Maryland Electron Ring Research Articles

Single-invariant nonlinear optics for a small electron recirculator

This paper describes the design and simulation of a proof-of-concept octupole lattice at the University of Maryland Electron Ring (UMER). This experiment tests the feasibility of nonlinear integrable optics, a novel technique that is expected to mitigate resonant beam loss and enable low-loss high-intensity beam transport in rings. Integrable lattices with large amplitude-dependent tune spreads, created by nonlinear focusing elements, are proposed to damp beam response to resonant driving perturbations while maintaining large dynamic aperture. At UMER, a lattice with a single octupole insert is designed to test the predictions of this theory. The planned experiment employs a low-current high-emittance beam with low space charge tune shift ($\ensuremath{\sim}0.005$) to probe the dynamics of a lattice with large externally-induced tune spread. Design studies show that a lattice composed of a 25-cm octupole insert and existing UMER optics can induce a tune spread of $\ensuremath{\sim}0.13$. Stable transport is observed in PIC simulation for many turns at space charge tune spread 0.008. A maximum spread of $\mathrm{\ensuremath{\Delta}}\ensuremath{\nu}=0.11$ (rms 0.015) is observed for modest octupole strength (peak $50\text{ }\text{ }\mathrm{T}/{\mathrm{m}}^{3}$). A simplified model of the system explores beam sensitivity to steering and focusing errors. Results suggest that control of orbit distortion to $<0.2\text{ }\text{ }\mathrm{mm}$ within the insert region is essential. However, we see only weak dependence on deviations of lattice phase advance ($\ensuremath{\le}0.1\text{ }\text{ }\mathrm{rad}$.) from the invariant-conserving condition.

Quadrupolar mode measurements for space charge dominated beams

On-line monitoring of beam quality requires non-invasive transverse phase space diagnostics. Emittance measurement is particularly challenging for high-intensity particle beams since space charge complicates the beam dynamics during measurement. Quadrupolar mode measurements have been empirically shown to provide information about the beam emittance, but so far only for small relative space charge effects, where the results depend on a linear theory. We present a quadrupolar mode measurement for space charge dominated beams with unsplit tunes using multi-turn resonant excitation. Results from experiments performed at the University of Maryland Electron Ring are compared to both analytic and numerical analysis of the rms envelope equations.

Steering Optimizations for the University of Maryland Electron Ring

Steering Optimizations for the University of Maryland Electron Ring

Initial Tests of Nonlinear Quasi-Integrable Optics at the University of Maryland Electron Ring

Initial Tests of Nonlinear Quasi-Integrable Optics at the University of Maryland Electron Ring

Long path-length experimental studies of longitudinal phenomena in intense beams

Intense charged particle beams are nonneutral plasmas as they can support a host of plasma waves and instabilities. The longitudinal physics, for a long beam, can often be reasonably described by a 1-D cold-fluid model with a geometry factor to account for the transverse effects. The plasma physics of such beams has been extensively studied theoretically and computationally for decades, but until recently, the only experimental measurements were carried out on relatively short linacs. This work reviews experimental studies over the past five years on the University of Maryland Electron Ring, investigating longitudinal phenomena over time scales of thousands of plasma periods, illustrating good agreement with simulations.

