Dynamics of an electron beam in the magnetic field of a betatron

Expressions for the vector potential and magnetic induction vector components have been obtained for a vertically asymmetric magnetic field of a betatron. The dynamics of the electron beam in the process of injection and acceleration in the electromagnetic field of the betatron has been investigated. It has been shown that the asymmetry of the magnetic field decreases the efficiency of the electron involvement in acceleration. The mutually related radial-vertical asymmetric oscillations of the electron beam in the asymmetric field lead to considerable losses of the beam particles on the walls and injector of the acceleration chamber. The results of these investigations may be useful in developing and tuning electron beam acceleration systems.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 42–46, December, 2004.     

The Dynamics of Electron Orbits during the Acceleration of Electrons in a Betatron

This paper presents a system of equations that describe the motion of charged particles in the electromagnetic field of a betatron. This system of equation was successfully used to study the behavior of the electron orbits and to determine the principal parameters of the electron beam in the electromagnetic field of a betatron during the electron acceleration and deceleration. The results of this study may find application in developing systems designed to accelerate electron beams. It has been shown that in the course of acceleration there is no damping of the betatron oscillations by the law B _z ^–1/2 and, correspondingly, no decrease in beam cross section. In contrast to the existing belief, the initial departure of the kinetic energy (momentum) of the injected electrons from the energy (momentum) of the electrons following the equilibrium orbit is not preserved in the course of acceleration. In the betatron chamber, the electron beam, when accelerated, does not constrict to form a ring but occupies a broad zone, whose dimensions are determined by the initial double amplitudes of the vertical and horizontal oscillations. Despite the large double amplitude of the oscillations of the beam particles, the average energy of the electrons differs from the energy of the electrons following the equilibrium orbit only slightly, and the departure of the average energy from the energy of the equilibrium electrons varies proportionally to the (varying) field of the betatron.     

Acceleration and radiation of externally injected electrons in laser plasma wakefield driven by a Laguerre-Gaussian pulse

By using three-dimensional particle-in-cell simulations, externally injected electron beam acceleration and radiation in donut-like wake fields driven by a Laguerre-Gaussian pulse are investigated. Studies show that in the acceleration process the total charge and azimuthal momenta of electrons can be stably maintained at a distance of a few hundreds of micrometers. Electrons experience low-frequency spiral rotation and high-frequency betatron oscillation, which leads to a synchrotron-like radiation. The radiation spectrum is mainly determined by the betatron motion of electrons. The far field distribution of radiation intensity shows axial symmetry due to the uniform transverse injection and spiral rotation of electrons. Our studies suggest a new way to simultaneously generate hollow electron beam and radiation source from a compact laser plasma accelerator.     

The Energy Spectrum of the Electron Beam of a Betatron

The process of extraction of an electron beam through the glass wall of a sealed-off acceleration chamber has been investigated. It has been shown that the electron beam extracted from the MIB-6E small-sized betatron has a nonuniform cross-sectional distribution of the particle flux density. This nonuniformity is due to the imperfection of the beam extraction devices and to the flaws in design of the extraction window of the accelerator chamber. The electrons extracted through the glass wall of the window lose a major portion of their energy. At the outlet of the chamber of the small-sized betatron, the spectrum of the electrons is not line. The half-width of the spectral line of the electron beam is, at best, 6% for a window glass thickness of 0.5 mm and about 15% for a glass thickness of 4 mm. The results of this study may find practical implementation in developing extracted electron beam formation systems.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 51–55, January, 2005.     

Capture of electrons for acceleration in a betatron with time and spatial variation of the magnetic field

It is shown that an additional pulsed magnetic field superimposed on the primary magnetic field of a betatron leads to time and spatial variation of the resulting magnetic field in the working gap of the accelerator. A mathematical model is developed for the capture of electrons for betatron acceleration with the additional pulsed magnetic field. It is shown that the time and spatial variation of the magnetic field in the working gap of the accelerator during electron injection leads to an increase in the efficiency of their capture for acceleration. The method of calculation permits a direct modeling of the capture of electrons for acceleration to obtain the highest efficiency.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 40–44, May, 1988.     

