Transverse Focusing Research Articles

Multistage Zeeman decelerator for molecular-scattering studies

We present a new concept for a multi-stage Zeeman decelerator that is optimized particularly for applications in molecular beam scattering experiments. The decelerator consists of a series of alternating hexapoles and solenoids, that effectively decouple the transverse focusing and longitudinal deceleration properties of the decelerator. It can be operated in a deceleration and acceleration mode, as well as in a hybrid mode that makes it possible to guide a particle beam through the decelerator at constant speed. The deceleration features phase stability, with a relatively large six-dimensional phase-space acceptance. The separated focusing and deceleration elements result in an unequal partitioning of this acceptance between the longitudinal and transverse directions. This is ideal in scattering experiments, which typically benefit from a large longitudinal acceptance combined with narrow transverse distributions. We demonstrate the successful experimental implementation of this concept using a Zeeman decelerator consisting of an array of 25 hexapoles and 24 solenoids. The performance of the decelerator in acceleration, deceleration and guiding modes is characterized using beams of metastable Helium ($^3S$) atoms. Up to 60 % of the kinetic energy was removed for He atoms that have an initial velocity of 520 m/s. The hexapoles consist of permanent magnets, whereas the solenoids are produced from a single hollow copper capillary through which cooling liquid is passed. The solenoid design allows for excellent thermal properties, and enables the use of readily available and cheap electronics components to pulse high currents through the solenoids. The Zeeman decelerator demonstrated here is mechanically easy to build, can be operated with cost-effective electronics, and can run at repetition rates up to 10 Hz

Creating and Steering Highly Directional Electron Beams in Graphene.

We put forward a concept to create highly collimated, nondispersive electron beams in pseudorelativistic Dirac materials such as graphene or topological insulator surfaces. Combining negative refraction and Klein collimation at a parabolic pn junction, the proposed lens generates beams, as narrow as the focal length, that stay focused over scales of several microns and can be steered by a magnetic field without losing collimation. We demonstrate the lens capabilities by applying it to two paradigmatic settings of graphene electron optics: We propose a setup for observing high-resolution angle-dependent Klein tunneling, and, exploiting the intimate quantum-to-classical correspondence of these focused electron waves, we consider high-fidelity transverse magnetic focusing accompanied by simulations for current mapping through scanning gate microscopy. Our proposal opens up new perspectives for next-generation graphene electron optics experiments.

The sTOF, a Favorable Geometry for a Time-of-Flight Analyzer.

A new geometry for the flight region in a time-of-flight mass spectrometer is presented. It consists of two opposing electrostatic sectors of about 255° each and straight sections with a length appropriate to the turns. The resulting geometry folds into a compact space. The first-order aberrations for position, angle, and energy are all zero. The transverse focusing properties are also excellent. For an energetic, high-divergence ion source such as laser ablation, the sTOF has higher resolution and ion transmission than a reflectron of similar physical size. Graphical Abstract ᅟ.

Nonlinear stability in the transport of intense bunched beams

The paper investigates the nonlinear coupling of envelope modes of oscillation for intense bunched beams. Initially, the analysis concentrates on the case of spherically symmetric beams for which longitudinal and transverse focusing forces are assumed to be the same. It is investigated how externally induced spherically symmetric breathing oscillations may nonlinearly drive the growth of ellipsoidal modes which can break the spherical beam symmetry. Next, a more general case in which the focusing forces are not symmetric such that the matched beam already presents an ellipsoidal shape is studied. It is found that depending on the parameters of the system, even a very small mismatch amplitude can drive an instability, which leads to an effective coupling of longitudinal and transversal envelope oscillations by means of the space-charge forces. Use is made of Poincaré plots and the stability index of periodic orbits to perform a detailed analysis of the location of the instability in the parameter space and how it affects the beam transport. Self-consistent numerical simulations are performed in order to verify the onset of the nonlinear instability and its effect on the evolution of the RMS size and emittance of the beam.

Scaling approach to tight-binding transport in realistic graphene devices: The case of transverse magnetic focusing

Ultra-clean graphene sheets encapsulated between hexagonal boron nitride crystals host two-dimensional electron systems in which low-temperature transport is solely limited by the sample size. We revisit the theoretical problem of carrying out microscopic calculations of non-local ballistic transport in such micron-scale devices. By employing the Landauer-Buttiker scattering theory, we propose a novel scaling approach to tight-binding non-local transport in realistic graphene devices. We test our numerical method against experimental data on transverse magnetic focusing (TMF), a textbook example of non-local ballistic transport in the presence of a transverse magnetic field. This comparison enables a clear physical interpretation of all the observed features of the TMF signal, including its oscillating sign.

