1. ALIGNMENT SENSITIVITY STUDIES FOR THE ILC DAMPING RINGS Kosmas Gr. Panagiotidis The Cockcroft Institute

2. Contents Overview of the ILC Luminosity and Emittance Generation of Emittance in a Storage Ring Sensitivity Studies Future Work

3. The International Linear Collider (ILC) is a proposed facility for future studies of fundamental particle physics. ILC will be designed to collide electrons and positrons at centre of mass energies of 500GeV or more, in order to make precision measurements of new phenomena, such as the Higgs boson and supersymmetry. The baseline configuration of the ILC [1] has been determined by the Global Design Effort. Figure 1:Schematic layout of ILC The International Linear Collider 30km

4. A fixed target has a high density of target particles, resulting in a good probability for interaction. Therefore, the intensity and emittance of the incident beam are not usually a major concern in fixed target experiments. In contrast, the density of a colliding beam target is extremely small compared to that of a solid target. The luminosity of a collider is determined by the density of the colliding bunches and the collision rate. For a linear collider concerning two colliding bunches of particles n 1 and n 2 colliding at a repetition rate f, the luminosity is given by where σ x and σ y are the horizontal and vertical beam sizes. Practical issues limit the charge per bunch and the repetition rate. Therefore, to enhance luminosity, one needs to reduce the beam sizes (and hence the emittances) as much as possible. Luminosity

5. Emittance The emittance is a measure of the phase space area (the area on a plot of momentum vs coordinate) occupied by particles in the beam, and is invariant in the absence of effects like radiation and acceleration. Thus, to get a small beam size at the IP, we need both very strong focusing (which is provided by the final focus magnets) and a very small emittance. The job of the damping rings is to use radiation effects to produce a beam with very small emittance. The lowest emittance ever achieved in a storage ring is 4.5 pm; to produce the design luminosity, the damping rings have to achieve a vertical emittance of 2 pm. Figure 2 : Phase-space ellipse

6. The two damping rings (one for the electron beam and one for the positron beam), situated coaxially around the Interaction Point (IP), form a major component of the ILC. Their purpose is to reduce the emittance of the beam, since, when created, neither the electron nor the positron bunches are compact enough to yield the high luminosity essential for the physics programme. The ILC Damping Rings Figure 3: Footprint of ILC positron ring and important parameters Circumference6.7km Energy5GeV Average current402mA

7. Types of Magnets used in the Damping Ring Dipole Magnets: They are used to bend the beam. Quadrupole Magnets: Their purpose is to focus the beam. Sextupole Magnets: They are used to correct the chromaticity.

8. Particle Trajectory and Steering Errors A dipole field error causes a distortion of the closed orbit and particles crossing the field error region get a vertical “kick”, as illustrated in figure 4. Depending on the sensitivity of the particular lattice, even a small error can lead to a large orbit distortion and this in turn means that in order to achieve successful operation of the ring, the alignments tolerances of magnetic components become very demanding. Dipole field error Closed Orbit Reference Trajectory Figure 4: Illustration of a dipole field error

9. Generation of emittance in a storage ring In storage ring operation the vertical emittance is typically dominated by magnet misalignments. Betatron coupling results in direct transfer of horizontal emittance into the vertical plane. The distortion on the closed orbit, resulting from this steering together with vertical sextupole misalignments, leads to a vertical beam offset in the sextupoles with respect to their magnetic center. Consequently, betatron coupling is introduced. Vertical misalignments in the sextupoles introduce a vertical kick to the beam that is dependent on the horizontal coordinate. This leads to each particle experiencing a different force in respect to their horizontal position in the bunch and consequently this also leads to vertical emittance growth. Rotations of quadrupoles around the beam axis have a similar effect to vertical misalignments of the sextupoles.

