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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Three-Dimensional Simulations of Electron Beams Focused by Periodic Permanent Magnets

A fully three-dimensional (3D) model of an electron beam focused by a periodic permanent magnet (PPM) stack has been developed. First, the simulation code MAFIA was used to model a PPM stack using the magnetostatic solver. The exact geometry of the magnetic focusing structure was modeled; thus, no approximations were made regarding the off-axis fields. The fields from the static solver were loaded into the 3D particle-in-cell (PIC) solver of MAFIA where fully 3D behavior of the beam was simulated in the magnetic focusing field. The PIC solver computes the time-integration of electromagnetic fields simultaneously with the time integration of the equations of motion of charged particles that move under the influence of those fields. Fields caused by those moving charges are also taken into account; thus, effects like space charge and magnetic forces between particles are fully simulated. The electron beam is simulated by a number of macro-particles. These macro-particles represent a given charge Q amounting to that of several million electrons in order to conserve computational time and memory. Particle motion is unrestricted, so particle trajectories can cross paths and move in three dimensions under the influence of 3D electric and magnetic fields. Correspondingly, there is no limit on the initial current density distribution of the electron beam, nor its density distribution at any time during the simulation. Simulation results including beam current density, percent ripple and percent transmission will be presented, and the effects current, magnetic focusing strength and thermal velocities have on beam behavior will be demonstrated using 3D movies showing the evolution of beam characteristics in time and space. Unlike typical beam optics models, this 3D model allows simulation of asymmetric designs such as non- circularly symmetric electrostatic or magnetic focusing as well as the inclusion of input/output couplers.

Kory, Carol L.↗
NASA NTRS2000

Two-Dimensional Array Beam Scanning Via Externally and Mutually Injection Locked Coupled Oscillators

Some years ago, Stephan proposed an approach to one dimensional (linear) phased array beam steering which requires only a single phase shifter. This involves the use of a linear array of voltage-controlled electronic oscillators coupled to nearest neighbors. The oscillators are mutually injection locked by controlling their coupling and tuning appropriately. Stephan's approach consists of deriving two signals from a master oscillator, one signal phase shifted with respect to the other by means of a single phase shifter. These two signals are injected into the end oscillators of the array. The result is a linear phase progression across the oscillator array. Thus, if radiating elements are connected to each oscillator and spaced uniformly along a line, they will radiate a beam at an angle to that line determined by the phase gradient which is, in turn, determined by the phase difference between the injection signals.The beam direction is therefore controlled by adjusting this phase difference. Recently, Pogorzelski and York presented a formulation which facilitates theoretical analysis of the above beam steering technique. This was subsequently applied by Pogorzelski in analysis of two dimensional beam steering using perimeter detuning of a coupled oscillator array. The formulation is based on a continuum model in which the oscillator phases are represented by a continuous function satisfying a partial differential equation of diffusion type. This equation can be solved via the Laplace transform and the resulting solution exhibits the dynamic behavior of the array as the beam is steered. Stephan's beam steering technique can be similarly generalized to two-dimensional arrays in which the beam control signals are applied to the oscillators on the perimeter of the array. In this paper the continuum model for this two-dimensional case is developed and the dynamic solution for the corresponding aperture phase function is obtained. The corresponding behavior of the resulting far-zone radiation pattern is displayed as well.

Pogorzelski, Ronald J.↗
NASA NTRS2001

Electron Beam-Cure Polymer Matrix Composites: Processing and Properties

Researchers from NASA and Oak Ridge National Laboratory are evaluating a series of electron beam curable composites for application in reusable launch vehicle airframe and propulsion systems. Objectives are to develop electron beam curable composites that are useful at cryogenic to elevated temperatures (-217 C to 200 C), validate key mechanical properties of these composites, and demonstrate cost-saving fabrication methods at the subcomponent level. Electron beam curing of polymer matrix composites is an enabling capability for production of aerospace structures in a non-autoclave process. Payoffs of this technology will be fabrication of composite structures at room temperature, reduced tooling cost and cure time, and improvements in component durability. This presentation covers the results of material property evaluations for electron beam-cured composites made with either unidirectional tape or woven fabric architectures. Resin systems have been evaluated for performance in ambient, cryogenic, and elevated temperature conditions. Results for electron beam composites and similar composites cured in conventional processes are reviewed for comparison. Fabrication demonstrations were also performed for electron beam-cured composite airframe and propulsion piping subcomponents. These parts have been built to validate manufacturing methods with electron beam composite materials, to evaluate electron beam curing processing parameters, and to demonstrate lightweight, low-cost tooling options.

