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First Order Perturbation Effects in Iron-Dominated Two-DimensionalSymmetrical Multipoles

Description: The effects of several perturbations are investigated. They are: modification of the shape of a pole, error excitation, displacement, and rotation of a pole. The effects are described in terms of changes of multipole coefficients. General relationships between some of these coefficients are described, and formulae are derived that allow their calculation for a model 2N-pole magnet. Numerical values of these coefficients are given for a quadrupole, sextupole, and octupole.
Date: April 1, 1969
Creator: Halbach, K.
Partner: UNT Libraries Government Documents Department

Forces and Stored Energy in Thin Cosine (n0) Accelerator Magnets

Description: We wish to compute Lorentz forces, equilibrium stress and stored energy in thin multipole magnets (Fig.1), that are proportional to cos(n{theta}) and whose strength varies purely as a Fourier sinusoidal series of the longitudinal coordinate z (say proportional to cos (2m-1){pi}z/L where L denotes the half-period and m = 1,2,3...). We shall demonstrate that in cases where the current is situated on such a surface of discontinuity at r = R (i.e. J = f({theta},z)), by computing the Lorentz force and solving the state of equilibrium on that surface, a closed form solution can be obtained for single function magnets as well as for any combination of interacting nested multi function magnets. The results that have been obtained, indicate that the total axial force on the end of a single multipole magnet n is independent (orthogonal) to any other multipole magnet i as long as n {ne} i. The same is true for the stored energy, the total energy of a nested set of multipole magnets is equal to the some of the energy of the individual magnets (of the same period length 2L). Finally we demonstrate our results on a nested set of magnets a dipole (n = 1) and a quadmpole (n=2) that have an identical single periodicity {omega}{sub 1}. We show that in the limiting 2D case (period 2L tends to infinity), the force reduces to the commonly known 2D case.
Date: March 18, 1996
Creator: Caspi, S.
Partner: UNT Libraries Government Documents Department

Preliminary study of using pipetron-type magnets for a pre-accelerator for the LHC

Description: One of the luminosity limitations of the LHC is the rather low injection energy (0.45 TeV) with respect to the collision energy (7 TeV). The magnetic multipoles in the main dipoles at low field and their dynamic behavior are considered to limit the achievable bunch intensity and emittance. We report on a preliminary study to increase the injection energy to 1.5 TeV using a two-beam pre-accelerator (LER) in the LHC tunnel. The LER is based on ''Pipetron'' magnets as originally proposed for the VLHC. The aim of the study is to assess the feasibility and to identify the critical processes or systems that need to be investigated and developed to render such a machine possible.
Date: June 1, 2006
Creator: de Rijk, G.; Rossi, L.; /CERN; Piekarz, H. & /Fermilab
Partner: UNT Libraries Government Documents Department

Effect of Wiggler insertions on the single-particle dynamics of the NLC main damping rings

Description: As they are expected to occupy a large portion of the lattice, wiggler insert ions will introduce significant linear and nonlinear perturbations to the single-particle dynamics in the NLC Main Damping Rings (MDR). The nonlinearities are of particular concern as a sufficiently large Dynamic Aperture (DA) is required for high injection efficiency. The main content of this report is a study of the wigglers impact on the DA of the NLC-MDR latest lattice design. The particle dynamics is modeled by transfer maps calculated by integration through the wiggler fields. For field representation we employed a 3D multipole expansion derived from the field data that were obtained with the aid of a magnet design code. Additional contents of this paper include an investigation of a simplified model of wiggler consisting of a sequence of standard magnet elements (where thin octupoles are used to represent the dominant nonlinearities) and the suggestion of a possible correction scheme to compensate the wiggler nonlinearities.
Date: July 30, 2003
Creator: Venturini, Marco
Partner: UNT Libraries Government Documents Department

Tracking of three variants of transition-free lattices for a proton driver

Description: Transition-free lattices are favored as possible realization of proton drivers. Several variants have been proposed, some of which have considerably different behavior. One of the main quantities used to characterize this behavior is the short term dynamic aperture (DA). In this note we study three different variants of such lattices, and show that the differences in DA among the lattices essentially disappear as soon as magnet multipole errors are included in the simulation. The tracking results can be understood in terms of the normal form based amplitude dependent tune shift and resonance strength coefficients.
Date: October 14, 2002
Creator: Johnstone, Bela Erdelyi and Carol
Partner: UNT Libraries Government Documents Department

