Kinetic Theory

# Kinetic Theory

## Kinetic Theory

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##### Presentation Transcript

1. Kinetic Theory

2. Particle Distribution Function

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

4. Total Derivative in Phase Space

5. Homework Problem 3.6, 3.7, 3.8

6. Examples of Distribution Functions

7. Maxwellian Distribution Functions

8. One-dimensional Maxwellian, cont’d

9. Thermal speed

10. charge x voltage = energy Equilibrium Distribution

11. Velocity Moments

12. Bulk flow velocity

13. Pressure tensor

14. Scalar pressure

15. Heat Flux

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

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

18. The momentum equation

19. Pressure Gradient Force

20. Pressure as Thermal Energy Density

21. Charge and Current Densities

22. 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.