Beam Envelope Research Articles

Enhancement of collimated low-energy broad-beam ion source with four-grid accelerator system

An application of a four-grid ion acceleration system for generating highly collimated low-energy (<1.5 keV) ion beams is presented. The four-grid system offers significantly reduced beam divergence angles for practical low-energy source designs compared to current two- and three-grid systems. Ion beam divergence of the entire beam envelope has been reduced to less than 2° at 250 and 750 eV. Results are also compared with a conventional three-grid system.

The role of the focusing field profile on the stability of periodically focused particle beams

In this paper, the role of the focusing field profile on the stability of periodically focused particle beams is investigated, paying special attention to the transport within the new regions of stability found recently for vacuum-phase advances well above 90° [R. Pakter and F. B. Rizzato, Phys. Rev. Lett. 87, 044801 (2001)]. In particular, a solenoidal focusing field profile that goes from a smooth sinusoidal-like function to a sharp-edged step-funcion as a continuous parameter is varied is considered. It is shown that the new regions are always present, but may be very sensitive to changes in the focusing field profile. Specifically, as the focusing field becomes more localized, the new regions become narrower, occur at higher vacuum phase advances, and present a larger number of nonlinear resonances and chaos in the beam envelope phase space. Although in all the cases analyzed here it was found that there is a relatively thick layer of regular trajectories isolating the matched solution from the chaotic region, self-consistent simulations show that envelope phase-space chaos may affect beam dynamics, leading to some small emittance growth.

Stability of the envelope evolution of a cold-fluid corkscrewing elliptic beam in a uniform-focusing magnetic field

The envelope oscillations of a cold-fluid corkscrewing elliptic beam in a uniform-focusing magnetic field are studied. In particular, by linearizing the generalized beam envelope equations, the eigenmodes of small-amplitude envelope oscillations are calculated for a cold-fluid corkscrewing elliptic beam oscillating about its equilibrium. All of the eigenmodes are shown to be stable.

Resonant beam behavior studies in the Proton Storage Ring

We present studies of space-charge-induced beam profile broadening at high intensities in the Proton Storage Ring (PSR) at Los Alamos National Laboratory. We investigate the profile broadening through detailed particle-in-cell simulations of several experiments and obtain results in good agreement with the measurements. We interpret these results within the framework of coherent resonance theory. With increasing intensity, our simulations show strong evidence for the presence of a quadrupole-mode resonance of the beam envelope with the lattice in the vertical plane. Specifically, we observe incoherent tunes crossing integer values, and large amplitude, nearly periodic envelope oscillations. At the highest operating intensities, we observe a continuing relaxation of the beam through space charge forces leading to emittance growth. The increase of emittance commences when the beam parameters encounter an envelope stop band. Once the stop band is reached, the emittance growth balances the intensity increase to maintain the beam near the stop band edge. Additionally, we investigate the potential benefit of a stop band correction to the high intensity PSR beam.

Cold phase fluid model of the longitudinal dynamics of space-charge-dominated beams

The dynamics of a longitudinally cold, charged-particle beam can be simulated by dividing the beam into slices and calculating the motion of the slice boundaries due to the longitudinal electric field generated by the beam. On each time step, the beam charge is deposited onto an (r, z) grid, and an existing (r, z) electrostatic field solver is used to find the longitudinal electric field. Transversely, the beam envelope equation is used for each slice boundary separately. In contrast to the g-factor model, it can be shown analytically that the repulsive electric field of a slice compressed to zero length is bounded. Consequently, this model allows slices to overtake their neighbors, effectively incorporating mixing. The model then effectively describes a cold fluid in longitudinal z, vz phase space. Longitudinal beam compression calculations based on this cold phase fluid model showed that slice overtaking reflects local mixing, while the global phase space structure is preserved.

Space charge dynamics of bright electron beams

The longitudinal dynamics and its coupling with the transverse dynamics of bunched beams with strong space charge are analyzed. We introduce a self-consistent Vlasov description for the longitudinal phase space similar to the familiar description for the transverse phase space using a Kapchinskij-Vladimirskij distribution. A longitudinal beam envelope equation is derived. An exact solution is then obtained when coupling to the transverse dynamics is ignored. This longitudinal envelope equation is coupled to the transverse envelope equation to form a set of coupled dynamical equations, which is then solved numerically. This analysis is prompted by the surprising results of recent experiments which showed that by driving an intense laser pulse into matter, which in turn creates a plasma, short bright relativistic electron bunches are produced, surprisingly narrowly focused. We find that because the space charge forces weaken with increasing transverse and longitudinal phase space, both the transverse and longitudinal emittance blowouts anticipated of bright compact bunches are mitigated by this coupling. It should be possible to capture these bunches into an rf cavity to accelerate to higher energies.

