Kinetic Theory.

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Presentation transcript:

Kinetic Theory

Particle Distribution Function

Density Function ns 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

Maxwellian Distribution Functions

One-dimensional Maxwellian, cont’d

Thermal speed

Equilibrium Distribution charge x voltage = energy

Velocity Moments

Bulk flow velocity

Pressure tensor

Scalar pressure

Heat Flux

Continuity equation: 0th moment of B-equation

Momentum Equation: 1st moment of B-equation

The momentum equation

Pressure Gradient Force

Pressure as Thermal Energy Density

Charge and Current Densities

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.