A Green's Function Method for the Solution of a Class of Two-dimensional Problems Involving Anisotropic Compressible Plasma (with an Application to the Unbounded Medium)†

Some Aspects of Wave Propagation and the Effect of the Boundaries and Excitations on the Electro-acoustic Spectrum in an Isotropic Compressible Plasma†

“…In recent studies (Sammadar andYildiz 1964, Yildiz 1964, Yildiz and Samaddar 1!J(3) some aspects of the surface wave phenomena were not clarified. For a cylindrically cold plasma and vacuum interface, it is known that the surface waves can exist ifthe equivalent dielectric constant £1 of the plasma assumes only negative values (for the various properties ofthe surface waves, see Barlow and Karbowski 1!J53, Cullen I !J54,Samaddar 1!J61, Samaddar and Yildiz 1963, 'I'amir and Oliner 1!J61, Wait.…”

“…In such a case an electromagnetic source will excite both optical and acoustical waves. Many authors (Field 1956, Kritz and Mintzer 1960, Abele 1961, Yildiz 1963and Yildiz and Silberg 1964 have considered the effects of the compressibility in a plasma. Moreover, the excitation of a compressible plasma half-space by a magnetic line current placed in the exterior medium has been considered by Hessel et al (1962), the scattering plane plasma waves from a plasma sphere by M2 Downloaded by [McGill University Library] Yildiz (HJ63a,b), the scattering by a perfectly conducting cylinder in a. compressible plasma by Sheshadri (1964), and the superluminal and radiational doppler spectrum in a cylindrically stratified compressible plasma by Yildiz (1964).…”

“…Many authors (Field 1956, Kritz and Mintzer 1960, Abele 1961, Yildiz 1963and Yildiz and Silberg 1964 have considered the effects of the compressibility in a plasma. Moreover, the excitation of a compressible plasma half-space by a magnetic line current placed in the exterior medium has been considered by Hessel et al (1962), the scattering plane plasma waves from a plasma sphere by M2 Downloaded by [McGill University Library] Yildiz (HJ63a,b), the scattering by a perfectly conducting cylinder in a. compressible plasma by Sheshadri (1964), and the superluminal and radiational doppler spectrum in a cylindrically stratified compressible plasma by Yildiz (1964). Hessel et al found that the interface can support a surface wave, and that the energy in an electromagnetic plane wave incident almost normally on the plasma half-space can be converted entirely into an acoustic wave if W is slightly higher than We' However, they did not look into the possibility of a transverse decay (surface wave), when W > We'…”

“…We shall nowderi ve coupled inhomogeneousKlein-Gordon type equations which prescribe the characteristics of the plasma modes and which have not been given previously in this form. Inhomogeneous Klein-Gordon equations, which correspond to one fluid, have been given by many authors for the isotropic plasma, see for example Cohen (U)61) and for a non-linear interaction, Yildiz (1964). Multiplying eqns, (1 c) by eNo/€o using the relationship given by (2a) and the usual definitions of w e 2 and Wi 2, we obtain two alternate expressions of Poisson's equation, where w c 2 and wi 2 will, respectively, enter into the following relations: v .…”

“…(9 c ) an.d (9 k), and accordingly 5 also modifies N,, N2, A-and A+ for the two-fluid model and yl, q2 and y for the one-fluid model (when ions are stationary). It is now clear that non-linear effects in the plasma must play a significant role (Yildiz 1964) in order to realistically account for various spectra such as the Doppler spectrum in turbulent plasma.…”