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Kinetic Theory

Kinetic Theory

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Kinetic Theory

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  1. Kinetic Theory

  2. Particle Distribution Function

  3. Density Function ns Number density, mass density, charge density

  4. The Boltzmann Equation: time variation of a distribution function

  5. Total Derivative in Phase Space

  6. Homework Problem 3.6, 3.7, 3.8

  7. Examples of Distribution Functions

  8. Maxwellian Distribution Functions

  9. One-dimensional Maxwellian, cont’d

  10. Thermal speed

  11. charge x voltage = energy Equilibrium Distribution

  12. Velocity Moments

  13. Bulk flow velocity

  14. Pressure tensor

  15. Scalar pressure

  16. Heat Flux

  17. Continuity equation: 0th moment of B-equation

  18. Momentum Equation: 1st moment of B-equation

  19. The momentum equation

  20. Pressure Gradient Force

  21. Pressure as Thermal Energy Density

  22. Charge and Current Densities

  23. Moments Measurements in Space Physics • Particle detector measures electric current produced by the charged particles • The electric field current, count-rate, is converted to number of density flux according to calibration • The flux can be converted to distribution function • The detector can select the energy range with energy resolution, as well as type of the particle species • Each detector has a finite field angle which determines the spatial resolution • The detector(s) scan over directions • Fluxes from all energy channels and all looking directions can be added together. • Moment factor can be added in the integration process to obtain moments, which are used as macroscopic quantities, such as density, velocity, temperature, (temperature) anisotropy • Satellite charge is a major problem in deriving correct distribution function • In the existence of multiple populations, “moments” may mean different things. Distribution functions have to be examined in this case.