Progress on muon parametric-resonance ionization cooling channel development

Description: Parametric-resonance Ionization Cooling (PIC) is intended as the final 6D cooling stage of a high-luminosity muon collider. To implement PIC, a continuous-field twin-helix magnetic channel was developed. A 6D cooling with stochastic effects off is demonstrated in a GEANT4/G4beamline model of a system where wedge-shaped Be absorbers are placed at the appropriate dispersion points in the twin-helix channel and are followed by short rf cavities. To proceed to cooling simulations with stochastics on, compensation of the beam aberrations from one absorber to another is required. Initial results on aberration compensation using a set of various-order continuous multipole fields are presented. As another avenue to mitigate the aberration effect, we optimize the cooling channel's period length. We observe a parasitic parametric resonance naturally occurring in the channel's horizontal plane due to the periodic beam energy modulation caused by the absorbers and rf. We discuss options for compensating this resonance and/or properly combining it with the induced half-integer parametric resonance needed for PIC.
Date: July 1, 2012
Creator: V.S. Morozov, Ya.S. Derbenev, A. Afanasev, K.B. Beard, R.P. Johnson, B. Erdelyi, J.A. Maloney
Partner: UNT Libraries Government Documents Department

Comparison of the dynamic apertures in the RHIC 100 GeV and 250 GeV polarized proton runs

Description: In this note we carry out dynamic aperture calcuations to understand the lifetime difference between the 2009 RHIC 100 GeV and 250 GeV polarized proton (p-p) runs. In these two runs the {beta}*s at the interatcion points (IPs) IP6 and IP8 are 0.7 m. We also compare the impacts of interaction region (IR) multipole errors with 2000 A and 5000 A triplet currents on the dynamic aperture. We calculated the dynamic apertures for RHIC 100 GeV and 250 GeV run lattices with same {beta}* = 0.7 m. We found that the dynamic apertures in units of mm are 12.5% and 4.3% smaller at 250 GeV than those at 100 GeV for particles with ({Delta}p/p0) = 3 x 0.0002828 and 3 x 0.0001414 respectively. However, in units of {sigma}, the dynamic apertures at 250 GeV are 36.4% and 51.7% bigger than those at 100 GeV. For particles with the same 3 x ({Delta}p/p0){sub rms}, the dynamic aperture at 250 GeV is almost twice of that at 100 GeV. We conclude that the lifetime difference for the 100 GeV and 250 GeV p-p runs with same {beta}* = 0.7 m lattices is mainly due to the fact that the relative rms momentum spread and rms transverse beam size are smaller than those at 100 GeV. If we install IR multipole errors of 5000 A triplet current to 100 GeV run, the dynamic apertures are reduced by 12.5% and 7% for particles with ({Delta}p/p0) = 3 x 0.0002828 and 3 x 0.0001414 particles, compared to that with IR multipole errors of 2000 A.
Date: January 1, 2011
Creator: Luo, Y.; Gu, X.; Fischer, W. & Trbojevic, D.
Partner: UNT Libraries Government Documents Department

Effect of Field Errors in Muon Collider IR Magnets on Beam Dynamics

Description: In order to achieve peak luminosity of a Muon Collider (MC) in the 10{sup 35} cm{sup -2}s{sup -1} range very small values of beta-function at the interaction point (IP) are necessary ({beta}* {le} 1 cm) while the distance from IP to the first quadrupole can not be made shorter than {approx}6 m as dictated by the necessity of detector protection from backgrounds. In the result the beta-function at the final focus quadrupoles can reach 100 km making beam dynamics very sensitive to all kind of errors. In the present report we consider the effects on momentum acceptance and dynamic aperture of multipole field errors in the body of IR dipoles as well as of fringe-fields in both dipoles and quadrupoles in the ase of 1.5 TeV (c.o.m.) MC. Analysis shows these effects to be strong but correctable with dedicated multipole correctors.
Date: May 1, 2012
Creator: Alexahin, Y.; Gianfelice-Wendt, E.; Kapin, V.V. & /Fermilab
Partner: UNT Libraries Government Documents Department

Sim Track User's Manual (v 1.0)

Description: SimTrack is a simple c++ library designed for the numeric particle tracking in the high energy accelerators. It adopts the 4th order symplectic integrator for the optical transport in the magnetic elements. The 4-D and 6-D weak-strong beam-beam treatments are integrated in it for the beam-beam studies. SimTrack is written with c++ class and standard template library. It provides versatile functions to manage elements and lines. It supports a large range of types of elements. New type of element can be easily created in the library. SimTrack calculates Twiss, coupling and fits tunes, chromaticities and corrects closed orbits. AC dipole and AC multipole are available in this library. SimTrack allows change of element parameters during tracking.
Date: January 27, 2010
Creator: Luo, Y.
Partner: UNT Libraries Government Documents Department


