Basic Concepts of Plasmas

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Introduction to Nuclear Engineering, Fall 2018

Basic Concepts of Plasmas

Fall, 2018

Kyoung-Jae Chung

Department of Nuclear Engineering

Seoul National University

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Atom: scientific approach

 Dalton’s atomic theory (John Dalton, 1808)

1. Elements are made of extremely small particles called atoms.

2. Atoms of a given element are identical in size, mass, and other properties; atoms of different elements differ in size, mass, and other properties.

3. Atoms cannot be subdivided, created, or destroyed.

4. Atoms of different elements combine in simple whole-number ratios to form chemical compounds.

5. In chemical reactions, atoms are combined, separated, or rearranged.

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3/47 Introduction to Nuclear Engineering, Fall 2018

The structure of atom

 Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and typically a similar number of neutrons. Protons and neutrons are called nucleons.

 More than 99.94% of an atom's mass is in the nucleus.

C

12 6

• Proton (p, H⁺)

- mass (m_p) = 1.67x10^-27 kg

- charge (q_p) = +1.6x10^-19 C (+e)

• Electron (e)

- mass (m_e) = 9.11x10^-31 kg - charge (q_e) = -1.6x10^-19 C (-e)

𝑚𝑚_𝑝𝑝

𝑚𝑚_𝑒𝑒 ≈ 1837 𝑞𝑞_𝑝𝑝

𝑞𝑞_𝑒𝑒 = 1

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What is a plasma?

 A Plasma is quasi-neutral gas of charged and neutral particles which exhibits collective behavior. (Francis F. Chen)

 Plasma is a gas in which a certain portion of the particles are ionized. (Wikipedia)

Heat / Energy

0°C 100°C ?°C

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Space plasmas

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The Sun’s energy

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Man-made fusion

노트북 배터리 1개 + 욕조 절반 물 (≥ 달걀컵 1개 분량 중수) = 200 MW

→ 55년 사용량

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ITER project

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Fusion in movies

 Magnetic confinement? Inertial confinement? Or, cold fusion?

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What are energy sources?

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Military plasmas

 Railgun

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Military plasmas

 Plasma shield

Boeing’s patent: protection system from explosive shockwaves

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Military plasmas

 EMP (electromagnetic pulse): nuclear-EMP or non-nuclear EMP

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Lightning

 Lightning is a sudden electrostatic discharge that occurs typically during a

thunderstorm. This discharge occurs between electrically charged regions of a cloud (called intra-cloud lightning or IC), between two clouds (CC lightning), or between a cloud and the ground (CG lightning).

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Plasmas in everyday life

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Plasmas in industry

반도체 식각

DRAM

인조 다이아몬드

플라즈마 용접

폐기물 소각

플라즈마 발파 플라즈마 코팅 플라즈마 로켓

플라즈마 전구 세라믹 가공 플라즈마 디스플레이

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Plasmas in biomedical application

Plasma surgery Plasma therapy

Plasma dentistry

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What is a plasma?

 Plasma is a collection of charged particles (positive ions, negative ions, electrons) and neutral particles (molecules, atoms, radicals).

Heat / Energy

H

₂

O  H

₂

+ O

₂

+ OH

 H + O

 H

⁺

+ O

⁺

+ e

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Composition of plasmas: H

₂

O example

 Thermal equilibrium is assumed.

K. J. Chung, Contrib. Plasma Phys. 53, 330 (2013)

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Generation of charged particles: electron impact ionization

Slow electron Fast electron

+ +

Acceleration

Electric field

+

^Proton

Electron

Acceleration Electric field

Ionization energy of hydrogen: 13.6 eV (~150,000K)

𝒂𝒂 = 𝑞𝑞𝑬𝑬 𝒎𝒎

 Electrons are easily accelerated by electric field due to their smaller mass than ions.

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Classification of plasmas

• 플라즈마는 기체와 달리 여러 온도가 존재

• T_e(전자온도) , T_i(이온온도) , T_g(중성입자온도)

• 저온 플라즈마 : Te (~10,000℃) >> T_i ≈ T_{g (~100℃)} → 비평형 플라즈마

• 고온(열) 플라즈마 : T_e ≈ T_i ≈ Tg (~10,000℃) → 평형 플라즈마

플라즈마 온도

플라즈마 밀도

• 플라즈마는 여러 밀도가 존재

• n_e(전자밀도) , n_i(이온밀도) , n_g(중성입자밀도)

• 저온 플라즈마 : n_g >> n_i ≈ n_e → 이온화 정도가 작고 대부분 기체상태(중성)로 존재

• 고온(열) 플라즈마 : n_g ≈ n_i ≈ n_e → 이온화 정도가 큼

얼마나 뜨거운가?

