Search Results (38 total)

A technique is described for the tomographic mapping of transverse phase space in beams with space charge. Most prior studies where performed at high energy where space charge was negligible and therefore not considered in the analysis. The tomographic reconstruction process is compared with results of simulations using the particle-in-cell code WARP. The new tomographic technique is tested for beams with different intensities (both emittance and space-charge dominated), and with different initial distributions. Effects of various errors in the data collection process on the reconstructed phase space are discussed. It is shown that the crucial factor is not necessarily the number of projections but the range of angles over which the projections are taken. This study also includes a number of experimental results on tomographic phase space mapping performed on the University of Maryland Electron Ring.

We present detailed calculations of RMS-envelope matching over a broad range of beam intensities for the University of Maryland Electron Ring (UMER). Containment of beams from zero current to extreme space charge, all without changing the strength of external focusing in the periodic lattice, is possible thanks to the high density of quadrupoles in UMER. In turn, the small-aspect ratio of the UMER magnets results in gradient or field profiles that are “all edges,” thus requiring special treatment when constructing accurate hard-edge models. Further, the results of matching calculations, for both symmetric and asymmetric FODO (alternating gradient) schemes, are compared with calculations from simple general expressions valid in the uniform-focusing approximation of the periodic lattice. Finally, some aspects of the source-to-FODO matching calculation/optimization problem are discussed, together with sensitivity studies of the matching solutions under realistic conditions. The examples from the UMER project, which include experimental results, emphasize the practical aspects of beam envelope matching.

Studies of the dynamics of longitudinal space-charge waves in space-charge dominated beams propagating through a transport channel with a long solenoid are performed at the University of Maryland. In this paper, we report some experimental results on the energy modulations converted from density modulations. By changing the working conditions of the electron gun, pure initial density modulations are generated. Energy perturbation waveforms are measured with a high-resolution energy analyzer. The experimental results are compared with both the linear theory and the simulation results. Good agreements are achieved for the relationship between the energy and current perturbation strengths.

We report a new experimental study of the growth of longitudinal energy spread in a space-charge-dominated electron beam, with a beam energy of several keV and beam current of approximately 100 mA. At relatively low beam densities, we measure growing energy spreads with distance along the transport channel, which are in remarkably good agreement with the theory of energy relaxation via Coulomb collisions. At higher beam densities, however, anomalous energy spreads exceeding the predictions of the relaxation theory are observed, which, we believe, could be caused by collective longitudinal-transverse instabilities observed in computer simulation studies. The onset of these instabilities occurs after several plasma periods according to calculations.

Characterization of beam energy spread in a space-charge dominated beam is very important to understanding the physics of intense beams. It is believed that coupling between the transverse and longitudinal directions via Coulomb collisions will cause an increase of the beam longitudinal energy spread. At the University of Maryland, experiments have been carried out to study the energy evolution in such intense beams with a high-resolution retarding field energy analyzer. The temporal beam energy profile along the beam pulse has been characterized at the distance of 25 cm from the anode of a gridded thermionic electron gun. The mean energy of the pulsed beams including the head and tail is reported here. The measured rms energy spread is in good agreement with the predictions of the intrabeam scattering theory. As an application of the beam energy measurement, the input impedance between the cathode and the grid due to beam loading can be calculated and the impedance number is found to be a constant in the operation region of the gun.

Theoretical and experimental work has been carried out to study the longitudinal space-charge effects in a retarding field energy analyzer. A one-dimensional, steady state model for both a monoenergetic beam and a thermal beam has been developed for this purpose. Potential improvements of using two-dimensional and time-dependent solutions are also briefly discussed. The study shows that, if the current density inside the device is higher than a critical value, the longitudinal space-charge effect and the formation of a potential minimum similar to the virtual cathode formation in an electron gun will distort the measured energy spectrum. The measured FWHM and the rms energy spread will be affected. The measured mean energy will also be shifted toward the low-energy side. By using a two-dimensional correction, the theoretical model also qualitatively explains the appearance of a visible tail at the high-energy side of the spectrum, as observed in experiments. According to the theory, to avoid this measurement distortion due to the longitudinal space charge, care has to be taken to limit the current density inside the device.

