Topic description

Particle accelerators such as the synchrotron radiation source BESSY II, operated by the Helmholtz-Zentrum in Berlin-Adlershof, play an important role in basic research. For example, such sources enable the investigation and further development of solar cells and catalysts for green hydrogen or batteries.

The interaction of beams of charged particles with the vacuum chamber of particle accelerators is typically described in the frequency domain by the complex-valued and frequency-dependent beam coupling impedance. The broadest possible knowledge of the beam coupling impedances of particle accelerator components is of crucial importance, e.g. to avoid beam instabilities or excessive (local) thermal loading of the components.

Both the computer-aided calculation and the measurement of broadband beam coupling impedances in the laboratory are still a challenge. At the Helmholtz-Zentrum Berlin, the undulator department has set up a test stand for measuring undulators [1]. In simple terms, undulators can be thought of as large permanent magnets with periodically changing polarity. These are placed in the beam line and periodically deflect the particle beam in a transverse plane so that the charged particles radiate energy in a longitudinal direction.

The test stand shown in Figure 1 is based on a Goubau line [2]. The enameled copper wire stretched from the left horn to the right plate is intended to emulate the beam of charged particles. To measure the undulators or undulator components, they are now placed in the test stand in such a way that the copper wire runs along the imaginary beam trajectory.The frequency-dependent reflection factor measured at the horn is used to estimate the beam coupling impedance of the respective particle accelerator component.

However, this reflection factor is not only determined by the properties of the structure to be tested, but is also significantly influenced by the properties of the test stand (geometry of the horn, distance between the plates, reflection at the plates).

The aim of the work is to investigate whether and how the properties of the structure can be calculated from the reflection coefficient. To this end, it will be investigated whether typical calibration methods known from microwave technology are suitable in principle, whether they may need to be modified or whether they are completely unsuitable for the application described above.

The work is supported by our partners M.Sc. Paul Volz and Prof. Dr. Atoosa Meseck from the Johannes Gutenberg University Mainz and the Helmholtz-Zentrum Berlin.

Tasks

• Familiarization with the topics of beam coupling impedance, Goubau lines and fundamentals of calibration methods from microwave technology
• Creating a simplified model to describe the high-frequency characteristics of the test stand
• Investigation of the propagation behavior of the electromagnetic fields along the Goubau line, e.g. depending on the aperture of the horn
• Evaluation of the suitability of common methods for calibration, so that the reflections measured at the test stand are largely determined by the particle accelerator component and not by the properties of the test stand
• If necessary, modification of existing methods for calibrating the reflections generated by the test stand

Keywords
algorithmics, high-frequency technology, field simulation, linear algebra

Type of work
Bachelor's thesis, Master's thesis (scope and level will be adapted accordingly)

Supervisor
Prof. Dr.-Ing. Thomas Flisgen

Literature
[1] P. Volz und A. Meseck, Impedance Studies for Elliptical In-Vacuum Undulator IVUE32, International Conference on Synchrotron Radiation Instrumentation, Hamburg, Germany, 2024
[2] B. Vaughn und D. Peroulis, “An updated applied formulation for the Goubau transmission line”, Journal of Applied Physics 126, 2019, https://doi.org/10.1063/1.5125141
[3] P. Volz und A. Meseck, “Goubau-Line Set Up for Bench Testing Impedance of IVU32 Components”, in Proc. IPAC’22, Bangkok, Thailand, July 2022, pp. 2719 – 2721 (https://accelconf.web.cern.ch/ipac2022/papers/thpopt053.pdf)
[4] P. Volz and A. Meseck, “Goubau-Line Set Up for Bench Testing Impedance of IVU32 Components”, J. Phys.: Conf. Ser. 2380 012026, 2022 (https://iopscience.iop.org/article/10.1088/1742-6596/2380/1/012026)

Topic description

Particle accelerators such as the famous Large Hadron Collider or synchrotron radiation sources such as BESSY II, PETRA IV and the Diamond Light Source play an important role in basic research. Particle collision facilities enable the characterization of subatomic particles, while synchrotron radiation sources are helpful, for example, in the investigation and further development of solar cells or catalysts for green hydrogen or batteries.

The interaction of beams of charged particles with the vacuum chamber of particle accelerators is typically described in the frequency domain by the complex-valued and frequency-dependent beam coupling impedance. Broadband knowledge of the beam coupling impedances is important, e.g. to avoid beam instabilities or excessive (local) thermal loading of the components. Figure 1 shows the electric field excited by a beam of charged particles in a simple test resonator.

