# Superconducting RF for high-beta accelerators

Instructors: Sergey Belomestnykh and Wencan Xu, Brookhaven National Laboratory

One-week course at USPAS 2011

Purpose and Audience

This graduate level course covers application of superconducting radio frequency (SRF) technology to contemporary high-beta accelerators: storage rings, pulsed and CW linacs, including energy recovery linacs (ERLs). The course will address physics and engineering aspects of using SRF in accelerators. It will cover beam-cavity interactions issues specific to superconducting cavities, a systems approach to designing SRF systems and engineering of superconducting cavity cryomodules. The course is intended for graduate students pursuing accelerator physics and graduate engineers and physicists who want to familiarize themselves with superconducting RF systems.

*Prerequisites: Classical mechanics, thermodynamics, electrodynamics, and physical or engineering mathematics, all at entrance graduate level.*

Objectives

Upon completion of this course, the students are expected to understand the physics underlying RF superconductivity and its application to accelerators, the advantages and limitations of SRF technology. The aim is to provide students with ideas and approaches enabling them to evaluate and solve problems related to application of superconducting cavities to accelerators, as well actively participate in engineering of SRF systems for various accelerators.

Instruction Method

This course includes a series of about 20 lectures and exercise sessions. Homework problems will be assigned which will be graded and answers provided in the exercise sessions. There will be an open-book, “take-home” final exam at the conclusion of the course.

Course Content

The course will include a brief introduction of the basic concepts of microwave cavities and the basic concepts of RF superconductivity. Then it will cover the beam-cavity interaction issues in accelerators: wake fields and higher-order modes (HOMs) in superconducting structures, associated with them bunched beam instabilities and approaches to deal with these instabilities (HOM absorbers and couplers, polarized cavities, etc.), bunch length manipulation with SRF cavities, beam loading effects, etc. Following that we will discuss a systems approach and its application to engineering of SRF systems for accelerators. Finally, we will address issues related to engineering of the SRF system components: cryostats, cavities, input couplers, HOM loads, and frequency tuners.

Reading Requirements

(*to be provided by USPAS*) “RF Superconductivity for Accelerators”, by H. Padamsee, J. Knobloch, and T. Hays, John Wiley & Sons, 2nd edition (2008).

It is * recommended* that students re-familiarize themselves with the fundamentals of electrodynamics at the level of “Fields and Waves in Communication Electronics“ (Chapters 1 through 11) by S. Ramo, J. R. Whinnery, and T. Van Duzer, John Wiley & Sons, 3rd edition (1994) or “Classical Electrodynamics” (Chapters 1 through 8) by J. D. Jackson, John Wiley & Sons, 3rd edition (1999).

Additional *suggested* reference books *(not provided by USPAS)*:

“Handbook of Accelerator Physics and Engineering”, edited by A. W. Chao and M. Tigner, World Scientific, 3rd print (2006)

“RF Superconductivity: Science, Technology, and Applications,” by H. Padamsee, Wiley-VCH (2009).

"Introduction to Wakefields and Wake Potentials" by P. B. Wilson, SLAC-PUB-4547 (1989).

"High Energy Electron Linacs: Application to Storage Ring RF Systems and Linear Colliders" by P. B. Wilson, SLAC-PUB-2884 (1982).

"Fundamental-Mode RF Design in e+e- Storage Ring Factories" by P. B. Wilson, SLAC-PUB-6062 (1993).

Credit Requirements

Students will be evaluated based on the following performances: final exam (40%), homework assignments and class participation (30%), Computer Lab project (20%).