We have developed a compact high-resolution retarding field energy analyzer for measuring the energy spread of space-charge-dominated electron beams. This energy analyzer has a cylindrical electrode to overcome the defocusing effects due to space-charge forces, beam trajectories, aperture effect, etc. The device provides excellent spatial and temporal information on the beam energy spread. Single-particle simulation shows that this energy analyzer has very good resolution for low-energy electron beams of several kilovolts and with large divergence angles. The energy analyzer has been tested with 2.5 keV, 60 mA electron beams. The measured energy spread is also compared with the theoretical calculations taking into account two main energy spread sources, namely, the Boersch effect and the longitudinal-longitudinal relaxation.

The appearance of rings of charge observed near the edge of beams from high-perveance guns is described with a simple ray tracing technique inspired by the particle-core model. We illustrate the technique, which has no analog in light optics, with examples from experiments employing solenoid focusing of an electron beam. The rings of charge result from the combined effects of external focusing and space-charge forces acting on paraxial fringe particles with relatively large initial transverse velocities. The model is independent of the physical mechanisms responsible for the fringe particles. Furthermore, the focal length for edge imaging in a uniform focusing channel is derived using a linearized trajectory equation for the motion of fringe particles. Counterintuitively, the focal length decreases as the beam current increases.

Air-core printed-circuit (PC) quadrupoles and dipoles have been developed for the University of Maryland electron ring, currently under construction. The quadrupoles and dipoles are characterized by very small magnetic fields (about 15 G at the aperture edge) and small aspect ratios (length/diameter < 1). We review the theory behind the design of the PC lenses and bending elements, and present general expressions for estimating the values of integrated field and integrated field gradient as functions of design parameters. The new quadrupole magnet represents an improvement over an earlier version which was based on an empirical approach. Further, we summarize the results of multipole content of the magnet fields as measured with a rotating coil apparatus of special construction. The results are compared with calculations with an iron-free magnetics code and are related to different types of errors in the manufacture and assembly of the PC magnets.

Space-charge modes similar to those observed in recent experiments appear in simulations of nonequilibrium charged particle beams with anisotropy. The modes couple degrees of freedom, causing energy transfer and equipartitioning without halo formation in just a few betatron wavelengths. The rate depends on a single free parameter quantifying the space-charge intensity of the final state. Traditional stability analyses are shown not to apply to high-intensity laboratory beams originating with a large perturbation from equilibrium.

We present experimental observations of the abnormal growth of localized nonlinear space-charge waves in space-charge dominated electron beams passing through a resistive channel. The energy width of the space-charge waves is measured on both ends of the channel. Previous experiments had shown that, for small initial perturbations, the energy width of the slow waves increases, while the energy width of the fast waves decreases, in agreement with linear theory. We report that in the nonlinear regime (large initial perturbations), the energy width of the fast wave increases, which is unexpected, and, to the best of our knowledge, no theory exists that would predict this phenomenon.

Experiments and particle-in-cell simulations demonstrate the appearance of wavelike transverse density variations in a space-charge dominated electron beam. Simulations show how an aperture located near the source gives rise to a nonequilibrium phase-space distribution with strong force imbalance confined to a sheath near the beam edge. Tracking of particles in this sheath, starting near the aperture's edge, reproduces well the onset of the perturbation. The subsequent evolution of the perturbation over about one meter suggests the appearance of a transverse wave. For the parameters investigated, simulations further indicate that the perturbation damps out over a few plasma periods without causing any rms emittance growth.

Experimental studies of high-power amplification in a novel three-cavity X-band gyroklystron are reported. The electron gun produces a 520 A beam of 470 keV electrons. The voltage flat top is nearly 2 μs and the beam's average velocity ratio is about 1. All cavities are designed to operate in the TE₀₁₁ coaxial mode near 8.6 GHz. Peak powers of 75–85 MW are measured. The resultant efficiency is near 32% and the gain is near 30 dB. This performance is in good agreement with simulations and represents nearly a threefold increase in the peak power capability of pulsed X-band gyroklystrons.