Measuring broadband beam coupling impedances of particle accelerator components is a challenge. Typically, test stands based on a wire are used for this purpose [1-6]. However, the introduction of a conducting wire into the structure significantly changes its high-frequency properties. On the one hand, a transverse electromagnetic wave can propagate through the wire in the longitudinal direction; on the other hand, the wire represents a significant disturbance of the high-frequency resonances, where a high longitudinal component of the electric field strength on the axis is expected. However, precise knowledge of the beam coupling impedances of these resonances is particularly important.

Recently, methods for the wireless measurement of beam coupling impedances have been proposed in the literature [7-9]. These methods do not require the insertion of a conductive wire into the structure. The high-frequency excitation is provided by couplers, which are attached to both sides of the structure (see Figure 2). These wireless methods appear promising as they overcome the above-mentioned disadvantages of the wired methods.

In this work, the properties of the wireless methods for highly resonant and for broadband accelerator components will be investigated by means of field simulations. The results based on scattering parameters are to be compared directly with the simulated beam coupling impedance. Advantages and disadvantages of wireless methods will be highlighted. The challenges of the concrete use of wireless methods in the measurement laboratory will also be considered.

The work is supported by our partner Dr.-Ing. Shahnam Gorgi Zadeh from the High Frequency Technology Group at CERN.

Tasks

• Familiarization with the topics of beam coupling impedance and the literature on wireless methods for measuring beam coupling impedances, including [7-9]
• Reproduction of basic simulation results in [7-9]
• Design of a resonant and a non-resonant test structure
• Creation of electromagnetic models of both structures
• Determination of the coupling impedances, in each case using wireless methods and directly using a numerical solver for beam coupling impedances
• Comparison of the results and working out the advantages and disadvantages of the wireless methods, possibly also in comparison to the methods based on a wire
• Discussion of possible difficulties in applying the methods in the laboratory

Keywords
algorithmics, high-frequency technology, field simulation

Type of work
Bachelor's thesis, Master's thesis (scope and level will be adapted accordingly)

Supervisor
Prof. Dr.-Ing. Thomas Flisgen

Literature
[1] P. Volz und A. Meseck, “Impedance Studies for Elliptical In-Vacuum Undulator IVUE32”, International Conference on Synchrotron Radiation Instrumentation, Hamburg, Germany, 2024
[2] P. Volz und A. Meseck, “Goubau-Line Set Up for Bench Testing Impedance of IVU32 Components”, in Proc. IPAC’22, Bangkok, Thailand, July 2022, pp. 2719 – 2721 (https://accelconf.web.cern.ch/ipac2022/papers/thpopt053.pdf)
[3] P. Volz and A. Meseck, “Goubau-Line Set Up for Bench Testing Impedance of IVU32 Components”, J. Phys.: Conf. Ser. 2380 012026, 2022 (https://iopscience.iop.org/article/10.1088/1742-6596/2380/1/012026)
[4] M. P. Sangroula, R. R. Lindberg, R. M. Lill und R. Zabel, “Measuring vacuum component impedance for the Argonne Advanced Photon Source upgrade”, Phys. Rev. Accel. Beams 23, Aug. 2020, doi.org/10.1103/PhysRevAccelBeams.23.082803
[5] S.Y. Kim, F. Stulle, C.K. Sung, K.H. Yoo, J. Seok, K.J. Moon et al.,“Characterization of the Goubau line for testing beam diagnostic instruments”, JINST 12 P12016, 2017, https://doi.org/10.1088/1748-0221/12/12/p12016
[6] V. G. Vaccaro, “Coupling impedance measurements: an improved wire method”, INFN, Rep. INFN/TC-94/023, pp. 1049–1052, 1994
[7] C. Antuono, A. Mostacci, A. Passarelli, C. Zannini, M. R. Masullo, and M. Migliorati, “A wireless method for beam coupling impedance bench measurement of resonant structures”, in Proc. 15th Int. Particle Accelerator Conf. (IPAC'24), Nashville, TN, USA, May 2024, paper THPC53, pp. 3124-3127.
[8] C. Antuono, M. Migliorati, A. Mostacci, and C. Zannini, “A Wireless Method for Beam Coupling Impedance Measurements of the LHC Goniometer”, in Proc. 68th Adv. Beam Dyn. Workshop High-Intensity High-Brightness Hadron Beams (HB’23), Geneva, Switzerland, Oct. 2023, pp. 407–410., doi:10.18429/JACoW-HB2023-THAFP05
[9] C. Antuono, M. Migliorati, A. Mostacci, E. Métral und C. Zannini, “A Wireless Method to Obtain the Impedance From Scattering Parameters”, in Proc. IPAC’22, Bangkok, Thailand, Jun. 2022, pp. 2213–2216, doi:10.18429/JACoW-IPAC2022-WEPOTK063