Wrenn, G.↗
NASA NTRS1998

Detailed characterization of the 1087 MeV/nucleon iron-56 beam used for radiobiology at the alternating gradient synchrotron

We report beam characterization and dosimetric measurements made using a 56Fe beam extracted from the Brookhaven National Laboratory Alternating Gradient Synchrotron (AGS) with a kinetic energy of 1087 MeV/nucleon. The measurements reveal that the depth-dose distribution of this beam differs significantly from that obtained with a 600 MeV/nucleon iron beam used in several earlier radiobiology experiments at the Lawrence Berkeley National Laboratory's BEVALAC. We present detailed measurements of beam parameters relevant for radiobiology, including track- and dose-averaged linear energy transfer (LET), fragment composition and LET spectra measured behind sample holders used in irradiations of biological samples. We also report measurements of fluence behind three depths (1.94, 4.68 and 9.35 g cm(-2)) of polyethylene targets with the 1087 MeV/nucleon beam, and behind 1.94 g cm(-2) of polyethylene with a 610 MeV/nucleon beam delivered by the AGS. These results are compared to earlier measurements with the 600 MeV/nucleon beam at the BEVALAC.

NASA Discipline Radiation Health↗
NASA NTRS2008

Five-Year Wilkinson Microwave Anisotropy Probe (WMAP)Observations: Beam Maps and Window Functions

Cosmology and other scientific results from the WMAP mission require an accurate knowledge of the beam patterns in flight. While the degree of beam knowledge for the WMAP one-year and three-year results was unprecedented for a CMB experiment, we have significantly improved the beam determination as part of the five-year data release. Physical optics fits are done on both the A and the B sides for the first time. The cutoff scale of the fitted distortions on the primary mirror is reduced by a factor of approximately 2 from previous analyses. These changes enable an improvement in the hybridization of Jupiter data with beam models, which is optimized with respect to error in the main beam solid angle. An increase in main-beam solid angle of approximately 1% is found for the V2 and W1-W4 differencing assemblies. Although the five-year results are statistically consistent with previous ones, the errors in the five-year beam transfer functions are reduced by a factor of approximately 2 as compared to the three-year analysis. We present radiometry of the planet Jupiter as a test of the beam consistency and as a calibration standard; for an individual differencing assembly. errors in the measured disk temperature are approximately 0.5%.

Hill, R.S.↗
NASA NTRS2008

Ion Beam Propulsion Study

The Ion Beam Propulsion Study was a joint high-level study between the Applied Physics Laboratory operated by NASA and ASRC Aerospace at Kennedy Space Center, Florida, and Berkeley Scientific, Berkeley, California. The results were promising and suggested that work should continue if future funding becomes available. The application of ion thrusters for spacecraft propulsion is limited to quite modest ion sources with similarly modest ion beam parameters because of the mass penalty associated with the ion source and its power supply system. Also, the ion source technology has not been able to provide very high-power ion beams. Small ion beam propulsion systems were used with considerable success. Ion propulsion systems brought into practice use an onboard ion source to form an energetic ion beam, typically Xe+ ions, as the propellant. Such systems were used for steering and correction of telecommunication satellites and as the main thruster for the Deep Space 1 demonstration mission. In recent years, "giant" ion sources were developed for the controlled-fusion research effort worldwide, with beam parameters many orders of magnitude greater than the tiny ones of conventional space thruster application. The advent of such huge ion beam sources and the need for advanced propulsion systems for exploration of the solar system suggest a fresh look at ion beam propulsion, now with the giant fusion sources in mind.

