1. NEW COMMENTS TO ILC BEAM ENERGY MEASUREMENTS BASED ON SYNCHROTRON RADIATION FROM MAGNETIC SPECTROMETER E.Syresin, B. Zalikhanov-DLNP, JINR R. Makarov-MSU K.Hiller, H.J. Schriber-DESY, Zeuthen

2. SCHEME OF MAGNET SPECTROMETER Scheme of magnetic spectrometer applied for ILC beam energy measurement.

3. GEANT SIMULATION R. Makarov E=250 GeV+50 MeV- blue histogram E=250 GeV-wight histogram Left SR fan spot edge SR fan left edge displacement  x left  7-8 μm SR fan right displacement  x right  5-6 μm Simulated energy resolution Required resolution 12 μm/50 MeV 2.5 μm/50 MeV

4. SIZE OF SR DETECTOR  Electron energy spread in bunch  Soft photon angle spread 12  rad at photon energy 20 keV and electron energy of 250 GeV. 750  m  Fringe field in the magnetic rigidity at magnetic field variation of  (Bl)/Bl ≈ 4∙10 -2 600  m  Interaction of hard SR photons with a vacuum pipe material became to additional SR at low energy and an increase of the SR fan horizontal size. The horizontal width of active detector area has been comparable with 1 mm at registration of soft SR. 1mm. 25  m.

5. ELECTRON ENERGY SPREAD Comparison of SR spot edges for monochromatic electrons at E=250 GeV (red color) and electron energy spread of ±125 MeV at E=250 GeV (white color) R. Makarov

6. GEANT SIMULATION K.H. Hiller Multiplicity of photons radiated by an electron whihin spectrometer magnet, GEANT simulation Average number of photons radiated by one electron Average photon energy SR calculations =(5/2·3 1/2 )·  ·eB/m·L mag /c=4.8 =(8·3 1/2 /45)·E cr =3.6 MeV E cr =0.66 E e 2 (GeV)·B(T)=11.6 MeV- critical photon energy  =1/137.

7. PHOTON ENERGY SPECTRUM K.H. Hiller Energy of photons radiated within the spectrometer magnet

8. SR calculation Power density

9. Photon Distribution

10. REFLECTION MIRRORS FOR SOFT SR The application of mirrors permits to avoid the problems related to SR radiation protection however the installation of mirrors reduces the energy resolution at fixed coordinate resolution and detector position. L am =40 m mirror-spectrometer magnet distance L m-d =10 m mirror-detector distance

11. REFLECTION OF SOFT SR RADIATION BY MIRROR φ max (rad) ≈ 0.08/E γ (keV)=4 mrad mirror critical angle at large atomic number Z and electron energy of 20 keV Dependence of Rh mirror reflectivity on photon energy. The mirror reflected surface is placed at angle of φ=3 mrad to beam axis.

12. DETECTOR SHIELDING AT MIRROR SCHEME The coordinate of left SR spot edge is equal to =8.3 cm. The coordinate of left hard SR spod edge corresponds to x SR =3.1 cm. The distance about Δx= 5 cm between soft SR channel and ILC beam pipe can be used for detector shielding and reduction of hard SR intensity. In this case we assume that before mirror the horizontal size of vacuum chamber pipe can be increased from 4 cm up 7 cm on a length of 40 m from middle of analyzed magnet. After mirror two special channels of length 10 m will be constructed to transportation of soft SR radiation to detector.

13. ENERGY RESOLUTION IN MIRROR SCHEME =1 ·10 -4 at detector coordinate resolution of δx=2 µm. MIRROR PARAMETERS d mir  25- 50 μm mirror thickness 0.6 mm vertical size of SR spot on mirror l mir =(LAM+L a-m ) 0.1  /2φ=65 cm length of left mirror The mirror reflect soft SR generated inside analyzing magnet on length of 0.1 LMM  30 cm at deflection angle of 0.1  /2  0.05 mrad.

14. MIRROR HEATING Mirror adsorption   >50-100 keV μμ0·0 /μμ0·0 /  0  50-100 keV, μ 0  5-10 cm 2 /g

15. Photon energy losses in both mirrors at photon energy    Q  ≈ N  (ε  /ε cr ) 1/3 ·d   ∙(2l mir  /L am  ) μ 0 ·d mir ·  0 /   Total energy losses in mirror per bunch Q  ≈ 3N  ∙(2l mir  /L am  ) μ 0 ·d mir ·  0 ≈3·10 14 eV≈45  J N  = 10 11 is the number of hard SR  -quants in the bunch, є cr = 11.4 MeV is the critical photon energy. Rh mirror (  =12.4 g/cm 3, d mir =25  m) Energy losses in mirror per train N bunch =4800 Q=N bunch Q  ≈200 mJ PHOTON ENERGY LOSS IN MIRROR

16. CREMNIUM DETECTOR Semiconductor SR detector scheme at sub μm resolution. Si  =2.3·10 5 Ohm·cm  =12  rel =  0  250 μs Ge  =47  ·cm  =16  rel =  0  7 ns  rel -charge relaxation time B.Zalikhanov

17. Si DETECTOR SIGNAL In Si detector pulse duration is defined by  RC str  50 ns C str =  0  S/d  1 nF-capacity of detector strip (S=2.5·10 -5 m 2, d=3  m) R=50  -resistance of amplifier Amplification conversion 50 V/1 nC V  1.5 V at number of electrons of 1.5·10 8

18. DETECTOR NOISE B. Zalikhanov Voltage fluctuation caused by heating noise ΔN – number of charge particles in detector strip Minimal  -quanta energy required for production of signal larger than heating noise W  =ΔN  E  = J i ·(kTC) 1/2 /e  50 keV J i =3.6 eV energy required for e-hall pair production Resolution related to current noise W 2   J i N c 1/2 ·(  rel /  c ) 1/2  60 keV N c  10 6 - number of free charges in Si (n si =1.1·10 10 cm -3 ),  c  d/  - E  2·10 -10 s - time of free charge collection on strip electrodes at  - =1.3 cm 2 /(V·s), E=1 kV/cm Ratio of heating and current noises to photon energy per strip (W  2 +W 2  2 ) 1/2 /N  E   10 -5 N  =10 6 - number of photon with energy of E   10 keV per strip

19. GAS AMPLIFICATION DETECTOR B. Zalikhanov Amplification coefficient N/N 0  10-100 N=N 0 exp (  d c-a ) P=50-100 Atm, d c-a  2 mm cathode anode distance  10-20 cm -1 Taunsend coefficient P in Torr, B=30·10 -3 V -1, E=V/d  0.5 kV/cm E an /E  10 electric field near anode (10-15  m) Number of soft photons at E  10 keV per strip Number of secondary electrons per strip After amplification at K=10 The signal at amplifier conversion of 5 V/1 nC N   10 6 N e  10 8 N e  10 9 V  1.5 V

20.  The position measurements of both horizontal edges for SR fan permits to determine the beam energy with a resolution of  E/E  5∙10 -5.  The energy resolution obtained in GEANT simulations corresponds to 12μm/50 MeV at electron energy of 250 GeV. The scaling sensitivity 12μm/50 MeV at electron energy of 250 GeV permits to reach the energy resolution of ΔE/E ≈5∙10 -5 at spatial resolution of 2-3 μm.  A high position resolution detectors (2-3 μm) for a low energy gamma registration within large radiation background are proposed. Detector production may be carried out by methods used in the microelectronic industry. Conclusion