Physics 777Plasma Physics and
Magnetohydrodynamics (MHD)
Instructor: Gregory Fleishman
Lecture 4. Linear Waves in the Plasma
30 September 2008
Plan of the Lecture
• MHD Waves
• Waves in Isotropic Plasma
• Waves in Magnetized Plasma
• Emission of Waves by a Given Electric Current
• Emission by Rectilinearly Moving Charge, General Derivation
Substitution of tensor components into coefficient A yields:
This Eq. has three roots
Neglecting ion contribution, we obtain two of three:
Section 2. Macroscopic Maxwell Equations. Linear response
Introduce polarization vector; continuity Eqn. is fulfilled:
Form displacement vector: D=E+4P; the most general (non-local) linear relation for statistically uniform medium reads:
Section 4. Emission of Waves by a Given
Electric Current
Recall:
where
is the Maxwellian tensor, j is an external electric current (including nonlinear plasma current in a general case).Let’s solve this inhomogeneous algebraic equation for E
- energy loss of a given current (from electrodynamics)
Section 5. Emission by Rectilinearly Moving Charge, General Derivation
Radiation field far away from the charge (from e/d)
Define and obtain: