Pierce Parameter Research Articles

Analysis and Simulation the Effect of the Pierce Parameter on the Output of the Free Electron Laser system

The free electron laser is considered one of these important and advanced inventions because it provides a laser beam within various wavelengths of the electromagnetic spectrum. In any laser system device, several parameters must be available on which the efficiency and performance of the laser system are dependent. The Pierce parameter is one of the important parameters in measuring the performance quality of the free electron laser. In this paper, the simulation results were obtained using the MATLAB program to show the important effect of the Pierce parameter on the performance of the free electron laser system. The simulation results showed that the values of the Pierce parameter ranged between (0.01 - 0.03) for the laser beam with long wavelengths, while it ranged between (0.001-0.0001) for the short wavelengths. The results showed an increase in the efficiency values of the free electron laser system with increasing the values of the Pierce parameter, which represents the ratio between the saturation power and the power of the electron; therefore, it can be used as a specific threshold to measure the efficiency of the laser system. Additionally, the simulation of the Pierce parameter has a direct relation to the small signal gain per unit length.

About theory of hybride TWTO and an amplifire with a complex permittivity

The purpose of this work is to construct a nonlinear theory of a hybrid between travelling wave tube (TWT) and an amplifier with a complex permittivity. Methods. The following model is considered: an ion-compensated one-dimensional electron beam penetrates the input travelling wave tube section, then flies into a medium with a complex permittivity, and then enters the output travelling wave tube section. A linear theory of this hybrid is constructed, and its results are compared with the results of the well-known linear theory of travelling wave tube. A nonlinear theory of this hybrid was constructed by a modified wave method, and the results were compared with the nonlinear travelling wave tube theory obtained by the classical Ovcharov–Solntsev’s wave method. In addition, to test the limits of applicability of the obtained results, a stationary nonlinear theory of the hybrid was constructed, obtained using the large particle method. The results of this theory were also compared with the stationary nonlinear travelling wave tube theory constructed using the large particle method. Results and conclusion. Based on the results of the developed theories, it is shown that, under certain parameters, the linear theory and nonlinear theories (both by the modified Ovcharov–Solntsev’s wave method and by the large particle method) make it possible to obtain comparable results both in the case of a classical travelling wave tube and for the hybrid under study. It is shown that under certain parameters, due to the resistive instability, the bunching of electrons can be noticeably improved and, as a result, the gain of the hybrid can exceed the gain in a classical travelling wave tube with the same parameters and the same total length of the device in the linear mode of operation. In the nonlinear mode of operation, the specified hybrid, with optimal environmental parameters, can have significantly higher values of output power and efficiency than travelling wave tube with the same value of the space charge parameter and the Pierce parameter.

Impacts of Multi-Dimensional Geometrical Uncertainties on Field Characteristics of Traveling-Wave Tube in Data-Driven Perspective

Recent prominent analyses on impacts of fabrication errors tend to start from Pierce parameters by assuming a normal distribution on them. We manage to analyze the complicated effects of multi-dimensional uncertainties directly from geometrical tolerances and present a general pattern for multi-dimensional geometrical uncertainty analysis on field characteristics. Aided by artificial neural networks (ANNs) which would get hold of the cost surface quickly and serve as rapid interfaces with a calculation speed several orders faster than full-wave code, Monte Caro analysis is accessible and effective to simulate the actual probabilistic distributions through a large-volume sampling on neural networks. Under such data-driven perspective which circumvents sophisticated theoretical analysis, the variations of geometrical parameters are analyzed as an entirety from the viewpoint of distribution. The dynamics of features of distributions of three field characteristics as well as geometrical parameters are therefore possible to be delved and analyzed. Such an analysis pattern is general since none of the steps presented cannot be readily transplanted to other topologies.

Efficiency enhancement of free-electron laser oscillator by kicking the electron beam orbit in a transverse gradient undulator

The conversion efficiency of a conventional free-electron laser (FEL) is on the level of Pierce parameter, which means that only a small portion of electron beam energy is converted into the electric field. Undulator tapering is a common way to enhance the FEL efficiency, however, it has limited effect when applying in the FEL oscillator. Inspired by the fast kicker developed in the high-repetition-rate FELs and storage rings, in this paper we propose to kick the electron beam orbit transversely in a transverse gradient undulator (TGU) after the FEL is saturated in oscillator. The electron beam will experience a different undulator strength after the beam orbit is deflected to the off-axis position. It can be regarded as a dynamic tapering method within the macrobunch while the dynamic detuning on the undulator strength with the normal tapering method is almost impossible in oscillator. Though the TGU will reduce the initial small-signal gain, the FEL efficiency still can be greatly enhanced. Numerical simulations demonstrated that the maximum FEL power can be enhanced to more than 3 times of the normal FEL oscillator.

Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic Fields

In this work, the radiation from electrons in multi-periodic undulator fields with symmetric and asymmetric harmonics was analyzed using generalized Bessel functions formalism. The asymmetric, symmetric, and anti-symmetric periodic magnetic fields with harmonics were studied in order to get the enhanced radiation of the high harmonics of undulator radiation (UR). The effect on the spontaneous and stimulated UR was explored. The exact integral forms for the Bessel coefficients were obtained for undulators with general symmetric and asymmetric field harmonics. Spectral properties of the radiation from several configurations of the undulator fields with harmonics were compared with each other. The resulting spontaneous UR spectrum and harmonic intensities were obtained analytically in the form of integrals and compared with the respective results that were obtained numerically with SPECTRA program. The dimensionless scaling parameter of a free electron laser (FEL)—the Pierce parameter (ρ)—was computed and compared for the different considered undulators. We studied the differences in the behavior of the high-gain single pass FEL harmonics and the spontaneous UR harmonics in the same undulators. The undulators with variable deflection parameter (k) were considered. The effect of the k parameter (deflection parameter for a common planar undulator) on the spontaneous UR and on the high-gain FEL radiation was explored. In this context, an experiment with variable strength undulators at FLASH 2 FEL was analyzed; the shorter saturated length in high harmonic self-seeding (HHSS) regime vs. self-amplified spontaneous emission (SASE) is explained.

Hard X-ray self-seeding commissioning at PAL-XFEL.

A wake monochromator based on a large-area diamond single crystal for hard X-ray self-seeding has been successfully installed and commissioned in the hard X-ray free-electron laser (FEL) at the Pohang Accelerator Laboratory with international collaboration. For this commissioning, the self-seeding was demonstrated with a low bunch charge (40 pC) and the nominal bunch charge (180 pC) of self-amplified spontaneous emission (SASE) operation. The FEL pulse lengths were estimated as 7 fs and 29.5 fs, respectively. In both cases, the average spectral brightness increased by more than three times compared with the SASE mode. The self-seeding experiment was demonstrated for the first time using a crystal with a thickness of 30 µm, and a narrow bandwidth of 0.22 eV (full width at half-maximum) was obtained at 8.3 keV, which confirmed the functionality of a crystal with such a small thickness. In the nominal bunch-charge self-seeding experiment, the histogram of the intensity integrated over a 1 eV bandwidth showed a well defined Gaussian profile, which is evidence of the saturated FEL and a minimal electron-energy jitter (∼1.2 × 10-4) effect. The corresponding low photon-energy jitter (∼2.4 × 10-4) of the SASE FEL pulse, which is two times lower than the Pierce parameter, enabled the seeding power to be maximized by maintaining the spectral overlap between SASE FEL gain and the monochromator.

Modelling a laser plasma accelerator driven free electron laser

Free-electron lasers (FEL) are the brightest, coherent sources of short wavelength radiation from the VUV into the x-ray. There is much research interest in reducing the cost and the size of FELs by utilising new accelerator techniques. Laser-plasma accelerator (LPA) are a promising accelerator for next generation compact FEL light sources with many potential advantages due to the high acceleration gradient and large peak currents they offer. The electron beams of a LPA typically have a smaller transverse emittance, a large energy spread and tend to be of shorter duration and higher current than conventional Radio Frequency (RF) accelerators. In this paper, a FEL driven by an electron beam from a typical LPA was simulated using the 3D FEL simulation code Puffin. It is shown that lowering the homogenous electron beam energy spread increases the radiation energy output in a short undulator and , as become less than the FEL, or Pierce parameter (), then the peak radiation energy increases and the saturation length reduces significantly as expected.

