The transverse evolution of the envelope of an intense, unbunched ion beam in a linear transport channel can be modeled for the approximation of linear self-fields by the Kapchinskij-Vladimirskij (KV) envelope equations. Here we employ the KV envelope equations to analyze the linear stability properties of so-called mismatch perturbations about the matched (i.e., periodic) beam envelope in continuous focusing, periodic solenoidal, and periodic quadrupole transport lattices for a coasting beam. The formulation is analyzed and explicit self-consistent KV distributions are derived for an elliptical beam envelope in a periodic solenoidal transport channel. This derivation extends previous work to identify emittance measures and Larmor-frame transformations to allow application of standard form envelope equations to solenoidal focusing channels. Perturbed envelope equations are derived that include driving sources of mismatch excitation resulting from focusing errors, particle loss, and beam emittance growth. These equations are solved analytically for continuous focusing and demonstrate a factor of 2 increase in maximum mismatch excursions resulting from sudden driving perturbations relative to adiabatic driving perturbations. Numerical and analytical studies are carried out to explore properties of normal mode envelope oscillations without driving excitations in periodic solenoidal and quadrupole focusing lattices. Previous work on this topic by Struckmeier and Reiser [Part. Accel. 14, 227 (1984)] is extended and clarified. Regions of parametric instability are mapped, new classes of envelope instabilities are found, parametric sensitivities are explored, general limits and mode invariants are derived, and analytically accessible limits are checked. Important, and previously unexplored, launching conditions are described for pure envelope modes in periodic quadrupole focusing channels.

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Stability properties of the transverse envelope equations describing intense ion beam transport

The capabilities and limitations of modern thermionic electron sources for producing high-emission-density (>10 A/cm/sup 2/) high-brightness beams are surveyed. The emphasis is on dispenser cathodes. The fabrication techniques and operating mechanisms that determine the operating limitations of existing commercial cathodes are discussed. In addition, cathode improvements that have been demonstrated in various prototype structures are described. >

Thermionic sources for high-brightness electron beams

Charged particle beams that are not perfectly matched or centered when injected into a focusing channel (or accelerator) have a higher total transverse energy than the equivalent ideal stationary beam. The excess energy ΔE represents free energy that can cause emittance growth. A general relationship between the possible emittance growth and ΔE is derived, and analytical results are presented for nonuniform, mismatched, and off‐centered beams.

Free energy and emittance growth in nonstationary charged particle beams

A free-electron laser (FEL) oscillator, driven by an rf linac, requires a train of electron bunches delivered to an undulator. The electron-beam brightness requirement exceeds that available from a conventional buncher. The demonstrated high peak brightness of laser-illuminated photoemitters indicates that the conventional buncher system might be eliminated entirely without the usual large loss in beam brightness that occurs in bunchers. A photoemitter with a current density of about 200 A/cm2 is located on an end wall of an rf cavity to accelerate a 60-ps bunch of electrons to 1 MeV as rapidly as possible. Preliminary experimental work and simulation calculations are presented.

High-Brightness Photoemitier Injector for Electron Accelerators

The High Current Experiment (HCX) at Lawrence Berkeley National Laboratory is part of the US program to explore heavy-ion beam transport at a scale representative of the low-energy end of an induction linac driver for fusion energy production. The primary mission of this experiment is to investigate aperture fill factors acceptable for the transport of space-charge-dominated heavy-ion beams at high space-charge intensity (line-charge density /spl sim/ 0.2 /spl mu/C/m) over long pulse durations (>4 /spl mu/s) in alternating gradient electrostatic and magnetic quadrupoles. This experiment is testing - at driver-relevant scale - transport issues resulting from nonlinear space-charge effects and collective modes, beam centroid alignment and beam steering, matching, image charges, halo, electron cloud effects, and longitudinal bunch control. We present the results for a coasting 1 MeV K/sup +/ ion beam transported through the first ten electrostatic transport quadrupoles, measured with beam-imaging and phase-space diagnostics. The latest additions to the experiment include measurements of the secondary ion, electron and atom coefficients due to halo ions scraping the wall, and four magnetic quadrupoles to explore similar issues in magnetic channels.

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The High Current Transport Experiment for heavy-ion inertial fusion

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.

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Relation between Field Energy and RMS Emittance in Intense Particle Beams

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 Wideroe 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.

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The Radio-Frequency Quadrupole - A New Linear Accelerator

The radio-frequency quadrupole (RFQ) is a new linear accelerator concept in which rf electric fields are used to focus, bunch, and accelerate the beam. Because the RFQ can provide strong focusing at low velocities, it can capture a high-current dc ion beam from a low-voltage source and accelerate it to an energy of 1 MeV/nucleon within a distance of a few meters. A recent experimental test at the Los Alamos Scientific Laboratory (LASL) has confirmed the expected performance of this structure and has stimulated interest in a wide variety of applications. We review the general properties of the RFQ, and present examples of applications of this new accelerator.

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The Radio-Frequency Quadrupole Linear Accelerator

Radio-frequency quadrupole (RFQ) linacs are becoming widely accepted in the accelerator community. They have the remarkable capability of simultaneously bunching low-energy ion beams and accelerating them to energies at which conventional accelerators can be used, accomplishing this with high-transmission efficiencies and low-emittance growths. The electric fields, used for radial focusing, bunching, and accelerating, are determined by the geometry of the vane tips. The choice of the best vane-tip geometry depends on considerations such as the peak surface electric field, per cent of higher multipole components, and ease of machining. We review the vane-tip geometry based on the "ideal" two-term potential function and briefly describe a method for calculating the electric field components in an RFQ cell with arbitrary vane-tip geometry. We describe five basic geometries and use the prototype RFQ design for the Fusion Materials Irradiation Test (FMIT) accelerator as an example to compare the characteristics of the various geometries.

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Radio-Frequency Quadrupole Vane-Tip Geometries

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.

T. P. Wangler

Papers

Relation between Field Energy and RMS Emittance in Intense Particle Beams

The Radio-Frequency Quadrupole - A New Linear Accelerator

The Radio-Frequency Quadrupole Linear Accelerator

Radio-Frequency Quadrupole Vane-Tip Geometries

Field energy and RMS emittance in intense particle beams