Prestudy of a VUV-FEL for MAX-lab
Sverker Werin
MAX-lab
Chapter and reference numbers are messed up by the HTML conversion!
MAX-lab is now starting to address the construction of a new injector for the two existing storage rings, which would open up possibilities for FEL activities at MAX. If a LINAC serving MAX II with 500 MeV electrons is achieved the very same injector would be able to run a Free Electron Laser in the Vacuum Ultraviolet (VUV FEL). This paper gives an overview of the capabilities of such a laser and the demands it poses on the injector. It is shown that laser action can be achieved for wavelengths down below 50 nm with peak powers over 350 MW.
- Introduction
This study is aimed at giving an preliminar picture of what can be expected from a VUV FEL placed at the intended new injector for MAX II. This aims at giving a firm starting point for future development and, hopefully, project realisation, and as such it should not only give hints of the possible parameters of a VUV FEL, but also build a base for future studies and design.
The MAX II storage ring gives a number of conditions that the injector has to fulfill. These are the base of the FEL activities as well. (see table 1.)
Table 1. The MAX II injector
Energy 500 MeV
RF Multiple of 500
MHz
Energy spread 0.1 %
Emittance 20 mm mRad
This injector should also operate as injector for MAX I (both for SR and pulsestrecher) and as a source for an IR FEL.
- Results
The results of this study show that a FEL built with moderate demands (initial parameters in Table 2) on the overall system will be able to operate down to 50 nm and with options to reach 25 nm (Figure 2). By improving the performance of the injector on one or a few points excellent operation with peak powers of several hundreds of mega watts can be foreseen (Figure 12 and Table 2, refined parameters). The brilliance of the refined case is compared to a set of third generation lightsource undulators and the two main short wavelength FEL projects in the world in Figure 1. (Please observe that these results do not take undulator errors into account. See the special section on errors below).
I propose that this refined set of parameters form the base for the future work with the VUV-FEL injector.
Figure 1. Comparison between different sources. (TTF at DESY, LCLS at Stanford, undulators at MAX II, BESSY II and ALS and a MAX-lab FEL)(additional data from [2]).
- The study
This study is based on a set of assumptions, which should be seen as an example. According to other desires or technical needs they may very well be altered.
- The laser should operate in so called "SASE" mode
(Self Amplified Stimulated Emission). The laser process starts
up from noice in the first part in the undulator and builds up
to a laser pulse towards the end. This excludes the needs for
an optical cavity, which is difficult to achieve at these wavelenghts.
- The undulator is a helical undulator. This gives good electron
beam focusing through the whole undulator, making it easier to
maintain the elctron beam over the fairly large distances needed.
The length is assumed to be 20 m.
- The undulator will be tapered. A taper, starting where the
laser reaches saturation, opens up possiblities to extract even
more energy out of the electron beam than the level at saturation.
- The laser should reach down to < 50 nm giving peak powers at several MW.
Table 2 . FEL parameters
Initial Refined
Wavelength 214 - 53 - 26 nm
5.8 - 23.4 - 47.7 eV
Electron energy 175- 350 - 500 MeV
Peak current 100 A 150 A
Energy spread (HWHM) 0.1% (sE/E = 0.085%) 0.07% (sE/E = 0.060%)
Emittance, normalized 20 mm mRad 10 mm mRad
e Beam radius (x & y) 0.5 mm 0.35 mm
taper begin at 10 m, 3 %, 5 m, 3 %, linear
linear
undulator period 0.035
length 20 m
K-value 0.707 (helical)
Undulator errors (sB) < 0.15 % *)
e pulse length > 1 ps (0.3 mm)
Macropulse rep. rate 10 Hz
Laser pulse length 500 fs
Peak flux (at 53 nm) 2*1025 photons/s 0.1%
Peak brilliance (at 53 6.7*1027 photons/s mm2 mR2
nm) 0.1%
Average flux**) (at 53 5*1018 photons/s 0.1%
nm)
Average brilliance**) 1.7*1021 photons/s mm2 mR2
(at 53 nm) 0.1%
*) Negligible influence seen at this level, further studies needed!
**) assuming populated microbunches at 50 MHz.
Three main wavelength cases have been used in this study: 214, 53 and 26 nm. These correspond to the same undulator settings with three different electron energies: 175, 350 and 500 MeV respectively. A set of initial parameters were defined, which correspond to a "conservative" injector and fair FEL performance (Table 2 initial parameters). These results were then analyzed regarding sensitivity to peak current, energy spread, emittance + electron beamsize. Also undulator taper and undulator errors were looked upon. This gave a new set of "refined" parameters (Table 2). This set gives good FEL performance and the injector is not far away into the extreme. The study was performed using the code TDA [1].
- Initial case
The gain of the FEL increases with the wavelength (Figure 2 with enlargements in Figure 3 and Figure 4). The overall layout on these curves are the same, with minor exceptions. The laser starts up from noice within the electron beam/spontaneous emission and rapidly reaches an exponential gain regime. The gain peaks at some point and saturation is reached (saturation length). Saturation occurs later in the undulator with shorter wavelengths. In this study taper (varying undulator strength by length) is used and sets in after 10 m in the undulator, this extracts more energy from the beam. 10 m is an appropriate choice for the 25 nm case (Figure 3). The laser thus reaches a second region of amplification.
In Figure 3 and Figure 4 (enlargements of Figure 2) it is clearly seen that even after a section with taper a new saturation level is reached, generating the final output power in these examples. The maximum extracted peak power is 20 - 120 MW.
In the following I have concentrated on the case with wavelength 53 nm. The sensitivity of this case to various parameters is given below.
Figure 2. Gain at different wavelenghts.
