1 / 28

Kinetic Theory

Kinetic Theory. Particle Distribution Function. Density Function n s. Number density, mass density, charge density. The Boltzmann Equation: time variation of a distribution function. Total Derivative in Phase Space. Homework. Problem 3.6, 3.7, 3.8. Examples of Distribution Functions.

kathi
Download Presentation

Kinetic Theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related