Electron optics with p-n junctions in ballistic graphene.

Electrons transmitted across a ballistic semiconductor junction are expected to undergo refraction, analogous to light rays across an optical boundary. In graphene, the linear dispersion and zero-gap band structure admit highly transparent p-n junctions by simple electrostatic gating. Here, we employ transverse magnetic focusing to probe the propagation of carriers across an electrostatically defined graphene junction. We find agreement with the predicted Snell's law for electrons, including the observation of both positive and negative refraction. Resonant transmission across the p-n junction provides a direct measurement of the angle-dependent transmission coefficient. Comparing experimental data with simulations reveals the crucial role played by the effective junction width, providing guidance for future device design. Our results pave the way for realizing electron optics based on graphene p-n junctions.

Ballistic miniband conduction in a graphene superlattice.

Rational design of long-period artificial lattices yields effects unavailable in simple solids. The moiré pattern in highly aligned graphene/hexagonal boron nitride (h-BN) heterostructures is a lateral superlattice with high electron mobility and an unusual electronic dispersion whose miniband edges and saddle points can be reached by electrostatic gating. We investigated the dynamics of electrons in moiré minibands by measuring ballistic transport between adjacent local contacts in a magnetic field, known as the transverse electron focusing effect. At low temperatures, we observed caustics of skipping orbits extending over hundreds of superlattice periods, reversals of the cyclotron revolution for successive minibands, and breakdown of cyclotron motion near van Hove singularities. At high temperatures, electron-electron collisions suppress focusing. Probing such miniband conduction properties is a necessity for engineering novel transport behaviors in superlattice devices.

Enhanced proton acceleration by intense laser interaction with an inverse cone target

The generation and control of high-quality proton bunches using focused intense laser pulse on an inverse cone target is investigated with a set of particle-in-cell simulations. The inverse cone is a high atomic number conical frustum with a thin solid top and open base, where the laser impinges onto the top surface directly, not down the open end of the cone. Results are compared with a simple planar target, where the proton angular distribution is very broad because of transverse divergence of the electromagnetic fields behind the target. For a conical target, hot electrons along the cone wall surface induce a transverse focusing sheath field. This field can effectively suppress the spatial spreading of the protons, resulting in a high-quality small-emittance, low-divergence proton beam. A slightly lower proton beam peak energy than that of a conventional planar target was also found.

Generation of femtosecond γ-ray bursts stimulated by laser-driven hosing evolution

The promising ability of a plasma wiggler based on laser wakefield acceleration to produce betatron X-rays with photon energies of a few keV to hundreds of keV and a peak brilliance of 1022–1023 photons/s/mm2/mrad2/0.1%BW has been demonstrated, providing an alternative to large-scale synchrotron light sources. Most methods for generating betatron radiation are based on two typical approaches, one relying on an inherent transverse focusing electrostatic field, which induces transverse oscillation, and the other relying on the electron beam catching up with the rear part of the laser pulse, which results in strong electron resonance. Here, we present a new regime of betatron γ-ray radiation generated by stimulating a large-amplitude transverse oscillation of a continuously injected electron bunch through the hosing of the bubble induced by the carrier envelope phase (CEP) effect of the self-steepened laser pulse. Our method increases the critical photon energy to the MeV level, according to the results of particle-in-cell (PIC) simulations. The highly collimated, energetic and femtosecond γ-ray bursts that are produced in this way may provide an interesting potential means of exploring nuclear physics in table top photo nuclear reactions.

Transverse characterization of focused Bessel beams with angular momentum applied to study degree of coherence

The transverse focusing properties at the ‘pseudo-focal’ plane of coherent Bessel beams with angular momentum are analyzed in detail. The transverse magnification of the central dark region of Bessel beams at this pseudo-focal plane is derived for the first time by calculating the ratio of the magnitude of the transverse components of the corresponding wave vectors before and after the focusing lens. We test our results experimentally with coherent laser Bessel beams and excellent agreement is observed. Then, an LED light source is used to generate Bessel beams. By modifying the coherence of the LED light source, we observe that by reducing coherence a smaller and shallower central dark region of Bessel beams with angular momentum is produced at the pseudo-focal plane. This technique can be used as a method to characterize the degree of coherence of vortex beams.

