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DESIGN AND SHIELDING OF A BEAM LINE FROM ELENA TO ATRAP USING ELECTROSTATIC QUADRUPOLE LENSES AND BENDS

Description: The construction of the Extra Low ENergy Antiprotons (ELENA) upgrade to the Antiproton Decelerator (AD) ring has been proposed at CERN to produce a greatly increased current of low-energy antiprotons for various experiments including anti-hydrogen studies. This upgrade involves the addition of a small storage ring and electrostatic beam lines. The 5.3-MeV antiproton beams from AD are decelerated down to 100 keV in the compact ring and transported to each experimental apparatus. In this paper, we describe an electrostatic beam line from the ELENA ring to the ATRAP experimental apparatus and magnetic shielding of the low-energy beam line against the ATRAP superconducting solenoid magnet. A possible rough conceptual design of this system is displayed.
Date: September 1, 2010
Creator: Yuri, Yosuke & Lee, Edward P.
Partner: UNT Libraries Government Documents Department

Solenoidal Fields for Ion Beam Transport and Focusing

Description: In this report we calculate time-independent fields of solenoidal magnets that are suitable for ion beam transport and focusing. There are many excellent Electricity and Magnetism textbooks that present the formalism for magnetic field calculations and apply it to simple geometries [1-1], but they do not include enough relevant detail to be used for designing a charged particle transport system. This requires accurate estimates of fringe field aberrations, misaligned and tilted fields, peak fields in wire coils and iron, external fields, and more. Specialized books on magnet design, technology, and numerical computations [1-2] provide such information, and some of that is presented here. The AIP Conference Proceedings of the US Particle Accelerator Schools [1-3] contain extensive discussions of design and technology of magnets for ion beams - except for solenoids. This lack may be due to the fact that solenoids have been used primarily to transport and focus particles of relatively low momenta, e.g. electrons of less than 50 MeV and protons or H- of less than 1.0 MeV, although this situation may be changing with the commercial availability of superconducting solenoids with up to 20T bore field [1-4]. Internal reports from federal laboratories and industry treat solenoid design in detail for specific applications. The present report is intended to be a resource for the design of ion beam drivers for Inertial Fusion Energy [1-5] and Warm Dense Matter experiments [1-6], although it should also be useful for a broader range of applications. The field produced by specified currents and material magnetization can always be evaluated by solving Maxwell's equations numerically, but it is also desirable to have reasonably accurate, simple formulas for conceptual system design and fast-running beam dynamics codes, as well as for general understanding. Most of this report is devoted to such formulas, but an introduction to ...
Date: November 1, 2007
Creator: Lee, Edward P. & Leitner, Matthaeus
Partner: UNT Libraries Government Documents Department

Precision matched solution of the coupled beam envelope equations for a periodic quadrupole lattice with space charge

Description: The coupled Kapchinskij-Vladimirskij (K-V) envelope equations for a charged particle beam transported by a periodic system of quadrupoles with self-consistent space charge force have previously been solved by various approximate methods, with accuracy ranging from 1% to 10%. A new method of solution is introduced here, which is based on a double expansion of the beam envelope functions in powers of the focal strength and either the beam's emittance or its dimensionless perveance. This method results in accuracy better than 0.1% for typical lattice and beam parameters when carried through one consistent level of approximation higher than employed in previous work. Several useful quantities, such as the values of the undepressed tune and the beam's perveance in the limit of vanishing emittance, are represented by very rapidly converging power series in the focal strength, with accuracy of .01% or better.
Date: February 1, 2002
Creator: Lee, Edward P.
Partner: UNT Libraries Government Documents Department

Emittance growth for the thermalization of space-charged nonuniformities

Description: Beams injected into a linear focusing channel typically have some degree of space-charge nonuniformity. In general, injected particle distributions with systematic charge nonuniformities are not equilibria of the focusing channel and launch a broad spectrum of collective modes. These modes can phase-mix and have nonlinear wave-wave interactions which, at high space-charge intensities, results in a relaxation to a more thermal-like distribution characterized by a uniform density profile. This thermalization can transfer self-field energy from the initial space-charge nonuniformity to the local particle temperature, thereby increasing beam phase space area (emittance growth). In this paper, we employ a simple kinetic model of a continuous focusing channel and build on previous work that applied system energy and charge conservation to quantify emittance growth associated with the collective thermalization of an initial azimuthally symmetric, rms matched beam with a radial density profile that is hollowed or peaked. This emittance growth is shown to be surprisingly modest even for high beam intensities with significant radial structure in the initial density profile.
Date: March 1, 2001
Creator: Lund, Steven M.; Barnard, John J. & Lee, Edward P.
Partner: UNT Libraries Government Documents Department