The seed energy fluctuation of hard X-ray self-seeding free electron laser

Self-seeding free electron lasers (FELs) are capable of generating fully coherent X-ray pulses. However, the stability of output pulse energy of hard X-ray self-seeding (HXRSS) FEL is poor. This letter reports the seed energy stability investigation of HXRSS FEL. For the purpose of a more stable HXRSS FEL, this work suggests a relatively broad bandwidth ρt of crystal monochromator, a relatively long electron bunch with energy jitter (r.m.s.) down to a quarter of FEL Pierce parameter ρ, and a larger Bragg angle θB to improve the seed energy stability. Moreover, the angle jitter (r.m.s.) between the SASE pulse incident direction and the crystal surface should be less than (ρ tan θB)/2, and the relative time jitter (r.m.s.) between the electron bunch and the seed should be less than half of the seed bump duration Tt.

Single-pass high-gain tapered free-electron laser with transverse diffraction in the postsaturation regime

It has been well known that the resonant interaction of an ultrarelativistic electron beam and the radiation field in the single-pass high-gain free electron laser (FEL) amplifier leads to the optical gain guiding. The transverse Laplacian term of the slowly varying wave equation in the linear regime can be approximated as a constant detuning parameter, i.e., |∇⊥2|∼kR/zR where kR is the resonant wave number and zR is the Rayleigh range of the laser. In the post-saturation regime, the radiation power begins to oscillate about an equilibrium for the untapered case while continues to grow by undulator tapering. Moreover, in this regime the gain guiding decreases and the simple constant detune is no longer valid. In this paper we study the single-pass high-gain FEL performance in the post-saturation regime with inclusion of diffraction effect and undulator tapering. Our analysis relies upon two constants of motion, one from the energy conservation and the other from the adiabatic invariant of the action variable. By constructing a two-dimensional axisymmetric wave equation and the coupled one-dimensional electron dynamical equations, the performance of a tapered FEL in the postsaturation regime can be analyzed, including the fundamental mode profile, the power efficiency and the scaled energy spread. We begin the analytical investigation with two different axisymmetric electron beam profiles, the uniform and bounded parabolic ones. It is found that the tapered FEL power efficiency can be smaller but close to the taper ratio provided the resonant phase remains constant and the beam-wave is properly matched. Such a tapered efficiency is nearly independent of transverse electron beam size before significant electron detrapping occurs. This is essentially different from the untapered case, where the power extraction efficiency is around the essential FEL gain bandwidth (or ρ, the Pierce or FEL parameter) and depends on the beam size. It is also found that the power enhancement due to undulator tapering is attributed more by the field increase outside the transverse electron beam than that inside the transverse electron beam. Several scaling properties on the taper ratio and the transverse electron beam size are also discussed in this paper.3 MoreReceived 29 January 2018DOI:https://doi.org/10.1103/PhysRevAccelBeams.21.060702Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsSynchrotron radiation & free-electron lasersAccelerators & Beams

Origin of Second-Harmonic Signals in Octave Bandwidth Traveling-Wave Tubes

In a helix traveling-wave tube (TWT) with a bandwidth exceeding one octave, the second harmonic of an input signal near the low end of the band will experience exponential growth. In such a case, we have found that the nonlinear electron orbits in the beam, as opposed to the orbital bunching exhibited in the linear electron orbits, are the main source for second-harmonic generation. This unexpected result is due to the synchronous amplification of the second harmonic. We demonstrate this phenomenon from the solution of the nonlinear equations that we have formulated that govern evolution of the second-harmonic field; these equations may include axial variations of the Pierce parameters. In several test cases, we compare the theory with simulation using the CHRISTINE large signal TWT code. Good agreement between theory and simulation is found.

