(7a)-(7d) results for transverse magnetic mode propagating through a PEC waveguide can be written as,
This is because for D'B' waveguide, the plates of the guide behave as perfect magnetic conductors for transverse electric components while they behave as perfect electric conductor for transverse magnetic mode. For the DB' waveguide at [alpha] = 0, there is no normal component of the electric filed at the guide surface while magnetic field has no tangential component.
where [A.sup.l(n).sub.m](k) are the expansion coefficients which define the electric field structure for the transverse magnetic mode TM mn with the indices m, n being the azimutal and radial number respectively.
Thus, we restrict our study only to the Transverse Magnetic modes (TM) which are modified by the plasma presence.
We found numerically the eigenfrequencies of the first symmetrical transverse magnetic modes [TM.sub.0n] modes in a radially inhomogeneous plasma confined in a cylinder through a strong magnetic field.
For example, using the expressions for the fields from , the transverse wave impedance for the transverse magnetic mode [Z.sub.TM] can be written as
Using (1), with an air-filled spherical cavity having an arbitrary radius [R.sub.a] = 150 [micro]m, the transverse wave impedance for the transverse magnetic mode [Z.sub.TM]([[??].sub.d,c] r) against radial distance for various intrinsic values of bulk DC wall conductivity is shown in Figure 1.
Similar to the treatment done in Case 1, using Equation (15e) and Equations (16), we can write the results for transverse magnetic mode propagating through a PMC waveguide as
For limiting cases, transverse impedance of DB wall is zero for transverse electric mode and infinitely high for transverse magnetic mode while it is non zero complex value for the intermediate situations.
This is because the plates of the guide behave as perfect electric conductors for transverse electric components while they behave as perfect magnetic conductor for transverse magnetic modes. For the reference PEC results, there is no tangential component of the electric filed at the guide surface while magnetic field has no normal component.
In conventional isotropic materials, these modes are electrically and magnetically polarized perpendicular to the direction of wave propagation and are often referred to as the transverse electric and transverse magnetic modes
. Furthermore, in isotropic materials the phase velocity does not depend on direction, while in anisotropic and cross-coupled materials, this is usually not the case.