Plasma Physics - Riassunti

Plasma Physics

→ See Maxwell equations

Electrodynamics in continuous media (macroscopic em)

This is a macroscopic equation

Internal charges + external (known) charges

for conduction depose

Localized, bound charges

→ polarization vector

Notation →

electric induction D

→ macroscopic vector

magnetic induction

Linear partial differential equation, but non-local behaviour

→ electrical susceptibility

→ propagation

Material possesses inertia → It doesn’t respond simultaneously to a stimulus

→ temporal and spatial dispersion

→ susceptibility electric tensor (ε) and electric conductivity

Properties of EM monochromatic wave in a medium depend on → the wave propagation in a medium depends on

phase velocity and frequency. There is a relation between the polarization vector and dispersive properties of the medium, the wave vector and the frequency.

→ MAXWELL EQS. IN A DISPERSIVE MEDIUM

dispersion tensor

Things are different along z and along the x-direction

so propagation index

→ E scalar (isotropy)

→ for the monochromatic wave →

even in vacuum (ε = isotropy) for the monochromatic wave E * K

longitudinal wave are not possible here.

Determination of (linear, circular,...)

Dispersion + Linear media + EM: Energy considerations

vacuum:

Conservation equation

Dispersion media:

→ conservation equation ← scaling changes with respect to ω

→ → averaging procedure over a fast period

→ → conservation of energy

conservation equation: → related to real part

→ related to the imaginary part

ε₀∫E_i * dE_i

∂t E_i

Di = ∫ε_ijE_i

E_i = ε_ijt* + ε_ij *

ε₀ = ε_iiε_ij + ε_ij =ε₀

Physical properties related to energy density.

X _∞ due to an impulse of the EN field.

fter the analytic continuation, we see that causality implies dispersion & correlations connection:

κατμεrs-κilling relations:

different physical properties (wave propagation, ε...) are connected

just assuming linear and non-local response + Fourier transform

analytic continuation.

ε is related to ω so we cannot imagine a non-dispersive medium.

Spatial Dispersion

The existence of the Fourier transform.

E(ω, x₀-)

T₀= f₀k x