Pierce 다이오드에서 플라즈마의 비선형 동력학적 거동

1차원 유체 모델을 사용하는 수치 코드를 개발하여 Pierce 다이오드에서 플라즈마에 대한 비선형 동력학적 거동을 연구하였다. Pierce 다이오드에서 플라즈마는 전극에서 방출되는 전자 전류와 전극 사이의 거리로 결정되는 Pierce 매개 변수가 변화함에 따라 안정하기도 하고 불안정해지기도 한다. 중성 및 비중성 Pierce 시스템의 동력학적 특성에 대해 해석적 및 수치적으로 연구하였다. Pierce 매개 변수의 값에 따라 플라즈마는 증폭 모드 또는 진동 모드를 가질 수 있으며, 진동 모드에서는 매개 변수가 감소함에 따라 계속적인 주기 배가 쌍갈림(period doubling bifurcation)을 일으키며 카오스 상태에 도달하게 된다. 이러한 거동에 대한 분석은 보다 복잡한 구조에서의 빔-플라즈마 상호작용에 대한 기본적인 이해를 위한 모델 및 카오스 제어를 위한 자료로서 사용될 수 있다. Nonlinear dynamical behaviors of plasma in the Pierce diode are investigated by a numerical code developed using a one dimensional fluid model. The plasma in Pierce diode is alternately stable and unstable as Pierce parameter is changed. The dynamical characteristics of neutral and non-neutral Pierce system is examined analytically and numerically. It alternately has growing and oscillatory mode as Pierce parameter varies. As Pierce parameter is decreased, each oscillatory mode undergoes a sequence of subharmonic period-doubling bifurcation and then culminate in a chaotic strange attractor. The analysis for this nonlinear behavior can be used as a model for understanding of beam-plasma interaction in more complex geometries and a data for chaos control.

Focusing properties of linear undulators

This paper investigates the focusing properties of linear magnetic undulators, i.e., devices characterized by weak defocusing properties in the horizontal (wiggling) plane and strongly focusing in the vertical plane. The problem of identifying the conditions that ensure the existence of the electron beam eigenstates in the undulator lattice for a given working point of electron beam energy Eb and resonant wavelengthr is studied. For any given undulator lattice, a bandlike structure is identified defining regions in the ðEb ;� rÞ plane where no periodic matching condition can be found, i.e., it is not possible to transport the electron beam so that optical functions are periodic at lattice boundaries. Some specific cases are discussed for the SPARC FEL undulator. I. INTRODUCTION Pure permanent magnet (PPM) undulators are imple- mented in single pass free-electron lasers (FEL) as inser- tion devices featuring a magnetostatic periodic (sinusoidal) field in the longitudinal (z) direction. The transverse magnetic field ensures coupling between the transverse wiggling motion of electrons and the transverse field of the amplified optical wave. The FEL power gain length, i.e., the exponential growth folding length, is Lg ¼ � u=ð4�� ffiffiffi p Þ, where � u is the undulator period andis the Pierce parameter (1-3), proportional to the cubic root of the current density. An FEL amplifier operating in self- amplified spontaneous emission has a saturation length Ls � 18-20Lg. We typically have Ls ranging from few meters in long wavelength (visible to near UV) devices, up to several tens of meters, in hard x-ray FEL amplifiers. The optimization process of the FEL parameters has to take into consideration the focusing properties of the undulator and the design of the electron transport lattice over the undulator length, in order to optimize the transverse beam size and maximize the current density, reducing therefore the gain length. The transport lattice of FEL amplifiers operating with high energy beams, as typical soft to hard x-ray sources (4-7), is based on a focusing-drift- defocusing-drift (FODO) scheme, alternated to a seg- mented undulator (8). The effect of a (linear) undulator is that of introducing a small perturbation to the FODO: a weak focusing in the vertical plane and a negligible effect in the horizontal plane. At lower beam energies, i.e., for FEL amplifiers operating at longer wavelengths from vis- ible to UV, the role of the undulator focusing becomes

Spurious Reflection of Space Charge Fields in TWTAs

The reflection of waves at the termination of a beam loaded traveling wave structure is considered. The presence of a bunched beam in the structure induces additional currents and voltages on the structure, which give rise to an additional reflection at the termination. This effect is first illustrated in a simple transmission line model, and then a formal field-based derivation for the reflection in a periodic structure is presented. Simple estimates for the magnitude of the reflection can be made based on the amplifier's Pierce parameter. Unlike the reflection due to a mismatched load, the spurious reflection due to the beam depends on signal power level. The spurious reflection can be simulated in large signal parametric codes, and examples of this are presented.

Counterstreaming electrons and ions in Pierce-like diodes.