Modeling HIF relevant longitudinal dynamics in UMER

The foremost challenge for Heavy-Ion Fusion (HIF) is achieving sufficiently low emittances and small energy spreads in the presence of intense space-charge, to achieve the high deposition densities necessary for pellet ignition. The University of Maryland Electron Ring (UMER) uses intense low-energy electron beams to access the scaled physics of HIF drivers. In particular, the long path-length propagation in UMER presents an opportunity to study, at realistic scales, the longitudinal beam dynamics and manipulations required for such a driver. With the use of induction modules, as in the ion machines such as NDCX-II, the resulting bunch dynamics show evidence of space-charge waves excited by an initial mismatch between the detailed initial beam distribution at the bunch ends and the applied focusing waveforms, persisting with multiple damped reflections propagating along the bunch flat-top. Using the induction module we are able to suppress space-charge waves with great accuracy, at amplitudes that include wave steepening prior to the formation of solitary wave trains. The longitudinal dynamics largely dominates when no containment fields are applied, coupling through the natural chromaticity of the ring even within the first turn. After subsequent turns, the bunch elongates and wraps the circumference of the machine multiple times; eventually reaching a point of instability that has also been shown through simulation, obtaining excellent agreement when the detailed longitudinal dynamics of the experiment are carefully incorporated into the model.

The University of Maryland Electron Ring Program

The University of Maryland Electron Ring (UMER) is a unique machine that uses scaled electron beams at nonrelativistic energies (10keV) to inexpensively model GeV beams of heavy ions over long path lengths (kilometers of transport distance). The UMER beam parameters correspond to space charge tune depressions, at injection, adjustable in the range of 0.14–0.85. Although a ring, many of the intense beam studies on UMER are applicable to linacs. This paper reviews the UMER program, which contains experimental, computational, and theoretical components. We outline the research areas of interest, recent accomplishments, and future plans, emphasizing the relevance to heavy ion drivers. Specific topics include longitudinal induction focusing and beam manipulations; generation and propagation of space charge waves, including large-amplitude solitons; bunch end interpenetration and observation of a multi-stream instability; beam halo studies; and diagnostic development.

Beam halo imaging with a digital optical mask

Beam halo is an important factor in any high intensity accelerator. It can cause difficulties in the control of the beam, emittance growth, particle loss, and even damage to the accelerator. It is therefore essential to understand the mechanisms of halo formation and its dynamics. Experimental measurement of the halo distribution is a fundamental tool for such studies. In this paper, we present a new high dynamic range, adaptive masking method to image beam halo, which uses a digital micromirror-array device. This method has been thoroughly tested in the laboratory using standard optical techniques, and with an actual beam produced by the University of Maryland Electron Ring (UMER). A high dynamic range ($\mathrm{DR}\ensuremath{\sim}{10}^{5}$) has been demonstrated with this new method at UMER and recent studies, with more intense beams, indicate that this DR can be exceeded by more than an order of magnitude. The method is flexible, easy to implement, low cost, and can be used at any accelerator or light source. We present the results of our measurements of the performance of the method and illustrative images of beam halos produced under various experimental conditions.

Smooth approximation model of dispersion with strong space charge for continuous beams

We apply the Venturini-Reiser (V-R) envelope-dispersion equations [M. Venturini and M. Reiser, Phys. Rev. Lett. 81, 96 (1998)] to a continuous beam in a uniform focusing/bending lattice to study the combined effects of linear dispersion and space charge. Within this simple model we investigate the scaling of average dispersion and the effects on beam dimensions and show that the V-R equations lead to the correct zero-current limits. We also introduce a generalization of the space charge intensity parameter and apply it to the University of Maryland Electron Ring and other machines. In addition, we present results of calculations to test the smooth approximation by solving the V-R original equations and also through simulations with the matrix code ELEGANT.

Longitudinal confinement and matching of an intense electron beam

An induction cell has successfully been demonstrated to longitudinally confine a space-charge dominated bunch for over a thousand turns (>11.52 km) in the University of Maryland Electron Ring [Haber et al., Nucl. Instrum. Methods Phys. Res. A 606, 64 (2009) and R. A. Kishek et al., Int. J. Mod. Phys. A 22, 3838 (2007)]. With the use of synchronized periodic focusing fields, the beam is confined for multiple turns overcoming the longitudinal space-charge forces. Experimental results show that an optimum longitudinal match is obtained when the focusing frequency for containment of the 0.52 mA beam is applied at every fifth turn. Containment of the beam bunch is achievable at lower focusing frequencies, at the cost of a reduction in the transported charge from the lack of sufficient focusing. Containment is also obtainable, if the confinement fields overfocus the bunch, exciting multiple waves at the bunch ends, which propagate into the central region of the beam, distorting the overall constant current beam shape.