• 저온 플라즈마 : 전자의 온도는 높지만 밀도가 낮고 대부분 저온의 중성입자이므로 뜨겁지 않음.

• 고온(열) 플라즈마 : 전자, 이온, 중성입자 모두 온도가 높아 뜨거움.

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Classification of plasmas

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Classification of plasmas

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History of plasmas

Irving Langmuir (1881-1957)

Nobel prize (1932)

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Concept of temperature

 Maxwell-Boltzmann distribution describes particle speeds in gases, where the particles do not constantly interact with each other but move freely between short collisions.

𝑓𝑓 𝑣𝑣 = 2 𝜋𝜋

𝑚𝑚 𝑘𝑘𝑘𝑘

3

𝑣𝑣

²

exp − 𝑚𝑚𝑣𝑣

²

2𝑘𝑘𝑘𝑘 𝑓𝑓 𝜀𝜀 = 2 𝜋𝜋

𝜀𝜀 𝑘𝑘𝑘𝑘

1/2

exp − 𝜀𝜀 𝑘𝑘𝑘𝑘

 Temperature: average kinetic energy at thermal equilibrium (K)

1 2 𝑚𝑚𝑣𝑣

²

= 3

2 𝑘𝑘𝑘𝑘

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Electron-volt unit

 The electron-volt (eV) unit is widely used for presenting the plasma temperature instead of Kelvin.

 Fluorescent lamp: a few eV

 Too hot? How can we touch such a hot plasma?

 What is the difference between energy and temperature?

 Unit conversion between K and eV

1 eV = (1.6x10^-19 C) x (1 V) = (1.6x10^-19 J) / (1.38x10^-23 J/K)

= 11,600K

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Boltzmann constant k

 The Boltzmann constant is a bridge between macroscopic and microscopic physics.

𝑃𝑃𝑃𝑃 = 𝑛𝑛𝑛𝑛𝑘𝑘 𝑃𝑃𝑃𝑃 = 𝑁𝑁𝑘𝑘𝑘𝑘 𝑛𝑛 (gas constant) = 8.31 JK

^-1

mol

^-1

𝑘𝑘 (Boltzmann constant) = 1.38x10

^-23

JK

^-1

𝑆𝑆 = 𝑘𝑘 ln𝑊𝑊

Macroscopic state No. of microscopic states 𝑘𝑘 = 𝑛𝑛

𝑁𝑁

_𝐴𝐴

 Entropy

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Maxwell-Boltzmann distribution function

 The Maxwell-Boltzmann distribution describes the probability of a particle's speed (the magnitude of its velocity vector) being near a given value as a function of the temperature of the system, the mass of the

particle, and that speed value.

𝑓𝑓 𝑣𝑣 = 2 𝜋𝜋

𝑚𝑚 𝑘𝑘𝑘𝑘

3 𝑣𝑣² exp −𝑚𝑚𝑣𝑣² 2𝑘𝑘𝑘𝑘

• Most probable speed

• Mean speed

• RMS speed

𝑣𝑣_𝑝𝑝 = 2𝑘𝑘𝑘𝑘 𝑚𝑚

𝑣𝑣 = 8𝑘𝑘𝑘𝑘 𝜋𝜋𝑚𝑚

𝑣𝑣_{𝑟𝑟𝑟𝑟𝑟𝑟} = 3𝑘𝑘𝑘𝑘 𝑚𝑚

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Pressure

 Pressure = the force per unit area applied in a direction perpendicular to the surface of an object (energy density).

 Units

 mmHg (millimeter of Hg, Torr) 1 atm = 760 mmHg = 760 Torr

 Pa (SI) = N/m²

1 atm = 101,325 Pa = 1,013.25 hPa 1 bar = 10⁵ Pa

 1 Pa = 7.5 mTorr

𝑝𝑝 = 𝑛𝑛𝑘𝑘𝑘𝑘

 Loschmidt number: No. of particles at 0°C and 1 atm: 2.7x10²⁵ m^-3

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Vacuum

 A volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure.

