Electron Beam Dynamics Research Articles

Particle‐in‐cell/Monte Carlo‐simulation of the discharge in helium initiated by a relativistic electron beam in the chamber with a magnetic mirror

AbstractA gas discharge is simulated and numerically studied in the gaseous helium in the region of the squeezed state of a single tubular magnetized relativistic electron beam at its partial reflection from a magnetic mirror. The code based on the particle‐in‐cell/Monte Carlo method was used. The electron beam dynamics, time evolution of phase portraits of particles, physical parameters, and spatial–time characteristics of plasma were calculated. It is shown that dense plasma appears in the cavity under the action of an electron beam in the form of a thin‐walled long cylinder of a large length; its electron concentration can be several units of 1011 cm−3. At the same time, it turned out that plasma is considerably inhomogeneous in length; its more dense part corresponds to the part of the squeezed state of a beam. The time dependence of the charge compensation of electrons on the helium atom concentration in the chamber was calculated. The dependence turned out to be decreasing since the rate of discharge development is increasing with the growth of the helium pressure in the cavity.

Dynamics of the super pinch electron beam and fusion energy perspective

The characterization of a high current, relativistic electron beam, designated the Super Pinch electron beam, has been performed using compact pulsed-power accelerators of various architectures with a novel diode geometry. The Thunderbird accelerator has an initial $1.5\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{s}$ rise time and 150-kA peak current. The drive voltage is compressed to produce a 12-ns 500-kV voltage pulse generating a $\ensuremath{\sim}40\text{\ensuremath{-}}\mathrm{kA}$ electron beam, which apparently exceeds the Alv\'en current limit although the useful current at small radius is an order of magnitude less. Using an insulated hollow cathode with a 0.5-cm anode-cathode gap, the large current is enabled by the evolution of plasma from the dielectric sleeve enveloping the cathode and a 0.5-mm wire anode. Post-shot recovery of the anode target and measurements of its deformation and damage allow an evaluation of the enhanced electron-beam focusing whereby significant beam energy is delivered to the record small, microscopic volume inside the anode target. The electron beam is seen to have conditions favorable to those needed to ignite compressed fuel in inertial confinement fusion. These results motivated a deeper insight using theoretical modeling with hybrid particle-in-cell codes. The modeling presented in this paper shows an electron beam radius of $<10\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ containing a current of 3--6 kA or $>500\text{ }\text{ }\mathrm{MA}/{\mathrm{cm}}^{2}$ current density. Scaling up the accelerator, such preferred focusing, target penetration, and affordability of the pulsed power generated electron beams open a new opportunity for the application of the mainstream pulsed power devices in the research and development of fusion energy.

Investigation of high current electron beam dynamics in linear induction accelerator for creation of a high-power THz radiation source

The work addresses the use of electron beam produced by the linear induction accelerator to generate terahertz radiation pulses of 100 MW power level based on a free electron laser scheme. The beam parameters required for efficient generation are given. The features of transverse beam dynamics when transporting the beam through the linac are investigated. Emphasis is put on the electron injector which geometry and operation parameters mainly determine the beam characteristics at the linac exit. Most of the possible factors contributing to the beam emittance gain in the accelerator are considered. The obtained analytical estimates are compared to the numerical simulation results. The experimental results on compressing and transporting the beam having the electron energy of 5 MeV and the current of 1 kA in the transport system of free electron laser are presented.

Kinetic theory of monochromatic waves bunching in a low-voltage beam discharge in rare gases

The kinetic theory of phase focusing, that is bunching in a low-voltage beam discharge in rare gases (LVBD) during the propagation of longitudinal electrostatic oscillations at the Knudsen numbers of the order of unity have developed. The anomalous relaxation of the almost monoenergetic electron beam in momentum and energy is described for the case when this process cannot be explained by electron–atom collisions. The paper has shown the important role of electrons that have the beam energy and isotropic directional distribution, which is formed as a result of elastic collisions between the beam electrons and atoms. The dependence of the anomalous relaxation length on parameters of the LVBD in rare gases is studied.The developed theory makes it possible to quantitatively interpret experimental data on the LVBD under conditions when the electron mean free path is of the order of the interelectrode gap. According to these data, regardless of the density of the charged particles in the LVBD plasma in rare gases, five Langmuir plasma wavelengths fit along the length of the anomalous relaxation of the electron beam. The study of the electron beam dynamics laws in a plasma is important for the development of plasma-electrical devices, where the beam discharge is applied, namely: widely used all-movable stabilizers, sources of intense electromagnetic radiation, controlled elements of electronic circuits, plasma chemical reactors, etc.

