For a constant temperature and pressure, a dynamic equilibrium is established between collisional excitations and radiative de-excitations, which lead to particular distribution of the atoms among different energy levels.
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Most of the atoms are at low-lying levels. The number of atoms at higher levels decreases exponentially with energy level. At low temperature, the faster the population drops at the higher levels. Only at very high temperatures, high-lying energy levels are occupied by an appreciable number of atoms. Taking log on both sides of Eq. Lagrangian multiplier for the most probable occupation of the j th level is given as. By adding values from Eqs.
PHYS 480 Outline
From Eqs. The change in the internal energy of the system in terms of thermodynamics equation can be written as. By comparing Eqs. Thus, Eq. In a system, most of the energy levels in an atom are degenerated, that is, atoms have several states with the same energy. To find out the population of an atom at a particular level, the population of each constituent state is required to be added together. Thus, each term in Eq. The Eq. The Einstein A coefficient gives the probability of spontaneous emission.
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A quantum of radiation is emitted by an atom when it de-excites from an excited level to a lower level, which is given as. As the radiation is emitted isotropically, thus the intensity is. Taking log and solving Eq.
By using Eq. Taking ratio of Eqs.
The Boltzmann equation gives only the relative number of atoms or ions in a particular excitation state with respect to the ground state and it does not provide the total number of atoms that have been ionized. In order to determine the total abundance of a given element, it is necessary to know how the atoms are distributed among their several ionization stages.
As the energies of free electrons are continuous, the Boltzmann expression analogous to Eq. Thus, the statistical weight for the free electron can be written as. We can write the integral in Eq. By replacing values of Pe and dPe in Eq. The integral on the right-hand side of Eq. By adding this value in Eq. By dividing Eqs. Kinetic theory provides the essential material for an introductory course on plasma physics as well as the basis for advanced kinetic theory. It offers a wide-range coverage of the field. The understanding of the most important plasma parameters, that is, plasma oscillations, plasma frequency, Debye shielding, Debye length, plasma temperature, and electron density, is important for studying plasmas.
Kinetic theory has a wide scope. Plasma kinetics mathematical equations that will aid the readers in understanding simple techniques on how to investigate plasma dynamics and kinetics are discussed in this chapter. Plasma understanding, waves, oscillations, frequencies, and applications are covered in kinetic theory.
In fact, we have attempted to present a precise discussion of plasma kinetic theory which includes the basic plasma parameters mathematical formulation for an easy understanding to the reader. Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3. Help us write another book on this subject and reach those readers.
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Plasma Kinetic Theory
Our readership spans scientists, professors, researchers, librarians, and students, as well as business professionals. Downloaded: Abstract The description of plasma using fluid model is mostly insufficient and requires the consideration of velocity distribution which leads to kinetic theory. Keywords plasma parameters kinetic theory particle distribution. Plasma kinetic equations Plasma physics involves phenomena that are related to dynamical processes in statistical mechanics.
Liouville distribution The fine-grained distribution function, which is precise in describing the microscopic conditions of many particles, would not by itself correspond to the coarse-grained quantities in the macroscopic view. In T-space, the microscopic state of the system is expressed by a point. Kinetic theory and the moment equations. Discontinuities and shock waves.
Electrostatic waves in a hot unmagnetied plasma. Waves in a hot magnetized plasma. Nonlinear effects. Collisional processes. However, no homework will be accepted after the official solution has been distributed normally, one week after its due date, via email.
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