Saturation of a one-sided multipactor in a decelerating electrostatic field

We analyze the saturation mechanism of a vacuum resonance microwave discharge (multipactor) where the decelerating electrostatic field returns electrons to the secondary-emission multiplying surface. It is found that the Coulomb defocusing of electron bunches prevails over their microwave focusing (toward the resonance phase of the field) in the stationary state, making it possible to extract superfluous secondary electrons when the electron bunches are reproduced on the discharge surface. Using this model, we determine the main characteristics of this multipactor, such as the magnitude and phase disposition of the resonant electron bunch. An explanation of the increase in the discharge power with increase in the secondary-emission coefficient is given. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 11, pp. 1097–1104, November, 1999.     

Multipactor discharge on a dielectric surface in the field of circularly polarized plane waves

The secondary-emission discharge (multipactor) on a dielectric surface irradiated by a plane TEM wave of circular polarization is analyzed theoretically. It is shown that interaction of electrons with the electromagnetic wave field can provide their return to the emission surface, which makes a multipactor possible even without any external static fields. Multipactor conditions for different reflection coefficients of the incident wave are found. The obtained results are used to estimate the throughput of the output window of a high-power vacuum microwave device. Specifically, it is established that decreasing the high-frequency field amplitude on the window surface when the mode of a partially standing wave is realized in the vicinity of the window does not always help raise its electric strength.     

介质窗横向电磁场分布下的次级电子倍增效应

本文利用自编P3D3V PIC程序, 数值研究了BJ32矩波导传输TE₁₀模式高功率微波在介质窗内、 外表面引发的次级电子倍增过程, 给出了次级电子3维空间位置分布特征、介质窗表面法向静电场分布规律以及电子数密度分布特性. 模拟结果表明: 对于介质窗内侧, 微波强场区域率先进入次级电子倍增过程; 而对于介质窗外侧, 则是微波弱场区域优先进入次级电子倍增过程. 形成机理可以解释为: 微波坡印廷矢量方向与介质窗外表面法向相同而与内表面法向相反, 内侧漂移运动导致强场区域电子易于被推回表面, 有利于次级电子倍增优先形成; 外侧漂移运动导致强场区域电子易于被推离表面, 不利于次级电子倍增形成. 准3维模型相对1维模型: 介质窗内侧次级电子倍增过程中, 次级电子倍增进入饱和时间长、饱和次级电子数目少、平均电子能量高、 入射微波功率低、沉积功率低; 介质窗外侧次级电子倍增过程中, 次级电子倍增进入饱和时间短、饱和次级电子数目少、平均电子能量低、 入射微波功率低、沉积功率低. 沉积功率与入射微波功率比值与微波模式、强度及介质窗内外侧表面关系不大, 准3维和1维模型计算结果均在1%–2%左右水平. 关键词： 高功率微波 介质表面次级电子倍增 粒子模拟 横向电磁场分布     

Statistical Theory of Two-Sided Multipactor

We develop a statistical theory of secondary-emission discharge (SED) taking the energy distribution of secondary electrons into account. The theory allows one to describe quantitatively the initial stage of development of a two-sided multipactor. For an arbitrary probability density of normal components of the ejection velocity and an arbitrary distance between the walls enclosing the microwave discharge plasma, we construct an analytical solution for the electron distribution function over transit times. The performed analysis is based on the results of a detailed study of conditions under which an electron reaches the opposite side. With allowance for the spread in thermal velocities, we derive a recurrence relation between the electron distribution functions over emission phases and formulate a general integral equation from which the resulting stationary distribution and the threshold of SED onset are determined.     