MULTI-PURPOSE MODES OF FORMATION OF ELECTRON BEAMS IN THE CYLINDRICAL MAGNETIC FIELD OF THE MAGNETRON GUN

The results of the study on the formation of electron beams by the magnetron gun at various configurations of the magnetic field in the beam transport channel are presented. A technique for modeling the processes of formation of electron flows and control of the distribution of beams by collimation is presented. Numerical simulation of the dynamics of electron beams in the magnetic field of the gun for its various configurations has been carried out. Experimental data on the transportation and collimation of electron beams are presented. The possibility of stable formation of an electron beam in the axial direction during its transportation is shown. Imprints of the collimated electron beam were obtained on metal targets. The possibility of controlling the beam diameter by varying the magnetic field is shown. Comparison of the results of numerical modeling and experimental data on the motion and collimation of the tubular electron flow is carried out.

Elliptical plasma-filled waveguide as a new standard short-period undulator.

Undulators as the sources of high-brilliance synchrotron radiation are of widespread interest in new generations of light sources and free-electron lasers. Microwave propagation in a plasma-filled elliptical waveguide can be studied as a standard short-period undulator. This structure as a lucrative insertion device can be installed in the storage ring of third- and fourth-generation light sources to produce high-energy and high-brilliance synchrotron radiation. In this article, the propagation of the transverse electric modes in a plasma-filled waveguide with an elliptical cross-section is investigated, and the field components, the cut-off frequencies and the electron beam trajectory are calculated. With due consideration of the electron beam dynamics and in order to achieve a standard short-period undulator, parameters such as the dimensions of the waveguide elliptical cross-section, the microwave frequency and the plasma density are calculated.

Design of 325 MHz RF grid-controlled high voltage thermionic cathode electron gun

The electron gun with high repetition rate and high average current has a very wide range of applications. This paper presents the design of a microwave grid-controlled high-voltage thermionic electron gun working in CW mode with a bunch repetition rate of 325 MHz and elaborates the experimental principles of this kind of electron guns. Firstly, simulation software EGUN, POISSON (Poisson Superfish) and GPT (General Particle Tracer) are used to accomplish the structure design of a300kV high-voltage DC electron gun and beam dynamics verification.Secondly, to feed the microwave into the gap between the cathode and the grid of the electron gunefficiently, design of a power supply with a scheme of impedance matching from the radio frequency power source to the cathode is completed.Accordingly, a 325 MHz dual-mode coaxial power supply device is designed, and its feasibility is verified and analyzed..

Electron dynamics for high-intensity hollow electron beams

Hollow Electron Lenses (HEL) will be installed at the High Luminosity Large Hadron Collider to provide a continuous and controlled depletion of beam halo particles by interaction with a superimposed hollow electron beam, of intensity as high as 5 A, and radii 1.1–2.2 mm for 7 TeV LHC operations. In this paper, issues related to the propagation of high intensity hollow electron beams are discussed and the simulations of the electron beam dynamics with feedback to the HEL design are presented. The main results are the rise of the electron beam accelerating voltage from 10 kV, as in the initial proposal, to 15 kV and the validation of the 5 T magnetic field at the main solenoids as being sufficient to guarantee a stable electron beam.

Classical patterns in the quantum rainbow channeling of high energy electrons

We are investigating the quantum dynamics of a well-collimated electron beam transmitting through planar channels of the Si crystal. Electron states were represented by wave packets while the electron beam is treated as an ensemble of noninteracting wave packets. We have investigated the relationship between classical caustic pattern and anharmonicity of the potential and analyzed how quantum dynamic depends on the wave packet impact parameter and beam's angular divergence. We found that the extrema of the electron trajectory period, considered as a function of the impact parameter, determine the shape of the caustic pattern. All wave packet probability densities have multiple maxima generated by a self-interference. Their sum, that represents probability density of an ensemble, was found to depends strongly on the beam angular divergence. For small divergence, most peaks of different wave packets are aligned causing wavelike behavior of the ensemble. For moderate angular divergence maxima of some wave packets, are aligned with minima of others, resulting in the emergence of the classical caustic pattern. We have shown and experimentally confirmed that the only indication that the observed caustic pattern is generated by the quantum dynamics is a slight systematic shift of the corresponding caustic maxima.

Accurate and confident prediction of electron beam longitudinal properties using spectral virtual diagnostics

Longitudinal phase space (LPS) provides a critical information about electron beam dynamics for various scientific applications. For example, it can give insight into the high-brightness X-ray radiation from a free electron laser. Existing diagnostics are invasive, and often times cannot operate at the required resolution. In this work we present a machine learning-based Virtual Diagnostic (VD) tool to accurately predict the LPS for every shot using spectral information collected non-destructively from the radiation of relativistic electron beam. We demonstrate the tool’s accuracy for three different case studies with experimental or simulated data. For each case, we introduce a method to increase the confidence in the VD tool. We anticipate that spectral VD would improve the setup and understanding of experimental configurations at DOE’s user facilities as well as data sorting and analysis. The spectral VD can provide confident knowledge of the longitudinal bunch properties at the next generation of high-repetition rate linear accelerators while reducing the load on data storage, readout and streaming requirements.