Results are presented for electron beam transport experiments in a 1-m-long straight section consisting of a solenoid and five short printed-circuit quadrupoles. A linear computer code for rms envelope matching, SPOT, is used for channel design, while final simulations with more realistic elements are obtained with a 21 / 2D version of WARP, a particle-in-cell code. Reasonable agreement is found between calculations and the effective beam envelope obtained from pictures of the beam on a movable phosphor screen. The results validate, within experimental errors, the use of short magnetic quadrupoles for the transport of space-charge dominated beams. The straight section constitutes the prototype matching section for an electron recirculator to be built at the University of Maryland.

The matching of charged particle beams into transport lines is usually done by using the rms envelope equations. The usual rms envelope equations, however, do not apply in the presence of bending magnets and a longitudinal momentum spread. A new set of equations is needed that simultaneously describes the rms envelopes of the beam and the dispersion function. A derivation is outlined in this paper. The new equations will make it possible to achieve proper matching of the rms envelopes and dispersion in the regime of highly space charge dominated beams.

The interplay between dispersion and space charge in circular accelerators or storage rings is investigated by looking for self-consistent, stationary solutions of the Vlasov-Poisson equation in the form of generalized Kapchinsky-Vladimirsky (KV) distributions. The smooth approximation is assumed. The results show a growth of the rms quantities describing the beam distribution with the longitudinal momentum spread, and the tune depression. This growth, however, is modest for realistic values of these parameters in strong focusing systems.

In high-current induction accelerators being considered for heavy ion inertial fusion and other applications, the resistive-wall instability in the long-wavelength range, may cause unacceptable beam energy spread. We have designed a small-scale low-cost electron beam experiment to investigate this instability in 1 m, 5–10 kΩ resistive-wall structures. In this Letter, we present the first experimental results on the interaction between a resistive wall and localized single space-charge waves in the long-wavelength range. The experiments have clearly demonstrated the growth of single slow waves due to the resistive-wall instability and the decay of single fast waves. The spatial growth/decay rates are measured and compared with theoretical analysis.

We derive a set of differential equations for the beam envelopes of an axisymmetric, bunched beam inside a perfectly conducting beam pipe. It is found that the beam dynamics are essentially independent of the form of bunch distribution in the free-space situation, however, in the presence of the beam pipe this is no longer the case. Analytic expressions involving infinite summations of Bessel functions are derived for the image potential and image fields of an ellipsoidally symmetric charge distributions in a beam pipe, in particular, the uniform density distribution. We simulate a simple beam transport system to demonstrate the application of these results.

The effective longitudinal focusing force of the radio-frequency (rf) field in an rf linear accelerator (linac) allows for the loss of particles due to the natural tail on the thermal equilibrium distribution. Equations are derived and numerical results are presented for the resulting fractional loss rate of particles from the rf bucket. This loss rate represents the best possible case. Existing accelerators have beams that are not in thermal equilibrium. Equipartitioning, mismatch, and phase oscillations, effects that are not treated here, can lead to emittance growth, the formation of nonthermal tails (halos), and greater particle losses. © 1996 The American Physical Society.

We analyze the image effects of a cylindrical pipe on continuous beams with elliptical symmetry. Differential equations involving the second-order spatial moments of a particle distribution are given. From the moment equations, a set of Kapchinskij-Vladimirskij-type equations is developed, which include the image effects of a cylindrical beam pipe. These equations are used to analyze the image effects for focusing, drift, defocusing, drift channels, sheet beams, and a magnetic quadrupole matching section. © 1996 The American Physical Society.

We report the experimental observation of the reflection and transmission of space-charge waves at the ends of bunched beams. The space-charge waves are produced in the form of localized perturbations on an initially rectangular electron beam which propagates in a periodic solenoid focusing channel. When the waves reach the beam ends, both reflection and transmission are observed from the experiment. The speed of the reflected and transmitted waves has been measured. A theoretical model is presented to offer an interpretation of the observed phenomena. The analysis shows that reflection does not occur if z_r≫λ/π, where z_r is the edge length and λ is the perturbation wavelength.

In the conventional design of rf linear accelerators (linacs) the charged-particle bunches are not in three-dimensional thermal equilibrium. For applications requiring high beam currents, the space charge couples the longitudinal and transverse particle motions. This leads to equipartitioning processes which cause unacceptable emittance growth and halo formation. A new design strategy for high-current rf linacs is proposed in which the bunches are in thermal equilibrium so that these effects do not occur. Analytic relationships and scaling laws for the design of such linacs are presented.