高功率微波作用下介质窗表面电子运动2维仿真

建立了真空中高功率微波作用下介质窗表面电子运动2维仿真模型,充分考虑了微波电磁场及介质表面静电场等影响因素。通过对不同电子出射初始角度和微波场参数(电场幅值、频率及电子出射时电场相位)对电子运动状态影响的仿真分析,得到了二次电子倍增过程中电子在复合场下的运动轨迹、电子重新返回介质表面的撞击能量及返回时间等状态参数,获得了电子运动状态参数随电子出射角度和微波场参数的变化规律。研究发现:电子出射角度对其运动状态有显著影响,电子存在运动轨迹最大的某一出射角度,该角度下电子拥有最大的撞击能量;微波电场幅值的增加将使电子撞击能量增加,返回时间减小,微波电场相位的变化使电子的撞击能量和返回时间呈周期振荡,这从本质上解释了电子数量在二次电子倍增过程中以微波频率两倍周期振荡的原因;随着微波频率的增加电子将由简单的类抛物线运动转变为复杂的振荡运动。     

介质材料二次电子发射特性对微波击穿的影响

以介质填充的平行板放电结构为例,本文主要研究了介质填充后微波低气压放电和微放电的物理过程.为了探究介质材料特性对微波低气压放电和微放电阈值的影响,本文采用自主研发的二次电子发射特性测量装置,测量了7种常见介质材料的二次电子发射系数和二次电子能谱.依据二次电子发射过程中介质表面正带电的稳定条件,计算了介质材料稳态表面电位与二次电子发射系数以及能谱参数的关系.在放电结构中引入与表面电位相应的等效直流电场后,依据电子扩散模型和微放电中电子谐振条件,分别探讨了介质表面稳态表面电位的大小对微波低气压放电和微放电阈值的影响.结果表明,介质材料的二次电子发射系数以及能谱参数越大,介质材料的稳态表面电位也越大,对应的微波低气压放电和微放电阈值也越大.所得结论对于填充介质的选择有一定的理论指导价值.     

Generation of ultrashort microwave pulses based on cyclotronsuperradiance

We have theoretically and experimentally investigated the superradiance from a bunch of electrons rotating in a homogeneous magnetic field. A RADAN-303B modulator equipped with a subnanosecond pulse slicer has been used to generate high current subnanosecond electron bunches (250 kV, 0.1-1 kA, 0.3-0.5 ns). Transverse momentum was imparted to the electrons by a kicker. It is shown that for the experimental observation of cyclotron superradiance from high current electron bunches the optimum conditions are the conditions of group synchronism, when the translational velocity of the bunch coincides with the group velocity of the radiation propagating in the waveguide. In the 35 GHz range microwave pulses with record short duration, down to 0.4 ns, with a peak power level up to 200 kW, have been obtained     

两种外磁场形式对介质面次级电子倍增的抑制

利用自编1D3V PIC程序,数值研究了不同外加磁场方式对次级电子倍增抑制的物理过程,给出了次级电子数目、平均能量、密度、运动轨迹、渡越时间、介质表面静电场及沉积功率等物理量时空分布关系。模拟结果表明:不同方向外加磁场抑制次级电子倍增的机理有所不同。轴向外加磁场利用电子回旋运动干扰微波电场对电子加速过程,使其碰壁能量降低以达到抑制二次电子倍增的效果;横向外加磁场利用电子回旋漂移过程中,电子半个周期被推离介质表面（不发生次级电子倍增）,半个周期被推回介质表面（降低电子碰撞能量）的作用机理,达到抑制二次电子倍增的效果。讨论了横向磁场在回旋共振下,电子回旋同步加速导致回旋半径增大,电子能量持续增加的特殊过程。两种外加磁场方式都可以通过增加磁场达到进一步抑制次级电子倍增的目的。轴向外加磁场加载容易,但对磁场要求较高;横向外加磁场需要磁场较低,但加载较为困难。     

Influence of the angular anisotropy of secondary emission on the characteristics of a two-sided multipactor

We study the influence of the thermal spread in ejection velocities of secondary electrons on the initial stage of development of a two-sided multipactor. The analysis employs a statistical method based on an exact analytical solution for the electron distribution function over times of transit through the vacuum gap. The obtained theoretical relations are used as the basis for a numerical algorithm which takes into account both the angular and energy distributions of secondary electrons and makes it possible to calculate quantitatively the main multipactor characteristics for the actual dependence of the secondary-emission ratio of the walls on the energy of bombarding electrons. Detailed numerical calculations of the multipactor zones are presented. It is shown that the presence of angular anisotropy can change significantly the conditions of production of the secondary-emission discharge as compared with the case of isotropic emission. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 5, pp. 406–415, May 2006.     

