Influence of the Third Harmonic Module on the Beam Size Maria Kuhn University of Hamburg Bachelor Thesis Presentation

FLASH Layout after the 2009 Upgrade Important elements of the beam line for emittance measurements Third harmonic module ACC39 Bunch compressor BC2 Diagnostics DBC2 Undulator – SASE process Why emittance measurement? for standard operation: beam with low transverse emittance in high-current peak indicator for beam size/ quality we determine the projected transverse emittance

Bunch Compression Four-bending-magnetic chicane curved sections: path length difference because of energy chirp of bunch head to tail acceleration off-crest small momentum: bunch head large momentum: bunch tail curvature of longitudinal phase space due to RF non-linear longitudinal compression forms the beam solution: third harmonic system

Third Harmonic Module Linearisation of longitudinal phase space after the first bunch compressor ACC39 off: long bunch tails, asymmetric bunches ACC39 on: linearises RF‘s sine shape

Third Harmonic Module Linearisation of longitudinal phase space after the first bunch compressor ACC39 off: long bunch tails, asymmetric bunches ACC39 on: linearises RF‘s sine shape overall RF field is flattened more effective bunch compression uniform intensity bunches

Third harmonic module cavity Problems: wakes are 3x stronger than in 1.3 GHz module non-symmetric structure Consequences: beam off-axis electrons are deflected transverse kicks Influence of Wake-Fields on Transverse Emittance

Third harmonic module cavity Problems: wakes are 3x stronger than in 1.3 GHz module non-symmetric structure Consequences: beam off-axis electrons are deflected transverse kicks Coupling of charged particles HOM field is excited cross section: wake-fields projected emittance grows

Data Analysis Diagnostic Section DBC2: four OTR monitors with well known transfer matrices measurement of transverse charge distribution

Data Analysis Diagnostic Section DBC2: four OTR monitors with well known transfer matrices measurement of transverse charge distribution calculation of the RMS beam size σ Phase space ellipse Twiss parameters √ √

Emittance Measurement Beam Size and 90% intensity cut

Emittance Measurement Beam Size and 90% intensity cut Normalized emittance: Emittance determination: (fit with χ 2 -method)

Trajectory Bump

Trajectory Amplitude in ACC39 Transfer matrix formulation Solution of equation of motion

Trajectory Amplitude in ACC39 Transfer matrix formulation Solution of equation of motion R1

Trajectory Amplitude in ACC39 Transfer matrix formulation Solution of equation of motion with R2 R3

Trajectory Amplitude in ACC39 Transfer matrix formulation Solution of equation of motion Resulting amplitude in the middle of the 3.9 GHz module with R4 R5

Results Emittance Measurement from 2010 Emittance Measurement from 2009 Diamonds: 3GUN Circles: 1GUN+2GUN Relative change of normalized emittance for different horizontal and vertical bump amplitudes

Error Analysis Image Analysis – Error of the beam size: 3% - 5% – Calibration of OTR monitors: 3% Emittance Calculation – Transfer matrices – Energy error: 2% quadrupole k-value – Error of normalized emittance: 2% horizontal and 4% vertical plane Trajectory – Calibration of steerer : 3% – Energy error (s.a.) – BPM calibration: 10% - 15% Statistical Errors – Beam size (CCD camera) < 5% Overall: 10% - 20% neglected

Conclusion The third harmonic module linearises the longitudinal phase space For standard operation the new system does not alter the projected transverse emittance The influence of wake-fields from the ACC39 cavities can be neglected

Results II Example plot x versus x‘ correlation between amplitude (x or y) and slope (x‘ or y‘) is linear at extreme amplitude: additional angle in the centre of the module Horizontal amplitude of 2.5mm in ACC39 Angle of 0.5mrad in the middle Additional amplitude at the end of the module of 0.5mm