EM Simulations for PETRA3 N. Baboi, DESY, Hamburg Introduction 1. Electrostatic simulations with MAFIA BPM for damping wiggler BPM for “standard” vacuum chamber 2. Simulations with Microwave Studio (MWS) Coupling between BPM-buttons BPM Workshop, Lüneburg, Nov. 30, 2006

PETRA3 Energy: 6 GeV Emittance: 1nm rad Current: 100 mA Bunches: 40 / 960

BPMs for PETRA3 235 BPMs (buttons) for various chamber sections

Monitor Constant 1/K FUR FDR FUL FDL

1. Electrostatic Simulations (MAFIA) Electrostatic calculation 1 V at one button calculate field distribution  monitor constant K through reflections  field for all 4 buttons combine these fields  FH and FV  KH and KV  coupling factor between beam and BPM-pickups = voltage at middle of BPM for 1 V at one button (in %)

1a. BPM for Damping Wiggler distance between buttons = 24 mm chamber: 30 x 120

BPM for Damping Wiggler: Coupling

BPM for Damping Wiggler: Monitor Constant FH FV

BPM for Damping Wiggler: Monitor Constant (2) 1/KH = 0.08 mm-1 1/KV = 0.06 mm-1 For 1 mm resolution need 8·10-5 resolution in FV Button distance 1/Kx [mm-1] 1/Ky [mm-1] Coupling [%] 20 0.074 0.070 12 24 0.083 0.061 10 31 0.093 0.045 7

1b. “Standard” Chamber 1/KH = 0.059 mm-1 for j = 55 deg 1/KV = 0.056 mm-1 for j = 55 deg R. Wanzenberg

2. Coupling between Buttons: UR – UL MAFIA-S: Electrostatic Simulation defined as vacuum ~0.9e-4V coupling to beam: 23% coupling to button ≈ 0.009%

Coupling between Buttons: UR – DR MAFIA-S: Electrostatic Simulation defined as vacuum ~0.12V coupling to button ≈ 10% BUT measurement (Neumann): -45dB -> 0.6%!

Coupling between Buttons Microwave Studio: S-parameters good agreement to measurements (normalized to 50 Ohm)

Coupling between Buttons Microwave Studio: Time Domain source port 1 port 3 electric (or magnetic) boundaries port 4 port 2

Coupling between Buttons Time Domain – Results

Coupling between Buttons “Beam” Simulation 1-4: ports 5: discrete port (source) port 1 port 3 discrete port 5 (S-Param, 10kW: practically I-source) electric boundaries port 2 port 4

Coupling between Buttons “Beam” Simulation - Results

Coupling between Buttons “Beam” Simulation - Results (2) Current / Voltage

Coupling between Buttons “Beam” Simulation - Results (3) Effect of other buttons worst case: other buttons are short-circuited => no difference!

3. Error Analysis: BPM for Straight Section chamber: 94 x 94 15 mm buttons (Meggitt) 5deg error in UR and DL pickups

Preliminary: BPM for Straight Section: Monitor Constant Without error With 5 deg error  10% error

Preliminary: BPM for Straight Sections Fields without/with angle error 5deg angle error