Amplitude nonuniformity of the magnetic field in a betatron

The effects of the amplitude nonuniformity of the magnetic field in a betatron on the forced and betatron radial oscillations of electrons during extraction (or discharge toward the target) at the end of the acceleration cycle are examined. The amplitude and phase dynamics of radial betatron oscillations are studied by means of an analog computer.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 5, pp. 104–109, May, 1969.     

Beschleunigung von Elektronen in einem Plasmabetatron

A plasma was produced by a high frequency electric quadrupole field (v=200 Megacycles) at gas pressures of 10^?4 to 5·10^?3 mm Hg in a quarz glass torus. The torus was placed between the poles of an air-core betatron with the following properties: radius of equilibrium orbit 20 cm, maximum accelerating field strength 80 V/cm, end energy 1.5 MeV. Associated with conduction currents of some 100 A, energetic Bremsstrahlung was observed and attributed to 1,2 MeV electrons. The number of accelerated electrons was of the order of 10¹¹ per pulse. The intensity and energy of the radiation, together with the time dependence of the plasma current, were observed as function of different parameters, such as the gas pressure, high frequency amplitude, induced acceleration field strength, for different gases. The energetic radiation disappears when, because of the self-induced magnetic field, the stability condition for the betatron equilibrium is no longer fulfilled.     

Enhanced betatron radiation by a modulating laser pulse in laser wakefield acceleration

We propose a new idea to enhance and control the betatron radiation by using a modulating laser pulse in laser wakefield acceleration. In this scheme, a high-power laser pulse is used for self-trapping and acceleration of the plasma electrons and the accelerated electron beam is modulated by a separately-propagating laser pulse for large amplitude betatron oscillations and microbunching. In this way, the relatively low power modulating laser pulse can enhance the X-ray photon flux and energy significantly. We performed two-dimensional particle-in-cell simulations to demonstrate the idea and the results show that a sub-TW laser pulse is enough for electron beam modulation and it can generate easily-controllable fs X-ray pulses with a wide range of photon energies from soft X-rays to hard X-rays.     

GYRAC: a compact, cyclic electron accelerator

The concept of the gyro-resonant accelerator (GYRAC), which is based on cyclotron resonance in a magnetic field that is increasing slowly in time, is presented. Previously published work shows that this results in an autoresonance in which the wave provides a synchronous acceleration of the electrons. Using a simple model makes it possible to design a particularly compact, cyclic electron accelerator; in a cavity with a 1-m radius and final magnetic field of 5 T, electron energy reaches 680 MeV, giving rise to synchrotron radiation of 1 keV. Assuming uniform fields and rescaling time, a Hamiltonian system is arrived at which has one degree of freedom and which, in first-order approximation is time independent. In a second-order approximation, a slow damping of the autoresonant oscillation is found. A paraxial model for beam and fields allows evaluation of the charge effects-the GYRAC then resembles the betatron. These results are illustrated by numerical three-dimensional simulations     

Elektronenbeschleunigung in einem Plasmabetatron mit und ohne hohem Leitungsstrom

A previous paper by Drees and Paul reported measurements on a plasma betatron. The study was continued using a betatron field with a vector potential taking into account the self magnetic field of a plasma current. The plasma was produced by a high frequency electric quadrupole field without an azimuthal magnetic field. The bremsstrahlung intensity of the accelerated electrons was observed as a function of gas pressure and accelerating field. The maximum energy of the electrons was 1.3 MeV compared to 1.5 MeV given by the field parameters. The maximum number in this energy range was about 10¹⁰ per pulse corresponding to a circulating runaway current of ～ 1 A. The conduction current was drasticly reduced by coating the inner wall of the quartz glass torus with a thin layer of graphite. This change in the plasma current did not influence the γ radiation intensity.     

