LECTURE II: ELEMENTARY PROCESSES IN IONIZED GASES Univerzitet Crne Gore LECTURE II: ELEMENTARY PROCESSES IN IONIZED GASES 4/7/2019 Dr Slavoljub Mijović University of Montenegro Faculty of Natural Sciences and Mathematics, Podgorica, MONTENEGRO E-mail: slavom@rc.pmf.cg.ac.yu 4/7/2019

COLLISIONS Particles undergo binary collisions- a simplification (see example 1,2) Plasmas may be collisional (e.g., fusion plasma) or collisionsless (e.g., solar wind). Space plasmas are usually collisionless. Ionization state of a plasma: Partially ionized: Earth‘s ionosphere or Sun‘s photosphere and chromosphere, dusty and cometary plasmas Fully ionized: Sun‘s corona and solar wind or most of the planetary magnetospheres Partly ionized, then ion-neutral collisions dominate; fully ionized, then Coulomb collisions between charge carriers (electrons and ions) dominate.

Example 1. A basic difference between neutral gases and plasmas is that in later case exists significant electromagnetic (microscopic) field. This field fluctuates very fast in time and sharply changes from point to point. In the same time this field influences charged particles’ movements by Lorenz’s force. Estimate the average value of the microscopic electric field in plasma for typical laboratory plasma conditions: Solution: If n is the number of charged particles per unit of plasma volume, then is the average distance between two neighbor charged particles. Finally the average microscopic electric field which one charged particle influences the nearest neighbor is approximately Putting in this formula known given values one can get a great value for Emik

Example 2. Estimate the average value of microscopic magnetic field in plasma with the same plasma conditions as in the example 1. Solution: If is temperature of a plasma and taking in mind that is the average velocity of thermal movement of particles in this plasma ( mass of electrons), then each electron influences the nearest neighbour by magnetic field, which value is approximately Putting in this formula the known values one can get

Collisions Elastic - occur when both momentum and kinetic energy are conserved. Inelastic - occur when momentum is conserved, but kinetic energy is not. The total momentum of any group of objects remains the same unless acted on by outside forces.

Example 3. Which part of the energy of an electron (in average) is given to an in rest atom per each elastic collision? Solution: During each elastic collision with a neutral at rest atom the electron gets momentum where is the change of the electron velocity as a vector. Thus, the energy of the atom increases because - is a scattering angle. From (1) one can see that the average energy loss of the electron during the collisions with atoms

Example 4. Electrons play dominant role in the processes of excitations and ionisations of atoms of a gas, and they are in the same time main carriers of the electric currents. This fact is mainly due to their low masses. In an electric field the electrons going to be accelerated to the greater values of velocities than ions, thus the processes with electrons are more effective. Determine the maximum change of the internal energy of the particles and during a non-elastic head-on collision under an assumption that the second particle is at rest in the moment of the collision. Consider the cases: and Solution: As it is well known in a general case, a collision of two particles of masses and describes by the laws of conversation of energy and momentum. I a case of a non-elastic collision a part of the kinetic energy of the particles go to internal energy excitation of the particles. In the case where the particle of mass before the collision was motionless and the collision is forehead (central), these two laws can be described as: (1) (2) where is the energy of the particles which is transformed in the internal energy. If we derive from eq. (1) and put in eq. (2), we can determine this value of the energy:

Example 3.-con’d (3) To find under which conditions the second particle gets the maximum value of this energy, one should calculate the first derivative of the expression (3) per velocity and put to be zero: (4) From (4) one can calculate the value for which has maximum: (5) Putting this values in eq. (3) one can get: (6)

The Parameters of a Collision-Microscopic Total Cross Section dx 

The Parameters of a Collision-Microscopic Total Cross Section The beam of projectiles Target particle More specific…

The Parameters of a Collision-Microscopic Total Cross Section The beam of projectiles

The Parameters of a Collision-Mean Free Path -total macroscopic cross section

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Definition of Cross Section?-con’d

Collision frequency and free path The neutral collision frequency, n, i.e. number of collisions per second, is proportional to the number of neutral particles in a column with a cross section of an atom or molecule, nnn, where nn is the density and n= d02 ( 10-20 m2) the atomic cross section, and to the average speed, <  > ( 1 km/s), of the charged particle. The mean free path length of a charged particle is given by: 4/7/2019

Coulomb collisions I Charged particles interact via the Coulomb force over distances much larger than atomic radii, which enhances the cross section as compared to hard sphere collisions, but leads to a preference of small-angle deflections. Yet the potential is screened, and thus the interaction is cut off at the Debeye length, D. The problem lies in determining the cross section, c. Impact or collision parameter, dc, and scattering angle, c. 4/7/2019

Coulomb collisions II The attractive Coulomb force exerted by an ion on an electron of speed ve being at the distance dc is given by: This force is felt by the electron during the fly-by time tc  dc/e and thus leads to a momentum change of the size, tc FC , which yields: For large deflection angle, c  90o, the momentum change is of the of the order of the original momentum. Inserting this value above leads to an estimate of dc , which is: 4/7/2019

Coulomb collisions III The maximum cross section, c = dc2, can then be calculated and one obtaines the electron-ion collision frequency as: Taking the mean thermal speed for ve , which is given by kBTe = 1/2 meve2, yields the expression: The collision frequeny turns out to be proportional to the -3/2 power of the temperature and proportional to the density. A correction factor, ln, still has to be applied to account for small angle deflections, where  is the plasma parameter, i.e. the number of particles in the Debye sphere. 4/7/2019

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