Introduction to Nuclear Engineering, Fall 2020
Basic Concepts of Plasmas
Fall, 2020
Kyoung-Jae Chung
Department of Nuclear Engineering
Seoul National University
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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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 (mp) = 1.67x10-27 kg
- charge (qp) = +1.6x10-19 C (+e)
• Electron (e)
- mass (me) = 9.11x10-31 kg - charge (qe) = -1.6x10-19 C (-e)
𝑚𝑝
𝑚𝑒 ≈ 1837 𝑞𝑝
𝑞𝑒 = 1
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
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
ITER project
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Fusion in movies
⚫ Magnetic confinement? Inertial confinement? Or, cold fusion?
What are energy sources?
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Military plasmas
⚫ Railgun
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
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
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
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
2O → H
2+ O
2+ OH
→ H + O
→ H
++ O
++ e
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Composition of plasmas: H
2O example
⚫ Thermal equilibrium is assumed.
K. J. Chung, Contrib. Plasma Phys. 53, 330 (2013)
Saha equation: degree of ionization in thermal equilibrium
⚫ The Saha ionization equation is an expression that relates the ionization state of a gas in thermal equilibrium to the temperature and pressure.
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Generation of charged particles: electron impact ionization
Slow electron Fast electron
+ +
Acceleration
Electric field
+
ProtonElectron
Acceleration Electric field
Acceleration Electric field
Ionization energy of hydrogen: 13.6 eV (~150,000K)
𝒂 = 𝑞𝑬 𝒎
➢ Electrons are easily accelerated by electric field due to their smaller mass than ions.
Classification of plasmas
• 플라즈마는 기체와 달리 여러 온도가 존재
• Te (전자온도) , Ti(이온온도) , Tg(중성입자온도)
• 저온 플라즈마 : Te (~10,000℃) >> Ti ≈ Tg (~100℃) → 비평형 플라즈마 (Non-equilibrium plasma)
• 고온(열) 플라즈마 : Te ≈ Ti ≈ Tg (~10,000℃) → 평형 플라즈마 (Equilibrium plasma)
플라즈마 온도
플라즈마 밀도
• 플라즈마는 여러 밀도가 존재
• ne (전자밀도) , ni(이온밀도) , ng (중성입자밀도)
• 저온 플라즈마 : ng >> ni ≈ ne → 이온화 정도가 작고 대부분 기체상태(중성)로 존재
• 고온(열) 플라즈마 : ng ≈ ni ≈ ne → 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
Classification of plasmas
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History of plasmas
Irving Langmuir (1881-1957)
Nobel prize (1932)
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.
𝑓 𝑣 = 𝑚 2𝜋𝑘𝑇
3/2
4𝜋𝑣2 exp −𝑚𝑣2 2𝑘𝑇
⚫ Temperature: average kinetic energy at thermal equilibrium (K)
1
2 𝑚𝑣
2= 3
2 𝑘𝑇
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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
Boltzmann constant k
⚫ The Boltzmann constant is a bridge between macroscopic and microscopic physics.
𝑃𝑉 = 𝑛𝑅𝑇 𝑃𝑉 = 𝑁𝑘𝑇
𝑅 (gas constant) = 8.31 JK-1mol-1
𝑘 (Boltzmann constant) = 1.38x10-23 JK-1
𝑆 = 𝑘 ln𝑊
Macroscopic state No. of microscopic states
𝑘 = 𝑅 𝑁
𝐴⚫ 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.
• Most probable speed
• Mean speed
• RMS speed
𝑣𝑝 = 2𝑘𝑇 𝑚
𝑣 = 8𝑘𝑇 𝜋𝑚
𝑣𝑟𝑚𝑠 = 3𝑘𝑇 𝑚 𝑓 𝑣 = 𝑚
2𝜋𝑘𝑇
3/2
4𝜋𝑣2 exp −𝑚𝑣2 2𝑘𝑇
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
𝑝 = 𝑛𝑘𝑇
⚫ 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.
𝑛 = 𝑝/𝑘𝑇
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.
Elastic collision
⚫ Conservation of momentum and energy
𝑚1, 𝑣1 𝑚2, 𝑣2 = 0
𝑚1, 𝑣1′
𝑚2, 𝑣2′ 𝜃1
𝜃2
𝜁𝐿 = 1
2 𝑚2𝑣2′2 1
2 𝑚1𝑣12
= 4𝑚1𝑚2
𝑚1 + 𝑚2 2 cos2 𝜃2
⚫ Energy transfer rate
𝜁ഥ𝐿 = 4𝑚1𝑚2
𝑚1 + 𝑚2 2 cos2 𝜃2 = 2𝑚1𝑚2 𝑚1 + 𝑚2 2
Average energy transfer rate by many collisions
Energy transfer rate by a single
collision
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Average energy transfer by collisions
⚫ 𝑚1 = 𝑚2 (electron-electron, ion-ion, neutral-neutral, ion-neutral) 𝜁ഥ𝐿 = 2𝑚1𝑚2
𝑚1 + 𝑚2 2 = 1 2
⚫ 𝑚1 ≪ 𝑚2 (electron-ion, electron-neutral) 𝜁ഥ𝐿 = 2𝑚1𝑚2
𝑚1 + 𝑚2 2 ≈ 2𝑚1
𝑚2 ≈ 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 𝑇𝑒 ≫ 𝑇𝑖 ≈ 𝑇𝑛 : Non-equilibrium
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
𝑚1, 𝑣1 𝑚2, 𝑣2 = 0
𝑚1, 𝑣1′
𝑚2, 𝑣2′, ∆𝑈 𝜃1
𝜃2
✓ Hint: ∆𝑈
𝑑𝑣2′ = 0 𝑎𝑡 ∆𝑈𝑚𝑎𝑥 𝜁𝐿 = ∆𝑈𝑚𝑎𝑥
1
2 𝑚1𝑣12
= 𝑚2
𝑚1 + 𝑚2 cos2 𝜃2
⚫ Energy transfer rate to internal energy ∆𝑈
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Average energy transfer to internal energy by collisions
⚫ 𝑚1 = 𝑚2 (electron-electron, ion-ion, neutral-neutral, ion-neutral) 𝜁ഥ𝐿 = 𝑚2
2 𝑚1 + 𝑚2 = 1 4
⚫ 𝑚1 ≪ 𝑚2 (electron-ion, electron-neutral) 𝜁ഥ𝐿 = 𝑚2
2 𝑚1 + 𝑚2 ≈ 1 2
⚫ 𝑚1 ≫ 𝑚2 (ion-electron, neutral-electron) 𝜁ഥ𝐿 = 𝑚2
2 𝑚1 + 𝑚2 ≈ 𝑚2
2𝑚1 ≈ 10−5~10−4
➢ Ionization (plasma generation)
➢ Excitation (light emission)
➢ Dissociation (radical production)
Various inelastic collisions in plasmas
⚫ Photon-induced reactions
➢ photo-excitation : h + N = N*
➢ photo-ionization : h + 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 = h + 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.
