Physics 777 Plasma Physics and Magnetohydrodynamics MHD Instructor
- Slides: 27
Physics 777 Plasma Physics and Magnetohydrodynamics (MHD) Instructor: Gregory Fleishman Lecture 4. Linear Waves in the Plasma 30 September 2008
Plan of the Lecture • • MHD Waves in Isotropic Plasma Waves in Magnetized Plasma Emission of Waves by a Given Electric Current • Emission by Rectilinearly Moving Charge, General Derivation
Section 1. MHD Waves (see Somov, Chapt. 15)
Fourier transform yields:
Section 2. Waves in Isotropic Plasma Transverse (free-space) modes
Longitudinal Waves Maxwellian Plasma where 1) Use iterations to solve
Ion Sound Waves
For if
Section 3. Waves in Magnetized Plasma
Zeros and Resonances Show that this means quasilongitudinal wave E||k if
Substitution of tensor components into coefficient A yields: This Eq. has three roots Neglecting ion contribution, we obtain two of three:
Asymptotic expressions
Zeros Neglecting ion contribution, we find: F w Z X
Normal waves for oblique propagation Simplifications: X O 1 Z 2 F-w A Whistler mode
Waves in Hot Plasma Recall: It is convenient to express this via Bessel functions
Maxwellian plasma
Bernstein Modes
Section 2. Macroscopic Maxwell Equations. Linear response Introduce polarization vector; continuity Eqn. is fulfilled: Form displacement vector: D=E+4 p. P; the most general (nonlocal) linear relation for statistically uniform medium reads:
Section 4. Emission of Waves by a Given Electric Current - energy loss of a given current (from electrodynamics) 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
where In the basis of the eigen-vectors Substitution yields: we obtain diagonal form
where
Section 5. Emission by Rectilinearly Moving Charge, General Derivation Radiation field far away from the charge (from e/d) Define and obtain:
Nonrelativistic case: Ultrarelativistic case:
We are looking for
Section 6. Homework • Derive formula for the energy emitted by a rectilinearly moving charge in a given field in the nonrelativistic case.
- Magnetohydrodynamics
- Right hand rule 1
- Difference between open cycle and closed cycle mhd system
- Mhd alyssa
- Predominant cell type
- Introduction to mhd
- Mhd titel
- Mhd equations
- Mhd
- Fcis lms
- Ballooning
- Concurrent project management
- P 777
- 16 777 216
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- Fração geratriz de 0 777
- Oceanic airlines 747
- Code strong in hospital
- 777
- Crc boeing 777
- 777.nine99
- Key tenets of ippd
- "boeing aircraft" 737 or 747 or 787 or 777 or t-x
- Properties of plasma
- Computational methods in plasma physics
- Instructor responsibilities and professionalism
- The virtual instructor
- Tipo de participantes