Additional acceleration and collimation of relativistic electron beams by magnetic field resonance at very high intensity laser interaction

For the interpretation of experiments for acceleration of electrons at interaction up to nearly GeV energy in laser produced plasmas, we present a new model using interaction magnetic fields. In addition to the ponderomotive acceleration of highly relativistic electrons at the interaction of very short and very intense laser pulses, a further acceleration is derived from the interaction of these electron beams with the spontaneous magnetic fields of about 100 MG. This additional acceleration is the result of a laser-magnetic resonance acceleration (LMRA) around the peak of the azimuthal magnetic field. This causes the electrons to gain energy within a laser period. Using a Gaussian laser pulse, the LMRA acceleration of the electrons depends on the laser polarization. Since this is in the resonance regime, the strong magnetic fields affect the electron acceleration considerably. The mechanism results in good collimated high energetic electrons propagating along the center axis of the laser beam as has been observed by experiments and is reproduced by our numerical simulations. PACS 41.75.Jv; 52.38.Kd; 52.65.Cc     

Radiative losses in plasma accelerators

We investigate the dynamics of a relativistic electron in a strongly nonlinear plasma wave in terms of classical mechanics by taking into account the action of the radiative reaction force. The two limiting cases are considered. In the first case where the energy of the accelerated electrons is low, the electron makes many betatron oscillations during the acceleration. In the second case where the energy of the accelerated electrons is high, the betatron oscillation period is longer than the electron residence time in the accelerating phase. We show that the force of radiative friction can severely limit the rate of electron acceleration in a plasma accelerator.     

场向传播的内磁层哨声波对辐射带高能电子的共振扩散

基于高斯分布的哨声波谱密度分布、偶极子背景磁场模型以及建立在卫星观测数据基础上的半经验电子密度纬度分布模型,对于等离子体层顶以外区域(4≤L≤7),计算了准线性当地及弹跳平均电子共振扩散系数,并估算了与磁层哨声波回旋共振导致的辐射带电子损失及加速时间尺度.结果表明,波粒共振相互作用区域取决于电子能量、波谱分布、电子赤道抛射角以及当地电子密度及背景磁场.哨声波共振频率除了与以上5个参量有关外,还与地磁纬度有关.赤道哨声波主要影响较低能量辐射带电子的加速,中高纬度哨声波主要作用于较高能量辐射带电 关键词： 共振波粒相互作用 地球辐射带 哨声波 回旋共振加速及散射沉降     

Generation of beams of charged particles with transverse energy

The paper describes the operation and construction of an electron gun designed to form beams with variable transverse energy and a variable spread of magnetic moments. Transverse energy is acquired by the electrons as the beam passes through a weakly non-adiabatic magnetic step, and in an adiabatic motion through a growing magnetic field. The small spread of magnetic moments of the beam electrons is achieved by fulfilling the so-called focusing conditions which ensure that the spread of moments resulting from different initial radii of the particles is compensated by their initial radial velocities.     

Stability of high-current beams of relativistic electrons in cyclic systems

Stability conditions of high-current thin beams of relativistic electrons against excitation of long-wave oscillations in a stellatron and modified betatron have been investigated theoretically. The influence of self electric and magnetic fields obtained from electron beam delayed potentials has been taken into consideration. The correspondent dispersion relation has been found. The electron beam of the modified betatron has been shown to be always unstable against excitation of the oscillations considered. Necessary and sufficient conditions for the elec-tron beam confinement in a stellatron have been found.     

Simplified equations for investigation of charged-particle dynamics in magnetic fields

A system of motion equations presented for charged particles in betatron magnetic fields makes it possible to conduct all particle dynamics calculations in relative units because the particle velocity components are expressed in terms of trajectory geometry using comparatively simple notation, and the conversion from relative to absolute units is easily carried out in terms of the radius of a fixed orbit and the magnetic induction of the field on it. This equation system has been used successfully to investigate particle dynamics in an electron beam extracted from a betatron and to determine the principal parameters of the beam; the results were confirmed in practice. Tomsk Polytechnic University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 29–35, March, 1998.     