Acceleration of nonmonoenergetic electron bunches injected into a wake wave

The trapping and acceleration of nonmonoenergetic electron bunches in a wake field wave excited by a laser pulse in a plasma channel is studied. Electrons are injected into the region of the wake wave potential maximum at a velocity lower than the phase velocity of the wave. The paper analyzes the grouping of bunch electrons in the energy space emerging in the course of acceleration under certain conditions of their injection into the wake wave and minimizing the energy spread for such electrons. The factors determining the minimal energy spread between bunch electrons are analyzed. The possibility of monoenergetic acceleration of electron bunches generated by modern injectors in a wake wave is analyzed.     

电子回旋共振放电中电子与微波互作用特性的粒子模拟和蒙特卡罗碰撞模拟

对电子回旋共振（ECR）放电电离过程中的电子与微波互作用特性进行了理论分析与数值模拟.采用粒子模拟（PIC）方法描述带电粒子与微波的互作用,采用蒙特卡罗碰撞（MCC）方法描述粒子间碰撞过程及带电粒子与边界的相互作用.编写了准三维的PIC/MCC数值模拟程序,并对放电过程中电子能量与微波场随时间、空间的演化进行了数值诊断. 关键词： 电子回旋共振放电 粒子模拟 蒙特卡罗方法 电离     

Generation of high-power electron beams in magnetron guns with secondary-emission cathodes

High-power electrons beams generated in a single injection magnetron gun with secondary-emission cathodes and in a set of such guns are studied. Hollow electron beams of current 50–100 A, electron energy 30–100 kV, and peak power 1–5 MW are obtained. The beams can be used as electron sources in accelerators and ordinary and multibeam high-power microwave devices.     

Influence of an external magnetic field on the threshold of multipactor onset on a dielectric surface

In this paper, we propose a theoretical model of the initial stage of development of a one-sided secondary-emission (multipactor) discharge on a dielectric surface. Consideration is based on a statistical method supported by an exact analytical solution for the transit-time distribution function of secondary electrons. The general integral equation allowing us to determine the stationary emission-phase distribution functions and the threshold of multiplicator onset in the presence of an external magnetic field is formulated. It is shown that the presence of an external magnetic field can significantly change the conditions of multipactor onset. It is found that the discharge-zone boundaries calculated within the framework of a statistical model are in qualitative agreement with the results obtained by the Monte-Carlo method. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 2, pp. 118–133, February 2007.     

高功率微波沿面闪络击穿机制粒子模拟

针对高功率微波介质沿面闪络击穿物理过程,首先建立了理论模型,包括:动力学方程、粒子模拟算法、二次电子发射, 以及电子与气体分子蒙特卡罗碰撞模型、电子碰撞介质表面退吸附气体分子机制;其次,基于理论模型,编制了1D3V PIC-MCC程序,分别针对真空二次电子倍增、高气压体电离击穿和低气压面电离击穿过程,运用该程序仔细研究了电子和离子随时间演化关系、电子运动轨迹、电子及离子密度分布、空间电荷场时空分布、电子平均能量、碰撞电子平均能量、碰撞电子数目随时间演化关系、电子能量分布函数、平均二次电子发射率以及能量转换关系。研究结果表明:真空二次电子倍增引发的介质表面沉积功率只能达到入射微波功率1%左右的水平,不足以击穿;气体碰撞电离主导的高气压体电离击穿,是由低能电子（eV量级）数目指数增长到一定程度导致的,形成位置远离介质表面,形成时间为s量级;低气压下的介质沿面闪络击穿,是在二次电子倍增和气体碰撞电离共同作用下,由于数目持续增长的高能电子（keV量级）碰撞介质沿面导致沉积功率激增而引发的,形成位置贴近介质沿面,形成时间在ns量级。     

