Fundamentals of Plasma Physics
190 Chapter 6. Cold plasma waves in a magnetized plasma modes. Parameter space is divided up into a finite number of regions, ca ...
6.2 Dielectric tensor 191 square root in Eq.(6.49) is √ B^2 − 4 AC= √ (RL−SP)^2 sin^4 θ+4P^2 D^2 cos^2 θ (6.54) and can only van ...
192 Chapter 6. Cold plasma waves in a magnetized plasma Bounded volume with no resonance andn^2 > 0 at some point in the bou ...
6.3 Dispersion relation expressed as a relation betweenn^2 xandn^2 z 193 taining two normal modes corresponding to two qualitati ...
194 Chapter 6. Cold plasma waves in a magnetized plasma For example, consider an antenna located in thex=0plane and having some ...
6.4 A journey through parameter space 195 n^2 xbecomes complex is called a region of inaccessibility and is a region where Eq.(6 ...
196 Chapter 6. Cold plasma waves in a magnetized plasma the plus or minus signs on the crosses in each bounded volume are establ ...
6.5 High frequency waves: Altar-Appleton-Hartree dispersion relation 197 can be accessed for any given plasma density and magnet ...
198 Chapter 6. Cold plasma waves in a magnetized plasma Perhaps the most important result of this era was a peculiar, but useful ...
6.5 High frequency waves: Altar-Appleton-Hartree dispersion relation 199 Equation (6.71) can be Taylor-expanded in the vicinity ...
200 Chapter 6. Cold plasma waves in a magnetized plasma suffices to keep only the leading term ofΓ.Thus, in this limit Γ≃ 2 ∣ ∣ ...
6.6 Group velocity 201 whistler dispersion for acoustic (a few kHz) waves in the ionosphere is n^2 −= ω^2 pe ∣ ∣ ∣ ωce ω cosθ ∣ ...
202 Chapter 6. Cold plasma waves in a magnetized plasma whereE ̃(k)is the amplitude of the mode with wavenumberk.The dispersion ...
6.7 Quasi-electrostatic cold plasma waves 203 6.7 Quasi-electrostatic cold plasma waves Another useful way of categorizing waves ...
204 Chapter 6. Cold plasma waves in a magnetized plasma verse parts El = ˆnnˆ·E Et = E−El (6.95) whereˆn=kˆ=n/nis a unit vector ...
6.8 Resonance cones 205 and then taking the vector derivative with respect tokto obtain 2 kxxSˆ +2kzˆzP+ ( k^2 x ∂S ∂ω +kz^2 ∂P ...
206 Chapter 6. Cold plasma waves in a magnetized plasma Suppose now that waves are being excited by a line sourceqδ(x)δ(z)exp(−i ...
6.8 Resonance cones 207 oscillating pointsource resonance cone ‘infinite’ potential on thissurface B Figure 6.4: Resonance cone ...
208 Chapter 6. Cold plasma waves in a magnetized plasma 6.9 Assignments Prove that the cold plasma dispersion relation can be w ...
6.9 Assignments 209 whereSP< 0 .By writing the source on thezaxis as f(z)= 1 2 π ∫ eikzz−iωtdkz and by solving the dispersion ...
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