10. Simulation Codes The studies presented here were performed using specialized codes for the modeling of accelerator systems, namely MAD (Methodical Accelerator Design [2] (version 8.23dl), and Merlin [3]. The simulations run with the aforementioned codes investigated the effect of magnet misalignments on specific beam parameters, namely on the vertical closed orbit, the dispersion and the vertical emittance ε y. A definition file for the present baseline damping ring lattice, referred to as the “OCS6” lattice, is available in the standard format used by MAD. This file describes the sequence of all elements that comprise the ring, but cannot be read directly by Merlin. Instead, MAD is used to produce a file that contains a detailed description of the lattice in a simplified format that can be recognized by Merlin. The simulations are then performed using Merlin. Using Merlin we are able to apply a random set of misalignments to a particular types of families of magnets and then calculate the effects of these misalignments on various properties of the beam.

11. Sensitivity of the y rms closed orbit to Quadrupole misalignments Figure 5 illustrates the closed orbit distortion for rms quadrupole vertical misalignments up to 10 μ m. The blue points show the average over 100 sets of errors with a given rms. The error bars indicate the 5th and 95th percentiles of each set of errors. Figure 5

12. Sensitivity of the Vertical Emittance ε y to Quadrupole tilts The above figure shows how the emittance is affected by quadrupole tilts (rotation of the magnet in respect to the reference trajectory). The error bars indicate the 5 th and 95 th percentiles of each set of errors Figure 6

13. Sensitivity of the Vertical Emittance ε y to Sextupole misalignments Figure 7 illustrates the effect of vertical sextupole misalignments to the vertical emittance; The error bars indicate the 5 th and 95 th percentiles of each set of errors. Figure 7

14. Conclusions The calculations based on the simulated data appear to be in reasonable agreement with theory and present acceptable errors. The simulations predict very accurately the trend of the effect to the lattice sensitivity in respect to each misalignment error, as expected by the theoretical formulae each case. Knowing these trends provides a clear understanding of how the machine responds to the different types of errors that are always present in everyday operation. A vertical emittance of 2pm (nominal specification for the ILC damping rings) is generated by vertical sextupole misalignments of the order of 60 μ m. An equal amount of vertical emittance is generated by quadrupole tilts of the order of 70 to 80 μ rad. It is unrealistic to expect that this level of precision can be achieved during commissioning of the machine. This effectively means that the machine will have to be tuned to the desired vertical emittance levels after construction and after successful beam circulation has been achieved.

15. Future Work The performed simulations took into account only one type of error each time. Of course, in reality all types of possible errors come into play simultaneously. To evaluate a simulation where all types of errors have been introduced into the model, one needs to be able to account for the effect of each type of error separately and that information is provided by the current studies. The next step of these studies is to try and simulate a more realistic model of the damping ring lattice, where all types of misalignment errors are present and evaluate it based on the knowledge acquired so far. Simulate the tuning procedure to achieve the necessary beam quality.

16. References 1. “ILC Baseline Configuration Document”, http://www.linearcollider.org/wiki/docu.php?id=bcd:bcd_home 2. http://mad.web.cern.ch/mad/ 3. http://www.desy.de/~merlin/ 4. A.W.Chao, M.Tigner, “Handbook of Accelerator Physics and Engineering”, World Scientific Publishing (Jun 1999) 5. S.Y. Lee, “Accelerator Physics”, World Scientific Publishing; 2Rev Ed edition (26 Jan 2005) 6. A.Wolski, J.Gao, S.Guiducci, “Configuration Studies and Recommendations for the ILC Damping Rings”, Lawrence Berkeley National Laboratory, February 4, 2006, http://repositories.cdlib.org/lbnl/LBNL-59449 7. A.Wolski, “Linear Dynamics for Particle Accelerators”, The Cockcroft Institute, Autumn Lecture Courses 2006, http://www.cockcroft.ac.uk/education.htm 8. A.Wolski, J.Jones, “Damping Rings Design and Physics Issues”, USPAS January 2007, Houston, Texas, http://www.cockcroft.ac.uk/education.htm 9. Hans Grote, F. Cristoph Iselin, “The MAD Program, User’s Reference Manual”, CERN/SL/90-13 (AP) Rev. 5, Geneva, Switzerland 1996

17. End of Presentation Thank you for your attention !