Periodic Quadrupole Research Articles

Fabrication and Powering Test of a High-Temperature Superconducting Periodic Quadrupole Driving a Short-Length Transport Line for Laser-Plasma Accelerators

Fabrication and Powering Test of a High-Temperature Superconducting Periodic Quadrupole Driving a Short-Length Transport Line for Laser-Plasma Accelerators

Analysis of single particle and collective beam effects in high intensity beams in a periodic quadrupole channel

In high intensity proton accelerators, there are two main mechanisms that can cause beam degradation: incoherent and coherent effects due to nonlinear space charge forces. The incoherent effects represent the single particle dynamics while the coherent effects represent the collective response of the beam. Of particular interest is the region above a zero current phase advance (σ0) of 90° where the (coherent) second-order envelope instability and the (incoherent) fourth-order particle resonance are seen to lead to emittance growth. Large emittance growth is also seen below the envelope instability region as the full current beam phase advance (σ) decreases. In the present study, we have studied the nonlinear effects in a high intensity beam propagating through a focusing-defocusing (FD) quadrupole channel for σ0 greater than 90°, both analytically, by studying the solutions of Kapchinsky-Vladimirsky (KV) equation and the particle core model, and through detailed particle-in-cell (PIC) simulations using the code. The KV envelope equation gives the collective response of the beam while the particle core model gives the contribution of the single particle effects. With pic simulations, which resemble the behavior of the real beams more closely as compared to envelope calculations or the particle core model, it is possible to study the evolution of the beam in a self-consistent manner. Our studies show, that it is possible to identify the specific process responsible for beam degradation in high intensity beams. It is also possible to identify which process dominates under different conditions. We further show that the width of the emittance increase stop band calculated from PIC simulations is wider than that calculated by the envelope equations and that the width depends on the length of the channel being studied. Published by the American Physical Society 2024

Engineered periodic quadrupole superstructure in ferroelectric thin films via flexoelectricity

Domain engineering of nanoferroelectrics becomes crucial due to the miniaturization of devices. Understanding the geometric ordering of nanodomains that self-organize into superstructures helps to develop modern domain engineering techniques. Here, using the phase field simulation, we find that large flexoelectricity in thin films can contribute to exotic in-plane needle-like and quadrupole superdomains. Our results indicate that by pressing a mesh of atomic force microscope tips on the film surface, the tip-induced flexoelectric field can tune the polarization nucleation during cooling and lead the nanodomains to evolve into periodic quadrupole patterns. Our work suggests a new approach to create and manipulate desired superstructures and offers a framework of developing engineering techniques in conjunction with phase-field modeling.

Stability Analysis of 300-GHz Sheet Electron Beam Transport in a Periodic Rectangular Quadrupole

A novel periodic magnetic focusing system is proposed. The stability of elliptical sheet beam transport in the magnetic field of a periodic rectangular quadrupole (PRQ) is studied and compared with that in the magnetic field of periodically cusped magnets (PCMs). Theoretically predicted matching conditions are verified by numerical simulations. An 11.7- kV, 35-mA, 0.32 mm $\times $ 0.06 mm elliptical sheet beam is confined in a 0.53 mm $\times $ 0.08 mm beam tunnel and transported over a distance of 30 mm. Both the PCM and PRQ have similar characteristics of electron beam distribution change, beam emittance, and beam transmission. The results of the initial stability analysis indicate that PCMs are preferable to PRQs because of their ability to confine the beam with a long magnet period.

Fabrication and cold test of prototype of spatially periodic radio frequency quadrupole focusing linac

A 325 MHz aluminum prototype of a spatially periodic RF quadrupole focusing linac was developed at the Institute of Modern Physics, Chinese Academy of Sciences, as a promising candidate for the front end of a high-current linac. It consists of an alternating series of crossbar H-type drift tubes and RF quadrupole sections. Owing to its special geometry, cavity fabrication is a major hurdle for its engineering development and application. In this paper, we report the detailed mechanical design of this structure and describe its fabrication process, including machining, assembly, and inspection. The field distribution was measured by the bead-pull technique. The results show that the field errors of both the accelerating and focusing fields are within an acceptable range. A tuning scheme for this new structure is proposed and verified. The cold test process and results are presented in detail. The development of this prototype provides valuable guidance for the application of the spatially periodic RF quadrupole structure.

Mitigation of envelope instability through fast acceleration in linear accelerators

The space-charge driven envelope instability can be of great danger in high intensity accelerators. Linear accelerators were designed to avoid this instability by keeping the zero current phase advance per lattice period below 90 degrees. In this paper, we report on the acceleration effects on the instability in a periodic solenoid and radio-frequency (RF) focusing channel and a periodic quadrupole and RF focusing channel using a three-dimensional envelope model and self-consistent macroparticle simulations. The simulation results show that the envelope instability can be mitigated with a reasonable accelerating gradient in both channels. This suggests that the zero current phase advance might be above 90 degrees in linear accelerators where the accelerating gradient is sufficiently high and opens additional freedom of transverse and longitudinal focusing in the accelerator design.

