Spectral Characteristics

Gives some characteristic numbers (energy, pulse length, power, brilliance, etc.) for FELs compared to third generation synchrotron radiation sources

Figure 6

Figure 6: Peak brilliance of XFELs and undulators for spontaneous radiation at TESLA and at the LCLS, Stanford [17], in comparison to the undulators at present third generation synchrotron radiation sources. In addition, also the spontaneous spectrum of an XFEL undulator is shown.

Figure 7

Figure 7: Average brilliance of XFELs and undulators for spontaneous radiation at TESLA and at the LCLS, Stanford [17], in comparison to the undulators at present third generation synchrotron radiation sources. In addition, also the spontaneous spectrum of an XFEL undulator is shown.

Figure 8

Figure 8: Number of photons per mode for the XFELs and undulators for spontaneous radiation at TESLA and at the LCLS, Stanford [17], in comparison to the undulators at present third generation synchrotron radiation sources. In addition, also the spontaneous spectrum of an XFEL undulator is shown. Please note that these curves were derived using Equation (10) with a peak brilliance scaled to a bandwidth Δ λ /λ =1.

As already mentioned, the characteristics of FEL radiation are high power, short pulse length, narrow bandwidth, spatial coherence and wavelength tunability. In this section, some examples will be given that shed light on the differences between the TESLA XFELs and state-of-the-art synchrotron radiation sources to illustrate the exceptional properties of an FEL. Table 1 gives an example of some typical photon beam parameters for one of the planned XFELs at TESLA (a detailed discussion of the properties of all XFEL undulators at TESLA can be found in the TDR Part V, Chap. 4).

Table 1: Photon beam properties of the SASE1 FEL at TESLA. In Chap. 4 photon beam parameters for all FEL devices and also the undulator parameters are presented.
 

Units

SASE1

Wavelength*

Å

1-5

Peak power

GW

37

Average power

W

210

Photon beam size (FWHM)**

µm

100

Photon beam divergence (FWHM)***

µrad

0.8

Bandwidth (FWHM)

%

0.08

Coherence time

fs

0.3

Pulse duration (FWHM)

fs

100

Min. pulse separation****

ns

93

Max. number of pulses per train****

#

11500

Repetition rate****

Hz

5

Number of photons per pulse

#

1.8 x 1012

Average flux of photons

#/sec

1.0 x 1017

Peak brilliance

B*****

8.7 x 1033

Average brilliance

B*****

4.9 x 1025

*Parameters are given for the shortest wavelength.

** Value at the exit of the undulator.

*** Far field divergence.

**** Values determined by the time structure of the electron beam in the accelerator. The average parameters for the SASE-1 FEL are given for the ultimate case when only this beamline is in operation.

***** In units of photons/( sec · mrad2 · mm2 · 0.1%bandwidth).



One of the key parameters to compare different radiation sources is their brilliance3. For partially coherent light sources (wigglers and undulators) the brilliance
[photons/( sec · mrad2 · mm2 · 0.1%bandwidth)] can be calculated from the spectral flux
[photons/( sec · 0.1%bandwidth)] divided by the photon beam's rms radius ∑ and divergence ∑' obtained from convolution of the electron beam and photon diffraction parameters as

img = img

(5)

img = img

(6)

img = img

(7)

In the case of full transverse coherence (e.g. FELs in saturation) ∑ and ∑ are related through

img

(8)

and Equation (5) can be transformed into

img

(9)

This means that the brilliance is simply given by the spectral flux divided by the transverse photon phase space.

As depicted in Fig. 6 the peak brilliance of the TESLA XFELs surpasses the spontaneous undulator radiation from today's state-of-the-art synchrotron radiation facilities by about eight or more orders of magnitude while the average brilliance is about four orders of magnitude higher (Figure 7). The peak brilliance is the brilliance scaled to the length of a single pulse while average brilliance is normalized to seconds at the highest possible repetition rate. Figure 8 shows the number of photons per mode, which can be expressed as

img

(10)

Eight orders of magnitude more photons per mode reflect the improved coherence of the FELs compared to the spontaneous emission of third generation SR sources. In summary, extremely short pulses, high intensity and full transverse coherence are the attractive features of the FEL radiation.

3 Note: In the US the European "brilliance" is mostly called "brightness". "Spectral brightness" is currently the preferred unit in the community.
(see: Report of the Working Group on Synchrotron Radiation Nomenclature – brightness, spectral brightness or brilliance?J. Synchrotron Rad. (2005). 12, 385)