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Behaviour of Electromagnetic Waves in Different Media and Structures Part 4

Tham khảo tài liệu 'behaviour of electromagnetic waves in different media and structures part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 78 Behaviour of Electromagnetic Waves in Different Media and Structures The oscillations of such a cavity are damped by energy lost to the walls in the form of heat. This heat comes from the currents circulating in the walls and is due to the finite conductivity of the metal of the walls. The total energy of the oscillations is the integral over the volume of the cavity of the energy density W I 0E2 Ao H2 dv 2 1 Ao 4nx 10 7 H m and o 1 X 10 9F m 3 36n where E and H are the electric and magnetic field vectors in volts meter and ampere-turns meter respectively. The cavity has been assumed to be empty. The total energy W in a particular mode decreases exponentially in time according to the expression got W Woe Q 4 where oo 2nf0 and Q is a quality factor of the mode which is defined by Q 2n energy stored in the cavity energy lost in one cycle 5 gọt The fields and currents decrease in time with the factor e Q . Most klystrons and klystrodes are built with cavities of radial-line types. Several types of reentrant cavities are shown in Fig. 1. It is possible to give for the type of cylindrical reentrant cavities a crude but instructive mathematical description in terms of approximate solutions of Maxwell s equations. Fig. 1. Resonant cavities a Coaxial cavity b Radial cavity c Tunable cavity d Toroidal cavity Electromagnetic Waves in Cavity Design 79 The principle or fundamental mode of oscillation of such cavity and the one with the longest free-space wavelength has electric and magnetic fields that do not depend on the azimuthal angle defining the half plane though both the axis and the point at which the fields are being considered. In addition the electric field is zero only at wall farthest apart from the gap and the magnetic field is zero only at the gap. In this mode the magnetic field is everywhere perpendicular to the plane passing through the axis the electric field lies in that plane. Lines of magnetic flux form circles about the axis and lines of electric flux