. (2014), vol. 135-136, pp. 432-465
↑ Cooray, V., Arevalo, L., Rahman, M., Dwyer, J., Rassoul, H. On the possible origin of X-rays in long laboratory sparks. J. Atmos. Sol. Terr. Phys. (2009), vol. 71, pp. 1890-1898
↑ Köhn, C., Chanrion, O., Neubert, T. Electron acceleration during streamer collisions in air. Geophys. Res. Lett. (2017), vol. 44, pp. 2604-2613
↑ Köhn, C., Chanrion, O., Babich, L.P., Neubert, T. Streamer properties and associated x-rays in perturbed air. Plasma Sour. Sci. Technol. (2018), vol. 27, 015017
↑ Köhn, C., Chanrion, O., Neubert, T. High-Energy Emissions Induced by Air Density Fluctuations of Discharges. Geophys. Res. Lett. (2018), vol. 45, https://doi.org/10.1029/2018GL077788
↑ Marode, E.; Bastien, F.; Bakker, M. (1979). "A model of the streamer included spark formation based on neutral dynamics". J. Appl. Phys. 50 (1): 140–146. Bibcode:1979JAP....50..140M. doi:10.1063/1.325697.
↑ Kacem, S.; et al. (2013). "Simulation of expansion of thermal shock and pressure waves induced by a streamer dynamics in positive DC corona discharges". IEEE Transactions on Plasma Science. 41 (4): 942–947. Bibcode:2013ITPS...41..942K. doi:10.1109/tps.2013.2249118. S2CID 25145347.
↑ Köhn, C.; Chanrion, O.; Babich, L. P.; Neubert, T. (2018). "Streamer properties and associated x-rays in perturbed air". Plasma Sources Science and Technology. 27 (1): 015017. Bibcode:2018PSST...27a5017K. doi: 10.1088/1361-6595/aaa5d8 .
↑ Köhn, C.; Chanrion, O.; Neubert, T. (2018). "High-Energy Emissions Induced by Air Density Fluctuations of Discharges". Geophys. Res. Lett. 45 (10): 5194–5203. Bibcode:2018GeoRL..45.5194K. doi:10.1029/2018GL077788. PMC 6049893 . PMID 30034044.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[Townsend1900-1] Townsend, J. S. (1900). "The Conductivity produced in Gases by the Motion of Negatively–charged Ions". Nature. 62 (1606): 340–341. Bibcode:1900Natur..62..340T. doi:10.1038/062340b0. ISSN 0028-0836. S2CID 4007488.

[Loeb1939-2] Leonard Benedict Loeb (1939). Fundamental processes of electrical discharge in gases. J. Wiley & Sons, inc. Retrieved 22 August 2012.

[LoebKip1939-3] Loeb, Leonard B.; Kip, Arthur F. (1939). "Electrical Discharges in Air at Atmospheric Pressure The Nature of the Positive and Negative Point-to-Plane Coronas and the Mechanism of Spark Propagation". Journal of Applied Physics. 10 (3): 142. Bibcode:1939JAP....10..142L. doi:10.1063/1.1707290. ISSN 0021-8979.

[Raether1939-4] Raether, H. (1939). "Die Entwicklung der Elektronenlawine in den Funkenkanal". Zeitschrift für Physik. 112 (7–8): 464–489. Bibcode:1939ZPhy..112..464R. doi:10.1007/BF01340229. ISSN 1434-6001. S2CID 124856050.

[Meek1940-5] Meek, J. (1940). "A Theory of Spark Discharge". Physical Review. 57 (8): 722–728. Bibcode:1940PhRv...57..722M. doi:10.1103/PhysRev.57.722. ISSN 0031-899X.

[6] Lu, X., Naidis, G., Laroussi, M., and Ostrikov, K. (2014) Guided Ionization Waves: Theory and Experiments. Physics Reports, Vol. 540, 123166.

[7] Laroussi, M.(2009) Low Temperature Plasmas for Medicine. IEEE Trans. Plasma Sci., Vol. 37, 714.

[Nijdamvan_de_Wetering2010-8] Nijdam, S; van de Wetering, F M J H; Blanc, R; van Veldhuizen, E M; Ebert, U (2010). "Probing photo-ionization: experiments on positive streamers in pure gases and mixtures". Journal of Physics D: Applied Physics. 43 (14): 145204. arXiv: 0912.0894 . Bibcode:2010JPhD...43n5204N. doi:10.1088/0022-3727/43/14/145204. ISSN 0022-3727. S2CID 44203888.