Three-dimensional envelope instability in periodic focusing channels

The space-charge driven envelope instability can be of great danger in high intensity accelerators and was studied using a two-dimensional (2D) envelope model and three-dimensional (3D) macroparticle simulations before. In this paper, we propose a three-dimensional envelope instability model to study the instability for a bunched beam in a periodic solenoid and radio-frequency (RF) focusing channel and a periodic quadrupole and RF focusing channel. This study shows that when the transverse zero current phase advance is below $90$ degrees, the beam envelope can still become unstable if the longitudinal zero current phase advance is beyond $90$ degrees. For the transverse zero current phase advance beyond $90$ degrees, the instability stopband width becomes larger with the increase of the longitudinal focusing strength and even shows different structure from the 2D case when the longitudinal zero current phase advance is beyond $90$ degrees. Breaking the symmetry of two longitudinal focusing RF cavities and the symmetry between the horizontal focusing and the vertical focusing in the transverse plane in the periodic quadrupole and RF channel makes the instability stopband broader. This suggests that a more symmetric accelerator lattice design might help reduce the range of the envelope instability in parameter space.

Spatially periodic radio-frequency quadrupole focusing linac

The new design for a spatially periodical rf quadrupole focusing linac is proposed. It consists of accelerating gaps formed between conventional cylindrical drift tubes, between drift tubes and rf quadrupoles with nonzero axial potential, and inside these rf quadrupoles, formed in the same way as in a conventional radio-frequency quadrupole (RFQ) linac with modulated electrodes. Such a combination provides both higher energy gain rate than conventional RFQ and stability of transverse motion for ion beams. The structure can be designed using various combinations of quadrupoles and drift tubes. Some options are considered in the paper using the smooth approximation method and computer simulation of beam dynamics. Transverse stability of particles has been studied. The proposed structure can provide suppression of rf defocusing effects on transverse beam dynamics. Some limitations of the spatially periodic rf quadrupole structure are mentioned.

Particle Orbits in Quadrupole–Duodecapole Halo Suppressor

Dynamics of continuous space-charged-dominated beam propagating through a periodic quadrupole–duodecapole focusing channel is studied both numerically and analytically using test–particle–core model and Particle-In-Cell (PIC) simulation code TOPOPIC. The results of TOPOPIC indicate that with initially matched beam, utilization of quadrupole–duodecapole channel results in less beam emittance growth and fewer halo particles than that in a pure quadrupole channel. The Poincare section of plot obtained from the test–particle–core model is used to systematically determine the beam intensity dependent resonant dominated behavior of the test–particles, which reveals the mechanism of the halo suppression in quadrupole–duodecapole channel. Results of study show that, for appropriate field strength, the nonlinear duodecapole force removes the resonant structures due to space charge. Motions of particles, originally trapped in the nonlinear resonant island or chaos region related to space charge, turn out to be along regular tori and these particles have less probability to get into beam halos.

The influence of transition metal solutes on the dislocation core structure and values of the Peierls stress and barrier in tungsten

Several transition metals were examined to evaluate their potential for improving the ductility of tungsten. The dislocation core structure and Peierls stress and barrier of 1/2〈111〉 screw dislocations in binary tungsten–transition metal alloys (W1−xTMx) were investigated using density functional theory calculations. The periodic quadrupole approach was applied to model the structure of the 1/2〈111〉 dislocation. Alloying with transition metals was modeled using the virtual crystal approximation and the applicability of this approach was assessed by calculating the equilibrium lattice parameter and elastic constants of the tungsten alloys. Reasonable agreement was obtained with experimental data and with results obtained from the conventional supercell approach. Increasing the concentration of a transition metal from the VIIIA group, i.e. the elements in columns headed by Fe, Co and Ni, leads to reduction of the C′ elastic constant and increase of the elastic anisotropy A = C44/C′. Alloying W with a group VIIIA transition metal changes the structure of the dislocation core from symmetric to asymmetric, similarly to results obtained for W1−xRex alloys in the earlier work of Romaner et al (2010 Phys. Rev. Lett. 104 195503). In addition to a change in the core symmetry, the values of the Peierls stress and barrier are reduced. The latter effect could lead to increased ductility in a tungsten-based alloy. Our results demonstrate that alloying with any of the transition metals from the VIIIA group should have a similar effect to alloying with Re.