Dynamics of self-accelerating electron beams in a homogeneous magnetic field

We examine the dynamics of electron beams that, in free space, are self-accelerating, in the presence of an additional magnetic field. We focus our attention in the case of Airy beams that follow parabolic trajectories and in generalized classes of beams associated with power-law trajectories. We study the interplay between beam self-acceleration and the circular motion caused by the magnetic field. In the case of Airy beams, using an integral representation, we find closed-form solutions for the electron wavefunction. We also derive asymptotic formulas for the beam trajectories both for Airy beams and for self-accelerating power-law beams. A ray optics description is rather useful for the interpretation of the beam dynamics. Our results are in excellent comparison with direct numerical simulations.

Model analysis of relativistic electron beam dynamics in a rarefied plasma

A mathematical model for describing the nonlinear dynamics of a relativistic electron beam in a rarefied plasma is discussed. The model can be applied for the analysis of the behavior of an electron beam in accelerators, as well as in electromagnetic radiation generators based on relativistic electron beams. The equation for the beam envelope and the results of its numerical solution are presented and shortly discussed.

Velocity bunching dynamics of attosecond electron beam in a DC-gun based high repetition-rate beamline

We investigate the possibility of generating attosecond electron beams with sub-fC charges and a beam energy of a few MeV from a DC-gun and two super-conducting linac based high repetition-rate photoinjector, a promising candidate for next-generation high-flux ultrafast electron diffraction (UED). Using two super-conducting linac photoinjectors, a cascade velocity bunching scheme is adopted to compress the picosecond long e-beam generated by the DC-gun. Thorough dynamic simulations showed that an electron bunch with 2×103 electrons could be compressed to a few hundreds of attoseconds. In such an ultra-low charge domain, space charge induced slice energy spread is identified to be the main obstacle for further compression, and the final bunch length will become shorter with the reduction of the bunch charge in the power function. Combining merits of the ultra-short bunch duration and the high repetition-rate, such extraordinary electron beams should have great potential to further improve the temporal resolving power of UED facilities.

Observation of the Dynamics of a Focal Spot Using a Long-Pulse Linear Induction Accelerator

A diagnostic has been developed to study the focusing dynamics of a high-power electron beam on a target. The diagnostic uses a pinhole camera to observe bremsstrahlung from the converter target. A data acquisition system yields images of the beam focal spot with a frame duration of 20 ns and an almost unlimited recording duration. The focal spot dynamics of a linear induction accelerator with an energy of 1.5 MeV, a current of 1.2 kA and a pulse duration of 350 ns were studied. The focal spot was found to be disrupted within the first 100 ns of the pulse. Defocusing has a complex 3-D character. The feasibility of additional cleaning of the target using an accelerator pre-pulse was shown. Stable beam focusing for up to 200 ns was demonstrated.

Submicropulse electron-beam dynamics correlated with short-range wakefields in Tesla-type superconducting rf cavities

We report direct observations of submicropulse beam centroid shifts (head-tail kicks) correlated with short-range wakefields generated by off-axis electron-beam steering in Tesla-type superconducting rf cavities. The experiments were performed at the Fermilab Accelerator Science and Technology (FAST) Facility using its unique configuration of a photocathode rf gun injecting beam into two separated nine-cell cavities. The cavities are in series with corrector magnets and beam position monitors (BPMs) located before, between, and after them. The off-axis steering in the cavity was guided by the rf BPM data and higher-order mode circuitry targeting the first and second dipole passbands. The centroid shifts of up to 300 μm from head to tail of the ∼10-ps-long micropulses at 500 pC/b in a 3-MHz pulse train were measured via optical transition radiation at a downstream screen with a Hamamatsu C5680 synchroscan streak camera. We also showed that we could compensate such kicks from the first cavity with the short-range wakefields (SRWs) in the second cavity, and we observed the dilution of the beam size in the tail of the pulses. A simple numerical model of the SRW effect in a single Tesla cavity is compared to the experiment successfully. In principle, these fundamental results may be scaled to cryomodule configurations of major free-electron laser (FEL) facilities such as the European XFEL, Linac Coherent Light Source or LCLS-II XFEL, and the conceptual international linear collider.

