CÓDIGO DE ÉTICA PARA INSPECTORES DE RECUBRIMIENTOS

In this section the basic properties of SR are briefly illustrated. A much more detailed description and discussion about SR and their properties can be found in several review articles and text books [79-82]. From classical electrodynamics it is well known that an electron emits electromagnetic radiation when accelerated. In the non-relativistic case (β = v/c << 1) the radiation emitted from an electron moving in a circular orbit has a doughnut-like pattern with dipole characteristics and an energy on the order of neV. If the electron is accelerated up to relativistic speeds (β≅ 1) this pattern gets transformed through the Lorentz transformation and

the angular distribution of the emitted radiation seen from in laboratory frame is concentrated in a cone with the small emission angle of

1/γ = mc2 / E [GeV], (4.1) where E is the particle energy. This radiation from relativistic electrons was first observed in 1947 by Elder et al. at the General Electric synchrotron in Schenectady, New York, and hence named synchrotron radiation [83]. While at first this radiation was more an unwanted parasitic effect, it was soon realized that it could be of great use as an intense and tunable radiation source. In fact, in the last twenty years many new accelerators and electron storage rings have been designed and constructed for the exclusively use of SR.

In order to keep the electrons in a circular orbit they have to be accelerated by dipole bending magnets (BM) which deflect them from their straight path. The bending radius R of such a BM depends on the particle energy E and the magnetic field B of the magnet with R= 3.335 E[GeV]/B[T]. Even though the whole electron storage ring is kept in ultra high vacuum (UHV), the electrons still suffer energy loss due to the emitted radiation and Coloumb interactions between each other. This results in the loss of electrons since an electron with less energy can no longer follow the prescribed path in the ring, and leads to the necessity of refilling the storage ring with electrons after a certain time, typically on the order of once or twice a day.

One of the advantages of SR is the well defined and reproducible x-ray beam. In order to achieve this, the electron beam in the storage ring has to be very well controlled. But the dipole magnets which bend the electrons on the circular orbit and therefore produce synchrotron radiation also disperse the electron beam. Therefore quadrupole and sextupole magnets have to be used to correct for the dispersion and refocus the electron beam to its original size and dispersion. The most important concept of such an arrangement of dipole, quadrupole and sextupole magnets, mounted in pairs to focus in both dimensions, is the Chasman-Green lattice which was developed for the National Synchrotron Light Source (NSLS) and is now used in most modern SR sources in the world.

A crucial feature of synchrotron sources compared to the standard x-ray sources is the broad spectrum emitted from the circulating electrons. The critical wavelength λc is defined as the

half power point of the spectrum. The critical wavelength is given by

λc = 5.59 R[m] /E3[GeV]. (4.2)

The long wavelength limit of the synchrotron spectrum is given by the electron-orbit frequency, which is typically in the ns or µs range. The spectrum falls off rapidly for wavelength shorter than λc and at λc/6 has only 1% of the maximum. Often instead of the

critical wavelength λc the critical energy Ec is used, which is given by

Ec = 2218 E3[GeV]/R[m] = 665 E2[GeV] B[T]. (4.3)

Figure 4.1 The total flux and brightness for several beamlines at three synchrotron sources (NSLS, ALS and APS) with different critical energies Ec. BM denotes the bending magnet

beamlines, U, X1 and UA the undulator beamlines, W, EPW X21, X25 and WIGA wiggler beamlines at the particular x-ray rings (plot made by S.Hulbert).

Generally the properties of different light sources can be compared in terms of the spectral flux, brightness and brilliance, with the following definitions:

Flux: photons emitted per second with the photon energy E and a band pass of ∆E/E = 0.1%. Brightness: same as Flux normalized for an horizontal acceptance angle ∆α = 1 mrad2. Brilliance: same as Brightness normalized to a source size of 1 mm2

A comparison of the total flux and brightness of several SR sources is shown in figure 4.1. The difference in their operating electron energies can be directly seen in the shift of the critical energy Ec. In addition to the higher photon energies the collimation of the radiation and the

lifetime of the electrons in the storage ring improves with the increase in the electron energy. On the other hand, radiation protection becomes more difficult. Considering (4.3) there are two ways to shift the critical photon energy Ec to higher values, minimizing the Radius R or

increasing the particle energy E. The more effective way is changing the latter parameter, since the increase in the critical energy goes with the third power of E and only linear in R. Furthermore the smallest R is limited by the maximum magnetic field B of the BM technically possible, which is about 10 Tesla. It should be noted that at most storage rings the applied field at the BM is in the order of 1 Tesla or lower in order to allow a high number of experimental stations, which is proportional to the number of bends.

