By Toshiyuki Shiozawa

*Waves in Relativistic Electron Beams *presents a sophisticated process classical electrodynamics with program 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 conception and relativistic electrodynamics, guiding them step-by-step in the course of the conception of free-electron lasers. The theoretical remedy all through this e-book is absolutely constructed via the standard three-d vector calculus. This e-book will be suggested as a graduate-level textbook or a reference publication within the fields of complex electromagnetic conception, relativistic electrodynamics, beam physics and plasma sciences.

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10. 20 ) where / 11 denotes the magnitude of a sinusoidally time-varying current. According to the law of charge conservation, time-varying charges appear at both ends of the wire. The charge density corresponding to these charges in frequency domain is expressed as 30 I. Basic Electromagnetic Theory _ p(r',w) = I [ h h] ~b(x')b(y') b(z'- -)- b(z' + -) . 16) are simplified. 11 ), we note some approximating relations. At both ends of the wire, we have an approximation for the phase term e - jklr-r'l = e - jkr [1 ± J"k -cos h e] .

7) For v << c, Eq. 8) If Eq. 8) should be in accordance with Newtonian mechanics, the second term on the right-hand side must correspond to the kinetic energy of a particle.

2) to the system /'by the Lorentz transformation. In order to transform Eqs. 8). For this purpose, letf(x,y,:,t) be an arbitrary scalar function of variables x, y, z, t. 8). 7) First, to find the transformation formulas for the field vectors E and B. 3. I), ()£- ()£ r rJy rJz iJB --- ---· +--' rJt = 0. ___ ( . , y E,. + 1,B,. ___, y 1 B, + 2 E r) - 0. ). 1 0) Eq. 3 ). Thus if Eqs. 1 0). 3. I). 7) to the z 42 2. 1 ), and combining to rearrange the resultant two equations, we get an_ -ay (E,. + vB,.