Source record↗
NASA NTRS2007

Dual-Beam Atom Laser Driven by Spinor Dynamics

An atom laser now undergoing development simultaneously generates two pulsed beams of correlated Rb-87 atoms. (An atom laser is a source of atoms in beams characterized by coherent matter waves, analogous to a conventional laser, which is a source of coherent light waves.) The pumping mechanism of this atom laser is based on spinor dynamics in a Bose-Einstein condensate. By virtue of the angular-momentum conserving collisions that generate the two beams, the number of atoms in one beam is correlated with the number of atoms in the other beam. Such correlations are intimately linked to entanglement and squeezing in atomic ensembles, and atom lasers like this one could be used in exploring related aspects of Bose-Einstein condensates, and as components of future sensors relying on atom interferometry. In this atom-laser apparatus, a Bose-Einstein condensate of about 2 x 10(exp 6) Rb-87 atoms at a temperature of about 120 micro-K is first formed through all-optical means in a relatively weak singlebeam running-wave dipole trap that has been formed by focusing of a CO2-laser beam. By a technique that is established in the art, the trap is loaded from an ultrahigh-vacuum magnetooptical trap that is, itself, loaded via a cold atomic beam from an upstream two-dimensional magneto-optical trap that resides in a rubidium-vapor cell that is differentially pumped from an adjoining vacuum chamber, wherein are performed scientific observations of the beams ultimately generated by the atom laser.

Thompson, Robert↗
NASA NTRS2005

Making AlN(x) Tunnel Barriers Using a Low-Energy Nitrogen-Ion Beam

A technique based on accelerating positive nitrogen ions onto an aluminum layer has been demonstrated to be effective in forming thin (<2 nm thick) layers of aluminum nitride (AlN(x)) for use as tunnel barriers in Nb/Al-AlN(x)/Nb superconductor/insulator/ superconductor (SIS) Josephson junctions. AlN(x) is the present material of choice for tunnel barriers because, to a degree greater than that of any other suitable material, it offers the required combination of low leakage current at high current density and greater thermal stability. While ultra-thin AlN films with good thickness and stoichiometry control are easily formed using techniques such as reactive molecular beam epitaxy and chemical vapor deposition, growth temperatures of 900 C are necessary for the dissociative adsorption of nitrogen from either nitrogen (N2) or ammonia (NH3). These growth temperatures are prohibitively high for the formation of tunnel barriers on Nb films because interfacial reactions at temperatures as low as 200 to 300 C degrade device properties. Heretofore, deposition by reactive sputtering and nitridation of thin Al layers with DC and RF nitrogen plasmas have been successfully used to form AlN barriers in SIS junctions. However, precise control over critical current density Jc has proven to be a challenge, as is attaining adequate process reproducibility from system to system. The present ion-beam technique is an alternative to the plasma or reactive sputtering techniques as it provides a highly controlled arrival of reactive species, independent of the electrical conditions of the substrate or vacuum chamber. Independent and accurate control of parameters such as ion energy, flux, species, and direction promises more precise control of film characteristics such as stoichiometry and thickness than is the case with typical plasma processes. In particular, the background pressure during ion-beam nitride growth is 2 or 3 orders of magnitude lower, minimizing the formation of compounds with contaminants, which is critical in devices the performance of which is dictated by interfacial characteristics. In addition, the flux of incoming species can be measured in situ using ion probes so that the dose can be controlled accurately. The apparatus used in the present ion-beam technique includes a vacuum chamber containing a commercial collimated- ion-beam source, a supply of nitrogen and argon, and an ion probe for measuring the ion dose. Either argon or nitrogen can be used as the feed gases for the ion source, depending on whether cleaning of the substrate or growth of the nitride, respectively, is desired. Once the Nb base electrode and Al proximity layer have been deposited, the N2 gas line to the ion beam is vented and purged, and the ion-source is turned on until a stable discharge is obtained. The substrate is moved over the ion-beam source to expose the Al surface layer to the ion beam (see figure) for a specified duration for the formation of the nitride tunnel barrier. Next, the Nb counter-electrode layer is deposited on the nitride surface layer. The Nb/Al- AlN(x)/Nb-trilayer-covered substrate is then patterned into individual devices by use of conventional integrated-circuit processing techniques.