𝜆 < 12,400 𝐼(𝑒𝑉) Å 𝐾. 𝐸. = ℎ𝜈 − 𝐼
ℎ𝜈 + 𝐴 → 𝑒 + 𝐴
+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.
𝑒 + 𝐴 → 2𝑒 + 𝐴
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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.
𝑒 + 𝐴 → 𝑒 + 𝐴
∗⚫ 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.
𝐴
∗→ 𝐴 + ℎ𝜈
Electron-induced reactions
⚫ Electron impact dissociation
Most responsible for the production of chemically active radicals in most of the plasmas.
𝑒 + 𝐴
2→ 𝑒 + 2𝐴
• 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).
𝑒 + 𝐴 → 𝐴
−• e + SF6 → SF6- (Electronegative plasma, electron loss)
• e + SF6 → SF5- + F (Dissociative attachment, negative ion, radical)
⚫ Negative ion generation
Recombination processes
⚫ Radiative recombination
Positive ions capture a free (energetic) electrons and combine with electrons to form new neutral atoms, radiating a photon.
𝑒 + 𝐴
+→ 𝐴 + ℎ𝜈
⚫ Electron-ion recombination
For electron-ion recombination, a third-body must be involved to conserve the energy and momentum. Abundant neutral species or reactor walls are ideal third-bodies. This recombination process typically results in excited neutrals.
𝑒 + 𝐴
++ 𝐴 → 𝐴
∗+ 𝐴
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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.
𝐴
+fast + 𝐴 slow → 𝐴 fast + 𝐴
+(slow)
Ar+ + Ar → Ar + Ar+
Collision parameters
⚫ Let 𝑑𝑛 be the number of incident particles per unit volume at 𝑥 that undergo an
“interaction” with the target particles within a differential distance 𝑑𝑥, removing them from the incident beam. Clearly, 𝑑𝑛 is proportional to 𝑛, 𝑛𝑔, and 𝑑𝑥 for infrequent collisions within 𝑑𝑥.
𝑑𝑛 = −𝜎𝑛𝑛𝑔𝑑𝑥 𝑑𝚪 = −𝜎𝚪𝑛𝑔𝑑𝑥
⚫ The collided flux: Γ(x) = Γ0 1 − 𝑒−𝑥/𝜆
⚫ Mean free path: λ = 1 𝑛𝑔𝜎
⚫ Mean collision time: 𝜏 = 𝜆 𝑣
⚫ Collision frequency: 𝜈 = 𝜏−1 = 𝑛𝑔𝜎𝑣 = 𝑛𝑔𝐾
⚫ Rate constant: 𝐾 = 𝜎𝑣
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Reaction rate
⚫ Reaction rate [reactions per volume and second, reactions/m3s]
𝑅𝑖 = 𝑛𝑒𝑛𝑔 < 𝜎𝑖 𝑣𝑒 𝑣𝑒 >𝑀= 𝑛𝑒𝑛𝑔𝐾
❖ Note that 𝑅𝑖 = 𝑛𝑔𝜎𝑖 𝑣 𝑛𝑒𝑣𝑒 = Σ𝑖 ∙ 𝜙 in nuclear reactor physics
⚫ Cross section vs Maxwellian-averaged rate constant
EEDF (electron energy distribution function)
⚫ It has a nearly Maxwellian energy distribution (not always)
𝑔𝑒 𝜀 = 2 𝜋
1 𝑘𝑇𝑒
3/2
𝜀1/2 exp − 𝜀 𝑘𝑇𝑒
⚫ For non-Maxwellian electron distribution, the reaction rate is obtained by
𝑅𝑖 = 𝑛𝑒𝑛𝑔 න
0
∞
𝑓𝑒 𝑣𝑒 𝜎𝑖 𝑣𝑒 𝑣𝑒4𝜋𝑣𝑒2𝑑𝑣𝑒
4𝜋𝑔𝑒 𝜀 d𝜀 = 4𝜋𝑣2𝑓𝑒(𝑣)d𝑣 𝜀 = 1
2𝑚𝑣2