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

Influence of the Third Harmonic Module on the Beam Size

Maria KuhnUniversity 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 ModuleLinearisation 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 ModuleLinearisation 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 cavityProblems:• wakes are 3x stronger than in 1.3 GHz module• non-symmetric structureConsequences:• beam off-axis• electrons are deflected• transverse kicks

Influence of Wake-Fields on Transverse Emittance

Influence of Wake-Fields on Transverse Emittance

Third harmonic module cavityProblems:• wakes are 3x stronger than in 1.3 GHz module• non-symmetric structureConsequences:• 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 MeasurementBeam Size and 90% intensity cut

Emittance MeasurementBeam Size and 90% intensity cut

Normalized emittance:

Emittance determination:

(fit with χ2-method)

Trajectory Bump

Trajectory Amplitude in ACC39Transfer matrix formulationSolution of equation of motion

Trajectory Amplitude in ACC39Transfer matrix formulationSolution of equation of motion

R1

Trajectory Amplitude in ACC39Transfer matrix formulationSolution of equation of motion

with

R2R3

Trajectory Amplitude in ACC39Transfer matrix formulationSolution 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 ACC39Angle of 0.5mrad in the middle Additional amplitude at the end of the module of 0.5mm