Plasma Physics 2
5. 5. Streamer breakdown mechanism
Korona discharge
Spark discharge
TU Eindhoven

Vylepsit …

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Lecture series contents
1.Townsend breakdown theory, Paschen‘s law
2.Glow discharge
3.Electric arc at low and high pressures
4.Magnetized low-pressure plasmas and their role in material deposition methods.
5.Brief introduction to high-frequency discharges
6.Streamer breakdown theory, corona discharge, spark discharge
7.Barrier discharges
8.Leader discharge mechanism, ionization and discharges in planetary atmospherres
9.Discharges in liquids, complex and quantum plasmas
10.Thermonuclear fusion, Lawson criterion, magnetic confinement systems, plasma heating and
intertial confinement fusion.

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2
Where are we on the IV chart
•At some conditions, the transition from Townsend to glow si not as „smooth“ and gradual as we
explained.
•At high fields, low currents and typically higher pressures, a filamentary structure typically
called a „Streamer“ starts to form
https://en.wikipedia.org/wiki/Streamer_discharge Explore video of streamer formation

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3
Streamer physics is a living topic
•Even though the interest peaked around the mid 2010s, it is still of interest
•There are no „definitive answers“, so whatever we are teaching here is an attempt to capture the
best current theory for streamer formation that will likely be improved in future.

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3
Streamer physics is a living topic
•Even though the interest peaked around the mid 2010s, it is still of interest
•There are no „definitive answers“, so whatever we are teaching here is an attempt to capture the
best current theory for streamer formation that will likely be improved in future.

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3
Streamer physics is a living topic
•Even though the interest peaked around the mid 2010s, it is still of interest
•There are no „definitive answers“, so whatever we are teaching here is an attempt to capture the
best current theory for streamer formation that will likely be improved in future.
•Streamers are important in geophysics, biophysics,  and in planetary plasma research, as well as
on-ground uses

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4
Examples of streamers
•There are no „definitive answers“, so whatever we are teaching here is an attempt to capture the
best current theory for streamer formation that will likely be improved in future.
Upper atmospheric lightning
Nanosecond discharge in liquid water
(M.Šimek, CAS, Praha)

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5
Terminology associated with streamers
Engineering / historical understanding of streamer = filamentary discharge
Physics description of a ”streamer head”

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Streamer formation and its similarities with Townsend > Arc transition
•In the previous description of glow discharge ignition, we have always assumed that the electron
avalanche creates charge carriers and these move around between the electrodes, forming a diffuse
discharge
•But it can occur that electron avalanche itself forms sufficient space charge and turns into a
plasma?

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Electron avalanche and its transition to quasineutral plasma
•Take the expression for the drift-diffusion flux of charge carriers
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•Approximate the diffusion coefficient as
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•And substitute to
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•a analogií Einsteinova vztahu pro elektrony:
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•šířící se elektronová lavina:

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Rostoucí a expandující elektronová lavina
•započítáme-li ionizaci a elektronový záchyt pak pro celkové počty elektronů a pozitivních i
kladných iontů platí:
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•elektrony se šíří k anodě driftovou rychlostí:
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•a difůze hraje také svou roli při expanzi laviny kolem její axiální osy:
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•pro lokální elektronovou hustotu pak platí (z rovnice kontinuity):
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•platí při tom, jak už bylo naznačeno:
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•kde je střední energie elektronů
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•pozitivní ionty (díky své asi sto krát nižší pohyblivosti) zůstávají vůči elektronům stabilní a
platí:
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•pokud zanedbáme záchyt elektronů a pro oblasti nedaleké od axiální osy pak:
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•čili hustota iontů roste exponenciálně směrem k anodě a klesá radiálně od axiální osy dle Gaussova
rozdělení

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Electron avalanche and its transition to quasineutral plasma
•If the avalanche has enough space and the external field E0 is large enough, the space charge
field E‘ becomes non-negligible
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•Electrons accumulate in the “head” of the streamer and the electric field drives further
ionization and causes expansion.
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•The expansion rate of the approx. spherical ”streamer head” is driven by the electric field of the
electrons themselves.
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•The field E‘ is proportional to R but the electron density is independent of E‘:
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•If the space-charge field becomes non-negligible compared to the external field, typically E‘ >
0.03 E0, the effects of space charge become dominant and the avalanche transforms into a “negative
streamer” – a filamentary type of plasma (quasineutral, collective)

