Part I

Object of Plasma Physics

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I. Object of Plasma Physics

1. Characterization of the Plasma State2. Plasmas in Nature3. Plasmas in the Laboratory

1. Characterization of the Plasma State

1.1 Definition of the Plasma State1.2 Historical Perspective1.3 Transition to the Plasma State1.4 Examples

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1.1 Definition of the Plasma State

1.1.1 Atomic Physics Brush-Up1.1.2 Thermodynamics Brush-Up1.1.2 Ionized Gases1.1.3 From Ionized Gas to Plasma1.1.4 The “Fourth State” of the Matter

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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

Looking at an Atom

• An “electron” cloud…

Looking inside an Atom

• Inside the “electron cloud”: Electrons, Protons and Neutrons

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Ionization Process

• Energetic electron causes ionization

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Nucleus

Atomic Structure

The real proportions inside an atom

8 miles

Electron

• 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):

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1.1.2 Thermodynamics Brush-up

u

f(u)

10.5

14

• 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

• 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

• 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

12

2 B

mA nk T

( )n f u du

• 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.

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1.1.3 Ionized Gases

3/ 2/212.4 10 i BU k Ti

n i

n T en n

• Solving Saha equation

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Example: Saha Equation

3/ 2/212.4 10 i BU k Ti

n i

n T en n

/2 21 3/ 22.4 10 i BU k Ti nn n T e

Example: Saha Equation (II)

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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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

From Ionized Gas to Plasma (II)

• (Long range) Coulomb force between two charged particles q1 and q2 at distance r:

r

1 22

04q qF

r

q2

q1

From Ionized Gas to Plasma (III)• (Short range) force between two neutral atoms (e.g.

from Lenard-Jones interatomic potential model)

attractiverepulsive

r

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.

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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