Design of a scaled recirculator for Heavy Ion Inertial Fusion

An alternative concept for Heavy Ion Inertial Fusion (HIF) is the use of a recirculator to accelerate ion beams to energies in the range of 50–100 GeV [1]. The physics of an ion recirculator can be explored by means of scaled experiments in a compact machine like the existing University of Maryland Electron Ring (UMER). UMER has been successfully used for the study of the fundamental physics of space-charge-dominated transport using a 10 keV electron beam with up to 100 mA of current (or 10 nC per a 100 ns pulse) [2]. Due to the low energy and high perveance, the UMER beam accesses the same range of intensities as an HIF driver. In this paper we report on a computational study for the design of an acceleration stage for UMER using an induction cell. Using the two-dimensional transverse slice model in the particle-in-cell code WARP we show that it is possible to accelerate the UMER beam up to 20 keV without major modifications to the machine. Such acceleration enables future experiments on transverse resonance crossing and studies on longitudinal pulse behavior.

Differential algebraic methods for single particle dynamics studies of the University of Maryland electron ring

The University of Maryland electron ring is a small low energy machine for the study of space-charge dominated beams. Differential algebraic methods as implemented in COSY INFINITY offer an accurate method to study and analyze single particle nonlinear dynamics. As a starting point for space-charge related studies, we undertook a comprehensive examination of the single particle nonlinear dynamics based on differential algebra methods. Quantities such as tunes, chromaticities, dispersion, amplitude dependent tune shifts, and resonance strengths were calculated, and robustness of the solutions with respect to errors tested. The model demonstrated that the earth’s magnetic field has a significant impact on the beam, and adds rich dynamics even in the absence of space charge. Initially we determined the tunes for which an injection-free idealization of the ring had the largest dynamic aperture. Our study then showed that the actual ring also had the largest dynamic aperture at these same tunes, and at these tunes was also least sensitive to errors. Comparison of predicted beam trajectories with measured data showed that the model was accurate for the examined area.

Scaled electron studies at the University of Maryland

Recent experiments performed on the University of Maryland Electron Ring (UMER) have demonstrated the advantages of using a scaled electron machine to economically investigate the nonlinear physics of a space-charge-dominated beam. This physics is important to larger and much more expensive machines, including accelerator systems for the study High Energy Density Physics and Heavy Ion Fusion. UMER has been successfully used for studying source and injector physics, developing diagnostics, and benchmarking simulations, as well as for investigating the special sensitivity of a space-charge-dominated machine to small deviations from the nominal design parameters. A description will also be presented of studies that utilize the downstream consequences of a controlled initial perturbation of the beam distribution for the study of both longitudinal and transverse beam physics. Current work to optimize ring operation will also be discussed.

Adiabatic thermal equilibrium theory for periodically focused axisymmetric intense beam propagation

An adiabatic equilibrium theory is presented for an intense, axisymmetric charged-particle beam propagating through a periodic solenoidal focusing field. The thermal beam distribution function is constructed based on the approximate and exact invariants of motion, i.e., a scaled transverse Hamiltonian and the angular momentum. The approximation of the scaled transverse Hamiltonian as an invariant of motion is validated analytically for highly emittance-dominated beams and highly space-charge-dominated beams, and numerically tested to be valid for cases in between with moderate vacuum phase advances (σv<90°). The beam root-mean-square (rms) envelope equation is derived, and the self-consistent nonuniform density profile is determined. Other statistical properties such as flow velocity, temperature, total emittance and rms thermal emittance, equation of state, and Debye length are discussed. Numerical examples are presented, illustrating the effects of the beam perveance, emittance, and rotation on the beam envelope and density distribution. Good agreement is found between theory and a recent high-intensity beam experiment performed at the University of Maryland Electron Ring [S. Bernal, B. Quinn, M. Reiser, and P. G. O’Shea, Phys. Rev. ST Accel. Beams 5, 064202 (2002)].

