1. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 1 Alexander Novokhatski April 13, 2016 Beam Heating due to Coherent Synchrotron Radiation. Alexander Novokhatski FCC Week 2016 The second Annual Meeting of the Future Circular Collider study April 13, 2016 Rome, Italy

2. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 2 Alexander Novokhatski April 13, 2016 introduction Synchrotron radiation is very important in all kinds of accelerators where bending magnets are used. They are electron-positron storage rings, high energy proton rings and linear accelerators, where bends or magnetic chicane for bunch compression are used. Increasing the intensity of the beam and decreasing the bunch length the coherent synchrotron radiation becomes important too. One dimensional CSR model explains well beam energy loss due to coherent radiation. However there are several other effects in the real three dimensional life. We will discuss slice energy spread growth and transverse forces action.

3. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 3 Alexander Novokhatski April 13, 2016 Why I got an interest in the CSR fields? Beautiful pictures watched on the YAG screen after the magnet when the electron beam is bent down in vertical direction

4. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 4 Alexander Novokhatski April 13, 2016 CSR numerical code To explain the nature of these interesting pictures, a special new 3d computer code was developed. It is based on a direct numerical solution of Maxwell equations for electromagnetic fields; and Newton’s equations for particle motion inside magnets and in excited electromagnetic fields. –A. Novokhatski, Phys. Rev. ST AB 14, 060707 (2011) In this way we include in consideration all coherent effects like CSR (coherent synchrotron radiation), wake fields excited by irregularities of the vacuum chamber, space charge fields and interaction of the CSR fields with the chamber walls. Electromagnetic fields excited by short bunches show properties of these fields much better in comparison with long bunches.

5. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 5 Alexander Novokhatski April 13, 2016 Edge CSR fields in the X-ray line Rrecently, we improved the algorithm and now the code can simulate 20 micron or even10 micron bunches. Using the code we simulate edge radiation in the dump magnet Magnified Initial beam direction Current beam direction Bunch field Fields on the YAG screen

6. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 6 Alexander Novokhatski April 13, 2016 Images of radiation. Calculated transverse magnetic fields. Bunch field Synchrotron radiation Edge radiation Calculated edge radiation is very similar to the images, which we have seen. In simulations the electron beam is bent in the horizontal direction An image of the experimental plot is upside down.

7. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 7 Alexander Novokhatski April 13, 2016 CSR physical picture The success in explaining the CSR images demonstrates the power of our numerical algorithm. We can use this algorithm to analyze the physical picture of the radiation. We use the electric field (force) lines to represent the radiation field. The next slide will show the radiation fields of a bunch in the 45 degree magnet at different positions of a bunch.

8. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 8 Alexander Novokhatski April 13, 2016 Field dynamics in a 45° magnet

9. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 9 Alexander Novokhatski April 13, 2016 Bunch self-field remakes itself V The upper field lines take the position of the lower lines The red arrow shows a bunch velocity vector The green arrows show the field line directions The lower field lines take the position of the upper lines

10. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 10 Alexander Novokhatski April 13, 2016 The picture becomes clear if we decompose the field =+ a field of a moving dipole a field of a bunch moving straight in initial direction Decomposition of the field of a bunch moving in a magnetic field into two fields:

11. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 11 Alexander Novokhatski April 13, 2016 Radiation forces Force lines show mainly deceleration forces from one side of a bunch and slight acceleration from the other side This means that a slice energy spread can be introduced by the CSR fields Also it can be seen that the transverse force is mainly from one side. We need to include the magnetic force to calculate the total traverse force. +Q is a real bunch

12. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 12 Alexander Novokhatski April 13, 2016 CSR calculations for a practical purpose. Here we present CSR calculations for a real magnet, which is used at LCLS as a dump magnet. It consists of three magnets and deflects the beam down in order to separate the electron beam from the X-ray beam Usually two electron beam energies are used: 4.3. GeV and 13.6 GeV. The magnetic field in the bends changes according the electron beam energy to keep the same trajectory The bunch length is 20 micron, the bunch charge is 180 pC.

13. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 13 Alexander Novokhatski April 13, 2016 Geometry of the dump magnet Blue line shows field distribution relative to longitudinal direction Red lines show walls of the beam chamber used in simulations

14. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 14 Alexander Novokhatski April 13, 2016 CSR fields in the beam pipe

15. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 15 Alexander Novokhatski April 13, 2016 Energy loss distribution Z-directionY-direction head tail Bunch shape

16. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 16 Alexander Novokhatski April 13, 2016 Energy loss averaged over a slice of a bunch

17. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 17 Alexander Novokhatski April 13, 2016 Phase plane Longitudinal coordinate energy head tail slice energy spread

18. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 18 Alexander Novokhatski April 13, 2016 Slice energy spread Typical measured energy spread Very good comparison of the curve shape with a measurement one

19. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 19 Alexander Novokhatski April 13, 2016 We may compare with incoherent energy spread due to quantum fluctuations of synchrotron radiation Matthew Sands “Physics of Electron Storage Rings” SLAC Report No 121, 1970 382 kV for 13.6 GeV 38 kV for 3.4 GeV

20. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 20 Alexander Novokhatski April 13, 2016 Transverse forces In 1D model the transverse force goes to zero with increasing energy In real life we may suspect that the force may exist as the energy loss has a slope in the transverse direction

21. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 21 Alexander Novokhatski April 13, 2016 Kick opposite to the bend direction (distribution) Z-direction Bend direction (Y) head tail

22. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 22 Alexander Novokhatski April 13, 2016 Vertical kick averaged over a slice of a bunch

23. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 23 Alexander Novokhatski April 13, 2016 We may compare with a formula (R.Talman force without logarithm) More than two times larger than CSR force

24. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 24 Alexander Novokhatski April 13, 2016 Z-direction Bend direction (Y) head tail Focusing-defocusing in perpendicular direction

25. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 25 Alexander Novokhatski April 13, 2016 Gradient of a horizontal kick Defocusing the tail Focusing the head

26. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 26 Alexander Novokhatski April 13, 2016 Comparison with magnet edge defocusing Karl L. Brown “A first and second-order matrix theory” SLAC Report No 75, 1972 Blue line shows relative field distribution Red lines show integrated edge defocusing

27. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 27 Alexander Novokhatski April 13, 2016 A kick due to a horizontal displacement of the beam *

28. OPERATED BY STANFORD UNIVERSITY FOR THE U.S. DEPT. OF ENERGY 28 Alexander Novokhatski April 13, 2016 Summary We have presented examples of additional CSR effects like slice energy spread, centrifugal force and focusing-defocusing in the perpendicular direction and with a possible kick. The effects may be comparable with well known effects like incoherent energy spread and edge defocusing. It will be interesting to check how these effects may be important for FCC. –Less magnetic field, but more magnets; longer bunches, but more charge The most important aspect of our numerical code is that a bunch is not rigid and the shape can be changed in the magnetic fields of bends or quadruples that may bring changes to the self fields. We will try to understand lattice and beam parameters and make first estimate of these effects for FCC. Thanks..