One-dimensional fluid model of ECR discharge with inhomogeneityeffects of external magnetic field

A one-dimensional fluid model of the microwave electron cyclotron resonance (ECR) discharge, which includes the inhomogeneity effects of the external magnetic field, is developed. We use fluid equations which are obtained from the one-dimensional Bolzmann equation expressed in terms of magnetic moment and parallel velocity. We model the plasma and sheath separately, and appropriate plasma-sheath boundary conditions are utilized. Microwave is represented by an energy flow, and treated by a ray tracing technique. For the argon discharge, we obtain various quantities such as the axial profiles of plasma density, electron temperature, electrostatic potential, fluid velocity, and microwave power deposition. The results of simulation compare well with the experimental observation of the mirror field effects on the plasma parameters     

低引导磁场下相对论亚纳秒电子束毫米波返波振荡器的粒子模拟

提出了一种Ka波段的相对论亚纳秒电子束毫米波慢波结构,在较低引导磁场情况下,运用粒子模拟(PIC)方法成功地模拟出器件中波束互作用的非线性物理演化过程,得到了一种超辐射状态下的微波辐射,它的产生与波相对于电子束滑移引起的电子束内电子间相互作用有关,辐射微波的峰值功率与电子束总电荷的平方成正比.粒子模拟有利于对超辐射这种束波互作用非线性物理现象的理解,并且对器件的设计有一定的参考价值.     

Investigation of multipactor breakdown in communication satellite microwave co-axial systems

Multipactor breakdown or multipactor discharge is a form of high frequency discharge that may occur in microwave components operating at very low pressures. Some RF components of multi-channel communication satellites have co-axial geometry and handle high RF power under near-vacuum conditions. The breakdown occurs due to secondary electron resonance, wherein electrons move back and forth in synchronism with the RF voltage across the gap between the inner and outer conductors of the co-axial structure. If the yield of secondary electrons from the walls of the co-axial structure is greater than unity, then the electron density increases with time and eventually leads to the breakdown. In this paper, the current due to the oscillating electrons in the co-axial geometry has been treated as a radially oriented Hertzian dipole. The electric field, due to this dipole, at any point in the coaxial structure, may then be determined by employing the dyadic Green’s function technique. This field has been compared with the field that would exist in the absence of multipactor.     

Energy-gain measurements from a microwave inverse free-electron-laser accelerator

Experiments are reported on inverse free-electron-laser acceleration, including for the first time observations of the energy change as a function of relative injection phase of the electron bunches. The microwave accelerating structure consists of a uniform circular waveguide with a helical wiggler and an axial magnetic field. Acceleration of the entire beam by 6% is seen for 6 MeV electron bunches at optimum relative phase. Experimental results compare favorably, for accelerating phases, with predictions of a three-dimensional simulation that includes large-orbit effects.     

电子回旋共振放电的电离特性PIC/MCC模拟(Ⅱ)——数值模拟与结果讨论

采用粒子模拟与蒙特卡罗相结合(PIC/MCC)的方法，应用电磁模型，编写了准三维的电子回旋共振(ECR)放电电离过程的模拟程序，得到了ECR放电过程中电子与离子的相空间分布、电磁场分布.通过对这些分布随时间演化的分析，得出ECR加热发生在ω≈ω_c0且垂直于轴向的区域；ECR区域，微波能量几乎全部耦合给电子，获得能量的电子通过与中性粒子的电离碰撞产生了大量的带电粒子；随着放电的进行，大量带电粒子通过频繁的碰撞，分布由各向异性逐渐趋于各向同性. 关键词： 电子回旋共振放电 粒子模拟 蒙特卡罗 电离