Note on cylindrical waves which propagate at the velocity of light
Abstract
The continuous linear acceleration of ultra relativistic particles in free space by an electromagnetic field requires the presence of a cylindrical wave component with phase velocity that differs negligibly from c and with nonvanishing electric field component in the direction of propagation. Certain geometries proposed for laser driven acceleration fail to satisfy these requirements. On the other hand, complex wave number plane wave fields which do satisfy these requirements were constructed. It is pointed out that any cylindrical wave with the required properties can be formed from superposition of plane waves of the form which was obtained. The situation is analogous to that which occurs in standard waveguide theory. There it is also true that any waveguide mode can be constructed by superposition of plane waves. Nevertheless, the study of the general properties of cylindrical waves has proved to be a very powerful tool for the analysis of waveguides and similar structures.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 April 1982
 Bibcode:
 1982STIN...8328311K
 Keywords:

 Cylindrical Waves;
 Propagation Velocity;
 Wave Propagation;
 Waveguides;
 Electromagnetic Fields;
 Linear Accelerators;
 Plane Waves;
 Relativistic Particles;
 Superposition (Mathematics);
 Communications and Radar