Description: The existence of multipole components in the dipole and quadrupole magnets is one of the factors limiting the beam stability in the RHIC operations. So, a realistic non-linear model is crucial for understanding the beam behavior and to achieve the ultimate performance in RHIC. A procedure is developed to build a non-linear model using the available multipole component data obtained from measurements of RHIC magnets. We first discuss the measurements performed at different stages of manufacturing of the magnets in relation to their current state in RHIC. We then describe the procedure to implement these measurement data into tracking models, including the implementation of the multipole feed down effect due to the beam orbit offset from the magnet center. Finally, the field quality analysis in the RHIC interaction regions (IR) is presented.
Date: June 25, 2007
Creator: BEEBE-WANG,J. & JAIN, A.
Partner: UNT Libraries Government Documents Department


Description: With the updated multipole magnet field errors in the interaction regions (IRs), detailed dynamic aperture studies are carried out around the current RHIC polarized proton (pp) working point. The beam parameters and {beta}*s are similar to those proposed for the next pp run. The effects on the dynamic apertures from nonlinear corrections, such as multipole field error correction in the IRs, second order chromaticity correction and horizontal third order resonance correction are evaluated. The sextupole components in the arc dipoles and the observed tune ripples are also considered.
Date: June 25, 2007
Creator: LUO,Y.; BAI, M.; BEEBE-WANG, J.; FISCHER, W.; JAIN, A.; MONTAG, C. et al.
Partner: UNT Libraries Government Documents Department

Forces in a Thin Cosine (nTheta) Helical Wiggler

Description: We wish to calculate the Lorentz body force associated with pure multipole helical magnetic fields (i.e, proportional to cos(n{theta})) whose strength varies purely as a Fourier sinusoidal series of the longitudinal coordinate z (say proportional to cos(2m-1){pi}z)/L, where L denotes the half-period of the wiggler field and m= 1,2,3... We also wish to apply such forces to the current sheet, and solve for the stress distribution required to maintain such a coil in equilibrium. In the calculations of Lorentz forces we include the self field contribution as well as possible contributions arising from additional nested helical windings. We shall demonstrate that in cases where the current is situated on a surface of discontinuity at r=R (i.e. J=f({theta},z)) and the Lorentz body force is integrated on that surface, a closed form solution for the stress distribution can be obtained and such a solution includes contributions from possible nested multi pole magnets. Finally we demonstrate that in the limiting 2D case where the field strength does not vary with z ( period 2L tends to infinity) the stress reduces to known 2D expressions.
Date: May 2, 1997
Creator: Caspi, S.
Partner: UNT Libraries Government Documents Department

Multipole Analysis of Circular Cylindircal Magnetic Systems

Description: This thesis deals with an alternate method for computing the external magnetic field from a circular cylindrical magnetic source. The primary objective is to characterize the magnetic source in terms of its equivalent multipole distribution. This multipole distribution must be valid at points close to the cylindrical source and a spherical multipole expansion is ill-equipped to handle this problem; therefore a new method must be introduced. This method, based upon the free-space Green's function in cylindrical coordinates, is developed as an alternative to the more familiar spherical harmonic expansion. A family of special functions, called the toroidal functions or Q-functions, are found to exhibit the necessary properties for analyzing circular cylindrical geometries. In particular, the toroidal function of zeroth order, which comes from the integral formulation of the free-space Green's function in cylindrical coordinates, is employed to handle magnetic sources which exhibit circular cylindrical symmetry. The toroidal functions, also called Q-functions, are the weighting coefficients in a ''Fourier series-like'' expansion which represents the free-space Green's function. It is also called a toroidal expansion. This expansion can be directly employed in electrostatic, magnetostatic, and electrodynamic problems which exhibit cylindrical symmetry. Also, it is shown that they can be used as an alternative to the Elliptic integral formulation. In fact, anywhere that an Elliptic integral appears, one can replace it with its corresponding Q-function representation. A number of problems, using the toroidal expansion formulation, are analyzed and compared to existing known methods in order to validate the results. Also, the equivalent multipole distribution is found for most of the solved problems along with its corresponding physical interpretation. The main application is to characterize the external magnetic field due to a six-pole permanent magnet motor in terms of its equivalent multipole distribution.
Date: January 9, 2006
Creator: Selvaggi, J
Partner: UNT Libraries Government Documents Department

