Optimal Compound Multi-Segment Cooling Method for High-Heat-Load X-Ray Mirrors

Fig. 2. Absorbed power density distribution of M1 at energy of 7.0 keV with grazing angle of 1.9 mrad. (a) Spontaneous radiation; (b) FEL fundamental radiation; (c) third harmonic radiation; (d) total power

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Fig. 3. Heat load distribution at each characteristic energy point in M1. (a) Meridian direction of reflector;(b) sagittal direction of reflector

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Fig. 4. Mirror cooling model and FEA model. (a) Mirror cooling structure; (b) enlarged view of mirror cooling structure; (c) FEA model of mirror cooling structure; (d) enlarged view of FEA model of mirror cooling structure

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Fig. 5. Temperature distribution after ray with energy of 7.0 keV incident on M1 mirror at grazing angle of 1.9 mrad

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Fig. 6. Thermal deformation of M1 mirror in meridian direction at each characteristic energy point

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Fig. 7. Thermal deformation after X-ray with energy of 7.0 keV incident on M1 mirror at grazing angle of 4.0 mrad under different cooling fin lengths

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Fig. 8. Residual height error after X-ray with energy of 7.0 keV incident on M1 mirror at grazing angle of 4.0 mrad under different cooling fin lengths

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Fig. 9. Schematic diagram of multi-stage compound cooling structure

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Table 1. Parameters for accelerator used in simultaneous radiation simulation

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Table 1. Parameters for accelerator used in simultaneous radiation simulation

Device	Parameter	Value
Electron beam	Electron energy /Gev	8
	Bunch charge /pC	100
	Average current /mA	0.1
	Peak current /A	1000
	Pulse duration /fs	100
	Emittance /（μm·rad）	0.4
	Repetition rate /MHz	1
Undulator	Peak magnetic field /T	1
	Period /mm	26
	Undulator length /m	4
	Number of segments	42
	Distance between segments /m	1

Table 2. Light source parameters under different photon energies
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Table 2. Light source parameters under different photon energies
Photon energy /keV 3.0 7.0 12.4 15.0
Bunch charge /pC 100 100 100 100
Electron energy /GeV 5 8 8 8
Pulse energy /μJ 930 1800 394 60
Source size（FWHM）/μm 49 48 50 50
Source divergence（FWHM）/μrad 5.5 2.7 1.7 1.3

Table 3. Material parameters in FEA

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Table 3. Material parameters in FEA

Material	Density /（kg·m^-3）	Elastic modulus /GPa	Yield stress /MPa	Poisson ratio	Thermal conductivity /（W·m^-1·K^-1）	Thermal expansion coefficient at temperature of 300 K /（ $10^{- 6}$ K^-1）
Silicon	2329	112.4	120	0.28	148	2.50
Copper	8900	110.0	220	0.34	391	1.75
In/Ga	6350				28

Table 4. S_R of M1 mirror under different energies
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Table 4. S_R of M1 mirror under different energies
Energy /keV
Grazing
angle /mrad
Total heat /W Simulated S_R
3.0 4.0 18.90 0.17
5.0 4.0 28.60 0.12
7.0 4.0 38.20 0.15
1.9 37.10 0.16
12.4 1.9 9.23 0.29
15.0 1.9 1.72 0.70

Table 5. Optimum cooling fin lengths under different energies
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Table 5. Optimum cooling fin lengths under different energies
Energy /keV Grazing angle /mrad Optimum cooling fin length /mm
3.0 4.0 156
5.0 4.0 109
7.0 4.0 53
1.9 148
12.4 1.9 64
15.0 1.9 65

Table 6. S_R under different energies after comprehensive optimization
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Table 6. S_R under different energies after comprehensive optimization
Energy /keV Grazing angle /mrad Total heat /W Simulated S_R
3.0 4.0 18.90 0.30
5.0 4.0 28.60 0.26
7.0 4.0 38.20 0.35
1.9 37.10 0.27
12.4 1.9 9.23 0.60
15.0 1.9 1.72 0.93

Table 7. Nominal heat load and working repetition rate before and after optimization at S_R=0.96

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Table 7. Nominal heat load and working repetition rate before and after optimization at S_R=0.96

Energy /keV	Grazing angle /mrad	Before Optimization		After Optimization		Repetition rate ratio
Energy /keV	Grazing angle /mrad	Total heat /W	Repetition rate /kHz	Total heat /W	Repetition rate /kHz	Repetition rate ratio
3.0	4.0	0.63	33.3	1.89	100	3.0
5.0	4.0	0.57	20.0	1.57	55	2.8
7.0	4.0	0.48	12.5	3.06	80	6.4
7.0	1.9	0.62	16.7	1.86	50	3.0
12.4	1.9	0.37	40.0	3.07	333	8.3
15.0	1.9	0.43	250.0	0.86	500	2.0

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Zhen Wang, Yajun Tong, Xiaohao Dong, Fang Liu. Optimal Compound Multi-Segment Cooling Method for High-Heat-Load X-Ray Mirrors[J]. Acta Optica Sinica, 2022, 42(23): 2334003

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