Analytical expressions for fringe fields in multipole magnets

Fringe fields in multipole magnets can have a variety of effects on the linear and nonlinear dynamics of particles moving along an accelerator beamline. An accurate model of an accelerator must include realistic models of the magnet fringe fields. Fringe fields for dipoles are well understood and can be modelled at an early stage of accelerator design in such codes as MAD8, MADX or ELEGANT. However, usually it is not until the final stages of a design project that it is possible to model fringe fields for quadrupoles or higher order multipoles. Even then, existing techniques rely on the use of a numerical field map, which will usually not be available until the magnet design is well developed. Substitutes for the full field map exist but these are typically based on expansions about the origin and rely heavily on the assumption that the beam travels more or less on axis throughout the beam line. In some types of machine (for example, a non-scaling FFAG such as EMMA) this is not a good assumption. In this paper, a method for calculating fringe fields based on analytical expressions is presented, which allows fringe field effects to be included at the start of an accelerator design project. The magnetostatic Maxwell equations are solved analytically and a solution that fits all orders of multipoles derived. Quadrupole fringe fields are considered in detail as these are the ones that give the strongest effects. Two examples of quadrupole fringe fields are presented. The first example is a magnet in the LHC inner triplet, which consists of a set of four quadrupoles providing the final focus to the beam, just before the interaction point. Quadrupoles in EMMA provide the second example. In both examples, the analytical expressions derived in this paper for quadrupole fringe fields provide a good approximation to the field maps obtained from a numerical magnet modelling code.Comment: 27 pages, 39 figures. The figures are new with respect to the previous version, Several mistakes also correcte

Multipole fringe fields

Abstract When creating an initial model of an accelerator, one usually has to resort to a hard edge model for the quadrupoles and higher order multipoles at the start of the project. Ordinarily, it is not until much later on that one has a field map for the given multipoles. This can be rather inconvenient when one is dealing with particularly thin elements or elements which are rather close together in a beamline as the hard edge model may be inadequate for the level of precision desired. For example, in the EMMA project, the two types of quadrupoles used are so close together that they are usually described by a single field map or via hard edge models. The first method has the desired accuracy but was not available at the start of the project and the second is known to be a rough approximation. In this paper, an analytic expression is derived and presented for fringe fields for a multipole of any order with a view to applying it to cases like EMMA. FRINGE FIELDS FOR DIPOLES In order to have fringe fields, given by a → B which satisfy Maxwell's equations, it is important to write all equations down explicitly. For Dipoles, it is sufficient to consider a two dimensional version of the equations Now, if we take B x = 0, we are left with together with which excludes all dependence on x. Further, we seek fringe fields which have a possible fall-off on axis given by the six parameter Enge function [1] with E(z) given by and all a i constants determined by models and/or experiment, or any function which decays sufficiently rapidly. Maxwell's equations (1) imply z . Both wave equations (for B y and B z ) can be easily solved to give Hence, if we ask that equations (1) be solved as well, we end up with If we further restrict ourselves to real magnetic fields, we obtain so B y and B z are given by twice the real and imaginary parts of the function e(z + iy) respectively. A possibility for having a magnetic field whose B y component fall off on axis is given by the six parameter Enge function [1] as which would force B z to have the form for some complex function E(z + iy). If we consider the simple case E(z + iy) = z + iy then equation

Accelerator system for the PRISM based muon to electron conversion experiment

The next generation of lepton flavor violation experiments need high intensity and high quality muon beams. Production of such beams requires sending a short, high intensity proton pulse to the pion production target, capturing pions and collecting the resulting muons in the large acceptance transport system. The substantial increase of beam quality can be obtained by applying the RF phase rotation on the muon beam in the dedicated FFAG ring, which was proposed for the PRISM project.This allows to reduce the momentum spread of the beam and to purify from the unwanted components like pions or secondary protons. A PRISM Task Force is addressing the accelerator and detector issues that need to be solved in order to realize the PRISM experiment. The parameters of the required proton beam, the principles of the PRISM experiment and the baseline FFAG design are introduced. The spectrum of alternative designs for the PRISM FFAG ring are shown. Progress on ring main systems like injection and RF are presented. The current status of the study and its future directions are discussed.Comment: Studies performed within the PRISM Task Force initiativ

Elovl5 is required for proper action potential conduction along peripheral myelinated fibers

Elovl5 elongates fatty acids with 18 carbon atoms and in cooperation with other enzymes guarantees the normal levels of very long‐chain fatty acids, which are necessary for a proper membrane structure. Action potential conduction along myelinated axons depends on structural integrity of myelin, which is maintained by a correct amount of fatty acids and a proper interaction between fatty acids and myelin proteins. We hypothesized that in Elovl5 (−/−) mice, the lack of elongation of Elovl5 substrates might cause alterations of myelin structure. The analysis of myelin ultrastructure showed an enlarged periodicity with reduced G‐ratio across all axonal diameters. We hypothesized that the structural alteration of myelin might affect the conduction of action potentials. The sciatic nerve conduction velocity was significantly reduced without change in the amplitude of the nerve compound potential, suggesting a myelin defect without a concomitant axonal degeneration. Since Elovl5 is important in attaining normal amounts of polyunsaturated fatty acids, which are the principal component of myelin, we performed a lipidomic analysis of peripheral nerves of Elovl5‐deficient mice. The results revealed an unbalance, with reduction of fatty acids longer than 18 carbon atoms relative to shorter ones. In addition, the ratio of saturated to unsaturated fatty acids was strongly increased. These findings point out the essential role of Elovl5 in the peripheral nervous system in supporting the normal structure of myelin, which is the key element for a proper conduction of electrical signals along myelinated nerves

Temperatura e pH de carcaças de bovinos abatidos sob inspeção municipal em Teresina, Piauí.

O objetivo deste trabalho foi avaliar a temperatura e o pH de carcaças não resfriadas de bovinos abatidos em estabelecimentos sob inspeção municipal em Teresina, Piauí, bem como o efeito do tempo de repouso pré-abate sobre estes parâmetros..

A Hard X-Ray Compton Source at CBETA

Inverse Compton scattering (ICS) holds the potential for future high flux, narrow bandwidth x-ray sources driven by high quality, high repetition rate electron beams. CBETA, the Cornell-BNL Energy recovery linac (ERL) Test Accelerator, is the world’s first superconducting radiofrequency multi-turn ERL, with a maximum energy of 150 MeV, capable of ICS production of x-rays above 400 keV. We present an update on the bypass design and anticipated parameters of a compact ICS source at CBETA. X-ray parameters from the CBETA ICS are compared to those of leading synchrotron radiation facilities, demonstrating that, above a few hundred keV, photon beams produced by ICS outperform those produced by undulators in term of flux and brilliance