Turbomolecular pump (TMP)

 No. of particles

 Calculate the number of particles at 1 mTorr.

𝑛𝑛 = 𝑝𝑝/𝑘𝑘𝑘𝑘

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Neutral mean free path

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Collision

 Collisions conserve momentum and energy: the total momentum and energy of the colliding particles after collision are equal to that before collision.

 Electrons and fully stripped ions possess only kinetic energy. Atoms and partially stripped ions have internal energy level structures and can be excited, de-

excited, or ionized, corresponding to changes in potential energy.

 It is the total energy, which is the sum of the kinetic and potential energy, that is conserved in a collision.

 Elastic: the sum of kinetic energies of the collision partners are conserved.

 Inelastic: the sum of kinetic energies are not conserved. ionization and excitation.

the sum of kinetic energies after collision is less than that before collision.

 Super-elastic: the sum of kinetic energies are increased after collision. de- excitation.

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Elastic collision

 Conservation of momentum and energy

𝑚𝑚₁, 𝑣𝑣₁ 𝑚𝑚₂, 𝑣𝑣₂ = 0

𝑚𝑚₁, 𝑣𝑣₁^′

𝑚𝑚₂, 𝑣𝑣₂^′ 𝜃𝜃₁

𝜃𝜃₂

𝜁𝜁_𝐿𝐿 =

12 𝑚𝑚²𝑣𝑣₂^′2

12 𝑚𝑚¹𝑣𝑣₁² = 4𝑚𝑚₁𝑚𝑚₂

𝑚𝑚₁ + 𝑚𝑚₂ ² cos² 𝜃𝜃₂

 Energy transfer rate [H/W]

𝜁𝜁�_𝐿𝐿 = 4𝑚𝑚₁𝑚𝑚₂

𝑚𝑚₁ + 𝑚𝑚₂ ² cos² 𝜃𝜃₂ = 2𝑚𝑚₁𝑚𝑚₂ 𝑚𝑚₁ + 𝑚𝑚₂ ²

Average energy transfer rate by many collisions

Energy transfer rate by a single

collision

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Average energy transfer by collisions

 𝑚𝑚₁ = 𝑚𝑚₂ (electron-electron, ion-ion, neutral-neutral, ion-neutral) 𝜁𝜁�_𝐿𝐿 = 2𝑚𝑚₁𝑚𝑚₂

𝑚𝑚₁ + 𝑚𝑚₂ ² = 1 2

 𝑚𝑚₁ ≪ 𝑚𝑚₂ (electron-ion, electron-neutral) 𝜁𝜁�_𝐿𝐿 = 2𝑚𝑚₁𝑚𝑚₂

𝑚𝑚₁ + 𝑚𝑚₂ ² ≈ 2𝑚𝑚₁

𝑚𝑚₂ ≈ 10⁻⁵~10⁻⁴

Table tennis ball (2.5 g)

Bowling ball (10 lb.)

Effective energy transfer (quick thermalization)

Hard to be thermalized

 Therefore, in weakly ionized plasma 𝑘𝑘_𝑒𝑒 ≫ 𝑘𝑘_𝑖𝑖 ≈ 𝑘𝑘_𝑛𝑛 : Non-equilibrium

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Inelastic collision

 The sum of kinetic energies are not conserved. Where is the lost energy?

 transferred to internal energy

 Atomic gases : electronic transition

 Molecules : excitation of rotational and vibrational states

𝑚𝑚₁, 𝑣𝑣₁ 𝑚𝑚₂, 𝑣𝑣₂ = 0

𝑚𝑚₁, 𝑣𝑣₁^′

𝑚𝑚₂, 𝑣𝑣₂^′, ∆𝑈𝑈 𝜃𝜃₁

𝜃𝜃₂

 Hint: ∆𝑈𝑈

𝑑𝑑𝑣𝑣₂^′ = 0 𝑎𝑎𝑎𝑎 ∆𝑈𝑈_{𝑟𝑟𝑚𝑚𝑚𝑚} 𝜁𝜁_𝐿𝐿 = ∆𝑈𝑈_{𝑟𝑟𝑚𝑚𝑚𝑚}

12 𝑚𝑚¹𝑣𝑣₁² = 𝑚𝑚₂

𝑚𝑚₁ + 𝑚𝑚₂ cos² 𝜃𝜃₂

 Energy transfer rate to internal energy ∆𝑈𝑈 [H/W]