Image-charge effects on the envelope dynamics of an unbunched intense charged-particle beam

The root-mean-squared (rms) envelope equations are derived and analyzed for an unbunched intense charged-particle beam in an alternating-gradient focusing field and a cylindrical conducting pipe. All higher-order image-charge effects from the cylindrical pipe are expressed in terms of so-called multiple moment factors in the rms beam envelope equations, and the multiple moment factors are evaluated. Numerical results show that for vacuum phase advance /spl sigma//sub /spl nu// < 90/spl deg/, the image-charge effects on the matched and slightly mismatched beam envelopes are negligibly small, at all orders, for all beams with arbitrary beam density profiles (including hollow density profiles) as well as for arbitrary small apertures (including beams with large aspect ratios). However, the main unstable region for the envelope evolution with image-charge effects, which occurs for 90/spl deg/ < /spl sigma//sub /spl nu// < 270/spl deg/, depending on the value of the normalized beam intensity SK / /spl epsiv/, is found to be narrower than its counterpart without image-charge effects.

Trans-equatorial ghost responses from east-west aperture synthesis arrays

A well-known property of radio synthesis telescopes is that spurious source responses decrease in amplitude with increasing angular separation between the interfering source and the field centre. This is due to both the delay beam (bandwidth smearing) and the primary beam envelope, as well as rejection by the synthesised beam itself. However, in certain special cases, ghost responses to sources far removed from the field centre can occur with significant amplitude. In particular, East-West linear arrays give rise to trans-equatorial ghosts, which are spurious responses to sources having declination equal in magnitude to that of the observed field, but opposite in sign. The trans-equatorial ghosts arise because the tracking required is independent of the sign of the declination. They can be present whenever the parent source is above the horizon and are then attenuated only by the primary beam – neither the delay beam nor the synthesised beam diminish the ghost response. Moreover, ghost sources may resemble real sources rather than easily recognised artifacts. Such ghosts have been seen in observations made with the Molonglo Observatory Synthesis Telescope, and in this case they are drawn out into small arcs by the minor departure of the telescope from an exact East-West array.

Propagation of laser radiation in anisotropic media

Weakly nonparaxial master equations are obtained for transverse components of the electric field envelope of laser beams and pulses propagating in an anisotropic medium with frequency dispersion and absorption (dichroism). It is demonstrated that, in the special case of a linear regime, the field is separated into ordinary and extraordinary waves and the propagation of the latter waves occurs through a mixed mechanism of diffraction and diffusion. It is shown that the derived equations are applicable to nonlinear-optical problems, including the description of the polarization structure of a soliton field in media with quadratic optical nonlinearity.

Bunching dynamics and transport window of intense ion beams in final beam buncher

A longitudinal compression is indispensable in a final stage of the heavy ion driver system using a particle accelerator. For the beam compression, an induction buncher applies the bunching voltage so as to make a considerable velocity tilt between the head and the tail of the beam bunch. However, the velocity tilt induces mismatch oscillation of the beam envelope due to the nonconformity between the beam particle velocity and the confinement force of the lens system. At the first step of design works for the beam transport line, the initial phase advance is decided to avoid resonance lines on the tune diagram. However, as the phase advance changes in the buncher by the velocity tilt, the beam bunch reenters in the resonance condition under certain circumstances. The transport region for avoiding the resonance condition is discussed on a phase diagram, as a function of the phase advance and the velocity tilt.

Precision matched solution of the coupled beam envelope equations for a periodic quadrupole lattice with space charge

The coupled Kapchinskij–Vladimirskij (K–V) envelope equations for a charged particle beam transported by a periodic system of quadrupoles with self-consistent space charge force have previously been solved by various approximate methods, with accuracy ranging from 1% to 10%. A new method of solution is introduced here, which is based on a double expansion of the beam envelope functions in powers of the focal strength and either the beam’s emittance or its dimensionless perveance. This method results in accuracy better than 0.1% for typical lattice and beam parameters when carried through one consistent level of approximation higher than employed in previous work. Several useful quantities, such as the values of the undepressed tune and the beam’s perveance in the limit of vanishing emittance, are represented by very rapidly converging power series in the focal strength, with an accuracy of 0.01% or better.

