K. R. Crandall

Relation between Field Energy and RMS Emittance in Intense Particle Beams

An equation is presented for continuous beams with azimuthal symmetry and continuous linear focusing, which expresses a relationship between the rate of change for squared rms emittance and the rate of change for a quantity we call the nonlinear field energy. The nonlinear field energy depends on the shape of the charge distribution and corresponds to the residual field energy possessed by beams with nonuniform charge distributions. The equation can be integrated for the case of an rms matched beam to yield a formula for space-charge-induced emittance growth that we have tested numerically for a variety of initial distributions. The results provide a framework for discussing the scaling of rms emittance growth and an explanation for the well-established lower limit on output emittance.

Beam halo formation from space-charge dominated beams in uniform focusing channels

In space-charge dominated beams the nonlinear space-charge forces produce a filamentation pattern, which results in a 2-component beam consisting of an inner core and an outer halo. The halo is very prominent in mismatched beams/sup 1-3/ and is a concern because of the potential for accelerator activation. We present new results about beam halo and the evolution of space-charge dominated beams from multiparticle simulation of initial laminar beams in a uniform linear focusing channel, and from a model consisting of single particle interactions with a uniform-density beam core/sup 4/. We study the energy gain from particle interactions with the space-charge field of the core, and we identify the resonant characteristic of this interaction as the basic cause of the separation of the beam into the two components. We identify three different particle-trajectory types, and we suggest that one of these types may lead to continuous halo growth, even after the halo is removed by collimators.<<ETX>>

RF Quadrupole Beam Dynamics

A method has been developed to analyze the beam dynamics of the radio frequency quadrupole accelerating structure. Calculations show that this structure can accept a dc beam at low velocity, bunch it with high capture efficiency, and accelerate it to a velocity suitable for injection into a drift tube linac.

Performance Characteristics of a 425-MHz RFQ Linac

A radio-frequency quadrupole (RFQ) focused proton linac has been developed and successfully tested at the Los Alamos Scientific Laboratory (LASL) for the purpose of evaluating its performance and applicability as a low-beta accelerator. The geometry of the structure was designed to accept a 100-keV beam, focus, bunch, and accelerate it to 640 keV in 1.1 m with a high-capture efficiency and minimum emittance growth. The accelerator test facility includes an injector, low-energy transport section for transverse matching, and a high-energy transport section for analysis of the beam properties. The accelerator cavity is exited through a manifold powered by a 425-MHz klystron. Diagnostic instrumentation was prepared to facilitate operation of the accelerator and to analyze its performance. Measurements of the beam properties are presented and compared with the expected properties resulting from numerical calculations of the beam dynamics.

The Radio-Frequency Quadrupole - A New Linear Accelerator

In many Laboratories, great emphasis now is placed on the development of linear accelerators with very large ion currents. To achieve this goal, a primary concern must be the low-velocity part of the accelerator, where the current limit is determined and where most of the emittance growth occurs. The use of magnetic focusing, the conflicting requirements in the choice of linac frequency, and the limitations of high-voltage dc injectors, have tended to produce lowvelocity designs that limit overall performance. The radio-frequency quadrupole (RFQ) linear accelerator, invented in the Soviet Union and developed at Los Alamos, offers an attractive solution to many of these low-velocity problems. In the RFQ, the use of RF electric fields for radial focusing, combined with special programming of the bunching, allows high-current dc beams to be captured and accelerated with only small beam loss and low radial emittance growth. Advantages of the RFQ linac include a low injection energy (20-50 keV for protons) and a final energy high enough so the beam can be further accelerated with high efficiency in a Wideröe or Alvarez linac. These properties have been confirmed at Los Alamos in a highly successful experimental test performed during the past year. The success of this test and the advances in RFQ design procedures have led to the adoption of this linac for a wide range of applications. The beam-dynamics parameters of three RFQ systems are described.

The Radio-Frequency Quadrupole: General Properties and Specific Applications

The radio-frequency quadrupole (RFQ) linac structure is being developed for the acceleration of low-velocity ions. Recent experimental tests have confirmed its expected performance and have led to an increased interest in a wide range of possible applications. We review the general properties of RFQ accelerators and present beam dynamics simulation results for their use in a variety of accelerating systems. These include the low-beta sections of the Fusion Materials Irradiation Test Accelerator, a 200-MHz proton linear accelerator, and a xenon accelerator for heavy ion fusion.

Emittance growth from charge density changes in high‐current beams

We use the relation between field energy and rms emittance, together with the property of charge‐density homogenization for intense nonuniform beams in linear focusing systems, to derive equations for emittance growth and minimum final emittance. We discuss three problems in which this charge redistribution mechnism is isolated: the 1‐D continuous sheet beam, the 2‐D continuous round beam, and the 3‐D spherical bunch. For each of the three problems, we identify and compare scaling parameters tha determine the emittance growth and minimum final emittance as a function of beam current, emittance, and external focusing strength. Numerical simulations are used to test the equations, to show that the charge redistribution mechanism results in very rapid emittance growth, and to study the detailed time evolution of the beams.

Operating Characteristics of a 2.0-MeV RFQ

A second radio-frequency quadrupole (RFQ) accelerator has been designed, constructed and operated at Los Alamos National Laboratory. The accelerators design parameters represent a major extension from the original Los Alamos RFQ, with the new accelerator being 2.5 times as long, having three times the output energy, and with 2.5 times the current limit. The new accelerators operating characteristics were studied for 3 months before disassembly to incorporate design modifications. Results are discussed.

Field energy and RMS emittance in intense particle beams

An equation is presented for continuous beam with azimuthal symmetry and continuous linear focusing; the equation expresses a relationship between the rate of change for squared rms emittance and the rate of change for a quantity we call the nonlinear field energy. The nonlinear field energy depends on the shape of the charge distribution and corresponds to the residual field energy possessed by beams with nonuniform charge distributions. The equation can be integrated for the case of an rms matched beam to yield a formula for space‐charge‐induced emittance growth that we have tested numerically for a variety of initial distributions. The results provide a framework for discussing the scaling of rms emittance growth and an explanation for the well‐established lower limit on output emittance.

Accelerator Column Models for Low-Current Beams

This paper describes three analytic approaches used to model electrostatic accelerator columns in beam-transport codes for low-current beams and compares the results of each approach with the results obtained by numerically calculating the electric field based on charge distribution on equipotential surfaces. The three analytic approaches described are (1) a cubic energy-gain approximation, (2) a cubic longitudinal electric-field approximation, and (3) the aperture equation. The first two approaches calculate impulse approximations at the apertures, whereas the third is an integration of particle trajectories through the column field. The conditions under which the solutions tend to break down are discussed.