HEL Beam dynamics: optimized magnetic system, correctors, collector

1. HEL Beam dynamics: optimized magnetic system, correctors, collector A. Barnyakov, D. Nikiforov, M. Arsentyava, A. Levichev BINP-CERN 29.05.2019

4. Magnetic fieldsin CST for new configuration Injection mode:  Injection energy and with proton beta=280 m at 450GeV => HEL e-beam 8.58 – 17.15 mmwhich correspond 3.45 T for gun and 3 T for main solenoid Flat top mode: Top energy and with proton beta=280 m at 7 TeV => HEL e-beam 2.17 – 4.34 mm which correspond 0.37 T for gun and 5 T for main solenoid

5. Beam dynamic: Injection mode Ø~25 mm(~31 mm prev.) Ø~36.1 mm For all beam dynamics simulations the real gun profile is used

6. Beam dynamic: Injection mode Ø~35.5 mm

7. Beam dynamic: Flat top mode

8. Beam dynamic: Flat top mode 5A The residual field inside hollow is no more than 30 kV/m (5A) and no more than 4kV/m (3A) in the end of main solenoid (which correspond previous simulations) 3A

9. Fields inside hollow 5A The max. residual field inside hollow (marker 2) is no more than 30 kV/m (5A). Max. field on outer beam boundary (marker 1) – 0.65 MV/m 3A The max. residual field inside hollow (marker 1) is no more than 3.6 kV/m (3A). Max. field on outer beam boundary (marker 2) – 0.35 MV/m

10. Corrector simulation (gun) Gun part correctors The bending solenoidwas adjusted to centered the beam in FLAT TOPE mode Main corr. Gun corr. Full deflection in the center of 1st main solenoid – 1.7 mm for injection mode The efficiency of gun corrector should be maximized as much as possible

11. Corrector simulation (gun_optimization) By 1200 Gs y Correction field linearalmost in all the vacuum chamber

12. Corrector simulation

13. Collector The key challenge for HEL collector is how to optimize it for two very different mode (cathode field: 0.37 T-> 3.45 T). We start with most critical INJECTION mode. For this mode we need at least 0.7 T to preserve acceptable beam size on the collector entrance, also we need space for diagnostics and for collector electrodes.

14. E-cooling collector model (typical) 1 – cooler vacuum chamber 2 – entrance of the collector 3 – collector deaccelerating electrode 4 – repeller 5 – collector electrode 6 – magnetic shielding 7 – collector body 8 – cooling system

15. 3 HEL collector model 2 3.45 Т on the cathode 1 5 4 7 6 1 – warm collector solenoid, 2 – antisolenoid, 3 – magnetic shielding, 4 –collector body, 5 – entrance electrode, 6 - repeller, 7 – cylindrical electrode (To reduce the output of low-energy electrons along the surface)

16. Warm solenoid Power: 33 kW Pressure_drop (per pancake): 1 atm Temp_delta: 20 K Field: 7000 Gs Hollow conductor: 14x14 mm, d = 9 mm Length: 280 mm Inner diameter: 160 mm Outer diameter: 300 mm N_wires: 100 Max_current: 1.7 kA To avoid steel saturation, we need to use massive shielding of solenoid (width – 15 mm)…….. 0.67 T

17. Collector transport model (injection)

18. Collector model 0.37 Т on the cathode

19. Collector transport model (flat top)

20. Local power density on collector surface FLAT TOP Max. Power density on collector 70 W/cm^2 INJECTION Max. Power density on collector 40 W/cm^2

21. Collector efficiency estimation One of the main characteristics of the collector is the secondary emission coefficient of the collector: - potential minimum on the beamline near the repeller – collector potential - magnetic field on the collector surface – magnetic field in the collector exit Sharapa A.N., Shemyakin A.V. Secondary electron current loss in electron cooling devices. Nucl. Instr. and Meth. A351 (1994) 295-299.

23. Beam correction on collector Corrected beam Uncorrected beam

24. Conclusion • Dynamics calculation for the flat top and the injection modes have been carried out. We used the latest magnetic field distribution and correctors • All simulations were performed for the irregular particles distribution with “peak” current density near the inner radius. The influence of this peak on the beam motion is not observed and this peak is saved during the motion. • In spite of stable regime, the particles have the complicated physics. In result the beam can slightly change the shape in time and the field inside the beam can be arisen, but the amplitude of this field in not more than 3% from the field near the outer beam radius at the end of the HEL. • Correctors have been simulated with different designs: different number of layers, coils, effective angle. Taking into account the field and current, all correctors can be used, but to reduce currents for correctors we need to use another type of conductors. • Dynamics calculation for the flat top and the injection modes in collector have been carried out, the parameters and the shapes of collector electrodes was defined

25. Bend TRK PIC dx, dy, dz1, 1, 1 mm^3 PIC and TRK solvers give the same results forthe beam after the bend, but here non-optimal grid is used due to PIC solver. In result the errors in the potential distribution and amplitude are arisen.

26. Bend with TRK solver and good grid 0.5x0.5x0.5 mm^3 1, 1, 1 mm^3 The comparison of the simulation for the same solvers gives the following result. The beam behavior is the same, but there is the difference between the amplitude and the distribution of the potential (kinetic energy). This is due to precision of the field simulation.

27. Potential asymmetry at the outer radius a 2.8 a If the beam was solid with parameters U0 = 15 keV, vb = 0.2 c I = 5 A, a = 30 mm, rb= 1.8 mm, potential difference is ΔUb ≈ 1.3 kV 12 kV 10.8 kV

28. Potential asymmetry and beam shape perturbation 1000 mm 3500 mm Faster Slower Particles starting from different azimuthal angles have different rotation velocity Non-zero electric field in the hollow increasing with the beam motion through the vacuum chamber Perturbation of the azimuthally uniform electron density