The theoretical analysis of the propagation of magnetohydrodynamic waves in a cylindrical plasma immersed in a steady inhomogeneous magnetic field is here undertaken by assuming a model field of two constant field regions joined by the field = A∇(l/r). We thus consider 'beach' and 'cliff' magnetic field configurations. The general solution of the coldplasma equations in the central (inhomogeneous field) region must be found numerically, but in the low-frequency case analytic solutions are obtained. The wave reflection and transmission found by applying boundary conditions at the constant field.Solutions are so obtained for a variety of cases, including simple reflection of the compressional and torsional modes, reflection of the compressional mode when the cutoff condition is encountered, absorption of the torsional mode at the ioncyclotron resonance, and conversion of one mode into the other after propagation through both of the above conditions. Finally, comparison is made with several recent experiments, which shows that the above theory is sufficient in the case that the wave frequency is not too close to the resonance frequency.The case of reflection of compressional waves from the cutoff shows good agreement between theory and experiment, except in the high field region, where apparently the waves are not confined by the magnetic field lines. Reflection of torsional waves close to the resonance condition shows disagreement in the transition region, where the experimental wave energy is as great as 4 times as large as that predicted both by the above theory and the WKB method.
Propagation of ion-cyclotron plasma waves in a weak inhomogeneous field