Wake-field generated by a line charge moving in the vicinity of a dielectric cylinder

The wake-field generated by a moving line charge in the vicinity of a dielectric cylinder is analyzed. It is shown that the emitted energy increases logarithmically with the kinetic energy ðg 1Þ of the line charge and decays exponentially as a function of the ratio h=R; where R is the cylinder radius and h is the distance of the line charge from the cylinder’s axis. Upon investigation of the angular distribution of the radiated energy we found it to be almost uniform in the nonrelativistic case, whereas for the relativistic case most of the emitted energy is radiated parallel to the direction of motion of the line charge. For a relativistic regime, the emitted energy is almost independent of the cylinder dielectric coefficient ðerÞ provided the latter is frequency-independent. Frequency dependence of er reduces significantly the deceleration of the line charge. For the ultra-relativistic case the transverse kick is inversely proportional to the kinetic energy and, as expected, increases as the line charge gets closer to the cylinder. Finally, a finite size bunch has been considered. As the transverse width of the bunch is increased, the total emitted energy also increases and the spectrum is broadened. r 2002 Elsevier Science B.V. All rights reserved. PACS: 41.60. m; 29.27. a; 87.64.Dz