Kaul, Anupama↗
NASA NTRS2004

Curing Composite Materials Using Lower-Energy Electron Beams

In an improved method of fabricating composite-material structures by laying up prepreg tapes (tapes of fiber reinforcement impregnated by uncured matrix materials) and then curing them, one cures the layups by use of beams of electrons having kinetic energies in the range of 200 to 300 keV. In contrast, in a prior method, one used electron beams characterized by kinetic energies up to 20 MeV. The improved method was first suggested by an Italian group in 1993, but had not been demonstrated until recently. With respect to both the prior method and the present improved method, the impetus for the use of electron- beam curing is a desire to avoid the high costs of autoclaves large enough to effect thermal curing of large composite-material structures. Unfortunately, in the prior method, the advantages of electron-beam curing are offset by the need for special walls and ceilings on curing chambers to shield personnel from x rays generated by impacts of energetic electrons. These shields must be thick [typically 2 to 3 ft (about 0.6 to 0.9 m) if made of concrete] and are therefore expensive. They also make it difficult to bring large structures into and out of the curing chambers. Currently, all major companies that fabricate composite-material spacecraft and aircraft structures form their layups by use of automated tape placement (ATP) machines. In the present improved method, an electron-beam gun is attached to an ATP head and used to irradiate the tape as it is pressed onto the workpiece. The electron kinetic energy between 200 and 300 keV is sufficient for penetration of the ply being laid plus one or two of the plies underneath it. Provided that the electron-beam gun is properly positioned, it is possible to administer the required electron dose and, at the same time, to protect personnel with less shielding than is needed in the prior method. Adequate shielding can be provided by concrete walls 6 ft (approximately equal to 1.8 m) high and 16 in. (approximately equal to 41 cm) thick, without a ceiling. The success of the present method depends on the use of a cationic epoxy as the matrix material in the prepreg tape, heating the prepreg tape to a temperature of 50 C immediately prior to layup, and exposing the workpiece to an electron-beam dose of approximately 2 Mrad. Experiments have shown that structures fabricated by the present method have the same mechanical properties as those of nominally identical structures fabricated by the prior method with electron beams of 3 to 4 MeV.

Byrne, Catherine A.↗
NASA NTRS2004

Compact Instrument for Measuring Profile of a Light Beam

The beamviewer is an optical device designed to be attached to a charge-coupled-device (CCD) image detector for measuring the spatial distribution of intensity of a beam of light (the beam profile ) at a designated plane intersecting the beam. The beamviewer-and-CCD combination is particularly well suited for measuring the radiant- power profile (for a steady beam) or the radiant-energy profile (for a pulsed beam) impinging on the input face or emerging from the output face of a bundle of optical fibers. The beamviewer and-CCD combination could also be used as a general laboratory instrument for profiling light beams, including beams emerging through small holes and laser beams in free space.

Papanyan, Valeri↗
NASA NTRS2012

Rapid Process to Generate Beam Envelopes for Optical System Analysis

The task of evaluating obstructions in the optical throughput of an optical system requires the use of two disciplines, and hence, two models: optical models for the details of optical propagation, and mechanical models for determining the actual structure that exists in the optical system. Previous analysis methods for creating beam envelopes (or cones of light) for use in this obstruction analysis were found to be cumbersome to calculate and take significant time and resources to complete. A new process was developed that takes less time to complete beam envelope analysis, is more accurate and less dependent upon manual node tracking to create the beam envelopes, and eases the burden on the mechanical CAD (computer-aided design) designers to form the beam solids. This algorithm allows rapid generation of beam envelopes for optical system obstruction analysis. Ray trace information is taken from optical design software and used to generate CAD objects that represent the boundary of the beam envelopes for detailed analysis in mechanical CAD software. Matlab is used to call ray trace data from the optical model for all fields and entrance pupil points of interest. These are chosen to be the edge of each space, so that these rays produce the bounding volume for the beam. The x and y global coordinate data is collected on the surface planes of interest, typically an image of the field and entrance pupil internal of the optical system. This x and y coordinate data is then evaluated using a convex hull algorithm, which removes any internal points, which are unnecessary to produce the bounding volume of interest. At this point, tolerances can be applied to expand the size of either the field or aperture, depending on the allocations. Once this minimum set of coordinates on the pupil and field is obtained, a new set of rays is generated between the field plane and aperture plane (or vice-versa). These rays are then evaluated at planes between the aperture and field, at a desired number of steps perceived necessary to build up the bounding volume or cone shape. At each plane, the ray coordinates are again evaluated using the convex hull algorithm to reduce the data to a minimal set. When all of the coordinates of interest are obtained for every plane of the propagation, the data is formatted into an xyz file suitable for FRED optical analysis software to import and create a STEP file of the data. This results in a spiral-like structure that is easily imported by mechanical CAD users who can then use an automated algorithm to wrap a skin around it and create a solid that represents the beam.