Computing the External Magnetic Scalar Potential due to an Unbalanced Six-Pole Permanent Magnet Motor

Description: The accurate computation of the external magnetic field from a permanent magnet motor is accomplished by first computing its magnetic scalar potential. In order to find a solution which is valid for any arbitrary point external to the motor, a number of proven methods have been employed. Firstly, A finite element model is developed which helps generate magnetic scalar potential values valid for points close to and outside the motor. Secondly, charge simulation is employed which generates an equivalent magnetic charge matrix. Finally, an equivalent multipole expansion is developed through the application of a toroidal harmonic expansion. This expansion yields the harmonic components of the external magnetic scalar potential which can be used to compute the magnetic field at any point outside the motor.
Date: February 12, 2007
Creator: Selvaggi, J.; Salon, S.; Kwon, O. & Chari, M. V. K.
Partner: UNT Libraries Government Documents Department

Calculations of Higher Multipole Components in a Large Superconducting Quadrupole Magnet

Description: We analyze the magnetic field of a finite length, large bore superconducting quadrupole magnet for use in a large aperture, high momentum magnetic spectrometer.In particular, we study the 12-pole and 20-pole components which would contribute to geometric aberations.The magnet is 130 cm long, has a pole radius of 4.3 cm, and the field is largely iron dominated.We analyze the magnet with a nominal field gradient of 276 gauss/cm.The field and/or the scalar potential is calculated with the program TOSCA and decomposed consistent with magnetostatic theory.We establish that the small multipole components are determined reliably and consistently.We find that although the absolute magnitude of the higher order multipoles can become quite large near the ends of the magnet, they reverse sign in this region and their contributions to the field integral are quite small.At the pole radius the integral contributions of the 12-pole (n=6) and 20-pole (n=10) are ~ 1.2*10^-2 and ~ 2.4*10^-
Date: November 1, 1990
Creator: Napolitano, James
Partner: UNT Libraries Government Documents Department

Measurement of the N --> Delta^+ (1232) Transition at High-Momentum Transfer by pi^0 Electroproduction

Description: We report a new measurement of the exclusive electroproduction reaction gamma*_p --> pi0_p to explore the evolution from soft nonperturbative physics to hard processes via the Q2 dependence of the magnetic (M1+), electric (E1+), and scalar (S1+) multipoles in the N --> Delta transition. 9000 differential cross section data points cover W from threshold to 1.4 GeV/c2, 4pi center-of-mass solid angle, and Q2 from 3 to 6 GeV2/c2, the highest yet achieved. It is found that the magnetic form factor G^*M decreases with Q2 more steeply than the proton magnetic form factor, the ratio E1+/M1+ is small and negative, indicating strong helicity nonconservation, and the ratio S1+/M1+ is negative, while its magnitude increases with Q2.
Date: September 1, 2006
Creator: Ungaro, M.; Stoler, P.; Aznauryan, I.; Burkert, V. D.; Joo, K.; Smith, L. C. et al.
Partner: UNT Libraries Government Documents Department

MEG (Magnetoencephalography) multipolar modeling of distributed sources using RAP-MUSIC (Recursively Applied and Projected Multiple Signal Characterization)

Description: We describe the use of truncated multipolar expansions for producing dynamic images of cortical neural activation from measurements of the magnetoencephalogram. We use a signal-subspace method to find the locations of a set of multipolar sources, each of which represents a region of activity in the cerebral cortex. Our method builds up an estimate of the sources in a recursive manner, i.e. we first search for point current dipoles, then magnetic dipoles, and finally first order multipoles. The dynamic behavior of these sources is then computed using a linear fit to the spatiotemporal data. The final step in the procedure is to map each of the multipolar sources into an equivalent distributed source on the cortical surface. The method is illustrated through an application to epileptic interictal MEG data.
Date: January 1, 2001
Creator: Mosher, John C.; Baillet, Sylvain; Jerbi, Karim & Leahy, Richard M.
Partner: UNT Libraries Government Documents Department

New corrector system for the Fermilab booster

Description: We present an ambitious ongoing project to build and install a new corrector system in the Fermilab 8 GeV Booster. The system consists of 48 corrector packages, each containing horizontal and vertical dipoles, normal and skew quadrupoles, and normal and skew sextupoles. Space limitations in the machine have motivated a unique design, which utilizes custom wound coils around a 12 pole laminated core. Each of the 288 discrete multipole elements in the system will have a dedicated power supply, the output current of which is controlled by an individual programmable ramp. This paper describes the physics considerations which drove the design, as well as issues in the control of the system.
Date: June 1, 2007
Creator: Prebys, E.J.; Drennan, C.C.; Harding, D.J.; Kashikhin, V.; Lackey, J.R.; Makarov, A. et al.
Partner: UNT Libraries Government Documents Department

