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. Equilibrium Distribution
charge x voltage = energy

12. Velocity Moments

13. Bulk flow velocity

14. Pressure tensor

15. Scalar pressure

16. Heat Flux

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

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

24. The momentum equation

25. Pressure Gradient Force

26. Pressure as Thermal Energy Density

27. Charge and Current Densities

28. 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.