Angular Polarization of Synchrotron radiation

Another important property of synchrotron radiation is the well defined angular distribution of its polarization. In the orbit plane the circulating electrons emit 100% linear polarized light, but with increasing elevation angle ψ above or below the orbit plane the x-rays become more and more circularly polarized, with an accompanying decrease in intensity. Figure 4.2 shows a typical example calculated from a BM at the NSLS for a photon energy of 7112 eV. In order to receive 75% circularly polarized rays one looses about half of the intensity. Carrying out experiments using circularly polarized light from a BM is always a trade off between the gain in the degree of circular polarization Pc and the loss in intensity I. Assuming Possion statistics

I P

FOM = _c2⋅

, (4.4)

and is plotted in figure 4.2. For the conditions shown here (NSLS, 2.8 GeV ring energy, photon energy of 7112 eV), the trade off between intensity loss and the degree of circular polarization, Pc, x-rays is optimized for an elevation angle, ψ, of about 0.9 mrad. The light is about 70%

circularly polarized, but has suffered about 40% loss of intensity.

Figure 4.2 degree of circularly polarization Pc (full line) and normalized

intensity (dashed line) with elevating angle from the orbit plane (ψ = 0 mrad).

0.0 0.1 0.2 0.3 0.4 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

degree of polarization

circular polarization

normalized intensity

figure of merit

normalized intensity

ψ

[mrad]

Insertion devices

One of the most important features in the Chaseman-Green lattice is the inclusion of dispersion free straight sections. These straight sections are used for radio frequency (RF) cavities providing energy to the circulating electrons, for quadrupole and sextupole magnets that focus the electron beam, for the electron injection line and in particular for insertion devices (ID). These IDs consist of periodic magnetic structures, which “wiggle” the electron trajectory in the straight section of the storage ring but avoid any net deflections or displacements of the electron beam from its original orbit in order not to affect the operation at the BM. The parameter characterizing ID’s is the deflection parameter K, defined as

c m B e K u π λ = 2 0 , (4.5)

with λu is the magnet period and B0 the magnetic field at the insertion device. This K parameter

describing the motion of the electron beam in an ID classifies the different devices. The maximum deflection angle of the orbit is

γ =

δ K . (4.6)

For K≤1 the insertion device is called undulator. The deflection angle δ is smaller than 1/γ and therefore the emitted photons stay in a narrow cone and can interfere with the radiation caused by the next bend of the electrons. This leads to coherent interference of the radiation of a single electron from the different magnetic periods of the ID’s and instead of a continuous spectrum a line spectrum with sharp peaks are observed at the wavelengths

) ½ 1 ( 2 2 2 K n u n + γ λ = λ , (4.7)

with n = 1, 3, 5 … (only odd harmonics have a non-zero contribution to the intensity in the orbit plane). Due to the coherent interference the intensity produced from the magnetic structure of an undulator scales with N2, where N is the number magnetic periods, and leads to a large increase in brightness and flux compared to that of a BM.

For insertion devices with long period lengths λu of the magnetic structure or high magnetic

fields B0 the parameter K becomes much larger than one, K >>1 and the ID is called a wiggler.

The radiation emitted from every magnetic pole adds incoherently and thus leads to a continuous spectrum similar to that of a bending magnet, but with a critical energy determined by the peak field in the magnetic structure of the wiggler. Within the deflection opening angle δ in (4.6) the intensity is 2N higher than from a bending magnet with the same critical energy. Leaving the orbit plane the elliptically polarized light produced from every half pole combines with the light from the next one and since they are of opposite sign the circular polarization cancels. Therefore the radiation produced by a wiggler is linearly polarized even above or below the orbit plane. However, these devices can be modified to tailor them for special applications or demands in polarization. Such an insertion device will be discussed in detail in the next section where a special multipole wiggler is installed at the X-13 beamline at the NSLS in order to produce circularly polarized x-rays in the orbit plane.

(c)

(b)

(a)

Figure 4.3 Experimental setup of X-13 beamline at the National Synchrotron Light Source at Brookhaven National Laboratory. (a) shows the X-13 straight section with the implemented Elliptical Polarized Wiggler (EPW). In (b) the beamline setup is depicted with both sections, the hard x-ray beamline X-13B going straight and the soft x-ray beamline, X-13A, where the x-ray beam is deflected by a small angle. (c) presents a side view of the X-13A beamline.