Impedance models for the Rapid Cycling Synchrotron 1 #
The RCS1 is the first circular machine in the muon collider complex. It accelerates the two muon/anti-muon bunches from 63 GeV to 300 GeV.
Assumptions for the impedance model #
A pure metallic beam pipe would face the issue of eddy currents because of the fast magnetic cycle. Solutions adopted in existing RCS is to have a ceramic (alumina) beam pipe with an outer (or inner at ISIS) RF shielding made of copper stripes. The inside part of the chamber is usually coated with Titanium Nitride for vacuum performance.
A few references for the JPARC vacuum chamber design:
- https://accelconf.web.cern.ch/p05/PAPERS/MPPP025.PDF
- https://accelconf.web.cern.ch/IPAC2012/papers/weppr056.pdf
- https://accelconf.web.cern.ch/abdwhb06/PAPERS/TUBX01.PDF
- JPARC CDR, from page 447 : https://cds.cern.ch/record/747209/files/34072617.pdf
- https://avs.scitation.org/doi/pdf/10.1116/1.1468656
- https://indico.fnal.gov/event/16269/contributions/36516/attachments/22688/28130/J-PARC-RCS-Vacuum-Chambers.pdf
- https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1591197
Similar to JPARC, we assume a ceramic chamber (10 mm thickness), with an inner TiN coating of 15 nm and an outer RF shielding made of copper stripes (0.5 mm thickness). Since IW2D simulates axisymetric structures, we approximate the copper stripes as an uniform copper layer.
The ceramic layer thickness assumed to be quite large: in JPARC CDR, quadrupole chambers are 7.5mm thick and dipole chambers are 15mm thick. This is becuase of the strength required to withstand the sintering process.
The material used has simply the same properties as a vacuum.
In this part we will create simple Resistive Wall impedance models using the PyWIT interface for IW2D, the materials library and IW2D for the actual computation.
Various classic materials will be used to visualize their properties. We start with pipes having an infinite thickness to then go to a more realistic one.
Chamber geometric parameters:
| Item | Unit | Value |
|---|---|---|
| Machine | / | RCSLE |
| Total machine length | m | 5990 |
| Average beta function | m | 50 |
| Chamber length | m | 5990 |
| Chamber geometry | / | Circular |
| Chamber inner radius | m | 30e-3 |
| Chamber material 1 | / | Titanium nitride TiN at 300K |
| Chamber thickness 1 | m | 15e-9 |
| Chamber material 2 | / | Ceramic |
| Chamber thickness 2 | m | 10e-3 |
| Chamber material 3 | / | Copper |
| Chamber thickness 3 | m | 5e-4 |
| Chamber material 4 | / | Vacuum |
| Chamber thickness 4 | m | Inf |
The materials used have the following properties:
| Material | DC Resistivity / Ohm m | epsilonr |
|---|---|---|
| TiN | 1 | |
| Copper | 1 | |
| Ceramic HA-997 | 50 |