Howard, Joseph↗
NASA NTRS2016

Beam-Forming Concentrating Solar Thermal Array Power Systems

The present invention relates to concentrating solar-power systems and, more particularly, beam-forming concentrating solar thermal array power systems. A solar thermal array power system is provided, including a plurality of solar concentrators arranged in pods. Each solar concentrator includes a solar collector, one or more beam-forming elements, and one or more beam-steering elements. The solar collector is dimensioned to collect and divert incoming rays of sunlight. The beam-forming elements intercept the diverted rays of sunlight, and are shaped to concentrate the rays of sunlight into a beam. The steering elements are shaped, dimensioned, positioned, and/or oriented to deflect the beam toward a beam output path. The beams from the concentrators are converted to heat at a receiver, and the heat may be temporarily stored or directly used to generate electricity.

Cwik, Thomas A.↗
DOE OSTI2022

E-Beam Irradiation Beamline at Jefferson Lab for Wastewater Treatment

Electron beam (e-beam) irradiation is an advanced method for removing the emerging organic contaminants in wastewater, such as 1,4-dioxane, and per- and polyfluoroalkyl sub?stances (PFAS), which have the potential to be regulated in the near future but are difficult to degrade by conventional treatment methods. This dissertation was based on a collabo?rating study between Jefferson Lab (Jlab) and Hampton Roads Sanitation District (HRSD) to evaluate the impacts of e-beam irradiation on the degradation of 1,4-dioxane and PFAS. It presents the detailed design of an e-beam irradiation beamline, the beamline simulation using general particle tracer (GPT), the installation, and the successful commissioning. The beamline is an extended section to the Upgraded Injector Test Facility (UITF) at Jlab, which is a continuous wave (CW), superconducting radio frequency (SRF) linear accelerator with an energy up to 10 MeV. To let the sample volume receive a significant and uniform dose distribution, the sample target was designed by investigating the dose distribution simulated with a Monte-Carlo code, FLUKA. The optimized beam energy was 8 MeV and the beam current for irradiation was ? 100 nA. With the use of a solenoid and a raster, the electron beam was expanded to the optimized size, 1? ? 15 mm, at the sample target. This dis?sertation also presents the irradiation experiments for 64 1,4-dioxane samples and 48 PFAS samples in different water matrices, including real wastewater, which were prepared and an?alyzed by HRSD. The absorbed doses of samples were obtained by designing a new method that combines the FLUKA simulation and dose mapping experiments. The irradiation re?sults showed that around 95% of 1,4-dioxane was removed at a low dose of ? 2 kGy, and PFAS was possibly removed at a lower dose compared to similar research. This work is a first implementation of SRF technology for wastewater irradiation. It pro?vides a valuable new research platform for wastewater remediation. This will be in support of future industrial applications of advanced SRF technologies and better understanding of the effect of e-beam irradiation on wastewater or water treatment.

Li, Xi↗
DOE OSTI2024

A Self Consistent 2D Simulation of Coherent Synchrotron Radiation Effects on Beam Dynamics

An increasing interest in high quality and high current electron beams necessitates a thorough understanding and prediction of coherent synchrotron radiation effects. The self-interaction of charged particles in a beam undergoing synchrotron motion is a physically significant process that is all too often computationally intensive with very little analytical results to rely on for the general case. The coherent spectrum of this interaction is of utmost importance to the design of free electron lasers (FELs) and an accurate assessment is imperative for their design. This work presents a novel implementation to the numerical simulation of charged particle beams. The simulation is a self-consistent approach including the self-fields generated by the beam of which coherent synchrotron radiation effects are of primary interest. A particle-in-cell model is used where a planar beam sampled by point particles is deposited on an encompassing grid at each timestep. The electromagnetic fields are calculated on the grid using the retarded potentials according to causality. The electromagnetic forces from the fields are interpolated on each particle which in turn advance in time. The simulation is benchmarked against well-established results for coherent synchrotron radiation effects. In addition, studies are provided that show the convergence of simulation results for increasing resolution. A study into the transverse beam size effects on beam dynamics is performed as well as a proof of concept where the simulation is used by a genetic algorithm to optimize the design parameters of a beam lattice. The results of these studies in tandem verify the efficacy of the simulation for its practical use in accelerator design or the study of synchrotron radiation effects

