Chapter 1
Synchrotron Light Sources

Zhentang Zhao

Shanghai Synchrotron Radiation Facility, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, 239 Zhangheng Road, Pudong New District, Shanghai, 201204, China

1.1 Introduction

Synchrotron light sources or storage ring light sources are indispensable large-scale scientific tools for basic and applied frontier research in various fields, ranging from materials science, energy science, life science, environmental science, to archaeological applications. Their development has evolved from the first generation to the third generation in the past five decades, and has now entered into the fourth generation phase with even higher brightness and coherence radiation based on the diffraction limited storage ring concept. Currently, there are over 50 synchrotron light sources in operation in more than 20 countries, and over 15 new synchrotron radiation facilities have been set up worldwide in various stages of commissioning, construction, design, or planning. In this chapter, we will introduce the basics of synchrotron radiation generation, storage ring physics, and radiation characteristics, which are of interest to synchrotron radiation users. We will also present the current status of the storage ring light source development across the world. This chapter is intended to cover only the basic concepts of synchrotron light source and review the current status on its development. For readers who are interested in the detailed physics and related technologies, we recommend the books or monographs in Refs [1-15].

1.2 Synchrotron Radiation Generation

When a relativistic electron moves on a curved path at nearly the speed of light, it emits electromagnetic radiation. This radiation was theoretically predicated and studied by Lienard, Wiechert, and Schott in around 1900, and its visible part was first observed at the 70 MeV GE electron synchrotron in 1947. Since then, this electromagnetic radiation has been called synchrotron radiation.

Synchrotron, a kind of circular particle accelerator, can accelerate charged particles from low energy to high energy or keep the particles circulating on the circular orbit at a constant energy for hours and days, which is referred to as storage ring. The electron storage ring is the core part of synchrotron light source. Relativistic electrons, circulating in the storage ring, generate synchrotron radiation when passing through three on-path major source components: the bending magnet, wiggler, and undulator magnets, as shown in Figure 1.1.

Figure 1.1 Synchrotron radiation from bending magnets, wigglers, and undulators [3].

(Cambridge University Press.)

This synchrotron radiation is extremely intense over a broad range of wavelengths from infrared through the visible and ultraviolet range, to the soft and hard X-ray part of the electromagnetic spectrum. Bending magnet radiation has broad spectrum and good photon flux; wiggler radiation provides higher photon energies and more photon flux; and undulator provides brighter radiation with smaller spot size and partial coherence.

1.2.1 Radiation from Bending Magnet

A bending magnet, also called a dipole magnet, consists of opposite poles, namely the north and south poles, which are on opposite sides of the magnet providing a homogeneous magnetic field.

As shown in Figure 1.2, when a relativistic electron of energy E travels on a circular trajectory in a dipole magnet of main field By = B and bending radius ?, where G = B? = p/e, the ratio of momentum to charge, is often called the magnetic rigidity, it radiates electromagnetic power confined in a cone with ±1/? opening toward its moving direction. Its radiation power can be expressed as,

where e is the electron charge, m0 is the electron rest mass, ßc is the electron moving speed, ? = E/(m0c2) is the Lorentz factor, and is the electron classical radius. Integrating the radiated power over an isomagnetic storage ring with constant ? gives an electron energy loss in one turn due to the synchrotron radiation as follows,

Figure 1.2 Synchrotron radiation from bending magnet.

In engineering units,

For an electron beam traveling through a dipole magnet of bending angle ?? with average current of Ib, the radiated power is,

For an electron beam circulating in storage ring (with average current of Ib and revolution time of T0), the total radiated power per turn is,

When an electron travels on the circular path in a dipole magnet, its emitting radiation on a fixed target outside the orbit circle comes only from a short arc of electron trajectory, this short synchrotron radiation pulse covers a wide continuous spectrum of photon energies from infrared to X-rays depending on the electron energy and the bending magnetic field. A so-called critical photon energy ?c (or critical frequency ?c) is defined as the photon energy which divides the synchrotron radiation into two spectral regions with equal radiated power,

In engineering units,

The significance of the critical photon energy is that it sets up the upper bund for the synchrotron radiation spectrum, and the spectral power falls rapidly for photon energies above this critical value. The complete spectral distribution of synchrotron radiation can be calculated using the Fourier transform of the radiation electric field,

The K5/3(x) above and K2/3(x) below are the modified Bessel functions. The on-axis spectral photon flux (defined as the number of photons per unit time) per unit solid angle in a bandwidth ??/? and for a circulating beam current Ib is a more useful parameter. It can be written as,

where a = e2/(2ch?0) is the fine structure constant. In engineering units, and with 0.1% bandwidth,

The on-axis photon flux per unit deflection angle is,

The photon flux at energy ? is given by,

and by integrating the photon flux for ? from zero to infinity, the total number of radiating photons per unit time is,

The total photon flux at energy ? for the storage ring with average beam current Ib is,

The total photon flux

1.2.2 Radiation from Undulator

Undulator and wiggler, or so-called insertion devices, consisting of a series of alternating magnet poles, deflect the electron periodically in opposite directions. They are installed in the storage ring straight sections and optimized for generating specific synchrotron radiation characteristics.

1.2.2.1 Planar Undulator Radiation

The radiation from planar undulator with Nu period has the same physical process as a short bending magnet, but the Nu times of oscillations that an electron performs in an undulator transform the radiation into quasi-monochramatic with finite line width and within a cone of . This makes the planar undulator radiation intensity effectively enhanced with reasonable radiation power (Figure 1.3).

Figure 1.3 Synchrotron radiation from undulator.

In a planar undulator with period length ?u and peak field B0, the main magnetic field is By = B0 sin(2ps/?u), and the average instantaneous radiation power of an electron traveling in planar undulator is,

where K is the so-called deflection parameter and is defined as,

The total energy emitted by an electron from the undulator with a length of Lu = Nu?u is,

The total average radiated power of an electron beam with current of Ib passing through the undulator is,

In engineering units,

Owing to the cooperative effect of radiation from different periods, the undulator radiation has line spectral characteristics. Its radiation wavelength, or photon energy at the nth harmonic, can be expressed as,

with the line width,

where n = 1, 3, 5, . is the harmonic number of radiation line, ?n = 2pc/?n, ??n = ?-n?1.

In the storage ring with circulating current Ib, the total on-axis undulator photon flux per unit solid angle is,

where a = e2/(2?0hc) is called the fine structure constant and Jm(k) is the Bessel function. In one measurement of a typical experiment, only one harmonic radiation is directed to the sample, and therefore, the radiation characteristics at specific wavelength and its tuning range is of great significance. As a more important parameter, the on-axis photon flux per unit solid angle at the nth harmonic is,

The on-axis photon flux at the nth harmonic is,

In engineering units of per 0.1% bandwidth,

1.2.2.2 Helical Undulator Radiation

The helical undulator has both horizontal and vertical field components, Bx = Bx0 sin(2ps/?u-f) and By = By0 sin(2ps/?u), which periodically vary in a sine wave with a period of ?u along its longitudinal direction. It is widely used for generating...