Bends and momentum dispersion during final compression in heavy ion fusion drivers

Description: Between the accelerator and fusion chamber the heavy ion beams are subject to a dramatic but vital series of manipulations, some of which are carried out simultaneously and involve large space charge forces. The beams' quality must be maintained at a level sufficient for the fusion application; this general requirement significantly impacts beam line design, especially in the considerations of momentum dispersion. Immediately prior to final focus onto a fusion target, heavy ion driver beams are compressed in length by typically an order of magnitude. This process is simultaneous with bending through large angles to achieve the required target illumination configuration. The large increase in beam current is accommodated by a combination of decreased lattice period, increased beam radius, and increased strength of the beamline quadrupoles. However, the large head-to-tail momentum tilt (up to 5%) needed to compress the pulse results in a very significant dispersion of the pulse centroid from the design axis. General design features are discussed. A principal design goal is to minimize the magnitude of the dispersion while maintaining approximate first order achromaticity through the complete compression/bend system. Configurations of bends and quadrupoles, which achieve this goal while simultaneously maintaining a locally matched beam-envelope, are analyzed.
Date: January 23, 2002
Creator: Lee, Edward P. & Barnard, John J.
Partner: UNT Libraries Government Documents Department

Efficient computation of matched solutions of the KV envelopeequation for periodic focusing lattices

Description: A new iterative method is developed to numerically calculate the periodic, matched beam envelope solution of the coupled Kapchinskij-Vladimirskij (KV) equations describing the transverse evolution of a beam in a periodic, linear focusing lattice of arbitrary complexity. Implementation of the method is straightforward. It is highly convergent and can be applied to all usual parameterizations of the matched envelope solutions. The method is applicable to all classes of linear focusing lattices without skew couplings, and also applies to parameters where the matched beam envelope is strongly unstable. Example applications are presented for periodic solenoidal and quadrupole focusing lattices. Convergence properties are summarized over a wide range of system parameters.
Date: January 3, 2006
Creator: Lund, Steven M.; Chilton, Sven H. & Lee, Edward P.
Partner: UNT Libraries Government Documents Department

Transverse centroid oscillations in solenoidially focused beam transport lattices

Description: Linear equations of motion are derived that describe small-amplitude centroid oscillations induced by displacement and rotational misalignments of the focusing solenoids in the transport lattice, dipole steering elements, and initial centroid offset errors. These equations are analyzed in a local rotating Larmor frame to derive complex-variable"alignment functions" and"bending functions" that efficiently describe the characteristics of the centroid oscillations induced by mechanical misalignments of the solenoids and dipole steering elements. The alignment and bending functions depend only on properties of the ideal lattice in the absence of errors and steering and have associated expansion amplitudes set by the misalignments and steering fields. Applications of this formulation are presented for statistical analysis of centroid deviations, calculation of actual lattice misalignments from centroid measurements, and optimal beam steering.
Date: August 1, 2008
Creator: Lund, Steven M.; Wootton, Christopher J. & Lee, Edward P.
Partner: UNT Libraries Government Documents Department

Drift Compression and Final Focus Options for Heavy Ion Fusion

Description: A drift compression and final focus lattice for heavy ion beams should focus the entire beam pulse onto the same focal spot on the target. We show that this requirement implies that the drift compression design needs to satisfy a self-similar symmetry condition. For un-neutralized beams, the Lie symmetry group analysis is applied to the warm-fluid model to systematically derive the self-similar drift compression solutions. For neutralized beams, the 1-D Vlasov equation is solved explicitly, and families of self-similar drift compression solutions are constructed. To compensate for the deviation from the self-similar symmetry condition due to the transverse emittance, four time-dependent magnets are introduced in the upstream of the drift compression such that the entire beam pulse can be focused onto the same focal spot.
Date: February 14, 2005
Creator: Qin, Hong; Davidson, Ronald C.; Barnard, John J. & Lee, Edward P.
Partner: UNT Libraries Government Documents Department

Drift Compression and Final Focus for Intense Heavy Ion Beams with Non-periodic, Time-dependent Lattice

