By Toshiyuki Shiozawa
Waves in Relativistic Electron Beams presents a complicated process classical electrodynamics with software to the new release of high-power coherent radiation within the microwave to optical-wave areas. particularly, it presents readers with the fundamentals of complicated electromagnetic thought and relativistic electrodynamics, guiding them step-by-step in the course of the concept of free-electron lasers. The theoretical therapy all through this publication is totally constructed via the standard 3-dimensional vector calculus. This publication will be advised as a graduate-level textbook or a reference publication within the fields of complicated electromagnetic thought, relativistic electrodynamics, beam physics and plasma sciences.
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Additional resources for Classical Relativistic Electrodynamics: Theory of Light Emission and Application to Free Electron Lasers
Example text
2). On the other hand, Gauss' laws for the electric and magnetic fields are expressed mathematically in the same form whether any closed surface S for describing the laws is at rest or moving. 4) where the surface integral and the volume integral are carried out over any closed surface S moving with velocity v and a volume V enclosed by S. 50 2. Foundations of Relativistic Electrodynamics 2. 7 Boundary Conditions for a Moving Boundary As shown in Fig. 3, let the boundary 5 between regions I and II be moving in an arbitrary direction with constant velocity v relative to the inertial system /, and then let us discuss the boundary conditions to be imposed on field vectors at the moving boundary 5.
6 Integral Representation of the Maxwell Equations in Moving Systems Consider a closed contour C moving with constant velocity v relative to the inertial system /, and an open surface S bounded by the closed contour C, as shown in Fig. 2. Then, let us discuss the integral representation of the Maxwell equations for the closed contour C and the open surface S. First, we consider Faraday's induction law, which states that if the amo unt of the magnetic flux linking the closed contour C is temporally changed, the electromotive force is produced around C with the magnitude equal to the negative time rate of change of the magnetic flux linking the contour C.
7), it is a universal law that is applicable to all types of energy, say nuclear, thermal or mechanical. In addition, note that the law has been well confirmed by experiments. 9 Relativistic Mechanics for a Material Particle Let us discuss how Newtonian mechanics for the motion of a material particle under the influence of external forces is modified in the special theory of relativity. For this purpose, we assume that the equation of motion and the energy conservation relation for a material particle in relativistic mechanics can be written formally in the same manner as in Newtonian mechanics.