Transportable Charge in a Periodic Alternating Gradient System

Lee, E. P.; Fessenden, T.J.; Laslett, L.J.

doi:10.1109/tns.1985.4333956

Cited by 27 publications

(24 citation statements)

References 4 publications

(2 reference statements)

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“…Although an accurate numerical solution for the beam envelope radii is easily obtained for specified beam and quadrupole lattice parameters, approximate analytical solutions continue to be useful for design studies, scaling, cost optimization, and physical understanding. Various analytical methods have been applied to solve these equations during the last twenty five years [3,4,5,6,7], with the degree of error decreasing from about 10% for the early smooth limit approximation to less than 1 % using the small parameter expansions employed by Anderson [6] and Lee [7]. In the present work the error is reduced to less than 0.1% for typical system parameters, but one may question the vdue of this new work since several approximations have been made in deriving the K-V equations, which may produce errors much larger than 0.1%, These approximations include the neglect of third order geometric abeaatians, non-linear components of quadrupole fringe fields, higher order magnetic multipoles, and deviations fiom the assumed flat space charge profile.…”

Section: Introductionmentioning

confidence: 99%

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

Lee

2002

Physics of Plasmas

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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 &om 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 mdepressed 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.

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Section: Introductionmentioning

confidence: 99%

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

Lee

2002

Physics of Plasmas

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“…Motivated by these limiting case results, for present purposes of analyzing leading order effects, we take F i = 0 and neglect image charge corrections. Results in the literature [19,11] can also be applied to calculate more elaborate image charge corrections.…”

Section: Core-particle Modelmentioning

confidence: 99%

A core-particle model for periodically focused ion beams with intense space-charge

Lund

Barnard

Bukh

et al. 2007

Nuclear Instruments and Methods in Physics Research Section A:

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A core-particle model is derived to analyze transverse orbits of test particles evolving in the presence of a core ion beam described by the KV distribution. The core beam has uniform density within an elliptical cross-section and can be applied to model both quadrupole and solenoidal focused beams in periodic or aperiodic lattices. Efficient analytical descriptions of electrostatic space-charge fields external to the beam core are derived to simplify model equations. Image charge effects are analyzed for an elliptical beam centered in a round, conducting pipe to estimate model corrections resulting from image charge nonlinearities. Transformations are employed to remove coherent flutter motion associated with oscillations of the ion beam core due to rapidly varying, linear applied focusing forces. Diagnostics for particle trajectories, Poincaré phase-space projections, and single-particle emittances based on these transformations better illustrate the effects of nonlinear forces acting on particles evolving outside the core. A numerical code has been written based on this model. Example applications illustrate model characteristics. The core-particle model described has recently been applied to identify physical processes leading to space-charge transport limits for an rms matched beam in a periodic quadrupole focusing channel [Lund and Chawla, Nuc. Instr. and Meth. A 561, 203 (2006)]. Further characteristics of these processes are presented here.

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“…Double-Helix Quadrupole (DHQ) Analysis The double-helix quadruple (DHQ) whose geometry is shown in Figure 6 has been described in Reference [2]. This magnet achieves a quadrupole field by the sinusoidal modulation of the axial position, z, of the turns in pairs of solenoid type coils according to the relationz (8) = h8 + An sin n8 where h is the helical advance per turn, An is the amplitude of the 27t modulation and n is the modulation frequency (n = 2 for the quadrupole.)…”

Section: 3mentioning

confidence: 99%

Superconducting Quadrupole Arrays for Multiple Beam Transport

Bangerter¹

2003

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The goal of this research was to develop concepts for affordable, fully functional arrays of superconducting quadrupoles for multi-beam transport and focusing in heavy ion fusion (HIF) accelerators. Previous studies by the Virtual National Laboratory (VNL) collaboration have shown that the multi-beam transport system (consisting of alternating gradient quadrupole magnets, a beam vacuum system, and the beam monitor and control system) will likely be one of the most expensive and critical parts of such an accelerator. This statement is true for near-term fusion research accelerators as well as accelerators for the ultimate goal of power production via inertial fusion. For this reason, research on superconducting quadrupole arrays is both timely and important for the inertial fusion energy (IFE) research program. This research will also benefit near-term heavy ion fusion facilities such as the Integrated Research Experiment (IRE) and/or the Integrated Beam Experiment (IBX).We considered a 2-prong approach that addresses the needs of both the nearer and longer term requirements of the inertial fusion program. First, we studied the flat coil quadrupole design that was developed by LLNL; this magnet is 150 mm long with a 50 mm aperture and thus is suitable for near term experiments that require magnets of a small length to aperture ratio. Secondly, we studied the novel double-helix quadrupole (DHQ) design in a small (3 x 3) array copfiguration; this design can provide an important step to the longer term solution of low-cost, easy to manufacture array constructions. Our Phase I studies were performed using the AMPERES magneto static analysis software. Consideration of these results led to plans for future magnet R&D construction projects.. The first objective of Phase I was to develop the concept of a superconducting focusing array that meets the specific requirements of a heavy ion fusion accelerator. Detailed parameter studies for such quadrupole arrays were performed. Based on these studies, the primary magnet parameters and the general features required for a complete array system (including vacuum and cryostat) were identified. Basic system concepts were formulated to serve as guides for future development work.A related issue was to compare the applicability and benefits of two different magnet technologies for use in such a quadrupole array. Analytical studies were performed for each of the two coil designs, a flat coil based on an HCX quadrupole designed by LLNL and a doublehelix quadrupole designed by AML. These studies have confirmed the feasibility of using either of the two coil designs in a small array.Advanced Magnet Laboratory, June 2003 DOE SBIR Phase I Final Report: DE-FG02-02ER83359

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Transportable Charge in a Periodic Alternating Gradient System

Cited by 27 publications

References 4 publications

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

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

A core-particle model for periodically focused ion beams with intense space-charge

Superconducting Quadrupole Arrays for Multiple Beam Transport

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