IPAC2011 - List of Keywords (longitudinal-dynamics)

Paper	Title	Other Keywords	Page
WEPC062	Second Order Achromats with Arbitrary Linear Transfer Matrices	quadrupole, sextupole, focusing, beam-transport	2160
	V. Balandin, R. Brinkmann, W. Decking, N. Golubeva DESY, Hamburg, Germany
	The most obvious method to construct a second order achromat with an arbitrary (predefined) linear transfer matrix is to take a bend magnet system arranged in an achromat like fashion with the total transfer matrix equal to the identity matrix, attach a drift-quadrupole block with the desired linear transfer matrix and then adjust the sextupoles installed in the first part in such a way that the total system becomes a second order achromat. Unfortunately this is not always possible and, in general, the parts of such a system can not be designed independently. In this paper we give the necessary and sufficient conditions which must be satisfied for both parts of the system in order to become a second order achromat. In addition we provide some practical recommendations showing how these conditions can be fulfilled. We formulate these necessary and sufficient conditions using the group-theoretical point of view for the design of magnetic optical achromats as introduced in . V. Balandin, R. Brinkmann, W. Decking, N. Golubeva, "Two Cell Repetitive Achromats and Four Cell Mirror Symmetric Achromats", Proc. IPAC'10, Kyoto, Japan (2010).

Paper

Title

Other Keywords

Page

WEPC062

Second Order Achromats with Arbitrary Linear Transfer Matrices

quadrupole, sextupole, focusing, beam-transport

2160

V. Balandin, R. Brinkmann, W. Decking, N. Golubeva
DESY, Hamburg, Germany

The most obvious method to construct a second order achromat with an arbitrary (predefined) linear transfer matrix is to take a bend magnet system arranged in an achromat like fashion with the total transfer matrix equal to the identity matrix, attach a drift-quadrupole block with the desired linear transfer matrix and then adjust the sextupoles installed in the first part in such a way that the total system becomes a second order achromat. Unfortunately this is not always possible and, in general, the parts of such a system can not be designed independently. In this paper we give the necessary and sufficient conditions which must be satisfied for both parts of the system in order to become a second order achromat. In addition we provide some practical recommendations showing how these conditions can be fulfilled. We formulate these necessary and sufficient conditions using the group-theoretical point of view for the design of magnetic optical achromats as introduced in *.
* V. Balandin, R. Brinkmann, W. Decking, N. Golubeva, "Two Cell Repetitive Achromats and Four Cell Mirror Symmetric Achromats", Proc. IPAC'10, Kyoto, Japan (2010).