Novel Hamiltonian method for collective dynamics analysis of an intense charged particle beam propagating through a periodic focusing quadrupole lattice

Identifying regimes for quiescent propagation of intense beams over long distances has been a major challenge in accelerator research. In particular, the development of systematic theoretical approaches that are able to treat self-consistently the applied oscillating force and the nonlinear self-field force of the beam particles simultaneously has been a major challenge of modern beam physics. In this paper, the recently developed Hamiltonian averaging technique [E. A. Startsev, R. C. Davidson, and M. Dorf, Phys. Rev. ST Accel. Beams 13, 064402 (2010)] which incorporates both the applied periodic focusing force and the self-field force of the beam particles, is generalized to the case of time-dependent beam distributions. The new formulation allows not only a determination of quasi-equilibrium solutions of the non-linear Vlasov-Poison system of equations but also a detailed study of their stability properties. The corrections to the well-known “smooth-focusing” approximation are derived, and the results are applied to a matched beam with thermal equilibrium distribution function. It is shown that the corrections remain small even for moderate values of the vacuum phase advance συ. Nonetheless, because the corrections to the average self-field potential are non-axisymmetric, the stability properties of the different beam quasi-equilibria can change significantly.

High-Power Microwave Generation by a Periodic Focusing Quadrupole Transport System

High-power microwave generation via a relativistic electron beam propagating through a periodic focusing quadrupole transport (PFQT) system is studied. Transverse confinement of e-beam in a PFQT system is provided by segmented cylindrical electrodes with applied oscillatory voltages <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">osc</sub> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> ) over 90 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> segments. With regard to transverse confinement, there is no applied axial guide magnetic field. An analytic theory of laser gain in the low-gain-per-pass limit is developed. Numerical computations of electron trajectories and gain are also presented. It is shown that the presence of transverse oscillation frequency due to PFQT leads to significant gain enhancement under appropriate conditions.

Approximate kinetic quasiequilibrium distributions for intense beam propagation through a periodic focusing quadrupole lattice

The transverse dynamics of an intense charged particle beam propagating through a periodic quadrupole focusing lattice is described by the nonlinear Vlasov-Maxwell system of equations, where the propagation distances play the role of time. To determine matched-beam quasiequilibrium distribution functions, one needs to determine a dynamical invariant for the beam particles moving in the combined applied and self-generated fields. In this paper, a perturbative Hamiltonian transformation method is developed which is an expansion in the particle’s vacuum phase advance � � � � v=2� , treated as a small parameter, which is used to transform away the fast particle orbit oscillations and obtain the average Hamiltonian accurate to order � � 3 . The average Hamiltonian is an approximate invariant of the original system, and can be used to determine self-consistent beam quasiequilibrium solutions that are matched to the focusing channel. The equation determining the average self-field potential is derived for general boundary conditions by taking into account the average contribution of the charges induced on the boundary. It is shown for a cylindrical conducting boundary that the average self-field potential acquires an octupole component, which results in the average motion of some beam particles being nonintegrable and their trajectories chaotic. This chaotic behavior of the beam particles may significantly change the nature of the Landau damping (or growth) of collective excitations supported by an intense charged particle beam.

Determination of electrodynamic parameters of the period of an accelerating structure with spatially periodic radio-frequency quadrupole focusing

The abandonment of a constant radio-frequency voltage across acceleration periods of the structure with a spatially periodic radio-frequency quadru pole focusing substantially expands the applicability range but complicates the tuning process of dynamic parameters. The possibility and necessity of applying the calculation is shown, when the accelerating structure is tuned. A procedure for calculating electrodynamic parameters of the acceleration period is proposed. The theoretical and experimental results are compared.

Experimental study of coherent betatron resonances with a Paul trap

Linear and nonlinear resonant instabilities of charged-particle beams traveling in periodic quadrupole focusing channels are studied experimentally with a compact non-neutral plasma trap. The present experiments are based on the idea that the collective motion of a beam in an accelerator is physically similar to that of a one-component plasma in a trap. A linear Paul trap system named ``S-POD'' (simulator for particle orbit dynamics) was developed to explore a variety of space-charge-induced phenomena. To emulate lattice-dependent effects, periodic perturbations are applied to quadrupole electrodes, which gives rise to additional resonance stop bands that shift depending on the plasma density. It is confirmed that an $m$th-order resonance takes place when the corresponding tune of an $m$th-order collective mode ${\ensuremath{\Omega}}_{m}$ is close to a half integer.