Hybrid MEG (Magnetoencephalography) source characterization by cortical remapping and imaging of parametric source models

Description: Reliable estimation of the local spatial extent of neural activity is a key to the quantitative analysis of MEG sources across subjects and conditions. In association with an understanding of the temporal dynamics among multiple areas, this would represent a major advance in electrophysiological source imaging. Parametric current dipole approaches to MEG (and EEG) source localization can rapidly generate a physical model of neural current generators using a limited number of parameters. However, physiological interpretation of these models is often difficult, especially in terms of the spatial extent of the true cortical activity. In new approaches using multipolar source models [3, 5], similar problems remain in the analysis of the higher-order source moments as parameters of cortical extent. Image-based approaches to the inverse problem provide a direct estimate of cortical current generators, but computationally expensive nonlinear methods are required to produce focal sources [1,4]. Recent efforts describe how a cortical patch can be grown until a best fit to the data is reached in the least-squares sense [6], but computational considerations necessitate that the growth be seeded in predefined regions of interest. In a previous study [2], a source obtained using a parametric model was remapped onto the cortex by growing a patch of cortical dipoles in the vicinity of the parametric source until the forward MEG or EEG fields of the parametric and cortical sources matched. The source models were dipoles and first-order multipoles. We propose to combine the parametric and imaging methods for MEG source characterization to take advantage of (i) the parsimonious and computationally efficient nature of parametric source localization methods and (ii) the anatomical and physiological consistency of imaging techniques that use relevant a priori information. By performing the cortical remapping imaging step by matching the multipole expansions of the original parametric source and the equivalent ...
Date: January 1, 2001
Creator: Baillet, S. (Sylvain); Mosher, J. C. (John C.); Jerbi, K. (Karim) & Leahy, R. M. (Richard M.)
Partner: UNT Libraries Government Documents Department


Description: Condensed phase physical and chemical processes generally involve interactions covering a wide range of distance scales, from short-range molecular interactions requiring orbital overlap to long-range coulombic interaction between local sites of excess charge (positive or negative monopoles). Intermediate-range distances pertain to higher-order multipolar as well as inductive and dispersion interactions. Efforts to model such condensed phase phenomena typically involve a multi-tiered strategy in which quantum mechanics is employed for full electronic structural characterization of a site of primary interest (e.g., a molecular solute or cluster), while more remote sites are treated at various classical limits (e.g., a molecular force field for discrete solvent molecules or a dielectric continuum (DC) model, if the solute is charged or has permanent multipole moments). In particular, DC models have been immensely valuable in modeling chemical reactivity and spectroscopy in media of variable polarity. Simple DC models account qualitatively for many important trends in the solvent dependence of reaction free energies, activation free energies, and optical excitation energies, and many results of semiquantitative or fully quantitative significance in comparison with experiment have been obtained, especially when detailed quantum chemical treatment of the solute is combined self consistently with DC treatment of the solvent (e.g., as in the currently popular PCM (polarized continuum model) approaches).
Date: November 1, 2006
Creator: NEWTON, M.D.
Partner: UNT Libraries Government Documents Department

Design and Measurement of the NSLS II Quadrupole Prototypes

Description: The design and measurement of the NSLS-II ring quadrupoles prototypes are presented. These magnets are part of a larger prototype program described in [1]. Advances in software, hardware, and manufacturing have led to some new level of insight in the quest for the perfect magnet design. Three geometric features are used to minimize the first three allowed harmonics by way of optimization. Validations through measurement and confidence levels in calculations are established.
Date: May 4, 2009
Creator: Rehak,M.; Jain, A. K.; Skaritka, J. & Spataro, C.
Partner: UNT Libraries Government Documents Department

Design of NSLS-II High Order Multipole Correctors

Description: Feasibility studies for two families of corrector magnets for NSLS-II are presented. The first family of magnets are generalizations of figure eight quadrupoles using rotationally symmetric breaks in the return yoke to fit in available space. Properties specific to figure eight magnet are identified. The second type of magnet is a combined sextupole/dipole trim.
Date: May 4, 2009
Creator: Rehak,M.; Danby, G.; Bengtsson, Jo; Jackson, J.; Skaritka, J. & Spataro, C.
Partner: UNT Libraries Government Documents Department