A comparison between MAFIA simulations and magnet measurements Michaela Marx 4 December 2006

1. FLASH Quadrupole (S-Band) Triplet Christoph A comparison between MAFIA simulations and magnet measurements Michaela Marx 4 December 2006 Triplet XFEL Beam Dynamics Meeting

2. Quadrupole Triplet: General Information • Triplet was designed in 1993 for the S-Band Linear Collider Test • Facility with a gradient of 17 T/m • aperture radius = 17.5 mm • total length: 300 mm, distance between thequadrupoles= 50 mm • - inner quadrupole 100 mm, • - two outer quads 50 mm each Figure shows the iron yoke – ¼ of the whole triplet outer quad outer quad inner quad 50 mm 50 mm 100 mm 50 mm 50 mm

3. The Simulation Model • The triplet was simulated by using the magneto-static module of the • program MAFIA • Due to symmetry conditions only one eighth of the geometry has been taken • into account for the calculation y [m] symmetry plane in beam direction filaments to simulate the coil windings x [m] beam direction MAFIA model: Cross-section of the iron yoke with filaments, 2d view, xy plane. MAFIA model: Iron yoke with filaments, 3d view.

4. y [mm] Settings for the current: Iinnerquad = 159.4 A Iouter quad = -136.6 A Iinner quad = 79.7 A Iouter quad = -68.3 A max. currents half currents X [mm] 0 2 6 10 14 positions of measurement Measurements for the Quadrupole Triplet • Various measurements have been done for the triplet by Y. Holler in 1996 • The field has been measured along the beam axis at different positions • in the horizontal direction at x = 2, 6, 10 and 14 mm; y = 0 mm Fields have been examined separately for the inner quad and for the outer quads: Iinner quad = 159.4 A Iouter quad = 0 A Iinner quad = 0 A Iouter quad = -136.6 A

5. Comparison between Measurement and MAFIA Simulation Measurement has an estimated x-position offset of nearly 2 mm! measurement Figure shows the field By along the beam axis. The difference of the MAFIA simulation results from the mesh resolution in the simulation model. No mesh line is given at the position where the measurement has been done.

6. Comparison between MAFIA simulation and measurement for S-Band Triplet 0.4 at center of inner quad (MAFIA) at center of outer quad (MAFIA) at center of inner quad (Measurement) 0.3 at center of outer quad(Measurement) 0.2 0.1 0 By along x-axis [T] -0.1 -0.2 -0.3 -0.4 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 x [m] Field Gradients outer quad: g=18.8 T/m Measurement MAFIA Currents: Iinner quad = 159.4 A Iouterquads = -136.6 A MAFIA Measurement inner quad: g=-22 T/m The field gradients are examined at the center of the inner quadrupole (lower curve) and at the center of the outer quadrupole (upper curve). Good agreement between simulation and measurement!

7. Outer Quadrupole: By vs. current 0.3 xoff=14.6mm (MAFIA) xoff=14mm (Measurement) 0.25 0.2 0.15 By(I) [T] @ x=14 mm, y=0, z=center of magnet 0.1 0.05 0 0 20 40 60 80 100 120 140 I [A] Inner Quadrupole: By vs. current 0 xoff=14.62mm (MAFIA) xoff=14mm (Measurement) -0.05 -0.1 -0.15 By(I) [T] @ x=14 mm, y=0, z=center of magnet -0.2 -0.25 -0.3 -0.35 0 20 40 60 80 100 120 140 160 I [A] Field vs. Current Field By vs. the current I for an outer quadrupole of the triplet. very good agreement between measurement and simulation. Field By vs. the current I for the inner quadrupole of the triplet. very good agreement between measurement and simulation.

8. The Quadrupole Triplet under current FLASH Conditions Triplet is not used as a triplet, but as a doublet … Iouter quad = -32.2 A Iinner quad = 5.3 A Iouter quad = 34.4 A Field By has been taken at different offset positions in x-direction:

9. Conclusions • Fields have been compared between Holler’s measurements and • a simulation with MAFIA • Good agreement for the field gradient and for the excitation curves • Problem: Absolute position of the HALL probe for the measurement is • unknown. To compare the measurement with the MAFIA • simulation the horizontal offset position was estimated from • the measurements.