ABSTRACT
Figure 2.2 On the left is a sketch of a bending magnet with the speed of the electrons ve-, the field B, the resulting force FL and the horizontal deflection angle fh. On the right is a sketch of a circular storage ring with the polygonal path of the electrons and the bending magnets. The diameter of the ring is denoted by DSR. At the bending magnets, the electrons are kicked by the Lorentz force to follow the storage ring curvature. This kick means accel-eration. From electrodynamics, it is well known that an accelerated charged particle radiates dipole radiation [see 2]. Therefore, this radiation appears at each of the bending magnets. In the non-
relativistic case, the field of the dipole radiation is concentrated on a ring around the center with the ring radius perpendicular to the acceleration direction, which is parallel to the force (see Fig. 2.3). However, at storage rings, the kinetic particle energy Eke-is some gigaelectron volts and the speed ve-of the electrons, given in units of the speed of light c, can be calculated using the following equation:
vc EE Ee ee ke--- -= - +ÊËÁ ˆ¯˜1 00 2 , (2.1)where the rest energy of an electron E0e-= m0e-c2 ª 0.51 MeV, and the rest mass of an electron m0e-ª 9.1 ◊ 10-31 kg. From this follows that for, for example, 1 GeV electrons, the speed is ve-= 0.9999999◊c, which consequently means that they move in a highly relativistic manner. At this speed, the relativistic aberration of light deforms the dipole radiation to a fan which is extremely collimated toward the forward direction [3]. The opening angle f of the radiation is f = - Ê
ËÁ ˆ ¯˜
= - - +
Ê
ËÁ ˆ
¯˜
È
Î
Í Í
˘
˚
˙ ˙ = +
Figure 2.3 Isosurfaces of dipole radiation calculated at different ve-. The effect of the relativistic aberration creates a beam radiating in (longitudinal) forward direction. See the text for explanation of the symbols.