Runaway electron beam dynamics at low plasma density in DIII-D: energy distribution, current profile, and internal instability

Parameters of the post-disruption runaway electron (RE) beam in the low density background plasma achieved after secondary deuterium injection are investigated in DIII-D. The spatially resolved RE energy distribution function is measured for the first time during the RE plateau stage by inverting hard x-ray bremsstrahlung spectra. It has maximum energy up to 20 MeV and a non-monotonic feature at 5–6 MeV observed only in the core of the beam supporting the possibility of kinetic instabilities. Results of Fokker-Plank modelling qualitatively support the formation of the non-monotonic distribution function. The RE current profile is reconstructed for the first time using the spatially resolved RE energy distribution. It is found to be more peaked than the pre-disruption plasma current, with higher internal inductance, suggesting preferential formation of REs in the core plasma or potentially a radially inward motion of REs. The accessed relatively low current (180 kA) RE beam is found to be MHD stable, likely due to its elevated safety factor profile. From this base stable equilibrium, an internal beam instability is accessed by ramping up the current. The instability leads to a sawtooth-like relaxation of the RE current profile, but drives no RE loss. An internal kink mode proposed as a candidate instability is supported by results of MARS-F modelling. Electron cyclotron emission (ECE) spectrum measured during the low density RE plateau is found to be bifurcated, with a break point at ≈ 100 GHz, suggesting resonant absorption of the ECE at low frequencies.

Analysis of Singularities and Internal Dynamics of Electron Beams

In this work we present an analysis of phase singularities in Laguerre-Gaussian beams. The cases to be analyzed are static and dynamic singularities. We consider the composition of canonical and kinetic currents around the singularities and velocities on each momentum state. We compare the behavior of time-dependent and stationary systems. We obtain the topological charge numbers that characterize the rotation of currents around the singularities. Finally, we present some analytical and numerical results to illustrate our model.

Electron beam dynamic study and Monte Carlo simulation of accelerator-based irradiation system for natural rubber vulcanization

This research focused on an electron beam accelerator system for natural rubber vulcanization. In this accelerator, electrons are generated from a 17-keV DC gun and accelerated in a 5-cell RF linac with a resonant frequency of 2996.39 MHz and an effective length of 22.15 cm. The RF macro-pulse has a length of 4 μs with a maximum repetition rate of 200 Hz. Electron beam dynamics in the linac were studied using software ASTRA. It was found that the electron beam can be accelerated to have average kinetic energy in a range of 1–3.86 MeV for accelerating gradients of 16.2 to 39.5 MV/m. This accelerating range corresponds to the RF peak powers of 0.32–1.49 MW. The beam dynamic simulation results were used as the inputs for GEANT4 Monte Carlo simulation of electrons in the irradiation system. The beams exit the linac and collide with a 50-μm titanium window. Then, they travel through 18 cm of air and penetrate in the rubber latex with optimal depths of 0.3–1.3 cm for electron beam energies of 1–3.85 MeV. At the rubber surface, rectangular apertures with well-defined effective area were considered to select the beams with more uniform transverse distribution. The effective volumes defined from the optimum depth and the effective irradiation area are 0.01–6.29 cm3 to obtain the required absorbed dose in a range of 50–150 kGy. The results from this study can be used to determine the parameters and conditions of the machine and the irradiation system for the practical operation.

The TeraFERMI Electro-Optic Sampling Set-Up for Fluence-Dependent Spectroscopic Measurements

TeraFERMI is the THz beamline at the FERMI free-electron-laser facility in Trieste (Italy). It uses superradiant Coherent Transition Radiation emission to produce THz pulses of 10 to 100 μ J intensity over a spectral range which can extend up to 12 THz. TeraFERMI can be used to perform non-linear, fluence-dependent THz spectroscopy and THz-pump/IR-probe measurements. We describe in this paper the optical set-up based on electro-optic-sampling, which is presently in use in our facility and discuss the properties of a representative THz electric field profile measured from our source. The measured electric field profile can be understood as the superimposed emission from two electron bunches of different length, as predicted by electron beam dynamics simulations.

ELECTRON BEAM DYNAMICS AT OUTPUT MAGNETRON GUN IN GRADIENT MAGNETIC FIELD

The results of numerical calculations based on the electron beam dynamics generated by a magnetron gun in the transport channel in a gradient magnetic field are presented. The dependence of the final transverse distribution on a target on the amplitude and gradient of the magnetic field was investigated. The possibility of controlling the transverse dimensions of the beam has been studied. It was found that the electron flux undergoes radial compression, the magnitude of which is determined by the form of the gradient magnetic field. The main dependences of the electron beam motion in a given magnetic field are modeled. The possibility of adjusting the beam diameter by varying the magnetic field is shown.