BEAM POSITION DIAGNOSTICS WITH HIGHER ORDER MODES ZHANG P. Księgarnia

Beam Position Diagnostics with Higher Order Modes in Third Harmonic Superconducting Accelerating Cavities

Higher order modes (HOM) are electromagnetic resonant fields. They can be excited by an electron beam entering an accelerating cavity, and constitute a component of the wake-field. This wake-field has the potential to dilute the beam quality and, in the worst case, result in a beam-break-up instability.

It is therefore important to ensure that these fields are well suppressed by extracting energy through special couplers. In addition, the effect of the transverse wake-field can be reduced by aligning the beam on the cavity axis. This is due to their strength depending on the transverse offset of the excitation beam. For suitably small offsets the dominant components of the transverse wake-field are dipole modes, with a linear dependence on the transverse offset of the excitation bunch. This fact enables the transverse beam position inside the cavity to be determined by measuring the dipole modes extracted from the couplers, similar to a cavity beam position monitor (BPM), but requires no additional vacuum instrumentation.

At the FLASH facility in DESY, 1.3 GHz (known as TESLA) and 3.9 GHz (third harmonic) cavities are installed. Wake-field in 3.9 GHz cavities are significantly larger than in the 1.3 GHz cavities. It is therefore important to mitigate the adverse effects of HOMs to the beam by aligning the beam on the electric axis of the cavities. This alignment requires an accurate beam position diagnostics inside the 3.9 GHz cavities. It is this aspect that is focused on in this thesis. Although the principle of beam diagnostics with HOM has been demonstrated on 1.3 GHz cavities, the realization in 3.9 GHz cavities is considerably more challenging. This is due to the dense HOM spectrum and the coupling of most HOMs amongst the four cavities in the third harmonic cryo-module.

1 Introduction
1.1 Free-electron Laser in Hamburg
1.2 Third Harmonic Cavities
1.3 Wakefields

2 Electromagnetic Eigenmode Simulations of the Third Harmonic Cavity
2.1 The Third Harmonic Cavity as a Periodic Structure
2.2 The Beam Pipe as a Circular Waveguide
2.3 Eigenmodes of an Ideal Third Harmonic Cavity

3 Measurements of HOM Spectra
3.1 Transmission Spectra of an Isolated Single Cavity
3.2 Module-Based Transmission Spectra
3.3 Beam-Excited HOM Spectra

4 Analysis Methods for Beam Position Extraction from HOM
4.1 Data Preparation
4.2 Direct Linear Regression
4.3 Singular Value Decomposition
4.4 k-means Clustering
4.5 Comparison of DLR, SVD and k-means Clustering

5 Dependencies of HOM on Transverse Beam O_- sets
5.1 Measurement Scheme
5.2 The Localized Dipole Beam-pipe Modes
5.3 Trapped Cavity Modes in the Fifth Dipole Band
5.4 Coupled Cavity Modes in the First and the Second Dipole Band

6 HOM-Based Beam Position Diagnostics
6.1 The Principle of Custom-built Test Electronics
6.2 Position Diagnostics with Trapped Cavity Modes
6.3 Position Diagnostics Based on a Band of Coupled Modes
6.4 Fundamental Limitations to Position Resolution

7 Conclusions
7.1 Summary
7.2 Future Studies on HOMBPM

A Mathematics
A.1 Direct Linear Regression
A.2 Singular Value Decomposition
A.3 Definitions of r2 and _r2
A.4 Definitions of Resolution
B Eigenmodes of an Ideal Third Harmonic Cavity
B.1 List of Eigenmodes
B.2 Electric Field Distributions
C Technical Details of the HOM Measurements

242 pages, Paperback

Po otrzymaniu zamówienia poinformujemy,
czy wybrany tytuł polskojęzyczny lub anglojęzyczny jest aktualnie na półce księgarni.