Physics of Phase Space Matching for Staging Plasma and Traditional Accelerator Components Using Longitudinally Tailored Plasma Profiles.

Phase space matching between two plasma-based accelerator (PBA) stages and between a PBA and a traditional accelerator component is a critical issue for emittance preservation. The drastic differences of the transverse focusing strengths as the beam propagates between stages and components may lead to a catastrophic emittance growth even when there is a small energy spread. We propose using the linear focusing forces from nonlinear wakes in longitudinally tailored plasma density profiles to control phase space matching between sections with negligible emittance growth. Several profiles are considered and theoretical analysis and particle-in-cell simulations show how these structures may work in four different scenarios. Good agreement between theory and simulation is obtained, and it is found that the adiabatic approximation misses important physics even for long profiles.

Electromagnetic design and beam dynamics simulation of a new superconducting accelerating structure for extremely low β protons**Supported by Major Research Plan of National Natural Science Foundation of China (91026001)

For the application of high intensity continuous wave (CW) proton beam acceleration, a new superconducting accelerating structure for extremely low β protons working in TE210 mode has been proposed at Peking University. The cavity consists of eight electrodes and eight accelerating gaps. The cavity's longitudinal length is 368.5 mm, and its transverse dimension is 416 mm. The RF frequency is 162.5 MHz, and the designed proton input energy is 200 keV. A peak field optimization has been performed for the lower surface field. The accelerating gaps are adjusted by phase sweeping based on KONUS beam dynamics. The first four gaps are operated at negative synchronous RF phase to provide longitudinal focusing. The subsequent gaps are 0° sections which can minimize the transverse defocusing effect. Solenoids are placed outside the cavity to provide transverse focusing. Numerical calculation shows that the transverse defocusing of the KONUS phase is about three times smaller than that of the conventional negative synchronous RF phase. The beam dynamics of a 10 mA CW proton beam is simulated by the TraceWin code. The simulation results show that the beam's transverse size is under effective control, while the increase in the longitudinal direction is slightly large. Both the TraceWin simulation and the numerical calculation show that the cavity has a relatively high effective accelerating gradient of 2.6 MV/m. On the whole, our results show that this new accelerating structure may be a possible candidate for superconducting operation at such a low energy range.

Design of a 10 MeV normal conducting CW proton linac based on equidistant multi-gap CH cavities**Supported by National Natural Science Foundation of China (11375122, 91126003)

Continuous wave (CW) high current proton linacs have wide applications as the front end of high power proton machines. The low energy part of such a linac is the most difficult and there is currently no widely accepted solution. Based on the analysis of the focusing properties of the CW low energy proton linac, a 10 MeV low energy normal conducting proton linac based on equidistant seven-gap Cross-bar H-type (CH) cavities is proposed. The linac is composed of ten 7-gap CH cavities and the transverse focusing is maintained by quadrupole doublets located between the cavities. The total length of the linac is less than 6 meters and the average acceleration gradient is about 1.2 MeV/m. The electromagnetic properties of the cavities are investigated by Microwave Studio. At the nominal acceleration gradient the maximum surface electric field in the cavities is less than 1.3 times the Kilpatrick limit, and the Ohmic loss of each cavity is less than 35 kW. Multi-particle beam dynamics simulations are performed with Tracewin code, and the results show that the beam dynamics of the linac are quite stable, the linac has the capability to accelerate up to 30 mA beam with acceptable dynamics behavior.

Simulation of dark current and dark current-induced background photons in the Thomson scattering X-ray source

A model of dark current generation in the photocathode radio-frequency (RF) gun is established in the Thomson scattering X-ray source, and dark current transport and losses along the beamline are simulated. A velocity bunching cavity is added between the RF gun and the first linac to achieve the longitudinal compression of the photoelectron bunches. Given the longitudinal acceleration and the transverse focusing of the bunching cavity, the dark current electrons with bunching are approximately three times more than those without bunching, and this condition aggravates the harm to the operation of the photoinjector. Numerous dark current electrons around the electron–laser interaction section hit against the pipe inner wall and two laser focusing mirrors, producing a large number of background photons. A simulation of the bremsstrahlung process using an MCNP code is presented, showing that the background photon yield is less than 2.1% of the scattering photon yield, which is acceptable for our application.

