1. 14.04.2005Collimation for the Linear Collider, Daresbury.1 Adam Mercer, German Kurevlev, Roger Barlow Simulation of Halo Collimation in BDS

2. 14.04.2005Collimation for the Linear Collider, Daresbury.2 Halo Collimation What is Halo –~ 10 4 of bunch particles at the BDS entry (TESLA) Standard Goals of Halo Collimation –High Luminosity –Machine protection from direct hit etc. and detector protection for acceptable backgrounds Two tasks for investigation –Transverse wake fields in small collimation apertures –Backgrounds and material damage analysis

3. 14.04.2005Collimation for the Linear Collider, Daresbury.3 Wake Fields Lattice element excitation when beam bunch passing through it that can hit: –the bunch itself (short-range wake) – energy loss or transverse kick –or the next bunches (long-range) – instabilities Wake Fields Classification –Longitudinal (energy loss) –Transverse (center mass offset results in kick in transverse angle) Geometric (on discontinuities) Resistive wall (finit conductivity) Surface roughness Transverse geometric and resistive wall effects are the most critical types for steep and tapered collimators

4. 14.04.2005Collimation for the Linear Collider, Daresbury.4 General Wake Fields Theory Usual approach is to get integrated forces and apply charge distribution moments (m=0 – monopole, m=1 – dipole, etc ) For a bunch particle e: Impedances: For example, for a round steep spoiler monopole and dipole components:

5. 14.04.2005Collimation for the Linear Collider, Daresbury.5 Collimators Wake Fields Theory-Geometric Below: α – taper angle, σ – bunch length, b – aperture radius or half width, h – horizontal half width) Round pipe (Yokoya) –Diffractive –Inductive Rectangular (Stupakov) –Diffractive –Intermediate –Inductive

6. 14.04.2005Collimation for the Linear Collider, Daresbury.6 Collimators Wake Fields Theory-Resistive Piwinski (according to Onoprienko) –Small offset (L – collimator length, σ z – bunch length, σ z – bunch length, σ – conductivity) No taper Tapered –Offset ~ half gap

7. 14.04.2005Collimation for the Linear Collider, Daresbury.7 Wake Fields Simulation Different type of codes –Full dimension in frequency or time domain to test analytical wake functions or get table data MAFIA, ECHO, … –Optical codes with phenomenological wake fields to get the effect on beam transport through the BDS Merlin –Written by Nick Walker (DESY) and Andre Wolski (LBL) –Set of C++ class libraries –Originally for linear collider, now does storage rings

8. 14.04.2005Collimation for the Linear Collider, Daresbury.8 Wake Fields in Merlin Merlin had a process for handling wake fields Now inserted Wake Functions (thanks to Frank Jackson) Bunch slices for wakes integration prepared and integration already implemented Momentum change on slice i

9. 14.04.2005Collimation for the Linear Collider, Daresbury.9 Merlin Example Particles feel integrated force from those in front  "banana bunch" Off-axis bunch after collimator, no wakefields. Looking down (from above) at the bunch. Exaggerated!

10. 14.04.2005Collimation for the Linear Collider, Daresbury.10 Merlin Example Particles feel integrated force from those in front  "banana bunch" Exaggerated! Off-axis bunch after collimator, with wakefields. Looking down (from above) at the bunch.

11. 14.04.2005Collimation for the Linear Collider, Daresbury.11 Comparison of MERLIN results with SLAC experiment Beam parameters used in experiment and simulation: Beam (bunch) charge Q_total = 2e+10 e - number of electrons in the bunch - Ne = 2e+10 Beam energy p0 = 1.19 GeV Lattice horizontal betta function betta_x = 3 m Horizontal emittance emit_x = 0.36 mm, emit_y = 0.16 mm, Lattice vertical betta function betta_y = 10 m (we used these ones to have minimal emittance grow - there are no exact values from experiment) Longitudinal bunch size sigma_z = 0.65 mm Squared aperture of the spoiler with the side width 38 mm (half width to use in wake formulas b1 = 1.9 mm)

12. 14.04.2005Collimation for the Linear Collider, Daresbury.12 SLAC Experimental results From SLAC report 2004

13. 14.04.2005Collimation for the Linear Collider, Daresbury.13 Merlin simulation result Vertical offset Y of the beam centroid is in mm as in experiment, mean Yp kick is in 10s mkrad units so our constant is close to the correct one. We used diffraction limit formula for transverse wake function. As a result in our case in Merlin we don't have effect of near wall wake fields as in ECHO code so it should be almost strait line. The table confirms also the following formula for rms kick: Krms=Kt/sqrt(3)

14. 14.04.2005Collimation for the Linear Collider, Daresbury.14 Backgrounds and material damage simulations Standard approach is to use industrial standard Finite Element Analysis or Finite Element Method code linked with beam transport code –SCRAPER-RTS&T + ANSYS –MAFIA + interface code + ANSYS –SUPERFISH + linking codes + ANSYS and other FEA codes –FronTier + ANSYS Plan to use available ANSYS code

15. 14.04.2005Collimation for the Linear Collider, Daresbury.15 Future project plan Wake fields for tapered collimators in Merlin Wake fields with higher order modes as in ECHO code for near wall wakes simulation in Merlin Tracking of all the spoilers until the IP Backgrounds and material damage simulations with Merlin and ANSYS plus probably some linking code