Transverse envelope dynamics of a 28.5-GeV electron beam in a long plasma.

The transverse dynamics of a 28.5-GeV electron beam propagating in a 1.4 m long, (0-2)x10(14) cm(-3) plasma are studied experimentally in the underdense or blowout regime. The transverse component of the wake field excited by the short electron bunch focuses the bunch, which experiences multiple betatron oscillations as the plasma density is increased. The spot-size variations are observed using optical transition radiation and Cherenkov radiation. In this regime, the behavior of the spot size as a function of the plasma density is well described by a simple beam-envelope model. Dynamic changes of the beam envelope are observed by time resolving the Cherenkov light.

An electrostatic storage ring for atomic and molecular science

An electrostatic storage ring with a circumference of 8.1 m was designed for the research of atomic and molecular science. The race-track ring consists of two 160° deflectors, four 10° deflectors and four quadrupole doublets. For the 160° deflectors, a cylindrical shape has been adopted. In this ring, there are four types of stable regions with and without waists of the beam envelope in the middle of the deflectors. A beam test was performed with 20-keV ion beams from an ECR ion source. The observed lifetimes of beams stored in each stable region were different under the same conditions, except for the tune values. The lifetimes did not depend much on the injected beam intensity for a current of less than about 100 nA. The design and performance of the electrostatic storage ring are presented.

Observation of plasma focusing of a 28.5 GeV positron beam.

The observation of plasma focusing of a 28.5 GeV positron beam is reported. The plasma was formed by ionizing a nitrogen jet only 3 mm thick. Simultaneous focusing in both transverse dimensions was observed with effective focusing strengths of order tesla per micron. The minimum area of the beam spot was reduced by a factor of 2.0+/-0.3 by the plasma. The longitudinal beam envelope was measured and compared with numerical calculations.

Fast damping in mismatched high intensity beam transportation

A very fast damping of beam envelope oscillation amplitudes was recently observed in simulations of high intensity beam transport, through periodic FODO cells, in mismatched conditions [V. Variale, Nuovo Cimento Soc. Ital. Fis. 112A, 1571--1582 (1999) and T. Clauser et al., in Proceedings of the Particle Accelerator Conference, New York, 1999 (IEEE, Piscataway, NJ, 1999), p. 1779]. A Landau damping mechanism was proposed at the origin of observed effect. In this paper, to further investigate the source of this fast damping, extensive simulations have been carried out. The results presented here support the interpretation of the mechanism at the origin of the fast damping as a Landau damping effect.

Stability of periodically focused intense particle beams.

A stability analysis of periodically focused intense particle beams based on the beam envelope equation is performed. We show that (i) the scenario, as the focusing field increases, is not the existence of a single threshold above which stable matched (equilibrium) solutions are absent, as generally believed, but the existence of successive regions of stability interrupted by gaps of instability; (ii) the beam can be focused to tighter radii using new stable matched solutions found for focusing field strengths greater than the previous threshold. Self-consistent simulations validate the findings.

Low energy beam transport for HIDIF

Low energy beam transport (LEBT) for a heavy ion inertial fusion (HIDIF, I. Hofmann and G. Plass, Report of the European Study Group on Heavy Ion Driven Inertial Fusion for the Period 1995–1998) facility suffers from high space charge forces and high ion mass. Space charge compensation reduces the necessary focusing force of the lenses and the radius of the beam in the LEBT, and therefrom the emittance growth due to aberrations and self fields is reduced. Gabor lenses (D. Gabor, Nature 160 (1947)) providing a stable space charge cloud for focusing and combine strong cylinder symmetric focusing with partly space charge compensation and low emittance growth. A high tolerance against source noise and current fluctuations and reduced investment costs could be other possible advantages. The proof of principle has already been demonstrated (J.A. Palkovic, Measurements on a Gabor lens for Neutralizing and Focusing a 30 keV Proton beam, University of Wisconsin, Madison, 1989; J. Pozimski, P. Groß, R. Dölling and T. Weis, First experimental studies of a Gabor plasma-lens in Frankfurt, Proceedings of the 3rd EPAC Conference, Berlin, 1992). To broaden the experiences and to investigate the realisation of a LEBT concept for the HIDIF injector an experimental program using two Gabor lenses for independent variation of beam radius and envelope angel at RFQ injection was started. Therefrom the first experimental results using a double Gabor lens (DGPL) LEBT system for transporting an high perveance Xe + beam are presented and the results of numerical simulations are shown.

