FEL2014 - List of Keywords (impedance)

Paper	Title	Other Keywords	Page
MOP003	Helical Undulator Radiation in Internally Coated Metallic Pipe	radiation, vacuum, undulator, synchrotron-radiation	26
	T.L. Vardanyan, A. Grigoryan, L.V. Hovakimyan, M. Ivanyan, A.V. Tsakanian, V.M. Tsakanov CANDLE SRI, Yerevan, Armenia
	The vacuum chambers of many advanced undulator sources are coated internally in order to reduce the impedance of the vacuum chamber or improve the vacuum performance. Although the impedances and radiation properties of the internally coated metallic pipes for straightforward moving charge are well studied, the peculiarities of the particles wiggling motion on the radiation characteristics in such structure are missed. In this paper we obtain exact expressions for the fields of a particle moving along a spiral path, as in the single-layer resistive as well as in the two-layer metallic waveguides, modelling NEG coating of the waveguide walls. Based on these results, it will be possible to obtain the necessary characteristics of the radiation of helical undulators, very close to reality. The solution is obtained as a superposition of a particular solution of inhomogeneous Maxwell's equations in a waveguide with perfectly conducting walls, and the solutions of the homogeneous Maxwell equations in the single-layer and double-layer resistive waveguides. Solution in the form of the multipole expansion for inhomogeneous Maxwell's equations for a waveguide with perfectly conducting walls, are also obtained in this study.

TUP023	Modeling CSR in a Vacuum Chamber by Partial Fourier Analysis and the Discontinuous Galerkin Method	synchrotron-radiation, synchrotron, radiation, vacuum	419
	D. A. Bizzozero, J.A. Ellison UNM, Albuquerque, New Mexico, USA R.L. Warnock SLAC, Menlo Park, California, USA
	Funding: Work supported by DOE contracts DE-FG-99ER41104 and DE-AC03-76SF00515. We continue our study of CSR* from a bunch on an arbitrary curved orbit in a plane, which used a Fourier transform in s-ct. The vacuum chamber has rectangular cross section with possibly varying horizontal width. We use the slowly varying amplitude approximation, and invoke a Fourier expansion in the vertical coordinate y, which meets the boundary conditions on the top and bottom plates and makes contact with the Bessel equation of the frequency domain treatment. The fields are defined by a PDE in s and x, first order in s, which is discretized in x by finite differences (FD) or the discontinuous Galerkin method (DG). We compare results of FD and DG, and also compare to our earlier calculations in 3D (paraxial) which did not use the Fourier series in y,. This approach provides more transparency in the physical description, and when only a few y-modes are needed, provides a large reduction in computation time. See FEL13 Proceedings MOPSO06: http://accelconf.web.cern.ch/AccelConf/FEL2013/papers/mopso06.pdf ** See PRST-AB 7 054403 (2004) and Jpn. J. Appl. Phys. 51 016401 (2012).

Paper

Title

Other Keywords

Page

MOP003

Helical Undulator Radiation in Internally Coated Metallic Pipe

radiation, vacuum, undulator, synchrotron-radiation

26

T.L. Vardanyan, A. Grigoryan, L.V. Hovakimyan, M. Ivanyan, A.V. Tsakanian, V.M. Tsakanov
CANDLE SRI, Yerevan, Armenia

The vacuum chambers of many advanced undulator sources are coated internally in order to reduce the impedance of the vacuum chamber or improve the vacuum performance. Although the impedances and radiation properties of the internally coated metallic pipes for straightforward moving charge are well studied, the peculiarities of the particles wiggling motion on the radiation characteristics in such structure are missed. In this paper we obtain exact expressions for the fields of a particle moving along a spiral path, as in the single-layer resistive as well as in the two-layer metallic waveguides, modelling NEG coating of the waveguide walls. Based on these results, it will be possible to obtain the necessary characteristics of the radiation of helical undulators, very close to reality. The solution is obtained as a superposition of a particular solution of inhomogeneous Maxwell's equations in a waveguide with perfectly conducting walls, and the solutions of the homogeneous Maxwell equations in the single-layer and double-layer resistive waveguides. Solution in the form of the multipole expansion for inhomogeneous Maxwell's equations for a waveguide with perfectly conducting walls, are also obtained in this study.

TUP023

Modeling CSR in a Vacuum Chamber by Partial Fourier Analysis and the Discontinuous Galerkin Method

synchrotron-radiation, synchrotron, radiation, vacuum

419

D. A. Bizzozero, J.A. Ellison
UNM, Albuquerque, New Mexico, USA
R.L. Warnock
SLAC, Menlo Park, California, USA

Funding: Work supported by DOE contracts DE-FG-99ER41104 and DE-AC03-76SF00515.
We continue our study of CSR* from a bunch on an arbitrary curved orbit in a plane, which used a Fourier transform in s-ct. The vacuum chamber has rectangular cross section with possibly varying horizontal width. We use the slowly varying amplitude approximation, and invoke a Fourier expansion in the vertical coordinate y, which meets the boundary conditions on the top and bottom plates and makes contact with the Bessel equation of the frequency domain treatment. The fields are defined by a PDE in s and x, first order in s, which is discretized in x by finite differences (FD) or the discontinuous Galerkin method (DG). We compare results of FD and DG, and also compare to our earlier calculations in 3D (paraxial) which did not use the Fourier series in y*,**. This approach provides more transparency in the physical description, and when only a few y-modes are needed, provides a large reduction in computation time.
* See FEL13 Proceedings MOPSO06: http://accelconf.web.cern.ch/AccelConf/FEL2013/papers/mopso06.pdf
** See PRST-AB 7 054403 (2004) and Jpn. J. Appl. Phys. 51 016401 (2012).