Fundamentals of Plasma Physics
7 Waves in inhomogeneous plasmas and wave energy relations 7.1 Wave propagation in inhomogeneous plasmas Thus far in our discuss ...
7.1 Wave propagation in inhomogeneous plasmas 211 Substituting Ampere’s law into the curl of Faraday’s law gives ∇×∇×E 1 = ω^2 c ...
212 Chapter 7. Waves in inhomogeneous plasmas and wave energy relations One way of interpreting this result is to state that the ...
7.2 Geometric optics 213 7.2 Geometric optics The WKB method can be generalized to a plasma that is inhomogeneous in more than o ...
214 Chapter 7. Waves in inhomogeneous plasmas and wave energy relations IfDis construed to be the Hamiltonian, then the first te ...
7.3 Surface waves - the plasma-filled waveguide 215 plasma to vacuum – in other words, the plasma has an edge or surface. A qual ...
216 Chapter 7. Waves in inhomogeneous plasmas and wave energy relations This result can also be used to solve for the transverse ...
7.3 Surface waves - the plasma-filled waveguide 217 We now consider an azimuthally symmetric TM mode propagating in a uniform cy ...
218 Chapter 7. Waves in inhomogeneous plasmas and wave energy relations Integration of Eq.(7.38) across the interface shows tha ...
7.4 Plasma wave-energy equation 219 Thus, in the limitω^2 P/c^2 ,ω^2 /c^2 <<k^2 << 1 /a^2 , Eq.(7.45) simplifies to ...
220 Chapter 7. Waves in inhomogeneous plasmas and wave energy relations and expressing this result as ∂w ∂t +∇·P=0 (7.53) where ...
7.5 Cold-plasma wave energy equation 221 taking of the real part is often not explicitly stated in linear relationships where it ...
222 Chapter 7. Waves in inhomogeneous plasmas and wave energy relations Integration of Eq.(7.56) taking into account the prescri ...
7.5 Cold-plasma wave energy equation 223 Ifωi= 0thenS,P, andDare all pure real. In this case ←→ K(ω)is Hermitian so that ←→ Kh= ...
224 Chapter 7. Waves in inhomogeneous plasmas and wave energy relations Since the energy density stored in the vacuum electric f ...
7.7 Negative energy waves 225 while the Hermitian part remains the same. There is now a new term involvingki.With the incorporat ...
226 Chapter 7. Waves in inhomogeneous plasmas and wave energy relations total system energy density in going from a situation wh ...
7.7 Negative energy waves 227 Since odd powers of oscillating quantities vanish upon time averaging, Eq.(7.96) becomes w ̄sys = ...
228 Chapter 7. Waves in inhomogeneous plasmas and wave energy relations so a negative energy wave hasω∂P/∂ω< 0 .If the dissip ...
8 Vlasov theory of warm electrostatic waves in a magnetized plasma 8.1 Uniform plasma It has been tacitly assumed until now that ...
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