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Average energy transfer to internal energy by collisions

 𝑚𝑚₁ = 𝑚𝑚₂ (electron-electron, ion-ion, neutral-neutral, ion-neutral) 𝜁𝜁�_𝐿𝐿 = 𝑚𝑚₂

2 𝑚𝑚₁ + 𝑚𝑚₂ = 1 4

 𝑚𝑚₁ ≪ 𝑚𝑚₂ (electron-ion, electron-neutral) 𝜁𝜁�_𝐿𝐿 = 𝑚𝑚₂

2 𝑚𝑚₁ + 𝑚𝑚₂ ≈ 1 2

 𝑚𝑚₁ ≫ 𝑚𝑚₂ (ion-electron, neutral-electron) 𝜁𝜁�_𝐿𝐿 = 𝑚𝑚₂

2 𝑚𝑚₁ + 𝑚𝑚₂ ≈ 𝑚𝑚₂

2𝑚𝑚₁ ≈ 10⁻⁵~10⁻⁴

 Ionization (plasma generation)

 Excitation (light)

 Dissociation (radical production)

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Various inelastic collisions in plasmas

 Photon-induced reactions

 photo-excitation : hν + N = N^*

 photo-ionization : hν + N = N⁺ + e

 Electron-induced reactions

 electron impact excitation : e + N = N^* + e

 electron impact ionization : e + N = N⁺ + 2e

 electron impact dissociation : e + N₂ = 2N + e

 super-elastic collision : N^** + e = N + e (fast)

 radiative recombination : N⁺ + e = hν + N

 dissociative recombination : e + N₂⁺ = 2N

 Ion-induced reactions

 charge exchange : N⁺(1) + N(2) = N(1) + N⁺(2)

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Photon-induced reactions

 Photo-ionization

The physical process in which an incident photon ejects one or more electrons from an atom, ion or molecule. This is essentially the same process that occurs with the photoelectric effect with metals. To provide the ionization, the photo wavelength should be usually less than 1000 Å, which is ultraviolet radiation.

𝜆𝜆 < 12,400 𝐼𝐼(𝑒𝑒𝑃𝑃) Å 𝐾𝐾. 𝐸𝐸 = ℎ𝜈𝜈 − 𝐼𝐼

ℎ𝜈𝜈 + 𝐴𝐴 → 𝑒𝑒 + 𝐴𝐴

⁺

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Electron-induced reactions

 Electron impact ionization

Electrons with sufficient energy (> 10 eV) can remove an electron from an atom and produce one extra electron and an ion.

𝑒𝑒 + 𝐴𝐴 → 2𝑒𝑒 + 𝐴𝐴

⁺

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Electron-induced reactions

 Electron impact excitation

Electrons with sufficient energy can also excite the electrons of an atom from the lower energy level to a higher energy level.

𝑒𝑒 + 𝐴𝐴 → 𝑒𝑒 + 𝐴𝐴

^∗

 De-excitation

The excited states of atoms are usually unstable and the electron configuration can soon return to its original ground sate, accompanied by the emission of a photon with a specific energy that equals the energy difference between the two quantum levels.

𝐴𝐴

^∗

→ 𝐴𝐴 + ℎ𝜈𝜈

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Electron-induced reactions

 Electron impact dissociation

Most responsible for the production of chemically active radicals in most of the plasmas.

𝑒𝑒 + 𝐴𝐴

₂

→ 𝑒𝑒 + 2𝐴𝐴

• e + O₂  2O + e (Chemically active O radical generation)

• e + CF₄  2e + CF₃⁺ + F (Dissociative ionization)

 Radical generation reactions

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Electron-induced reactions

 Electron attachment

Electron can attach to an electronegative atom to form a negative ion, for example, a halogen atom or an oxygen atom (electron-capture ionization).

𝑒𝑒 + 𝐴𝐴 → 𝐴𝐴

⁻

• e + SF₆  SF₆^- (Electronegative plasma, electron loss)

• e + SF₆  SF₅^- + F (Dissociative attachment, negative ion, radical)

 Negative ion generation

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Recombination processes

 Radiative recombination

Positive ions capture a free (energetic) electrons and combine with electrons to form new neutral atoms, radiating a photon.