[wormeester_2010-9] Wormeester, G; Pancheshnyi, S; Luque, A; Nijdam, S; Ebert, U (2010). "Probing photo-ionization: simulations of positive streamers in varying N₂:O₂-mixtures". J. Phys. D: Appl. Phys. 43 (50): 505201. arXiv: 1008.3309 . Bibcode:2010JPhD...43X5201W. doi:10.1088/0022-3727/43/50/505201. S2CID 56165202.

[koehn_brems_photo_2017-10] Köhn, C; Chanrion, O; Neubert, T (2017). "The influence of bremsstrahlung on electric discharge streamers in N₂, O₂ gas mixtures". Plasma Sources Sci. Technol. 26 (1): 015006. Bibcode:2017PSST...26a5006K. doi: 10.1088/0963-0252/26/1/015006 .

[Lehtinen+Marskar2021-11] 1 2 Lehtinen, Nikolai; Marskar, Robert (2021). "What Determines the Parameters of a Propagating Streamer: A Comparison of Outputs of the Streamer Parameter Model and of Hydrodynamic Simulations". Atmosphere. 12 (12): 1664. doi: 10.3390/atmos12121664 . hdl: 11250/2977612 .

[Lehtinen2021-12] Lehtinen, Nikolai (2021). "Physics and Mathematics of Electric Streamers". Radiophys Quantum El. 64: 11–25. doi:10.1007/s11141-021-10108-5.

[13] Kochkin, P., Köhn, C., Ebert, U., van Deursen, L. Analyzing x-ray emissions from meter-scale negative discharges in ambient air. Plasma Sour. Sci. Technol. (2016), vol. 25, 044002

[14] Köhn, C., Ebert, U. Calculation of beams of positrons, neutrons, and protons associated with terrestrial gamma ray flashes. J. Geophys. Res. Atmos. (2015), vol. 120, pp. 1620-1635

[15] Köhn, C., Ebert, U. Angular distribution of Bremsstrahlung photons and of positrons for calculations of terrestrial gamma-ray flashes and positron beams. Atmos. Res. (2014), vol. 135-136, pp. 432-465

[16] Cooray, V., Arevalo, L., Rahman, M., Dwyer, J., Rassoul, H. On the possible origin of X-rays in long laboratory sparks. J. Atmos. Sol. Terr. Phys. (2009), vol. 71, pp. 1890-1898

[17] Köhn, C., Chanrion, O., Neubert, T. Electron acceleration during streamer collisions in air. Geophys. Res. Lett. (2017), vol. 44, pp. 2604-2613

[18] Köhn, C., Chanrion, O., Babich, L.P., Neubert, T. Streamer properties and associated x-rays in perturbed air. Plasma Sour. Sci. Technol. (2018), vol. 27, 015017

[19] Köhn, C., Chanrion, O., Neubert, T. High-Energy Emissions Induced by Air Density Fluctuations of Discharges. Geophys. Res. Lett. (2018), vol. 45, https://doi.org/10.1029/2018GL077788

[20] Marode, E.; Bastien, F.; Bakker, M. (1979). "A model of the streamer included spark formation based on neutral dynamics". J. Appl. Phys. 50 (1): 140–146. Bibcode:1979JAP....50..140M. doi:10.1063/1.325697.

[21] Kacem, S.; et al. (2013). "Simulation of expansion of thermal shock and pressure waves induced by a streamer dynamics in positive DC corona discharges". IEEE Transactions on Plasma Science. 41 (4): 942–947. Bibcode:2013ITPS...41..942K. doi:10.1109/tps.2013.2249118. S2CID 25145347.

[22] Köhn, C.; Chanrion, O.; Babich, L. P.; Neubert, T. (2018). "Streamer properties and associated x-rays in perturbed air". Plasma Sources Science and Technology. 27 (1): 015017. Bibcode:2018PSST...27a5017K. doi: 10.1088/1361-6595/aaa5d8 .

[23] Köhn, C.; Chanrion, O.; Neubert, T. (2018). "High-Energy Emissions Induced by Air Density Fluctuations of Discharges". Geophys. Res. Lett. 45 (10): 5194–5203. Bibcode:2018GeoRL..45.5194K. doi:10.1029/2018GL077788. PMC 6049893 . PMID 30034044.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]