The dynamics of Pierce-like diodes is investigated for ions moving with arbitrary velocities opposite to as well as in the direction of electron propagation. By application of an integral formalism that is able to account for mobile streaming ions, equilibrium solutions for the diode in an external circuit are derived. The stability of the uniform equilibrium for the short-circuited diode and for counterstreaming species is investigated. In this case, new oscillatory unstable branches appear that destabilize the diode for all values of \ensuremath{\alpha}, where \ensuremath{\alpha} is the Pierce parameter. This contrasts with the diode with co-moving ions being stable for sufficiently small values of \ensuremath{\alpha}. These new branches coincide with the Pierce-Buneman modes for initially resting ions. If \ensuremath{\Vert}${\mathit{v}}_{\mathit{i}0}$\ensuremath{\Vert}/${\mathit{v}}_{\mathit{e}0}$ is increased, where ${\mathit{v}}_{\mathit{s}0}$ are the injection velocities (s=e,i), a stronger destabilization is observed for counterstreaming in comparison to co-streaming with maximum growth rate in the range of ${\mathit{v}}_{\mathit{i}0}$\ensuremath{\approxeq}-2${\mathit{v}}_{\mathit{e}0}$ for a hydrogen plasma. It is furthermore shown that the familiar picture of waves (Fourier modes) must be substantially modified to meet the physics of bounded plasmas.

Finite ion velocity effects on the stability of Pierce-like diodes

The stability of Pierce-like plasma diodes is investigated for arbitrary ion injection velocities. A recently developed integral formalism that accounts for ion dynamical effects is applied to derive a generalized dispersion relation for electrostatic perturbations. Its evaluation exhibits several new features, such as the appearance of growing oscillatory modes, which become Pierce–Buneman modes in the limit of initially resting ions, and of weakly damped oscillatory modes, which become undamped ion plasma oscillations in this limit. The stability of this bounded plasma system is shown to be controlled by the new control parameter α̂=α(1+μ̂)1/2, where α is the Pierce parameter and μ̂≡mev2e0/miv2i0 the ratio of electron and ion kinetic energy at the emitter.

Pierce-type dispersion relation for an intense relativistic electron beam interacting with a slow-wave structure

A Pierce-type dispersion relation is derived for the interaction of an intense relativistic electron beam with a cylindrical slow-wave structure of arbitrary corrugation depth. It is shown that near a resonance, the Pierce parameter can be expressed in terms of the vacuum dispersion function and the beam current. The dispersion relation is valid in both the low-current (Compton) regime and the high-current (Raman) regime. The dispersion characteristics of the interaction, such as the linear instability growth rate and bandwidth, are analyzed for both regimes.

To the theory of induced scattering of electromagnetic waves by an electron beam in a regular waveguide

In this work, a formula for the amplification parameter (analogous to the Pierce parameter in travelling-wave tube theory) of regular waveguide modes is deduced in the case of induced scattering by an electron beam with an arbitrary electron density distribution in the cross section. The presence of an axial magnetic field transporting a beam along the interaction region is taken into account. Obtained results can be used for calculation of the amplification in free electron lasers with electromagnetic, magnetostatic or electrostatic pump and a definite beam transverse profile. In particular, expressions for amplification coefficients in the case of a thin-wall hollow electron beam propagating in a cylindrical waveguide, that takes into account the excitation of beam waves (space charge in TWT theory), are found. An analysis of the dependence of amplification on the guiding magnetic field value and hollow beam radius is carried out.

The Pierce diode with an external circuit. I. Oscillations about nonuniform equilibria

The nonuniform (nonlinear) equilibria of the classical (short circuit) Pierce diode and the extended (series RLC external circuit) Pierce diode are described, and the spectrum of oscillations (stable and unstable) about these equilibria are worked out. It is found that only the external capacitance alters the equilibria, though all elements alter the spectrum. In particular, the introduction of an external capacitor destabilizes some equilibria that are marginally stable without the capacitor. Computer simulations are performed to test the theoretical predictions for the case of an external capacitor only. It is found that most equilibria are correctly predicted by theory, but that the continuous set of equilibria of the classical Pierce diode at Pierce parameters (α=ωpL/v0) that are multiples of 2π are not observed. This appears to be a failure of the simulation method under the rather singular conditions rather than a failure of the theory.