basic concepts of plasmas · 2020. 1. 9. · electrons and fully stripped ions possess only kinetic...

Introduction to Nuclear Engineering, Fall 2019

Basic Concepts of Plasmas

Fall, 2019

Kyoung-Jae Chung

Department of Nuclear Engineering

Seoul National University

2/47 Introduction to Nuclear Engineering, Fall 2019

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.


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.

C612

• 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)

𝑚𝑚𝑝𝑝𝑚𝑚𝑒𝑒

≈ 1837𝑞𝑞𝑝𝑝𝑞𝑞𝑒𝑒

= 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


Space plasmas


The Sun’s energy


Man-made fusion

노트북 배터리 1개 + 욕조 절반 물(≥ 달걀컵 1개 분량 중수) = 200 MW→ 55년 사용량


ITER project


Fusion in movies

Magnetic confinement? Inertial confinement? Or, cold fusion?


What are energy sources?


Military plasmas

Railgun


Military plasmas

Plasma shield

Boeing’s patent: protection system from explosive shockwaves


Military plasmas

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

http://www.google.co.kr/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwj01rjJ-8zZAhVBpJQKHceDAQcQjRx6BAgAEAY&url=http://m.chosun.com/svc/article.html?sname%3Dnews%26contid%3D2010102200297&psig=AOvVaw0OBNavM_WTsWUq2ODL_2P6&ust=1520056940480108http://www.google.co.kr/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwj01rjJ-8zZAhVBpJQKHceDAQcQjRx6BAgAEAY&url=http://m.chosun.com/svc/article.html?sname%3Dnews%26contid%3D2010102200297&psig=AOvVaw0OBNavM_WTsWUq2ODL_2P6&ust=1520056940480108


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).


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


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

H2O H2 + O2 + OH H + O H+ + O+ + e


Composition of plasmas: H2O example

Thermal equilibrium is assumed.K. J. Chung, Contrib. Plasma Phys. 53, 330 (2013)


Generation of charged particles: electron impact ionization

Slow electron Fast electron

+ +

Acceleration

Electric field

+ Proton

Electron

Acceleration

Electric field

Acceleration

Electric field

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

𝒂𝒂 =𝑞𝑞𝑬𝑬𝒎𝒎

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

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

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.


History of plasmas

Irving Langmuir(1881-1957)Nobel prize (1932)

http://en.wikipedia.org/wiki/File:Langmuir-sitting.jpghttp://en.wikipedia.org/wiki/File:Langmuir-sitting.jpg


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 =2𝜋𝜋

𝑚𝑚𝑘𝑘𝑘𝑘

3𝑣𝑣2 exp −

𝑚𝑚𝑣𝑣2

2𝑘𝑘𝑘𝑘𝑓𝑓 𝜀𝜀 =

2𝜋𝜋

𝜀𝜀𝑘𝑘𝑘𝑘

1/2exp −

𝜀𝜀𝑘𝑘𝑘𝑘

Temperature: average kinetic energy at thermal equilibrium (K)

12𝑚𝑚𝑣𝑣2 =

32𝑘𝑘𝑘𝑘


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.

𝑃𝑃𝑃𝑃 = 𝑛𝑛𝑛𝑛𝑘𝑘 𝑃𝑃𝑃𝑃 = 𝑁𝑁𝑘𝑘𝑘𝑘

𝑛𝑛 (gas constant) = 8.31 JK-1mol-1

𝑘𝑘 (Boltzmann constant) = 1.38x10-23 JK-1

𝑆𝑆 = 𝑘𝑘 ln𝑊𝑊

Macroscopic state No. of microscopic states

𝑘𝑘 =𝑛𝑛𝑁𝑁𝐴𝐴

Entropy


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 =2𝜋𝜋

𝑚𝑚𝑘𝑘𝑘𝑘

3𝑣𝑣2 exp −

𝑚𝑚𝑣𝑣2

2𝑘𝑘𝑘𝑘

• Most probable speed

• Mean speed

• RMS speed

𝑣𝑣𝑝𝑝 =2𝑘𝑘𝑘𝑘𝑚𝑚

𝑣𝑣 =8𝑘𝑘𝑘𝑘𝜋𝜋𝑚𝑚

𝑣𝑣𝑟𝑟𝑟𝑟𝑟𝑟 =3𝑘𝑘𝑘𝑘𝑚𝑚


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


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


Neutral mean free path


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

𝑚𝑚1, 𝑣𝑣1 𝑚𝑚2, 𝑣𝑣2 = 0

𝑚𝑚1, 𝑣𝑣1′


𝜃𝜃1𝜃𝜃2

𝜁𝜁𝐿𝐿 =12𝑚𝑚2𝑣𝑣2

′2

12𝑚𝑚1𝑣𝑣1

2=

4𝑚𝑚1𝑚𝑚2𝑚𝑚1 + 𝑚𝑚2 2

cos2 𝜃𝜃2

Energy transfer rate [H/W]

�𝜁𝜁𝐿𝐿 =4𝑚𝑚1𝑚𝑚2𝑚𝑚1 + 𝑚𝑚2 2

cos2 𝜃𝜃2 =2𝑚𝑚1𝑚𝑚2𝑚𝑚1 + 𝑚𝑚2 2

Average energy transfer rate by many collisions

Energy transfer rate by a single collision


Average energy transfer by collisions

𝑚𝑚1 = 𝑚𝑚2 (electron-electron, ion-ion, neutral-neutral, ion-neutral)