(The gain is given from the inital power of 1 mW, thus it
equals power in mW)
- Current
In Figure 5 the gain at different peak currents is given (initial case: 100A). The saturation length decrease with more current and the output power increases. By tuning the position and strength of the taper, which was not optimised, the output power can be enhanced.
- Emittance
The electron beam emittance is a key parameter for the electron density in the beam. As mentioned above a helical undulator was chosen for this study as this gives a uniform focusing force in both the vertical and horisontal planes. Further the examples have been tuned to achieve a more or less parallel electron beam through the undulator with no actual waist. The electron beam radius in the simulations for the three different cases of emittances are given in Figure 6.
The three settings effects the gain as shown in Figure 7 (initial case 2.0*10-5). By reducing the emittance and beamsize, the saturation length further decreases and the ouput power increses. (Please compare the "saturation power" as the figure is lying slightly in output power as the taper is not optimised for each case.) I have here not evaluated the possibility of actually placing an electron beam waist in the beginning of the undulator to shorten the gainlenght further.
- Energy spread
One more very critical point is the energy spread (Figure 8). Above it is assumed a spread of 0.35 MeV (0.1% HWHM), and small variations lead to changes in saturation length and output power.
- Linewidth
The linewidth of the emitted radiation is rather difficult to judge from these calculations. By plotting the gain (output power) at the end (20 m) of the undulator an estimate can be achieved (Figure 9). This implies a linewidth sl/l = 0.5 %.
Without an optical cavity for the laser the linewidth will unfortunately be far from fourier transform limited. Instead there is a certain amount of power available defined by the output power. This power will be used to amplify any of the wavelengths within the gain profile present at startup. Thus the exciting radiation will have a linewidth equal to the gain width.
- Optical beamsize
So far nothing has been mentioned about the optical beamsize. Figure 10 shows as an example the optical beamsize for the refined case in Figure 12. At 0 m the value makes a sharp drop, this is due to a given input value ( 1 mW) to the program. The optical mode generated by the electron beam directly takes overhand and grows within the electron beam. At 5 m saturation is approached, and the amplification decreases. At this point the optical mode starts to expand. Around 7 m new amplification is achieved by the taper in the undulator and the optical mode is focused down slightly. When the amplification slows down after 15 m the optical modes starts to grow again.
The optical mode is diffraction limited throughout the undulator, with in principle a large divergence. The reason for not expanding rapidly is the "focusing" supplied by the strong amplification. New photons are added but only within the electron beam .
- Undulator errors
The undulator errors described by the simulation tool used refers to the RMS errors in peak magnetic field. The size of the problem grows quite significantly when errors are introduced, and the "error noice" in the calculations is difficult to suppress, while at the same time the calculation times grows sharply.
The analysis (Figure 11) shows that a sK = sB = 1*10-3 (K is the undulator parameter and B the magnetic field in the undulator) is well acceptable, while if the errors grow to 5*10-3 it is not. (This translates into sB / B = 0.14 % and 0.71 %) On the other hand a funny effect is seen: the saturation power increases with errors, while the power extracted by the use of taper decreases. At the same time it must be stressed that the numerical errors in these simulations increase at lengths over 15 m. All this indicates that a more thorough analysis of undulator errors must be done.
- Refined case
All the factors discussed above opens up for a FEL which is "one step better" at several points compared to the initial case of Table 2:
- current 150 A (100)
- emittance 1*10-5 m Rad(2*10-5 )
- energy spread 0.5 MeV (0.7 MeV)
- taper beginning at 5 m (10)
By introducing these improvements the result is boosted by a fair amount (Figure 12). The ouput power has grown to 350 MW, and still it is not optimized. In the other end one can see that the undulator can be reduced to a mere 7 m and still output powers above 100 MW can be reached.
- Subsystems
- Acceleratorsystem
The acceleratorsystem is regarded as the whole system starting with the electron gun, prebuncher, pulseformers, linear accelerator (LINAC) and bunchcompressors. The demands given above, can only be fulfilled by a careful design and cooperation of all or several of these systems.
- Transport line
The transport line from the LINAC output to the FEL undulator must fulfill certain criteria, though none seems too difficult. It must be tunable to form the electron beam size to the actual optical size needed under different conditions in the undulator.
- Undulators
For this study a helical undulator is chosen. This is a complexity in the design which might show to be too big. The reason for this choice, though, is that the undulator itself provides focusing in both the horisontal and vertical plane. This gives the possibility to easily conserve the electron beam size through the undulator. Another choice would be a planar undulator built in sections with focusing applied between the different sections, or other means of focusing within the undulator structure.
Neither the period nor the excitation in the undulator should pose any problems. The difficulties lie rather in the exceptional length of the device and the demands on undulator errors. If tuning of the undulator is not required the construction will become easier, which implies that tuning takes place by energy shift out from the LINAC. Rapid tuning though will need changes in the undulator fields.
Table 3. Undulator data
Type helical
K-value 0.707 (or
variable)
Period 0.035 m
Length 20 m
Errors, sB 0.15 %
Start-up from noice
The principle for start up of the SASE process from noice is not completely understood. The priniple is proved in operation in the long wavelength region but no experience exist in the VUV. In the FEL community there is no real worry on this point, the question is rather on how fast the process starts up. The first actual results in the wavelengthregion in question will come from the Tesla Test Facility (TTF) [2] in Hamburg early 1998. Models discussed briefly during the workshop "Advanced Technologies for generating VUV radiation" (Daresbury GB, 1997) point towards the proceess normally starting faster than predicted by the available simulation codes.
- Simulation tools
This study is performed by the use of the code TDA[ ]. This code is well established and tested against other codes with good results [] . The code is set up on a SUN-SPARC station under UNIX, unfortunately giving long computation times compared to the original CRAY version.
- References