Duffin, Dallan [Old Dominion Univ., Norfolk, VA (U↗
DOE OSTI2023

Pulsed-Beam Transmission Electron Microscopy and Radiation Damage

Here, we review the use of pulsed electron-beams in transmission electron microscopes (TEMs) for the purpose of mitigating specimen damage. We begin by placing the importance of TEMs with respect to materials characterization into proper context, and we provide a brief overview of established methods for reducing or eliminating the deleterious effects of beam-induced damage. We then introduce the concept of pulsed-beam TEM, and we briefly describe the basic methods and instrument configurations used to create so-called temporally structured electron beams. Following a brief overview of the use of high-dose-rate pulsed-electron beams in cancer radiation therapy, we review historical speculations and more recent compelling but mostly anecdotal findings of a pulsed-beam TEM damage effect. This is followed by an in-depth technical review of recent works seeking to establish cause-and-effect relationships, to conclusively uncover the presence of an effect, and to explore the practicality of the approach. These studies, in particular, provide the most compelling evidence to date that using a pulsed electron beam in the TEM is indeed a viable way to mitigate damage. Throughout, we point out current gaps in understanding, and we conclude with a brief perspective of current needs and future directions.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Investigation of resistive magnetic field generation by intense proton beams in dense plasmas

Current and future applications of intense proton sources abound, including radiography, cancer therapy, warm dense matter generation, and inertial confinement fusion. With increasingly efficient acceleration and focusing mechanisms, proton current densities may soon approach and exceed 10 10 A/cm 2 , e.g., via intense laser drivers. Simulations have previously shown that in this current density regime, beam-induced field generation plays a significant role in beam transport through dense plasmas. Here, we present a theoretical model for the generation of resistive magnetic fields by intense proton beam transport through solid density plasmas. The theoretical evolution of the magnetic field profile is calculated using an analytic model for aluminum resistivity, heat capacity, and stopping power, applicable from cold matter to hot plasma. The effects of various beam and material parameters on the field are investigated and explained for both monoenergetic and Maxwellian proton beams. For a proton beam with Maxwellian temperature 5 MeV and total energy 10 J, the model calculates resistive magnetic fields up to 150 T in aluminum. In conclusion, the calculated field profiles from several beam cases are compared with 2D hybrid particle-in-cell simulations, with good agreement found in magnitude and time scale.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

An adaptive masking method for beam halo measurement by a digital micro mirror device

We report that in high intensity particle beams, irregularities in cathode emission, scattering effects, dark current and space charge forces can lead to a common phenomenon termed beam halo with associated emittance growth, beam loss and overall beam quality degradation. It is of fundamental interest and practical importance to precisely monitor such beam halo, which could offer valuable insights into the experimental strategy for the suppression of this undesired feature. A Digital Micro mirror Device (DMD) is a computer-controlled micro-electrical-mechanical system that contains a compact array of physically independent reflective mirrors. Using a standard DMD, we come up with an adaptive masking method for halo measurement, which demonstrates superior robustness and efficiency comparing to the conventional approaches as confirmed by simulation and experimental results. Our development includes an integrated package of hardware, software and a graphic user interface (GUI) that is robust and portable and can be applied as a beam halo diagnostic for electron guns or radiating charged particle beams in general.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Improved calibration of rf cavities for relativistic electron beams: Effects of secondary corrections and experimental verification

In the aspect of longitudinal beam bunching, the bunching strength can be controlled by the rf cavity phase and voltage. However, these machine parameters are different from those that interact with the beam itself. In order to gain control of the beam-cavity interaction, cavity calibration must be performed. Furthermore, it relies on fitting the beam energy gain versus cavity phase to a calibration function. Under the conventional assumption of relativistic beam conditions, the calibration function is a first harmonic sinusoidal function (a sinusoidal function with a period of 2π). However, this expression is insufficient for a high-voltage bunching cavity. Due to beam acceleration inside the cavity, an energy bias and a second harmonic function should be included to modify the conventional calibration function, even for a relativistic electron beam. In this paper, we will derive this modification and provide a comparison to both the Coherent Electron Cooling Experiment and the IMPACT T simulation, respectively.

43 PARTICLE ACCELERATORS↗