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Plasma Physics 2
Adam Obrusník, adamobrusnik@physics.muni.cz
Tomáš Hoder, hoder@physics.muni.cz

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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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Discharges – what this Lesson covers?

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Contents of this lesson
̶Transition from glow to arc, mechanisms, fundamental properties of arcs.
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̶Physics of arc plasmas, analytical models for high power LTE arcs.
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̶A short but important note on vacuum arcs
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̶Applications of arc plasmas

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Observation of the transition between Glow Dischage and Arc Discharge

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Glow > Arc transition mechanics
Visuals first: https://www.youtube.com/watch?v=VAwnxIc0-6E
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Pressure increase or power increase

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Glow > Arc transition mechanics
Q: What happens if you start increasing plasma power in glow discharge?
A1: Plasma gets generally more dense
A2: Cathode sheath gets thinner even though voltage keeps growing.
A3: Electric field in the cathode drop increases.
A4: More ions bombard the cathode surface.

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Glow > Arc transition mechanics
Q: When will this stop? What do you think happens to the cathode?
A1: It gets hot (more ions) => thermoemission of electrons
A2: It is subject to locally strong electric field => field emission
We get 2 new effects that further boost the plasma density!

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Glow > Arc transition mechanics
̶First, let’s qualitatively assess this on the quantum mechanics level.
̶Heating up the metal ensures that there are more and more electrons getting over the work function
barrier.
̶Electric field close to the metal surface further reduces the energy barrier for electrons to get
out.
Interesting Q: what is the plasma density in metals?
A: About 1029 m-3, so there is enough electrons J.
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Diagram, engineering drawing Description automatically generated

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Glow > Arc transition mechanics
̶At high E fields, the field emission effect lowers the barrier to such extent, that electron
emission becomes mostly insensitive to metal temperature.
̶
̶Current densities in an arc discharge actually can and do reach MA/m2 (that is mega-Amperes)
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Macroscopic treatment of electrode processes
̶The aforementioned processes at the cathode are very important for sustaining an arc plasma.
̶Thermionic emission is well described by so-called Richardson’s law, which connects emitted
current density with surface temperature and work function as:
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̶Where AG is a material-specific constant (tabulated) and W is the work-function of the material.
̶Interestingly, the AG constant is only mildly sensitive to the material
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Macroscopic treatment of electrode processes
̶The aforementioned processes at the cathode are very important for sustaining an arc plasma.
̶To account for the fact that the electric field at the electrode facilitates easier emission (also
known as Schottky effect/Schottky emission), the Richardson law can be modified as:
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̶
̶
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Where we see that the electric field is effectively reducing the work function of the material, as
expected from the QM perspective.
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Structure and properties of an arc plasma, z-pinch effect

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Structure and parameters of an arc
̶An arc plasma is mostly the positive column
̶Anode and cathode falls are typically highly constricted to the surface (10s of micrometers –
milimeter)
̶At the electrode, an arc imprint can be either constricted to spot(s) or diffuse
̶Voltage drop in the cathode sheath is very small – 10-50 V
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Structure and parameters of an arc
̶There are generally two types of arc plasmas – equilibrium and non-equilibrium
̶The type depends on current but also on the pressure
̶Thermal arcs have been operated up to 1 MW of plasma power.

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Structure and parameters of an arc
̶There are generally two types of arc plasmas – equilibrium and non-equilibrium
̶The type depends on current but also on the pressure
̶Thermal arcs have been operated up to 1 MW of plasma power.

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Pinch effect in arc plasmas
̶The high currents in arc plasmas generate substantial magnetic fields
̶These fields lead to further constriction of the discharge channel – Benett’s z-pinch
Apparent pressure which constricts the arc channel is proportional to the quare root of the current
density
balance of forces:

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Arc plasma as a conductive fluid, Saha equation, Ellenbaas-Heller equation

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Arc as a conductive fluid
̶In the 20th century, various applications for high-power arcs have appeared (t.b.d. later)
̶Coincidentally, it turns out that high power arc plasma is much easier to model than e.g. glow
discharge plasmas due to several simplifying factors:
1.The sheath is thin (micrometers)
2.Voltage drop in sheath is small (10 V) => kinetic effects simpler
3.Gas and electron temperatures are equal (local Thermodynamic equilibrium)
4.Ionization degree is high and electron energy distribution function is Maxwellian
5.
This allows us to compute some plasma properties analytically, which is much more difficult for the
glow discharge and other non-LTE discharges.

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Saha ionization equation
̶Describes ionization degree for an LTE plasma
̶Connects the density of the (i+1)-th ionization state ions with i-th state ions => we can
calculate ionization degree only based on the local temperature.

