Part I Object of Plasma Physics BACK. I. Object of Plasma Physics 1. Characterization of the Plasma...
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![Page 1: Part I Object of Plasma Physics BACK. I. Object of Plasma Physics 1. Characterization of the Plasma State 2. Plasmas in Nature 3. Plasmas in the Laboratory.](https://reader036.fdocuments.us/reader036/viewer/2022062408/56649f265503460f94c3d9ff/html5/thumbnails/1.jpg)
Part I
Object of Plasma Physics
BACK
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I. Object of Plasma Physics
1. Characterization of the Plasma State
2. Plasmas in Nature
3. Plasmas in the Laboratory
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1. Characterization of the Plasma State
1.1 Definition of the Plasma State
1.2 Historical Perspective
1.3 Transition to the Plasma State
1.4 Examples
BACK
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1.1 Definition of the Plasma State
1.1.1 Atomic Physics Brush-Up
1.1.2 Thermodynamics Brush-Up
1.1.2 Ionized Gases
1.1.3 From Ionized Gas to Plasma
1.1.4 The “Fourth State” of the Matter
BACK
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BACK 1.1.1 Atomic Physics Brush-Up
How do atoms really look like?
Atoms in a Silicon crystal as seen through a Scanning Tunnel Microscope
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Looking at an Atom
• An “electron” cloud…
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Looking inside an Atom
• Inside the “electron cloud”: Electrons, Protons and Neutrons
m10105.0
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Ionization Process
• Energetic electron causes ionization
m10105.0
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Nucleus
Atomic Structure
The real proportions inside an atom
8 miles
Electron
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• A velocity distribution function represents how many particles have a certain velocity
• Example 1: a stream of particles, with (one-dimensional) velocities u1=0.5 (m/s):
BACK
1.1.2 Thermodynamics Brush-up
u
f(u)
10.5
14
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• Example 2: counter-streaming particles, half with (one-dimensional) velocities u1=0.5 (m/s) and half with u2=-0.5 (m/s):
Thermodynamics Brush-up (II)
u
f(u)
10.5-0.5
7
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• Example 3: a system with a velocity spread and density n (m-3).
• In general the distribution is normalized to the density:
• For a discrete distribution:
Thermodynamics Brush-up (III)
f(u)
( )i i ii i
n f u u n
u10.5 u-0.5
0 ( ) ( ) ( )i i i iu f u f u n u
( ) 1 ( )i i ii
u du n n u du
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• Thermal equilibrium: all the components of the system have the same temperature or average kinetic energy
• At thermal equilibrium the velocity distribution function becomes a Maxwellian:
• The constant A is found by imposing
Thermodynamics Brush-up (IV)
21( ) exp( / )
2 Bf u A mu k T
1
2
2 B
mA n
k T
( )n f u du
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• An ionized gas is characterized, in general, by a mixture of neutrals, (positive) ions and electrons.
• For a gas in thermal equilibrium the Saha equation gives the expected amount of ionization:
• The Saha equation describes an equilibrium situation between ionization and (ion-electron) recombination rates.
BACK
1.1.3 Ionized Gases
3/ 2/212.4 10 i BU k Ti
n i
n Te
n n
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• Solving Saha equation
BACK
Example: Saha Equation
3/ 2/212.4 10 i BU k Ti
n i
n Te
n n
/2 21 3/ 22.4 10 i BU k Ti nn n T e
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Example: Saha Equation (II)
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Backup: The Boltzmann Equation
The ratio of the number density (in atoms per m^3) of atoms in energy state B to those in energy state A is given by
NB / NA = ( gB / gA ) exp[ -(EB-EA)/kT ]
where the g's are the statistical weights of each level (the number of states of that energy). Note for the energy levels of hydrogen
gn = 2 n2
which is just the number of different spin and angular momentum states that have energy En.
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BACK
1.1.4 From Ionized Gas to Plasma
• An ionized gas is not necessarily a plasma • An ionized gas can exhibit a “collective behavior” in
the interaction among charged particles when when long-range forces prevail over short-range forces
• An ionized gas could appear quasineutral if the charge density fluctuations are contained in a limited region of space
• A plasma is an ionized gas that presents a collective behavior and is quasineutral
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From Ionized Gas to Plasma (II)
• (Long range) Coulomb force between two charged particles q1 and q2 at distance r:
r
1 22
04
q qF
r
q2
q1
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From Ionized Gas to Plasma (III)
• (Short range) force between two neutral atoms (e.g. from Lenard-Jones interatomic potential model)
attractiverepulsive
r
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1.1.5 The “Fourth State” of the Matter
• The matter in “ordinary” conditions presents itself in three fundamental states of aggregation: solid, liquid and gas.
• These different states are characterized by different levels of bonding among the molecules.
• In general, by increasing the temperature (=average molecular kinetic energy) a phase transition occurs, from solid, to liquid, to gas.
• A further increase of temperature increases the collisional rate and then the degree of ionization of the gas.
BACK
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The “Fourth State” of the Matter (II)
• The ionized gas could then become a plasma if the proper conditions for density, temperature and characteristic length are met (quasineutrality, collective behavior).
• The plasma state does not exhibit a different state of aggregation but it is characterized by a different behavior when subject to electromagnetic fields.
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The “Fourth State” of the Matter (III)BACK