Excitation of an upper hybrid wave by two intense laser beams and particle acceleration

This Letter presents an investigation of the excitation of an upper hybrid wave (UHW) by cross focusing of two intense laser beams in a collisionless hot magnetoplasma, when relativistic and ponderomotive nonlinearities are operative. The electric vectors of the two beams are polarized along uniform static magnetic field and the beams propagate perpendicular to the static magnetic field. Analytical expressions for the beam width of the laser beams, electric vector and power of the excited UHW and energy gain have been obtained. The UHW generation at the difference frequency and particle acceleration has also been studied. The nonlinear coupling between intense laser beams and UHW is so strong that UHW gets excited and a large fraction of the laser beam energy gets transferred to UHW and this UHW accelerates electrons. It has been shown that the presence of a magnetic field affects significantly the power of the UHW and energy gain by the electron in the presence of the UHW.     

锐真空-等离子体边界倾角对激光尾波场加速中电子注入的影响

超短超强激光脉冲在气体等离子体中激发的尾波场加速在过去40年里有了长足的发展,人们已经在厘米加速距离内获得了数GeV的准单能电子加速,激光尾波加速的最高电子能量已经达到8 GeV.为了进一步提升加速电子束的稳定性和品质,多种电子注入方式先后被提出.本文研究了基于锐真空-等离子体边界面的密度跃变注入,着重讨论了不同角度的倾斜边界面对注入电子品质的影响.二维粒子模拟研究表明,与倾角为0°的垂直边界面相比,在合适的倾斜边界角下,第二个尾波空泡内产生的注入电量可以有近三倍的提升,同时偏振方向与入射面平行的驱动激光可以增加第一个空泡内注入电子的电量.根据不同激光入射角度时尾波场中电子自注入的起始位置差异,分析了电子电量与横向振荡增强的原因.这些研究有利于提升基于Betatron运动的尾波场辐射及其应用.     

外加静电场的聚焦激光脉冲真空加速电子方案

采用五阶修正的聚焦激光光场方程模拟研究了由Singh提出的在电子和激光脉冲作用尾部阶段施加外场的加速方案,将Singh方案中采用的外加磁场改成了外加电场,并且考虑了光束的纵向电场和光束衍射效应.模拟结果显示,电子可以从加速相位阶段被外场导入下一个加速相位阶段而不进入减速相位阶段,因此电子能获得比不加外场方案更高的净能增益. 关键词： 强激光 激光加速     

On the amplification mechanism of the ion-channel laser

The amplification mechanism of the ion-channel laser (ICL) in the low-gain regime is studied. In this concept, a relativistic electron beam is injected into a plasma whose density is comparable to or lower than the beam's density. The head of the electron beam pushes out the plasma electrons, leaving an ion channel. The ion-focusing force causes the electrons to oscillate (betatron oscillations) about the axis and plays a role similar to the magnetic field in a cyclotron autoresonance maser (CARM). Radiation can be produced with wave frequencies from microwaves to X-rays depending on the beam energy and plasma density: ω~2γ^3/2ω_pe, where γ is the Lorentz factor of the beam and ω_pe is the plasma frequency. Transverse (relativistic) bunching and axial (conventional) bunching are the amplification mechanisms in ICLs; only the latter effect operates in free-electron lasers. The competition of these two bunching mechanisms depends on beam velocity ν_0z; their dependences on ν_0z cancel for the cyclotron autoresonance masers. A linear theory is developed to study the physical mechanisms, and a PIC (particle-in-cell) simulation code is used to verify the theory. The mechanism is examined as a possible explanation for experimentally observed millimeter radiation from relativistic electron beams interacting with plasmas