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9
Electron avalanche and its transition to quasineutral plasma
We can have a look at the (minimum) streamer physics through equations
https://arxiv.org/pdf/physics/0508109.pdf
•Electrons are created in ionization collisions and lost through attachment
•Positive are created through collisions and depend only on local electron density => streamers are
so fast, that positive ions do not have time to be transported.
•Same for negative ions, which are formed by attachment

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10
Raether-Meek criterion
•The Raether-Meek criterion states the condition for streamer breakdown.
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•If the space charge field is E‘ > 0.03 E0, the streamer forms.
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•Through numerical modeling, this can be translated to „Townsend terminology“ arriving at
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•This can be understood as a criterion describing at what conditions will an avalanche transition
to a streamer, as opposed to a situation when an avalanche serves as a “seed” of charge carriers
for igniting glow discharge plasma
Glow discharge - Wikipedia Example images of positive streamer discharge trees in technical air
at... | Download Scientific Diagram

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Positive vs negative streamers
•Experience shows that there are two types of streamers – those propagating from a cathode and
those propagating from an anode.
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•In positive streamers, the dominant ionization mechanism is photoionization.
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•In negative streamers, the dominant ionization mechanism is direct electron-impact ionization.
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•In both cases, the ionization occurs mostly in the streamer head, because the electric field is
strong there.
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Cathode streamer = positive streamer
Anode streamer = negative streamer

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Statistical nature of breakdown in gases
•Same as with Townsend breakdown, the streamer breakdown is also a statistical/random phenomenon!
•After Wijsman (1943) and his work on statistical breakdown through Townsend mechanism, other
theories have emerged which could also capture the transition from a Townsend mechanism to a
streamer mechanism , e.g.Hodges (1985):
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Including attachment in Wijsman theory
Purely streamer breakdown with avalanches transitioning
into streamers
Unified ignition probability, considering both Townsend
breakdown and Streamer breakdown
Breakdown probability for Townsend breakdown:
[Wijsman]
Breakdown probability for streamer breakdown:

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•With increasing pressure, the ignition probaibility curve is shifting towards higher E and its
shape is changing too
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•Qualitatively, this is similar to Townsend breakdown but the physics behind is a bit more complex
J
Statistical nature of breakdown in gases
4 kPa
9.3 kPa
26.7 kPa

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•Not-so-historically (1980s-2000s), streamers were researched y prof Mirko Cernak.
•An important technique for quantifying streamers is TCSPC = time-correlated single-photon counting
pioneered a.o. by Tomas Hoder
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•By time-correlating the origin of individual photons, light was emitted with the exponential
spatial resolution up to 1 microsecond before the streamer, which suggested the Townsend mechanism
The Brno trace in streamer research J
Chart Description automatically generated

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•Explaining the fundamentals through simulations – Zdeněk Bonaventura and team.
Bonaventura, Bourdon:
Ebert, Teunissen:
The Brno trace in streamer research J

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Q: What do you think could happen when we have such a propagating plasma structure?
But what happens next with the streamers?
A1: Streamer reaches a counter-electrode
•Conductive channel is formed
•Electric field drops significantly
•We see an arc plasma forming if the power supply can support it.
•We see a spark plasma forming if the power supply cannot support an arc
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A2: Streamer does not reach a counter-electrode
•The counter electrode is large and far
•Ionization stops to increase and ultimately starts to decrease in space because the plasma is
expanding to a large volume.
•Streamers can exist as semi-stable structures in time, called corona discharge
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Corona and Arc Discharge Corona discharge - Wikipedia

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CORONA DISCHARGE
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Corona discharge
•If the field is highly non-uniform, e.g. close to sharp tips surrounded by ground, a corona
discharge can appear
•There is no counter-electrode to reach but streamers still form and consume some energy
•Sometimes referred to as partial discharge
positive corona at 125 kV
in atmosphere
Corona Discharge | COMSOL Blog

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17
Corona discharge
•Corona can form in the proximity of both a positive and negative tip
Positive corona – tip is extended by a positive streamer
Negative corona – negative streamers propagate towards the tip
Photoionization important
Appears as diffuse glow around a wire.
Stable in all gases.
Secondary emission and volume ionization important
Has a glow discharge structure.
Appears as a series of luminous spots.
Stable only in electronegative gases.