Scaled electron experiments at the University of Maryland

The University of Maryland Electron Ring (UMER) and the Long Solenoid Experiment (LSE) are two electron machines that were designed explicitly to study the physics of space-charge-dominated beams. The operating parameters of these machines can be varied by choice of apertures and gun operating conditions to access a wide range of parameters that reproduce, on a scaled basis, the full nonlinear time-dependent physics that is expected in much costlier ion systems. Early operation of these machines has demonstrated the importance of the details of beam initial conditions in determining the downstream evolution. These machines have also been a convenient tested for benchmarking simulation codes such as WARP, and for development of several novel diagnostic techniques. We present our recent experience with multi-turn operation as well as recent longitudinal and transverse physics experiments and comparisons to simulation results. Development of novel diagnostic techniques such as time-dependent imaging using optical transition radiation and tomographic beam reconstruction are also described.

Measurement and simulation of the time-dependent behavior of the UMER source

Control of the time-dependent characteristics of the beam pulse, beginning when it is born from the source, is important for obtaining adequate beam intensity on a target. Recent experimental measurements combined with the new mesh-refinement capability in WARP have improved the understanding of time-dependent beam characteristics beginning at the source, as well as the predictive ability of the simulation codes. The University of Maryland Electron Ring (UMER), because of its ease of operation and flexible diagnostics has proved particularly useful for benchmarking WARP by comparing simulation to measurement. One source of significant agreement has been in the ability of three-dimensional WARP simulations to predict the onset of virtual cathode oscillations in the vicinity of the cathode grid in the UMER gun, and the subsequent measurement of the predicted oscillations.

Tomography as a diagnostic tool for phase space mapping of intense particle beams

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.

RMS envelope matching of electron beams from “zero” current to extreme space charge in a fixed lattice of short magnets

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.

Commissioning of the University of Maryland Electron Ring (UMER): Advances toward multiturn operation

The University of Maryland Electron Ring (UMER) is a low-energy, high current recirculator for beam physics research [M. Reiser et al., in Proceedings of the 1999 Particle Accelerator Conference, New York, NY (IEEE, New York, 1999), p. 234]. Ring construction is completed for multiturn operation of beams over a broad range of intensities and initial conditions. UMER is an extremely versatile experimental platform with a beam current of up to 100mA and a pulse length as long as 100ns. UMER is addressing issues in beam physics relevant to many applications that require intense beams of high quality, such as advanced concept accelerators, free electron lasers, spallation neutron sources, and future heavy-ion drivers for inertial fusion. The primary focus of this paper is to present experimental results in the areas of beam steering and multiturn operation of the ring. Unique beam steering algorithms now include measurement of the beam response matrix at each quadrupole and matrix inversion by singular value decomposition. With these advanced steering methods, transport of an intense beam over four turns (144 full lattice periods) of the ring has been achieved.

UMER: An analog computer for dynamics of swarms interacting via long-range forces

Some of the most challenging and interesting problems in nature involve large numbers of objects or particles mutually interacting through long-range forces. Examples range from galaxies and plasmas to flocks of birds and traffic flow on a highway. Even in cases where the form of the interacting force is precisely known, such as the 1/ r 2-dependent Coulomb and gravitational forces, such problems present a formidable theoretical and modeling challenge for large numbers of interacting bodies. This paper reports on a newly constructed, scaled particle accelerator that will serve as an experimental testbed for the dynamics of swarms interacting through long-range forces. Primarily designed for intense beam dynamics studies for advanced accelerators, the University of Maryland Electron Ring (UMER) design is described in detail and an update on commissioning is provided. An example application to a system other than a charged particle beam is discussed.