Intense ion beam propagation in a reactor sized chamber

We consider the physics of the ballistic transport of intense ion beams in a heavy ion fusion reactor chamber filled with low pressure Flibe gas. We consider first a single beam envelope model and show via a simple case that emittance growth is an issue in the chamber as well as in the accelerator. We develop a model for the neutralization of beam space-charge by the electrons produced by gas ionization by the beam and derive an expression for the evolution of the neutralization factor as the beam propagates into the chamber. We then extend the envelope model from a one species beam to a beam of ions of several charge states by considering the entire beam as a set of subbeams (one for each charge state) each described with coupled envelope equation. The fully electromagnetic PIC code BPIC was used to investigate the behavior in greater detail. A parametric study of the sensitivity of the final spot radius at the target versus the ion beam stripping and gas ionization cross-sections (which are characterized by large uncertainties) shows that, in the studied regime (Hylife-II parameters), the accessible window of cross-sections for ballistic transport in the chamber through neutral Flibe gas is eventually small. The temperature evolution for each species and the emittance growth for the entire ion beam was studied for a typical scenario and indicates that a fair amount of the initial electric potential energy carried by the beam as it enters the chamber is converted into temperature and transverse emittance. The high temperature of the ionization-produced electrons prevents a full charge neutralization of the ion beam as it approaches the target. It is shown that focusing a beam array or pre-ionizing a fraction of the background gas may help in reducing the focal spot.

Injector for the University of Maryland Electron Ring (UMER)

The electron beam injector constructed by FM technologies for the University of Maryland Electron Ring (UMER) program is described. The program will use an electron beam to model space-charge-dominated ion beams in a recirculating linac for heavy ion inertial fusion, as well as for high-current muon colliders. The injector consists of a 10 keV, 100 mA electron gun with 50–100 nsec pulse width and a repetition rate of 120 Hz. The e-gun system includes a 6-mask, rotatable aperture plate, a Rogowski current monitor, an ion pump, and a gate valve. The injector beamline consists of a solenoid, a five-quadrupole matching section, two diagnostic chambers, and a fast current monitor. An independent diagnostic chamber also built for UMER will be used to measure horizontal and vertical emittance, current, energy, energy spread, and the evolution of the beam envelope and profile along the injector beamline.

Theory and simulation of ion noise in microwave tubes

Since there is always some ambient gas in electron beam devices, background ionization is ubiquitous. For long pulse times, the electrostatic potentials associated with this ionization can reach significant levels and give rise to such observed phenomena as phase noise in microwave tubes. This noise is usually associated with the motion of ions in the device; therefore, it is called ion noise. It often manifests itself as a slow phase fluctuation on the output signal. Observations of noise in microwave tubes such as coupled-cavity traveling wave tubes (CC-TWTs) and klystrons have been discussed in the literature. In this paper, a hybrid model is discussed in which the electron beam is described by the beam envelope equation, and the ions generated by beam ionization are treated as discrete particles using the one-dimensional equations of motion. The theoretical model provides good qualitative as well as reasonable quantitative insight into the origin of ion noise phenomena. The numerical results indicate that the model reproduces the salient features of the phase oscillations observed experimentally. That is, the scaling of the frequency of the phase oscillations with gas pressure in the device and the sensitive dependence of the phase oscillations on the focusing magnetic field. Two distinct time scales are observed in simulation. The fastest time scale oscillation is related to the bounce motion of ions in the axial potential wells formed by the scalloping of the electron beam. Slower sawtooth oscillations are observed to correlate with the well-to-well interactions induced by the ion coupling to the electron equilibrium. These oscillations are also correlated with ion dumping to the cathode or collector. As a practical matter, simulations indicate that the low frequency oscillations can be reduced significantly by using a well-matched electron beam propagating from the electron gun into the interaction circuit.