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Write the dispersion relation for electromagnetic waves in a plasma. - Write Ohm's Law for isotropic conductivity. - Write Ohm's Law for anisotropic conductivity. - Write the dielectric tensor - Derive the dielectric tensor. - Write the identity matrix. - Write the definition equation of the electron cyclotron frequency. - Derive the definition equation of the electron cyclotron frequency. - What do dispersion relations do? They link frequency to wave-number for waves. Write the definition equation of the refractive index. - Write the definition of group velocity. - Write the definition of phase velocity. - Write the equation for the resultant polarisation in terms of the electron number density and the magnetic field. - Write the definition equation of the dipole moment. - Write down the electric and magnetic field equations for a Hertzian dipole in spherical co-ordinates. - Write the definition equation of the Poynting flux. - Derive the Poynting flux for a Hertzian dipole. - Write the equation for the differential power. - Write the equation for the differential power radiated from a Hertzian dipole. - What is Thomson scattering? The interaction between an electromagnetic wave and a free electron. Write the definition equation of the differential scattering cross section. - Write the equation for the magnitude of the average Poynting flux. - Write the equation for the classical electron radius. - What is Rayleigh scattering? The interaction between electromagnetic waves and atomic electrons. Write the equation of motion for a Hydrogen electron interacting with an electromagnetic wave. - Write the relation between the cross-sections of Thomson and Rayleigh scattering. - Write the equation for the total power radiated by a relativistic electron as it accelerates. - What is electron cyclotron emission? It is the energy emitted by a non-relativistic electron which is gyrating in a magnetic field. What is gyroresonant emission? It is the energy emitted by a relativistic electron which is gyrating in a magnetic field. Write the equation for the gyrofrequency of a relativistic electron. - Derive the equation for the gyrofrequency of a relativistic electron. - Write the mass continuity equation. - Write the energy equation for magnetohydrodynamics. - Write Euler's equation for magnetohydrodynamics. - Write the induction equation. - Which dissipative processes are neglected in ideal magnetohydrodynamics. Finite viscosity, electrical conductivity, and thermal conductivity.