1. DRAFT Simulation of Errant Beams in the BDS How many bunches will damage beamline components or quench SC coils? Analysis Steps 1.Use TRANSPORT with BDS optics Model FF9 to mis-steer beam and find the maximum angle of incidence and minimum beam size at various locations. 2. Use EGS4 to simulate energy deposition where bunches encounter material. L. Keller, 10 Oct. 2005

2. Examples of FF Soft Bend Mis-settings which Steer Bunches into the Final Doublet This example is analyzed here because it has the largest angle of incidence (76 µrad).

3. 2 mm s.s. beampipe Iron Pole Regions for scoring E_dep Bunch at grazing angle EGS4 Model where Errant Bunches Hit Near Betatron Quad X or Y (cm) Beam axis Axial distance, arbitrary location (cm) (This shows the worst case where the magnet pole is touching the beampipe)

4. Regions for scoring E_dep 2 mm s.s. beampipe SC Cu coil 30 cm long Copper Protection Collimator Bunch at grazing angle EGS4 Model where Errant Bunches Hit Near the Final Doublet bunch ΔX X (cm) Beam axis Axial distance, arbitrary location (cm)

5. Beam Line Section 250 GeV Beam Size (µ) σ x σ y Inc. Angle Sigma Z on pipe Hit Location Comments SS Pipe (°C/ b) Quad Pole (°C/ b) Cu Coll. (°C/ b) β coll., Ver. kick 72 2.3400 µr0.6 cm803- QB0 offset 1000 µ, bunch hits near QB2, 140 m away β coll., Hor kick 40 1.0400 µr10 cm1152- QB1 offset 1000 µ, bunch hits near QB3, 105 m away β coll., Hor kick 20 1.490 deg---25,000Bunch hits AB3 headon Final Doublet, Hor kick from B1 635 3576 µr 830cm0.7 See next slide 160 (full bunch on lip) Large beam size and small incident angle reduce maximum ΔT. See slide 6 for E_dep in SC coil. Examples of Mis-steering in the BDS Maximum ΔT/ 2x10 10 bunch at the Hit Location 1. Fracture temperature of iron approximately 200 °C 2. Temperatures approx. 2.5x higher for 500 GeV beam => smaller beam, higher energy 3. Aluminum pipe ΔT approx. 1/3 SS pipe

6. Length of copper protection collimator 250 GeV Beam Size (µ) σ x σ y Inc. Angle Sigma Z on Pipe E dep in Copper SC Coil (mj/g) Comments 0 cm635 3576 µr830 cm7 With no protection collimator the bunch is spread over a long length of beam pipe 30 cm635 3576 µr830 cm58 Most of the bunch hits the lip of the protection collimator, hence large energy dep. for a relatively short collimator 50 cm635 3576 µr830 cm5 Irreducible minimum since shower spray from the inner edge becomes azimuthally isotropic 100 cm635 3576 µr830 cm4 Irreducible minimum since shower spray from the inner edge becomes azimuthally isotropic Energy Deposition for Mis-steered Beam Hitting Near Final Doublet Maximum joules/gram per 2 x 10 10 bunch in QF1 SC Copper Coil 1.N. Mokov: Tevatron experience shows “fast” (1/2 msec) limit is 0.5 mj/g 2.E_dep approx. 2.5x higher for 500 GeV beam => smaller beam, higher energy

7. Summary In the collimation sections, the grazing angle on the beam pipe protects normal magnets for many tens of bunches. A single bunch hitting a collimator or absorber head-on causes melting over a considerable length and radius. The relatively large beam and small angle of incidence hitting the beam pipe near the final doublet slows physical damage, but not quenches, for tens of bunches. Adding a protection collimator upbeam of the final doublet does not prevent quenches from a missteered beam since enough beam scrapes the inner edge of the collimator. It’s hard to put error bars on these numbers – simulating total energy deposition for electromagnetic showers in small volumes, it fraught with difficulties.