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17
Corona discharge
•Corona can form in the proximity of both a positive and negative tip
Positive corona – tip is extended by a positive streamer
Negative corona – negative streamers propagate towards the tip

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Negative corona structure
•The negative corona has a structure similar to a glow discharge with highly asymmetrical
electrodes
negativní
ionty
pozitivní
ionty
struktura doutnavého výboje
v případě Trichelova pulzu v
negativní koróně

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17
Trichel pulses in negative corona
•Trichel pulses are kHz – MHz oscillations inherent to negative corona discharges.
•The fundamental physics is driven by the nature of the plasma:
1.A negative streamer starts to form
2.Ionization grows exponentially
3.Formed charge carriers start to shield the external E field.
4.At some point, the external field is shielded perfectly by the discharges => no more corona
5.Plasma takes some characteristic time to “dissipate” – that time scale is typically microseconds,
determined by the plasma ambipolar diffusion time scale.
6.As the plasma dissipates, external field starts to dominate again
7.A negative streamer starts to form …

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Trichel pulses in negative corona
Time recording of a Trichel pulse (Sigmond 1973):
We see electron multiplication, space charge formation and ultimately a glow discharge structure –
but what is the dynamics behind it?

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23c
Trichel pulses in negative corona – current measurement
Photoemission coefficient
p-CuI > p-brass
Has no effect on the maximum but it affects the rise time!
First current peak sensitive to material, second current
peak is not!

-streamer initiation and generation of energetic photons.
First peak is probably the impact of the streamer
onto the cathode – probably the first Trichel pulse
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-for repeated Trichel pulses, it is likely that transient glow
discharge starts to form, as qualitatively outlined
a few slides back.

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23d
Trichel pulses in negative corona – emission measurement
Nitrogen emission in time and space before the Trichel pulse:
Nitrogen emission, current and E field in time and space during the Trichel pulse:

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SPARK DISCHARGE
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Spark discharge
•If a sufficient amount of current is available and the streamer reaches a counter-electrode, what
we call a spark discharge starts to form.
•This can be understood as an. early stage of an arc discharge but arc itself will operate only if
the power supply can provide ample current.

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Spark discharge (Janda, Machala 2010)
•If the voltage is pulsed at the right frequency and duty cycle, the spark can be transient.
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•Interesting special case of this plasma source, used at UK Bratislava.

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Spark discharge formation (Janda, Machala 2016)
•The IV measurements of a pulsed spark discharge shed more lithght onto how it is formed.
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•We see around 1.2 us, that if the discharge would not be stopped, the current would run away
exponentially and an arc discharge would be formed.
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•We also see the voltage decreasing, as the plasma is becoming ore conductive.

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Spark discharge formation (Janda, Machala 2016)
•Measurements of electron density in spark plasma suggest that the plasma densities reach full
ionization
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•If the supply of power is not interrupted by the power supply at microsecond scales, the plasma
will thermalize and an arc discharge will form.

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APPLICATION OVERVIEW
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Corona discharge applications
•Corona discharge is often unwanted, appearing on high voltage components where it induces loss
power.
•One major application are electrostatic precipitators. In these devices, corona discharge softly
charges microparticles of combustion products so that they can be captured and not contaminate the
environment.
Deutch-Anderson efficiency:
Drift of a charged microparticle
Loss power on HV lines
flow rate

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Spark discharge applications
•Historically spark plugs… we all know where that is going J
•Understanding of sparks, Trichel pulses, etc.. is still super important in circuit breakers
because it affects how fast you are able to switch current on/off in the grid.
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Amazon.com: BOSCH 9614 OE Fine Wire Double Iridium Spark Plug - Pack of 4 : Automotive Circuit
Breakers: What They Are and Their Types | by Anshuman Rathor | Medium

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Streamer „applications“
•Understanding streamers is absolutely crucial in geophysics, biophysics and planetary plasmas.
•Thanks to the, we can understand upper atmospheric lighting
•They also help to elucidate how life started to form – plasma was one of the “activation channels”
converting inorganic molecules to organic ones.
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Upper-atmospheric lightning - Wikipedia Photo Shows Red Jellyfish Sprite Lightning During a Texas
Storm

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Takeaways
•What is a streamer, positive and negative
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•What are the main physics phenomena
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•What happens when a streamer reaches a counter-electrode
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•The few applications of streamers and their importance for fundamental science.