Requirement document
ESS reference
Optimizations of the superconducting linac
Creation date : 2010/07/13
Page 1 / 6
Requirement document
for the
framework of the optimization of the
geometrical betas and number of cells for
the superconducting linac resonators
WP 2
ESS Accelerator
PBS code: 1.2.1.1.1.2 and 1.2.2.2.1.1
Originator
Name
Fonction
Date
Visa
Reviewer
R. Duperrier
Name
S. Peggs
Approver
Name
System engineer of the
Fonction WP 2 leader of the Accelerator Fonction
Accelerator Design Update
Design Update
2010/07/13
Date
Date
Visa
Visa
M. Lindroos
Coordinator of the Accelerator
Design Update
This document is the property of the ESS AB. It can copied or disseminate without the authorization of the ESS AB.
Reduced ESS
reference
RD for Optimizations of the superconducting linac
Page 2 / 6
Release
No.
1
2
3
4
Date
Revision Description
2010/07/13 Distances between cryomodule wall and cavity have been
changed.
2010/07/14 Two different currents have been included.
2010/07/15 Frequencies for the different sections are added.
2010/09/12 Additional informations for the constraints of the optimisation
DISTRIBUTION LIST
Internal
External
Mats Lindroos, Steve Peggs, Mohamad Eshraqi, Aurélien
Ponton, S. Bousson, G. Devanz
This document is the property of the ESS AB. It can copied or disseminate without the authorization of the ESS AB.
Reduced ESS
reference
RD for Optimizations of the superconducting linac
Page 3 / 6
TABLE OF CONTENTS
1. Scope of the system ............................................................................................... 4
1.1. Identification ............................................................................................................................ 4
1.2. Purpose .................................................................................................................................... 4
1.3. Stakeholders ............................................................................................................................ 4
2. Requirements .......................................................................................................... 4
2.1. Functional requirements......................................................................................................... 4
2.2. Performance requirements ..................................................................................................... 5
2.3. Interface requirements (definition of the interfaces) ............................................................ 5
3. Verification methods ............................................................................................... 6
4. Traceability matrix ................................................................................................... 6
5. References ............................................................................................................... 6
This document is the property of the ESS AB. It can copied or disseminate without the authorization of the ESS AB.
Reduced ESS
reference
RD for Optimizations of the superconducting linac
Page 4 / 6
1. Scope of the system
1.1. Identification
The framework of the optimization of the geometrical betas and number of cells of the superconducting
linac resonators establishes the guidelines to conduct the single particle studies that allow determining
the values for these parameters in agreement with the requirements described hereafter.
1.2. Purpose
The described framework allows defining clear and documented pre-requisites to conduct the
optimizations and establishes a common basis for the layout comparisons. It is an essential part of the
selection process for several important parameters of the superconducting linac.
1.3. Stakeholders
The system engineer, WP2 and WP5 define the framework. The optimizations are performed by WP2.
2. Requirements
2.1. Functional requirements





The sought efficiency is the best real estate gradients.
The layouts must respect the state of art for designing high current proton linac:
o continuity of the longitudinal acceptance,
o low rate for the phase advance per meter evolution, the zero current phase advance
change has to be negligible compared to the zero current phase advance for each
focusing period,
o the provided acceptance has to be large enough to avoid loss in presence of
imperfections.
The layout has to provide realistic spaces for the insertion of magnets, cavities, beam
instrumentations, pumping systems, bellows.
Number of cells per resonator and number of cavities per cryomodules will be optimized.
Transverse focusing will be based on either two warm magnets in a warm section (SNS like) or
two superconducting quadrupoles in a common cryomodule (Tesla like, no warm to cold
transition).
This document is the property of the ESS AB. It can copied or disseminate without the authorization of the ESS AB.
Reduced ESS
reference
RD for Optimizations of the superconducting linac
Page 5 / 6
2.2. Performance requirements











The proton superconducting linacs will have to cover two possible energy ranges [50,
2500] MeV and [100, 2500] MeV.
Two peak currents will be studied, 50 and 75 mA.
Layouts based on the energy range [50, 2500 MeV] will contain: one section with spoke
resonator and two sections with elliptical cavities.
Layouts based on the energy range [100, 2500 MeV] will contain three sections with elliptical
cavities.
Sections with spoke resonators will use one single geometrical beta and a frequency of
352.21 MHz.
Sections with elliptical cavities will use either one or two or three different geometrical betas and
a frequency of 704.42 MHz.
Spokes will be based on either 2 or 3 or 4 stems.
Elliptical cavities will be based on either 4 or 5 or 6 cells.
No limitation for the power coupler per resonator will be considered.
The longitudinal acceptance has to provide a safe factor equal to 8 times the expected rms
bunch size, the longitudinal rms emittance (zz') is assumed to be equal to 0.5 .mm.mrad.
Two maximum accelerating gradients for each resonator will be considered:
o 6 or 8 MV/m for the spokes,
o 15 or 20 MV/m for the high betas elliptical cavities, the low beta sections being scaled
according to the law Eacc [MV/m] = g*(18,2-5,7*g)*B[mT]/50.
2.3. Interface requirements

Distances for the warm magnet version:
o distance between quadrupoles equal to 400 mm,
o distance quadrupole and cryomodule wall equal to 200 mm,
o distance between cryomodule wall and cavity equal to 300 and 450 mm (spokes and
ell.),
o distance between cavities equal to 300 and 400 mm (spokes and ell.),
o quadrupole length equal to 250 and 400 mm (spokes and ell.),
o cavity length equal to the number of cells times 0,5x with  the geometrical reduced
speed and  the wavelength of the resonator.

Distances for the cold magnet version:
o distance between quadrupoles equal to 400 mm,
o distance quadrupole and cryomodule wall equal to 250 mm,
o distance between cryomodule wall and cavity equal to 300 and 450 mm (spokes and
ell.),
o distance between cavities equal to 300 and 400 mm (spokes and ell.),
o quadrupole length equal to 250 and 400 mm (spokes and ell.),
o distance between quadrupole and cavity equal to 400 mm,
This document is the property of the ESS AB. It can copied or disseminate without the authorization of the ESS AB.
Reduced ESS
reference
RD for Optimizations of the superconducting linac
Page 6 / 6
o cavity length equal to the number of cells times 0,5x with  the geometrical reduced
speed and  the wavelength of the resonator.
3. Verification methods and outputs
An algorithm to obtain optimized layout in agreement with requirements has to be established and
documented. Parametric plots showing that the algorithm allows finding optimum values will be
detailled.
The required production yield for each resonator will be provided.
4. Traceability matrix
This is a table that traces the requirements in this document to the higher level requirements or if this is
a top level requirements document, it should trace to the User Requirements or needs
5. References
M. Eshraqi, All the ESS cryos, SPL/ESS meeting, Lund, Sweden, june 2010.
This document is the property of the ESS AB. It can copied or disseminate without the authorization of the ESS AB.