By Toshiyuki Shiozawa
Waves in Relativistic Electron Beams presents a sophisticated process classical electrodynamics with software to the iteration of high-power coherent radiation within the microwave to optical-wave areas. in particular, it presents readers with the fundamentals of complicated electromagnetic thought and relativistic electrodynamics, guiding them step-by-step during the thought of free-electron lasers. The theoretical therapy all through this publication is totally built via the standard three-d vector calculus. This ebook will be suggested as a graduate-level textbook or a reference publication within the fields of complex electromagnetic thought, relativistic electrodynamics, beam physics and plasma sciences.
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6) denote the change in frequency or the Doppler shift in frequency produced by the relative motion of two inertial systems. As is evident from the above discussion, in relativity, the frequency and wave numbers are transformed as a cluster, or more precisely, as a four-vector in the same manner as the space-time coordinates. With the aid of the transformation formula for frequency, we can find the constitutive relations for a moving temporally dispersive medium or a moving medium with frequency dispersion.
For example, it is well known that the precursor of an electromagnetic pulse is propagated with the velocity of light in vacuum, c in these media as well. 3 Transformation of Electromagnetic Quantities According to the special theory of relativity, the Maxwell equations hold in all inertial systems. In other words, when we move from one inertial system to another by the Lorentz transformation, the form of the Maxwell equations is kept invariant. If a physical law is form-invariant under a transformation as in the above example, the physical law is referred to as covariant under the transformation.
2cosfJ + i0 sine) . Iohe -jkrH +l,. - 2I cos (} . 16). The final results for the electric and magnetic field components in spherical coordinates are obtained as follows: E,. 26) 2 · (} H- =I 0-hk- e -jkr[} - + -1- ]sm rp 4n kr ( kr? 10 Electromagnetic Radiation in Unbounded Space Ecp = H,. = H8 = 0. 28) As stated in the preceding subsection, the radiation fields, which decay in inverse proportion to the distance from the origin, predominate at large distances (kr >> 1) from the origin where an electric dipole is located.