Electromagnetic fields in the cylindal cavity having discontinuous media
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概要
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In the conventional microwave measurements of plasma electron density, few of the distorted electromagnetic fields of the resonant cavity which is caused by plasma are considered. To calculate the correct plasma electron density we analysed the electromagnetic fields of the cavity which consists of two media. If we think a cylinder which has the radius a and dielectric constant ε_1 in the cylindrical resonant cavity with its radius b, the resonant modes E_<omo> have only the axial electric components and an azimuthal magnetic components. The first medium (dielectric constant ε_1) [numerical formula] The second medium which consists of the space between onc cylinder with its dielectric constant ε_1 and the metal walls of th eresonant cavity with its radius b. Let the dielectric constant of the second medium be ε_2,then we have the electromagnetic fields considering the boundary condition at wall E_z=0 as shown in the next equations, [numerical formula] Here, k_1 and k_2 are eigenvalues of the first and the second medium respectively, r is the distance from origin in the radial direction, J_0 is the zero order and J_1 is the first order Bessel Functions. The expressions of the electromagnetic fields in the hollow resonant cavity are as same as that in the equation (1) but different dielectric constant and eigenvalue, i.e, [numerical formula] We can easily value the ratios of the magnitudes of electromagnetic fields with cylindrical hollow resonant cavity to that of the cavity with discontineous media, comparing equatioa (1) with equations (2) and (3). We can eliminate ε_2,k_2 appeared in the equation (2) using that H_ψ is continuous at γ=a. Then we have the equation easy comparable with equation (1). [numerical formula] If we divide the equation (1), the first equation of the (2), the equation (2)' and the equation (3) by A_1k_1^2,A_1ωε_1k_1,and A_1k^2 respectively, we can get the normalized forms of these equations. Eigure 1 shows one field distributions, having the resonant frequency 4000MC/S, the resonant mode E_<θ10>, b/a=4.1,specific dielectric constant ε_1=0.1 and ε_2=1.0. Figure 2 shows another field distributions having the resonant frequency 9400MC/S, the resonant mode E_<020>, b/a=4.0,ε_1=0.1 and ε_2=1.0. In Figures the ratio of the magnitude of the field of the cavity with the discontineous media to that of the hollow cavity at γ=0 and γ=a.
- 山梨大学の論文
- 1961-12-20
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