**Computer Lab and Codes**

- During the Computer Lab sessions students will be working on a project using computer codes ABCI and SUPERFISH. The codes will be installed on the USPAS computers. The other codes that will be available on the USPAS computers are: MathCAD, MATLAB, Microsoft Office.
- Please keep in mind that commercial software (MathCAD, MATLAB, Microsoft Office) will not be available for installation on students' laptops due to licensing issues. Students will have to use USPAS computers to have access to these software if they do not have it. However, it will be sufficient to use Open Office or Google Docs instead although it may be a bit less convenient.
- ABCI code and documentation can be downloaded from the ABCI Home Page. It is available in Windows and Linux versions.
- SUPERFISH can be downloaded from the LANL Accelerator Code Group Download Area for Poisson Superfish. It has only Windows version.

**Computer Lab Project**

The objective of this project is to compare two different single-cell geometries of superconducting RF cavities for a high-current storage ring, such as a third-generation light source, using two computer codes: SUPERFISH and ABCI. The cavity fundamental mode frequency is 500 MHz, the accelerating voltage is 2 MV, the beam pipe diameter is 100 mm, the peak surface electric filed should not exceed 40 MV/m, the peak surface magnetic field should not exceed 100 mT, the Nb cavity is assumed to operate at 4.5 K. Beam parameters: the average current is 500 mA, the rms bunch length is 10 mm, the beam repetition frequency is 50 MHz.

**Elliptical cavity**

- Start with the provided sample ABCI input file.
- Run ABCI, make sure you understand how to run the program and review the results. Consult ABCI manual as necessary.
- Make an input file for SUPERFISH. Run SUPERFISH, review the results. Confirm that the fundamental mode frequency if 500 MHz (±1 MHz). Consult SUPERFISH manual as necessary.
- If the beam pipe diameter is not 100 mm, modify the geometry correspondingly, keeping the resonant frequency at 500±1 MHz.
- Calculate the cavity figures of merit, make sure that the peak fields stay within constrains.
- Calculate parameters of at least 5 lowest HOMs.
- Try to optimize the cavity geometry for better performance. Keep the geometry non-reentrant (Why do we want to do this?). Stay within constrains.
- We encourage you to develop a script using you favorite software (MATLAB, MathCAD, Excel,...) for generating new geometries.
- For the optimal geometry create ABCI input file.
- Run ABCI for the rms bunch length of 10 mm. Calculate the HOM loss factor.

**Quarter Wave Resonator (QWR)**

- Start with the provided sample SUPERFISH input file.
- Run SUPERFISH, make sure you understand how to run the program and review the results. Confirm that the fundamental mode frequency if 500 MHz (±1 MHz). Consult SUPERFISH manual as necessary.
- If the beam pipe diameter is not 100 mm, modify the geometry correspondingly, keeping the resonant frequency at 500±1 MHz.
- Calculate the cavity figures of merit, make sure that the peak fields stay within constrains.
- Calculate parameters of at least 5 lowest HOMs.
- Try to optimize the cavity geometry for better performance. Keep the geometry to be QWR (your optimization may try to morph the cavity to become more like a pillbox cavity with a nose-cone, so make sure that the length of the cavity coaxial part is close to the quarter-wave). Stay within constrains.
- We encourage you to develop a script using you favorite software (MATLAB, MathCAD, Excel,...) for generating new geometries.
- For the optimal geometry create ABCI input file.
- Run ABCI for the rms bunch length of 10 mm. Calculate the HOM loss factor.

**Comparison of two geometries**

- Based on the simulation results: i) compare performance of two cavities at fundamental mode (R/Q, Q0, RF power loss, peak fields, …); ii) compare HOM performance of two cavities (frequencies of HOMs, R/Q’s, HOM power, …).
- Write a report summarizing the results of your simulations and comparison of two geometries, make conclusions.

**Lecture Notes and Homework Problems**

**Monday**

*Fundamentals of RF and microwave engineering*

*Basic concepts of RF superconductivity*

**Tuesday**

*Derivation of the RF power formula for a beam loaded cavity can be found in RF_power_with_beam_loading.pdf*

**Wednesday**

**Thursday**

**Friday**

*Fabrication techniques and cavity preparation*

Questions? Send email to S. Belomestnykh or W. Xu.