Collisions

1
Collisions

• Vacuum and Pressure
• Elastic and inelastic collisions
• Collision cross section, mean free path and
  collision frequency
• Coulomb collisions
• Various collision frequencies

2
Vacuum and Pressure

• Degree of vacuum indicated by pressure
• Units of pressure
• mm Hg (millimeter of mercury from mercury
  manometers)
• 1 atm(standard atmosphere at 0oC)760 mm Hg
• Torr, mTorr (International Standard) 1 atm760
  Torr
• Pa(pascal)N/m2 (International Standard)
• 1 atm1. 01325x105 Pa 1 Torr133. 32 Pa
• Meaning of pressure
• Pressure depends on temperature as well as number
  density
• Perfect gas law
• with Boltzmann constant k, kT300oK300/11604
  eV
• np/kT101325/(3001. 602x10-19/11604)2 .
  447x1025 molecules(atoms)/m3
• 1mTorr --gt 2 . 447x1025 / 760000 3. 2x1019 /m3

3
Basic Concepts of Collisions

• Collisions of charged particles in a plasma
• collisions with neutral atoms and molecules
• dominant in partially ionized plasmas
• collisions with other charged particles (Coulomb
  collisions)
• dominant in high-temperature plasmas
• Elastic and inelastic collisions
• elastic collision the sum of kinetic energies
  of the collision partners are conserved.
• inelastic collision the sum of kinetic energies
  are not conserved. ionization and excitation
• super-elastic the sum of kinetic energies are
  increased after collision. de-excitation

4
Fundamental Collision Parameters
Hard sphere collision
of particles colliding in dx
fraction of incident particles colliding in dx
Uncollided flux

• Collision parameters
• collision cross section ?(v)
• mean free path ?mfp 1/(nn?) ? 1/p
• collision frequency ? v/ ?mfp nnlt?vgt Knn ?
  p
• reaction rate K lt?vgt

5
Results of Collisions

• Plasma diffusion and other transport processes
• Transfer energy between particles
• Responsible for the electrical resistivity of the
  plasma

Complexity of Collision Processes

• The concept of collision in a plasma is subtle
• Relative velocity dependency of collision
  processes
• Integrated effects of interactions between
  particles of all velocities
• Effective collision frequency depends on the
  specific process

6
Binary Coulomb Interaction inside the Debye Sphere
Parallel momentum change
electron
v
Coulomb logarithm
7
Coulomb Collisions Large-angle scattering and
small-angle collisions
Effective collision cross-section

• Impact parameters for small angle Coulomb
  scattering
• minimum from Coulomb force balance
• maximum from Debye length
• ratio gives importance of small angle scattering

8
Coulomb Logarithm
for
with
for
, the quantum mechanical effect need to be
accounted for
For electrons, Te 10eV
For protons, Te 10keV
9
Coulomb Logarithm
10
Coulomb Logarithm for electron-ion collisions
11
Coulomb Logarithm with Quantum Mechanical Effect
Classically,
Quantum mechanically by considering Debye
shielding potential,
Using the Born approximation,
for
, small angle contributions with
are negligible, so
The actual quantum mechanical effect is to remove
the contributions at large impact parameters
between ?D and (?D/ ?qm )ro leaving