1. Undulator parameters choice/wish based on a simplified XFEL cost model Jürgen Pfingstner 29 st of July 2015

2. Content 1.Motivation: Tolerance studies 2.Undulator parameters and cost

3. 1. Motivation: Tolerance studies

4. Undulator tolerance studies Motivation: Undulator imperfection increase undulator saturation length and reduce X-ray output power. Tolerances for the following quantities (and others) have to be specified: – Beam jitter. – Phase errors: break length, phase shifter accuracy, phase error of undulator magnet. – Undulator field strength errors. – Undulator mechanical alignment: vertical, horizontal. – Undulator jaws misalignment: pitch, roll, gap, horizontal shift. Main reference (so far): paper from H.D. Nuhn et al. (FEL2011) collects experience from tolerance studies from LCLS-I and the European XFEL. Strategy is used for LCLS-II undulator design and supposedly also for the PAL FEL (same structure). Strategy of studies: some basic undulator simulation results (GENESIS tolerance studies) are extended to predict other tolerances.

5. Problems with the tolerance studies Results could be specific to the undulator and beam parameters. Hence, it is necessary to have a realistic undulator module. Two issues have to been handled before the tolerance studies can start: 1.Undulator section parameters: The undulator has been mostly overtaken from the SwissFEL. But are these parameters the best for our goal of minimal cost? Some more insides about the cost relations are necessary. Simplified cost model. 2.The beam optics of the undulator section So far beam optics has been designed to be a simple FODO lattice. Weak focusing of undulator is not take into account. Beta-function is distorted. Adapted optics design is necessary.

6. 2. Undulator parameters and cost

7. Cost scaling with beam energy E Question: Which undulator parameters server or goal of cost minimization best? -Is it better to go to higher energy and simplify the undulator design? -Or should the undulator be as fancy as possible? Method: Establish a simplified cost model to answer this question. -Scope of this model is not a detailed cost estimate. -Only the relative cost of different contributions are compared. -The cost C is evaluated for different final beam energy E but the same/similar X-ray properties (λ γ, P γ ). Model: C L (E) … Linac cost C U (E) … Undulator cost C F … Fix cost Fix costs include all energy independent costs: gun, injector, laser heater, bunch compressors, bunch spreader, collimation system, photon beam lines, experimental area, and buildings to house these systems.

8. Linac cost The cost of the linac is estimated based in the current parameters. No parameter optimization options have been implemented. c LM … Linac module cost per metre (including RF). c B … Building cost per metre. L L … Linac length. E… Final beam energy. E inj … Beam energy after injector. g… Acceleration gradient. f L … RF filling factor of linac. N str … Number of cavities per module. L str … Length of one structure. L LM … Linac module length C LM … Cost of one linac module. C l_sup … Support, vacuum, and cooling. C guide … Wave guides, LLRF. C kly … Cost for klystrons. C mod … Cost for modulators. C bpm … BPM cost. C qp … Quadrupole cost.

9. Undulator cost scaling: -Saturation length L SAT increases linear with E. -But for high E one can go to higher λ u and cost/metre should go down. -Wild guess for a cost scaling s und (E): -Help from undulator experts needed. Undulator cost The cost of the undulator is calculated in the same fashion as for the linac.

10. Comment on X-ray power When changing the beam energy, it is assumed that the X-ray wavelength λ γ stays the same. Therefore the undulator period λ u has to be changed according to We assume that K can be kept at about the same level. In this case also the X-ray output power P γ is changed as This scaling is relatively weak however. E.g. E from 6 to 4GeV (33%), P γ reduced by 42%. This reduction is small for FEL power relations, where one talks about orders of magnitudes. The power loss can be compensated by adding few modules for tapering. Hence we assume that power level can be chosen nearly independent of the undulator parameters. Tapering is not the standard in nowadays FEL’s operation. It has to be investigated why!

11. Comparison C-band and X-band machine (used parameters) Two machines (C-band and X- band) are compared. C-band parameters adapted from SwissFEL. X-band parameters are according to our design. Linac filling factor has been increase for X-band (in blue, 6% linac cost reduction). Only the relation of the costs to each other is considered. Therefore costs are given in arbitrary units [a.u.].

12. Comparison C-band and X-band machine (absolute cost) Undulator cost scaling with E. Relation of linac and undulator cost. Implications for design. Relation to fix costs at 6 GeV.

13. Conclusions: Undulator parameters Linac is the clear cost driver of an XFEL and it scales linear with energy. Undulator cost is comparable small (even for very advanced designs). Hence, the energy has to be reduced as much as possible. For the same X-ray wavelength this can only be done with more advanced undulator designs: Therefore, design is driven to as low E as possible, with as fancy undulators as available. E.g., 1cm instead of 1.5cm undulator, E can be reduced from 6 to 5 GeV. This can also be seen in the historical development of XFELs at the Å-level: – First generation (LCLS1): 16 GeV beam, with 3 cm out-of-vacuum undulator. – Second generation (SACLA, SwissFEL): 5-6 GeV beam, with 1.5 cm in-vacuum undulator. Example for X-band: λ u of 1 cm instead of 1.5 cm, E from 6 to 5 GeV.

14. Comparison C-band and X-band machine (relative cost) Relative cost saving W is defined as: For higher E, W approaches the saving for only the linac. For lower E, fix costs reduce W. Undulator cost influences W only weakly.

15. Conclusions: Relative cost Maximal possible win W is about 40% if only a linac would be build. – 2.4 times the gradient would suggest about 60% win. – But higher gradients need more klystrons and modulators per metre. For our energy range (5-6 GeV), fix cost determine strongly the remaining win: – 150 a.u: W = 20% – 100 a.u: W = 23% – 50 a.u: W = 29% – 0 a.u: W = 37% To make the best out of the X-band technology, fix costs have to be reduced wherever possible. The absolute cost can be also reduced by going to smaller beam energies if the undulator technology allows for that.

16. Possible improvements to the model Improvements of the current model – Undulator cost scaling should be revised with undulator experts. – Many component prices are rough estimates and should be revised with experts. Model extensions: – Power consumption cost. – A more detailed evaluation of the fix cost (pure guess at the moment). Implementation of optimization capabilities: – At the moment, the model only adds up the costs of the current layout. – No capabilities for an optimization of the subsystems (e.g. linac, undulator) has been added so far. – Such optimizations could probably be included in the current model if desired by the designer of the subsystems.

17. Discussion: Undulator parameters optimization Reduced undulator wavelength reduces linac cost. Are there new developments in the undulator design that could be used? There are already undulators with shorter period length, but K value is drastically reduced. Tradeoff for minimal cost could be found with the cost model and information about undulator development. Interesting information from Avni: wake field issues at the SwissFEL. This may require more conservative design

18. Thank you for your attention!