𝑒𝑒 + 𝐴𝐴

⁺

→ 𝐴𝐴 + ℎ𝜈𝜈

 Electron-ion recombination

For electron-ion recombination, a third-body must be involved to conserve the energy and momentum conservation. Abundant neutral species or reactor walls are ideal third-bodies. This recombination process typically results in excited neutrals.

𝑒𝑒 + 𝐴𝐴

⁺

+ 𝐴𝐴 → 𝐴𝐴

^∗

+ 𝐴𝐴

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Ion-induced reactions

 (resonant) Charge exchange (or charge transfer)

The cross section for resonant charge transfer is large at low collision energies, making this an important process in weakly ionized plasmas.

𝐴𝐴 𝑓𝑓𝑎𝑎𝑓𝑓𝑎𝑎 + 𝐴𝐴 𝑓𝑓𝑠𝑠𝑠𝑠𝑠𝑠 → 𝐴𝐴 𝑓𝑓𝑎𝑎𝑓𝑓𝑎𝑎 + 𝐴𝐴

⁺

(𝑓𝑓𝑠𝑠𝑠𝑠𝑠𝑠)

Ar⁺ + Ar  Ar + Ar⁺

 [H/W] Survey the applications of charge exchange.

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Collision parameters

 Let 𝑑𝑑𝑛𝑛 be the number of incident particles per unit volume at 𝑥𝑥 that undergo an

“interaction” with the target particles within a differential distance 𝑑𝑑𝑥𝑥, removing them from the incident beam. Clearly, 𝑑𝑑𝑛𝑛 is proportional to 𝑛𝑛, 𝑛𝑛_𝑔𝑔, and 𝑑𝑑𝑥𝑥 for infrequent collisions within 𝑑𝑑𝑥𝑥.

𝑑𝑑𝑛𝑛 = −𝜎𝜎𝑛𝑛𝑛𝑛_𝑔𝑔𝑑𝑑𝑥𝑥 𝑑𝑑𝚪𝚪 = −𝜎𝜎𝚪𝚪𝑛𝑛_𝑔𝑔𝑑𝑑𝑥𝑥

 The collided flux: Γ(x) = Γ₀ 1 − 𝑒𝑒^{−𝑚𝑚/𝜆𝜆}

 Mean free path: λ = 1 𝑛𝑛_𝑔𝑔𝜎𝜎

 Mean collision time: 𝜏𝜏 = 𝜆𝜆 𝑣𝑣

 Collision frequency: 𝜈𝜈 = 𝑛𝑛_𝑔𝑔𝜎𝜎𝑣𝑣 = 𝑛𝑛_𝑔𝑔𝐾𝐾

 Rate constant: 𝐾𝐾 = 𝜎𝜎𝑣𝑣

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Reaction rate

 Reaction rate [reactions per volume and second, reactions/m³s]

𝑛𝑛_𝑖𝑖 = 𝑛𝑛_𝑒𝑒𝑛𝑛_𝑔𝑔 < 𝜎𝜎_𝑖𝑖 𝑣𝑣_𝑒𝑒 𝑣𝑣_𝑒𝑒 >_𝑀𝑀= 𝑛𝑛_𝑒𝑒𝑛𝑛_𝑔𝑔𝐾𝐾

 Note that 𝑛𝑛_𝑖𝑖 = 𝑛𝑛_𝑔𝑔𝜎𝜎_𝑖𝑖 𝑣𝑣 𝑛𝑛_𝑒𝑒𝑣𝑣_𝑒𝑒 = Σ_𝑖𝑖 � 𝜙𝜙 in nuclear reactor physics

 Cross section vs Maxwellian-averaged rate constant

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EEDF (electron energy distribution function)

 It has a nearly Maxwellian energy distribution (not always)

𝑓𝑓

_𝑒𝑒

𝜀𝜀 = 2 𝜋𝜋

𝜀𝜀 𝑘𝑘𝑘𝑘

_𝑒𝑒

1/2

exp − 𝜀𝜀 𝑘𝑘𝑘𝑘

_𝑒𝑒

 For non-Maxwellian electron distribution, the reaction rate is obtained by

𝑛𝑛_𝑖𝑖 = 𝑛𝑛_𝑒𝑒𝑛𝑛_𝑔𝑔 �

0

∞𝑓𝑓_𝑒𝑒 𝑣𝑣_𝑒𝑒 𝜎𝜎_𝑖𝑖 𝑣𝑣 𝑣𝑣_𝑒𝑒𝑑𝑑𝑣𝑣_𝑒𝑒