=12

𝑚𝑚1 ≪ 𝑚𝑚2 (electron-ion, electron-neutral)


≈2𝑚𝑚1𝑚𝑚2

≈ 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

𝑘𝑘𝑒𝑒 ≫ 𝑘𝑘𝑖𝑖 ≈ 𝑘𝑘𝑛𝑛 : 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

𝑚𝑚1, 𝑣𝑣1 𝑚𝑚2, 𝑣𝑣2 = 0


𝑚𝑚2, 𝑣𝑣2′ ,∆𝑈𝑈

𝜃𝜃1𝜃𝜃2

Hint:∆𝑈𝑈𝑑𝑑𝑣𝑣2′

= 0 𝑎𝑎𝑎𝑎 ∆𝑈𝑈𝑟𝑟𝑚𝑚𝑚𝑚𝜁𝜁𝐿𝐿 =∆𝑈𝑈𝑟𝑟𝑚𝑚𝑚𝑚12𝑚𝑚1𝑣𝑣1

2=

𝑚𝑚2𝑚𝑚1 + 𝑚𝑚2

cos2 𝜃𝜃2

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


Average energy transfer to internal energy by collisions

𝑚𝑚1 = 𝑚𝑚2 (electron-electron, ion-ion, neutral-neutral, ion-neutral)

�𝜁𝜁𝐿𝐿 =𝑚𝑚2

2 𝑚𝑚1 + 𝑚𝑚2=

14

𝑚𝑚1 ≪ 𝑚𝑚2 (electron-ion, electron-neutral)


2 𝑚𝑚1 + 𝑚𝑚2≈

12

𝑚𝑚1 ≫ 𝑚𝑚2 (ion-electron, neutral-electron)


2 𝑚𝑚1 + 𝑚𝑚2≈

𝑚𝑚22𝑚𝑚1

≈ 10−5~10−4

Ionization (plasma generation) Excitation (light) Dissociation (radical production)


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)


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 <12,400𝐼𝐼(𝑒𝑒𝑃𝑃) Å

𝐾𝐾.𝐸𝐸 = ℎ𝜈𝜈 − 𝐼𝐼

ℎ𝜈𝜈 + 𝐴𝐴 → 𝑒𝑒 + 𝐴𝐴+



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+

http://upload.wikimedia.org/wikipedia/commons/2/27/Ionization_energies.pnghttp://upload.wikimedia.org/wikipedia/commons/2/27/Ionization_energies.png



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



Electron impact dissociation

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

𝑒𝑒 + 𝐴𝐴2 → 𝑒𝑒 + 2𝐴𝐴

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

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

Radical generation 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


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


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.


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, 𝑛𝑛𝑔𝑔, and 𝑑𝑑𝑥𝑥 for infrequent collisions within 𝑑𝑑𝑥𝑥.

𝑑𝑑𝑛𝑛 = −𝜎𝜎𝑛𝑛𝑛𝑛𝑔𝑔𝑑𝑑𝑥𝑥 𝑑𝑑𝚪𝚪 = −𝜎𝜎𝚪𝚪𝑛𝑛𝑔𝑔𝑑𝑑𝑥𝑥

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

Mean free path: λ =1𝑛𝑛𝑔𝑔𝜎𝜎

Mean collision time: 𝜏𝜏 =𝜆𝜆𝑣𝑣

Collision frequency: 𝜈𝜈 = 𝜏𝜏−1 = 𝑛𝑛𝑔𝑔𝜎𝜎𝑣𝑣 = 𝑛𝑛𝑔𝑔𝐾𝐾

Rate constant: 𝐾𝐾 = 𝜎𝜎𝑣𝑣


Reaction rate

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

𝑛𝑛𝑖𝑖 = 𝑛𝑛𝑒𝑒𝑛𝑛𝑔𝑔 < 𝜎𝜎𝑖𝑖 𝑣𝑣𝑒𝑒 𝑣𝑣𝑒𝑒 >𝑀𝑀= 𝑛𝑛𝑒𝑒𝑛𝑛𝑔𝑔𝐾𝐾

Note that 𝑛𝑛𝑖𝑖 = 𝑛𝑛𝑔𝑔𝜎𝜎𝑖𝑖 𝑣𝑣 𝑛𝑛𝑒𝑒𝑣𝑣𝑒𝑒 = Σ𝑖𝑖 � 𝜙𝜙 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)

𝑓𝑓𝑒𝑒 𝜀𝜀 =2𝜋𝜋

𝜀𝜀𝑘𝑘𝑘𝑘𝑒𝑒

1/2

exp −𝜀𝜀𝑘𝑘𝑘𝑘𝑒𝑒

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

𝑛𝑛𝑖𝑖 = 𝑛𝑛𝑒𝑒𝑛𝑛𝑔𝑔 �0

∞𝑓𝑓𝑒𝑒 𝑣𝑣𝑒𝑒 𝜎𝜎𝑖𝑖 𝑣𝑣𝑒𝑒 𝑣𝑣𝑒𝑒𝑑𝑑𝑣𝑣𝑒𝑒

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basic concepts of plasmas · 2020. 1. 9. · electrons and fully stripped ions possess only kinetic...

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