• V. Balandin, W. Decking, N. Golubeva
  DESY, Hamburg

The problem of errors, arising due to finite BPM resolution in the reconstructed orbit parameters, is one of the standard problems of the accelerator physics. Even so for the case of uncoupled motion the covariance matrix of reconstruction errors can be calculated "by hand", the usage of the obtained solution, as a tool for designing of a "good measurement system", is not straightforward. A better understanding of this problem is still desirable. We make a step in this direction by introducing dynamics into this problem, which seems to be static. We consider a virtual beam obtained as a result of the application of a reconstruction procedure to ‘‘all possible values'' of BPM reading errors. This beam propagates along the beam line according to the same rules as any real beam and has all beam dynamical characteristics, such as emittances, dispersions, betatron functions, and all these values describe the properties of the BPM measurement system. As an application we formulate requirements for the BPM measurement system of high-energy intra-bunch-train feedback system of the European XFEL Facility in terms of the introduced concepts of error emittance and error Twiss parameters.

• B. Faatz, N. Baboi, V. Balandin, W. Decking, S. Düsterer, J. Feldhaus, N. Golubeva, T. Laarmann, T. Limberg, D. Nölle, E. Plönjes, H. Schlarb, S. Schreiber, F. Tavella, K.I. Tiedtke, R. Treusch
  DESY, Hamburg
• J. Bahrdt, R. Follath, M. Gensch, K. Holldack, A. Meseck, R. Mitzner
  Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Elektronen-Speicherring BESSY II, Berlin
• M. Drescher, V. Miltchev, J. Roßbach
  Uni HH, Hamburg

FLASH has been a user facility since 2005, delivering radiation in the wavelength range between 7 and 47 nm using the SASE principle. In order to increase user beam time and improve the radiation properties delivered to users, a major extension of the user facility called FLASH II has been proposed by DESY in collaboration with the HZB, which is a seeded FEL over the parameter range of FLASH. As logical continuation, the HHG development program started with sFLASH, will result in direct seeding. Because in the foreseeable future there will probably not be HHG seed lasers available at high repetition rates down to wavelengths of 4 nm, a cascaded HGHG scheme will be used to produce short wavelengths. After a first design report, the project now enters its preparation phase until the decision for funding will be taken. During this time, the FLASH beam parameters after the present upgrade 2009/2010 will be characterized and the present design will be re-evaluated and adjusted. In addition, complete start-to-end simulations will complete the simulations which have been performed so far, including a complete design of the extraction area.

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

A straight drift-quadrupole system, though not being an achromat, can transport certain incoming beam ellipses without introducing first-order chromatic distortions. Several examples of such apochromatic beam transport are available in the literature. In this paper we show that the possibility of apochromatic focusing is a general property: For every drift-quadrupole system there exist an unique set of Twiss parameters (apochromatic Twiss parameters), which will be transported through that system without first order chromatic distortions. Moreover, we prove that at the same time the apochromatic Twiss parameters bring the second order effect of the betatron oscillations on the shift of the average bunch path length to the minimal possible value and also minimize the effect of betatron oscillations on bunch lengthening for Gaussian beam. As an example we consider the application of the apochromatic focusing concept to the design of matching sections and phase shifter of the post-linac collimation section of the European XFEL Facility.

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

An achromat is a focusing system, in which as large a number of higher order aberrations as possible is canceled by symmetries of the linear optics and the rest is corrected by the usage of third and higher order multipoles. The first achromats ever considered were repetitive achromats, in which the cancellation of higher order aberrations relies on appropriate selection of cell tunes. Later on achromats, employing mirror symmetry, were also developed. In this paper we remove one superfluous constraint on the linear optics in the theory of four cell mirror symmetric achromats, make an accurate consideration of two cell repetitive achromats, and compare the number of multipoles required for each of those achromats. Moreover, we contribute a point of view, from which both approaches to the achromat design become identical. As a practical application we consider the design of the arcs of the post-linac collimation section of the European XFEL Facility.

• N. Golubeva, V. Balandin, W. Decking
  DESY, Hamburg

We consider a beam line, in which pure betatron oscillations are transversely uncoupled, but which has nonzero horizontal and vertical dispersions simultaneously. We show that transverse oscillations in such a beam line could be chromatically coupled if the horizontal dispersion is nonzero in the vertical bending magnets and vice versa. We also show that the ability of sextupoles to generate chromatic coupling terms depends on the relation between sextupole tilt angles and the direction of the dispersion vector at the sextupole locations. We discuss different approaches to the setup of sextupole tilt angles depending on chromatic aberrations taken for correction. As a practical application we consider the usage of tilted sextupoles in the design of the beam switchyard at the European XFEL Facility.