Description: In the currently envisioned configurations for heavy ion fusion, it is necessary to longitudinally compress the beam bunches by a large factor after the acceleration phase. Because the space-charge force increases as the beam is compressed, the beam size in the transverse direction will increase in a periodic quadrupole lattice. If an active control of the beam size is desired, a larger focusing force is needed to confine the beam in the transverse direction, and a non-periodic quadrupole lattice along the beam path is necessary. In this paper, we describe the design of such a focusing lattice using the transverse envelope equations. A drift compression and final focus lattice should focus the entire beam pulse onto the same focal spot on the target. This is difficult with a fixed lattice, because different slices of the beam may have different perveance and emittance. Four time-dependent magnets are introduced in the upstream of drift compression to focus the entire pulse onto the sam e focal spot. Drift compression and final focusing schemes are developed for a typical heavy ion fusion driver and for the Integrated Beam Experiment (IBX) being designed by the Heavy Ion Fusion Virtual National Laboratory.
Date: February 14, 2005
Creator: Qin, Hong; Davidson, Ronald C.; Barnard, John J. & Lee, Edward P.
Partner: UNT Libraries Government Documents Department

Drift compression and final focus options for heavy ionfusion

Description: A drift compression and final focus lattice for heavy ion beams should focus the entire beam pulse onto the same focal spot on the target. The authors show that this requirement implies that the drift compression design needs to satisfy a self-similar symmetry condition. For un-neutralized beams, the Lie symmetry group analysis is applied to the warm-fluid model to systematically derive the self-similar drift compression solutions. For neutralized beams, the 1D Vlasov equation is solved explicitly and families of self-similar drift compression solutions are constructed. To compensate for the deviation from the self-similar symmetry condition due to the transverse emittance, four time-dependent magnets are introduced in the upstream of the drift compression such that the entire beam pulse can be focused onto the same focal spot.
Date: January 18, 2005
Creator: Qin, Hong; Davidson, Ronald C.; Barnard, John J. & Lee, Edward P.
Partner: UNT Libraries Government Documents Department

Drift compression and final focus of intense heavy ion beams

Description: The longitudinal and transverse dynamics of a heavy ion fusion beam during the drift compression and final focus phase is studied. A lattice design with four time-dependent magnets is described that focuses the entire beam pulse onto a single focal point with the same spot size.
Date: May 2003
Creator: Qin, Hong; Davidson, Ronald C.; Barnard, John J. & Lee, Edward P.
Partner: UNT Libraries Government Documents Department

Cold phase fluid model of the longitudinal dynamics ofspace-charged dominated beams

Description: The dynamics of a longitudinally cold, charged-particle beam can be simulated by dividing the beam into slices and calculating the motion of the slice boundaries due to the longitudinal electric field generated by the beam. On each time step, the beam charge is deposited onto an (r, z) grid, and an existing (r, z) electrostatic field solver is used to find the longitudinal electric field. Transversely, the beam envelope equation is used for each slice boundary separately. In contrast to the g-factor model, it can be shown analytically that the repulsive electric field of a slice compressed to zero length is bounded. Consequently, this model allows slices to overtake their neighbors, effectively incorporating mixing. The model then effectively describes a cold fluid in longitudinal z, v{sub z} phase space. Longitudinal beam compression calculations based on this cold phase fluid model showed that slice overtaking reflects local mixing, while the global phase space structure is preserved.
Date: March 1, 2002
Creator: de Hoon, Michiel J.L.; Lee, Edward P.; Barnard, John J. & Friedman, Alex
Partner: UNT Libraries Government Documents Department

Plasma neutralization models for intense ion beam transport in plasma

Description: Plasma neutralization of an intense ion pulse is of interest for many applications, including plasma lenses, heavy ion fusion, cosmic ray propagation, etc. An analytical electron fluid model has been developed based on the assumption of long charge bunches (l{sub b} >> r{sub b}). Theoretical predictions are compared with the results of calculations utilizing a particle-in-cell (PIC) code. The cold electron fluid results agree well with the PIC simulations for ion beam propagation through a background plasma. The analytical predictions for the degree of ion beam charge and current neutralization also agree well with the results of the numerical simulations. The model predicts very good charge neutralization (>99%) during quasi-steady-state propagation, provided the beam pulse duration {tau}{sub b} is much longer than the electron plasma period 2{pi}/{omega}{sub p}, where {omega}{sub p} = (4{pi}e{sup 2}n{sub p}/m){sup 1/2} is the electron plasma frequency, and n{sub p} is the background plasma density. In the opposite limit, the beam pulse excites large-amplitude plasma waves. The analytical formulas derived in this paper can provide an important benchmark for numerical codes, and provide scaling relations for different beam and plasma parameters.
Date: May 1, 2003
Creator: Kaganovich, Igor D.; Startsev, Edward A.; Davidson, Ronald C.; O'Rourke, Sean & Lee, Edward P.
Partner: UNT Libraries Government Documents Department