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In linear beam dynamics transverse motion of particles can be treated separately in the horizontal and vertical plane. This can be achieved by proper selection, design and alignment of beam transport magnets. Fabrication and alignment tolerances, however, will introduce, for example, rotated quadrupole components where only upright quadrupole fields were intended. In other cases like colliding beams for high energy physics large solenoid detectors are installed at the collision points to analyse secondary particles. Such solenoids cause coupling which must be compensated.

Transverse and longitudinal beam dynamics as discussed in earlier chapters is governed by purely single-particle effects where the results do not depend on the presence of other particles or any interactive environment. Space-charge effects were specifically excluded. This restriction is sometimes too extreme and collective effects must be taken into account where significant beam intensities are desired. In most applications high beam intensities are desired and it is therefore prudent to test for the appearance of space charge and other intensity effects.

While discussing self fields of a charged particle bunch, we noticed a significant effect from nearby metallic surfaces. The dynamics of individual particles as well as collective dynamics of the whole bunch depends greatly on the electromagnetic interaction with the environment. Such interactions must be discussed in more detail to establish stability criteria for particle beams.

Ever since J.C. Maxwell formulated his unifying electromagnetic theory in 1873, the phenomenon of electromagnetic radiation has fascinated the minds of theorists as well as experimentalists. The idea of displacement currents was as radical as it was important to describe electromagnetic waves. It was only 14 years later when G. Hertz in 1887 succeeded to generate, emit and receive again electromagnetic waves, thus, proving experimentally the existence of such waves as predicted by Maxwell’s equations. The sources of the radiation are oscillating electric charges and currents in a system of metallic wires. In this text, we discuss the generation of electromagnetic radiation emitted by free electrons from first principles involving energy and momentum conservation as well as Maxwell’s equations.

After Schott’s [1] unsuccessful attempt to explain atomic radiation with his electromagnetic theory no further progress was made for some 40 years mainly because of lack of interest. Only in the mid 1940s did the theory of electromagnetic radiation from free electrons become interesting again with the successful development of circular high-energy electron accelerators.

The phenomenon of synchrotron radiation has been introduced in a conceptual way and a number of basic relations have been derived. In this chapter we will approach the physics of synchrotron radiation in a more formal way to exhibit detailed characteristics. Specifically, we will derive expressions for the spatial and spectral distribution of photon emission in a way which is applicable later for special insertion devices.

Synchrotron radiation from bending magnets is characterized by a wide spectrum from microwaves up to soft or hard x-rays as determined by the critical photon energy. To optimally meet the needs of basic research with synchrotron radiation, it is desirable to provide radiation characteristics that cannot be obtained from ring bending magnets but require special magnets. The field strength of bending magnets and the maximum particle beam energy in circular accelerators like a storage ring is fixed leaving no adjustments to optimize the synchrotron radiation spectrum for particular experiments.

Synchrotron radiation is emitted when electromagnetic fields exert a force on a charged particle. This opens the possibility to apply external fields with specific properties for the stimulation of electrons to emit more radiation.