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Ellenbaas-Heller Equation
for a gas
for a plasma

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Plasma as a conductive fluid
̶If the plasma is in LTE, it is actually easier to simulate and model than a milder non-LTE plasma.
̶You do not have to worry about electron mobilities, ion mobilities.
̶You do not have to worry about kinetic processes because they are already included in the
thermodynamic properties‘ variations
̶You do not have to solve the problematic Poisson equation because ne=ni.

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Plasma as a conductive fluid

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A short but important note on vacuum arcs

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Vacuum arcs
̶It turns out that arc plasma does not need gas background to operate.
̶The plasma is ignited in the metal vapors that are emitted from the cathode
̶Vacuum arcs have been ignited at pressures of 10-4 or even 10-6 Pa

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Vacuum arcs
̶Vacuum arcs are very different from conventional arcs that operate at 1000 Pa – 1 atm.
̶In the cathode spot, the plasma density can reach 1025-1026 m-3 (yes, over 1 atm of plasma) even
if it is surrounded by high vacuum
̶The remarkable gradient in plasma properties causes hypersonic expansion of the plasma plume,
which attains the drift velocity of
10 – 50 km/s (Mach 20 – Mach 120)
̶It has been extensively researched for
satellite electric propulsion, but the main
applications are PVD coatings.
Development of a High-Reliability Vacuum Arc Thruster System | Journal of Propulsion and Power

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Applications of arc plasmas

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Application – Lighting
̶Sodium arc lamps – only scalable source of large-area lighting before the recent scaling of LEDs.
Low ionization potential of sodium and pleasant emission current made them the most energy
efficient source of lighting until ca 2020
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̶Xenon arc lamps for automotive applications – also surpassed by LEDs.
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̶HID lamps (high-intensity discharge) – typically operated in mercury vapors with dopants. But
mercury does not produce UV, it emits through blackbody radiation.
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LED vs Sodium lamps vs Metal Halide - Paragon 6274 Xenon Arc Lamp Metal-halide lamp - Wikipedia

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Application – Welding
̶Plasma welding is probably the most widely used application of arcs.
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̶Apart from regular welding machines that you can find in every dad’s garage, there are highly
specialized devices for industrial use.
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̶These devices typically combine arc cathode with the welded piece as an anode and there is active
gas flow through the cathode.
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̶Enables high-precision welding and joining.
Applied Sciences | Free Full-Text | A Convenient Unified Model to Display the Mobile Keyhole-Mode
Arc Welding Process Plasma Welding - Ionix Oy

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Application – Circuit breakers
̶If a high-power circuit is disconnected, there is a lot of energy that needs to be dissipated.
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̶That energy can be dissipated into forming a plasma discharge.
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̶Obviously, the discharge is parasitic, unwanted => people use gases which are really bad for
generating plasma. Typically SF6
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̶These gases are called “electronegative” gases, because they prefer to form negative ions rather
than positive.
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̶In Prague, there is a big research centre of EATON working on these – job opprotunity.

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Application – Circuit breakers
̶If a high-power circuit is disconnected, there is a lot of energy that needs to be dissipated.
̶
̶That energy can be dissipated into forming a plasma discharge.
̶
̶Obviously, the discharge is parasitic, unwanted => people use gases which are really bad for
generating plasma. Typically SF6

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Application – Plasma Catalysis
̶Plasma catalysis is an emerging “green” application. Where not only arc plasmas ar used.
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̶The idea is converting waste gases to value-added chemicals, e.g. converting CH4 from biomass to
H2 or converting CO2 to syngas, that can be re-used as fuel.
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̶Arc plasmas are used rather often in this type of projects because of their scalability, fast
switching times, robustness, and off-the-shelf availability.
Plasma arc waste recycling - A simple introduction Arc Plasmatron - Plasma Dynamics

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Application – Plasma Spraying
̶Extremely important in all mechanical industries
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̶Solid microparticles melted or evaporated in the plasma and deposited onto substrates to form hard
/ low friction / thermal barrier coatings.
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̶This is used especially for jet engine turbine blades or for mechanically stressed components in
power generation applications.
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̶Alternative/parallel to low pressure PVD – plasma
spraying is much faster but produces much
“dirtier” and rougher materials.
Atmospheric Plasma Spray | Oerlikon Metco Plasma Spray Coating - Plasma Arc Spraying & Plasma
Coating Companies

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Take aways
̶Mechanisms of arc plasma formation
̶Surface phenomena – thermoemission and field emission and what they depend on.
̶Properties of an arc discharge
̶Modeling strategies for high power LTE arcs – Saha, Ellenbaas-Heller, non-linear thermodynamic
properties.
̶Overview of applications
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