C. K. Allen

Optimal transport of particle beams

Abstract The transport and matching problem for a low energy transport system is approached from a control theoretical viewpoint. We develop a model for a beam transport and matching section based on a multistage control network. To this model we apply the principles of optimal control to formulate techniques aiding in the design of the transport and matching section. Both nonlinear programming and dynamic programming techniques are used in the optimization. These techniques are implemented in a computer-aided design program called SPOT. Examples are presented to demonstrate the procedure and outline the results.

Optimal transport of low energy particle beams

The transport and matching problem for a low energy transport system is approached from a control theoretical viewpoint. We model the beam dynamics and transport section using the KV envelope equations. To this model we apply the principles of optimal control to formulate techniques which aid in the design of the transport and matching section. The techniques are applied to the example of an H-beam transport and matching system.

Study of beam dynamics for an intense, high-brightness H− beam to design an efficient low-energy beam transport using ESQ lenses

With an aim of transporting an initially diverging high-perveance (generalized beam perveance 2IbI0β3γ3 = 0.003), high-brightness (normalized brightness ∼1011 A/(m rad)2) H− beam and finally focusing it without any significant emittance dilution, a detailed simulation scheme has been set up incorporating the various nonlinear forces due to the beam and the external focusing elements, e.g., due to space charges, geometrical and chromatic aberrations. The analysis is done following a particular hierarchy to identify the mechanism of emittance growth; this procedure is used to optimize the lens parameters. A combination of six electrostatic quadrupole lenses is configured to deliver a satisfactory solution. The estimated emittance growth is a factor of about 1.6, and this is mainly due to chromatic aberrations. A relatively small group of particles is found to be responsible for the emittance growth. The analysis highlights a number of important issues, e.g., sensitivity to the beam distribution, beam current, lens misalignments, etc. An ESQ LEBT system with some novel features in terms of compactness and mechanical rigidity is developed, and its essential characteristics are described.

Efficient low‐energy beam transport for intense, high‐brightness H− beams in high energy accelerators: Perspectives and a solution using ESQ lenses (abstract)a)

The characteristics of a 30 mA, 35 kV H− beam from a volume source have been determined using emittance measurements. A low energy‐beam transport (LEBT) system consisting of six electrostatic quadrupole lenses and a short (about 5 cm long) single‐stage einzel lens is designed with the aim of transporting the beam over a distance of about 30 cm and focusing a clean, matched beam into a radio‐frequency quadrupole accelerator of the Superconducting Super Collider. The system parameters are chosen on the basis of simulation of beam dynamics. The emittance growth in the LEBT section is within a factor of about 1.5 and this satisfies the requirement of the emittance budget. The LEBT system is designed to be mechanically rugged.

High‐brightness H− beam transport using ESQ lenses

Development of an efficient low‐energy beam transport section (LEBT) is an important issue in accelerator research. An experiment is undertaken to build up an electrostatic quadrupole (ESQ) lens system with an aim to transport a 30 mA, 35 kV H− beam, with normalized beam brightness of ∼8×1010 A/(m‐rad)2, over a length of about 30 cm and match it into a radio‐frequency‐quadrupole. Beam parameters of a Penning‐Dudnikov type ion source at the AT‐1 test stand at Los Alamos National Laboratory are used. The LEBT section consists of six electrostatic quadrupole lenses. The apparatus is designed by detailed computer code simulation of beam dynamics. An emittance growth of about 80% is predicted in transporting the beam through the ESQ system. The ESQ lens system is fabricated. Tests of the system are planned to validate the design parameters, voltage hold‐off of the quadrupole assembly, etc. Critical issues on the design of the apparatus and its fabrication will be discussed.

Solution of Laplace’s equation by the method of moments with applications to charged particle transport

A fast approximation method to the 3D electrostatic problem is developed. The method of moments procedure is outlined for the particular case of Laplace’s equation. The resulting matrix‐vector equation is solved by a conjugate gradient algorithm. These techniques are then implemented with a computer code running on a PC and used to solve example problems.

An ESQ lens system for low energy beam transport experiments on the SSC test stand

A low-energy beam transport system is designed with the aim of transporting 30 mA, 35 kV H/sup -/ beam from a volume source and focusing it into an RFQ. The characteristics of the beam from the source are determined analyzing the emittance data. The behavior of the beam through the LEBT is studied using simulation codes. The system parameters are optimized so that the LEBT has a very modest contribution to the emittance growth (here a factor of about 1.5) and the emittance budget of the linac section is maintained.<<ETX>>

Electrostatic focusing and RFQ (radio frequency quadrupole) matching system for a low-energy H- beam

1407_65The conceptual design of an electrostatic quadrupole (ESQ) system for focusing and matching a 30 mA, 35 kV H- beam into a radio frequency quadrupole (RFQ) accelerator has been developed. The design procedure involves two steps. First, a linear beam optics code which solves the K-V envelope equations is used to design a lens system based on a hard-edge focusing function. The beam envelope, in conjunction with the lens parameters, should satisfy several constraints concerning electric breakdown, image forces, spherical and chromatic aberrations. Next, a practical lens design is developed. The field gradient is calculated numerically with a 3-D Laplace solver and the fringe-field integrals are evaluated to obtain the nonlinear forces up to the third order. The results from the Laplace solver generate input to a modified PARMILA code, and the beam propagation and emittance growth in the system are evaluated. Preliminary analysis shows an emittance growth of about 50%. Design of the apparatus and experimental plans are discussed.

Study of emittance growth and its control for a low energy H− beam transport system

A compact 6‐lens electrostatic quadrupole lens system in conjunction with a short, single einzel lens section has been developed with the aim of transporting a 30 mA, 35 kV H− beam [normalized beam brightness of about 1011 A/(m‐rad)2] over a length of about 30 cm and focusing it into an RFQ. The effect of a neutral background gas on the measurements of the beam from the ion source is studied in order to evaluate reliably the input beam parameters for the lens design. The beam dynamics calculations have been made using simulation codes for typical H− beam parameters from two different ion sources; a magnetron type and a volume source type. The simulation results show a relatively modest emittance growth, that is within about 50–60% even in the case of an input beam with very small beam radius (1.1 mm) and very large divergence (72 mrad).

A moment method Laplace solver for low energy beam transport codes

A moment method technique for solving Laplaces equation is presented. The technique is then extended to Poissons equation to include space charge. The procedure is implemented on a PC and applied to the cases of an electrostatic quadrupole lens and an ellipsoidal bunch in a grounded pipe.<<ETX>>