Stable Sheet-Beam Transport in Periodic Nonsymmetric Quadrupole Field

Stable sheet electron-beam transport is critical for sheet-beam microwave device which is attractive for high-power millimeter wave to terahertz-regime radiation. This paper studies the stable sheet-beam transport in periodic nonsymmetric quadrupole field. First, the conditions for stable round- and sheet-beam transport in periodic magnetic quadrupole field are deduced. In the deduction, we find that the symmetric quadrupole field and the space-charge field of sheet beam are not well matched. In order to settle this problem, we use periodic nonsymmetric quadrupole field instead of periodic symmetric quadrupole field to transport sheet beam. Finally, 3-D PIC simulations verify the conditions for stable sheet-beam transport and show that periodic nonsymmetric quadrupole field is intrinsically well suited for sheet-beam transport.

Propagation of the intense relativistic sheet electron beam with a quasi-rectangular cross section

The sheet electron beam with a quasi-rectangular cross section has been proposed to carry intense current. Obviously different from the elliptical sheet electron beam with the same high aspect ratio, this kind of beam is almost uniform in thickness, and can be generated by the cold metal cathode. Besides, the uniform thickness leads to uniform beam power in the horizontal direction, implying less modes but better counteraction between the beam and microwave. In addition, the uniform thickness make the width of the propagation system,including the cold cathode, the microwave cavities and the focusing magnets,easily changed. Firstly,the space-charge electric field of the sheet electron beam was analyzed numerically, then the focusing magnets, including the periodic cusped magnets and quadrupole magnets, were designed according to the space-charge electric field for beam matching. To validate the above theoretical analysis, particle-in-cell simulation was performed, which shows that the 300 keV, 3 kA sheet electron beam can be well focused by the 0.163 T periodic cusped magnetic fields with the 0.064 T quadrupole magnetic fields. More than 98% of the total current has been propagated through the distance of 300 mm.

A core-particle model for periodically focused ion beams with intense space-charge

A core-particle (CP) model is derived to analyze transverse orbits of test-particles evolving in the presence of a core ion beam that has uniform density within an elliptical cross-section. The model can be applied to both quadrupole and solenoidal focused beams in periodic or aperiodic lattices. Efficient analytical descriptions of electrostatic space-charge fields external to the beam core are derived to simplify model equations. Image-charge effects are analyzed for an elliptical beam centered in a round, conducting pipe to estimate model corrections resulting from image-charge nonlinearities. Transformations are employed in diagnostics to remove coherent flutter motion associated with oscillations of the ion beam core due to rapidly varying, linear applied-focusing forces. Diagnostics for particle trajectories, Poincaré phase-space projections, and single-particle emittances based on these transformations better illustrate the effects of nonlinear forces acting on particles evolving outside the core. A numerical code has been written based on this model. Example applications illustrate model characteristics. The CP model described has recently been applied to identify physical processes leading to space-charge transport limits for an rms-envelope matched beam in a periodic quadrupole focusing-channel [S.M. Lund, S.R. Chawla, Nucl. Instr. and Meth. A 561 (2006) 203]. Further characteristics of these processes are presented here.

Efficient computation of matched solutions of the Kapchinskij-Vladimirskij envelope equations for periodic focusing lattices

A new iterative method is developed to numerically calculate the periodic, matched beam envelope solution of the coupled Kapchinskij-Vladimirskij (KV) equations describing the transverse evolution of a beam in a periodic, linear focusing lattice of arbitrary complexity. Implementation of the method is straightforward. It is highly convergent and can be applied to all usual parameterizations of the matched envelope solutions. The method is applicable to all classes of linear focusing lattices without skew couplings, and also applies to all physically achievable system parameters -- including where the matched beam envelope is strongly unstable. Example applications are presented for periodic solenoidal and quadrupole focusing lattices. Convergence properties are summarized over a wide range of system parameters.

Space-charge transport limits of ion beams in periodic quadrupole focusing channels

It has been empirically observed in both experiments and particle-in-cell simulations that space-charge-dominated beams suffer strong growth in statistical phase-space area (degraded quality) and particle losses in alternating gradient quadrupole transport channels when the undepressed phase advance σ 0 increases beyond about 85 ∘ per lattice period. Although this criterion has been used extensively in practical designs of strong focusing intense beam transport lattices, the origin of the limit has not been understood. We propose a mechanism for the transport limit resulting from strongly chaotic classes of halo particle resonances near the core of the beam that allow near-edge particles to rapidly increase in oscillation amplitude when the space-charge intensity and the flutter of the matched beam envelope are both sufficiently large. When coupled with a diffuse beam edge and/or perturbations internal to the beam core that can drive particles outside the edge, this mechanism can result in large and rapid halo-driven increases in the statistical phase-space area of the beam, lost particles, and degraded transport. A core–particle model is applied to parametrically analyze this process. Extensive self-consistent particle in cell simulations is employed to better quantify properties of the space-charge limits and to verify core–particle model predictions.