GEANT4 simulations for beam emittance in a linear collider based on plasma wakefield acceleration

Alternative acceleration technologies are currently under development for cost-effective, robust, compact, and efficient solutions. One such technology is plasma wakefield acceleration, driven by either a charged particle or laser beam. However, the potential issues must be studied in detail. In this paper, the emittance evolution of a witness beam through elastic scattering from gaseous media and under transverse focusing wakefields is studied.

Design and experiments of RF transverse focusing in S-Band, 1 MeV standing wave linac

S-Band standing wave (SW) linacs in the range of 1–10MeV have many potential industrial applications world wide. In order to mitigate the industrial requirement it is required to reduce the overall size and weight of the system. On this context a 2856MHz, 1MeV, bi-periodic on axis coupled self transverse focused SW linac has been designed and tested. The RF phase focusing is achieved by introducing an asymmetric field distribution in the first cell of the 1MeV linac. The pulsed electron beam of 40keV, 650mA and 5µs duration is injected from a LaB6 thermionic gun. This paper presents the structure design, beam dynamics simulation, fabrication and experimental results of the 1MeV auto-focusing SW linac.

Design study of low energy beam transport line for ion beams of the post-accelerator at RAON

Low-energy ions produced by the ion source pass through the focusing and acceleration sections. During this process, the ions accumulate energy and are finally transported to the apparatus that utilizes them for a specific purpose. Thus, in order to increase the transmission efficiency of the ion beams, the low energy beam transport (LEBT) system must minimize the beam loss and the emittance growth. The LEBT system is designed and optimized to transmit 132Sn16+ and 58Ni8+ beams of the post-accelerator at RAON that is the accelerator complex for the rare isotope science. The post-accelerator LEBT line comprises solenoids and electrostatic quadrupoles for transverse focusing and a multi-harmonic buncher for longitudinal focusing. This paper presents the results of the optical design and beam tracking for the post-accelerator LEBT obtained by using TraceWIN and TRACK codes.

On a class of ideal focusing systems for energy analysis

Every plane electrostatic system produces pair of orthogonal curve families -- field lines and equipotentials, which can be associated with trajectories and lines of constant action of some mechanical system. The pair of opposite parallel line charges has a two-dimensional representation on a plane perpendicular to charge lines. Such electrostatic system is used as trajectories/action generator. Both action and its arbitrary function are orthogonal to particle trajectories simultaneously. This fact can be used to regularize result two-dimensional potential function and to optimize three-dimensional charged particle motion. The method is applied to create charged particle energy analyzer with an ideal focusing in the symmetry plane. The system useful property is that its energy dispersion tends to infinity when the angle between direction to detector and initial velocity tends to π. Also, for some simple examples it was shown that together with the ideal focusing in a plane of symmetry the system has transversal first order focusing for some initial angles.

Control of focusing fields for positron acceleration in nonlinear plasma wakes using multiple laser modes

Control of transverse wakefields in the nonlinear laser-driven bubble regime using a combination of Hermite-Gaussian laser modes is proposed. By controlling the relative intensity ratio of the two laser modes, the focusing force can be controlled, enabling matched beam propagation for emittance preservation. A ring bubble can be generated with a large longitudinal accelerating field and a transverse focusing field suitable for positron beam focusing and acceleration.

Proton acceleration in underdense plasma by ultraintense Laguerre–Gaussian laser pulse

A three-dimensional (3D) particle-in-cell (PIC) simulation is used to investigate witness proton acceleration in underdense plasma with a short intense Laguerre–Gaussian (LG) laser pulse. Driven by the LG10 laser pulse, a special bubble with an electron pillar on the axis is formed in which protons can be well confined by the generated transversal focusing field and accelerated by the longitudinal wakefield. The risk of scattering prior to acceleration with a Gaussian laser pulse in underdense plasma is avoided, and protons are accelerated stably to much higher energy. In the simulation, a proton beam has been accelerated to 7 GeV from 1 GeV in underdense tritium plasma driven by a 2.14 × 1022 W cm−2 LG10 laser pulse.