The effect of crossed fields on the velocity distribution of hollow electron beams

An analysis of the effect of radial electric and longitudinal magnetic fields on the axial velocity distribution of electrons in a hollow beam was carried out on a simplified model. Two results, both consistent with experimental observations, were obtained. First, the longitudinal velocity spread (or equivalent temperature) increases with distance from the axis. Second, the retarding potential at which all electrons are collected also increases with distance from the axis; this indicates that the energy of the slowest electrons at the beam edge is decreased as a result of the crossed fields. The radial electric field, which is greatest near the beam edge and zero on the axis, converts some of the longitudinal energy of the electrons into rotational energy. This kind of scattering is analyzed by a perturbation method whereby the transverse motion of the incident beam is considered harmonically bound by the magnetic field. The spectrum of the energy absorbed in the rotational mode is shown to be velocity dependent and thus to give rise to distortion in the Maxwellian distribution of the incident beam.     

A low potential collector employing an asymmetrical electrode in an axially-symmetric magnetic field

A collector for a beam-type tube with an axial magnetic focusing field can be made to operate at a potential near cathode potential without returning secondary electrons, if the beam is deflected and caused to pass an asymmetrical electrode properly positioned in the axially symmetric magnetic focusing field. Collection takes place in a region of radial electric field. Experimental results on such a device indicate successful operation, provided the velocity spread in the beam is not too large.     

Phase velocity of a transverse electric wave propagating in a magnetized electron beam

In this paper three-dimentional simulations are carried out to the phase velocity of a transverse electric wave which propagates in a relativistic electron beam magnetized by a wiggler field and an axial guide magnetic field. Results show that the phase velocities are quite different from each other as the axial guide magnetic field changes its direction.     

The Linear and Self-Consistent Nonlinear Theory of the Electron Cyclotron Maser Instability

In this paper the linear and nonlinear theory of the electron cyclotron maser instability is considered. The configuration used to study the maser instability consists of relativistic electrons gyrating about and drifting along a uniform magnetic field within a parallel plate waveguide. Relativistic effects associated with the gyrating electrons are responsible for excitation of the transverse electric mode in the waveguide. Linear theory shows that the growth rate maximizes when the axial beam velocity coincides with the axial wave group velocity of the excited electromagnetic wave. This allows us to perform the nonlinear analysis in a frame where both the axial wave number and axial beam velocity vanish. We have found that the maser instability exists only if the perpendicular beam energy exceeds a threshold value. Our analysis also describes the temporal nonlinear evolution of the field amplitude and frequency of a single excited wave. The nonlinear wave dynamics are self-consistently determined from the nonlinear particle orbits through the force and wave equations. The nonlinear analysis shows that there are two possible mechanisms for the saturation of the unstable wave: 1) depletion of the available free energy associated with the rotating particles and 2) phase trapping of the gyrating electrons in the wave. The initial beam parameters determine which of the two mechanisms is responsible for saturation. Competition between the two saturation mechanisms leads to a peaking in the energy conversion efficiency as a function of beam energy. Numerical results of the nonlinear formalism show that energy conversion efficiencies from the particles to the wave can be as high as 60 percent in the beam frame. Furthermore, by appropriately contouring the external magnetic field, among other things, efficiencies as high as 70 percent can be realized.     

Power Enhancement of a Small-Orbit Coaxial Cyclotron Autoresonance Maser (CARM) by Employing an External Radial Electrostatic Field

A proposal is presented to enhance the saturation power of a small-orbit coaxial cyclotron autoresonance maser (CARM) by employing an external electrostatic voltage. Nonlinear simulations show possible increase of 22% of the saturation power with high gain of 67 dB for a transverse electric mode at frequency of 140 GHz. Influences of initial parameters on the saturation power are simulated. It is found that due to the use of an external electrostatic field, saturation power of the wave is sensitive to the ratio of the transverse velocity to the axial velocity, as well as to the spread of the transverse velocity. The physical mechanism of the power enhancement may be that the radial force produced by the radial electrostatic field superposes an extra motion on the electron beam and thus causes an extra energy coupling between the electron beam and the radial electric component of the wave.     

Increase of Gyrotron Output Power at High-Order Axial Mode Through an After-Cavity Excitation of the Next Transverse Mode

In the experimental study on the frequency tuning of a double-beam gyrotron, an unexpected abrupt increase of the output power was observed for some magnetic field values corresponding to the excitation of high-order axial modes (HOAM). This effect can be explained through an after-cavity interaction of the spent but bunched electron beam with the neighboring transverse mode which has the same azimuthal but the next (i.e., greater by one) radial index with respect to the operating mode. The calculations show that under certain conditions the cyclotron synchronism between the electron beam and the next radial mode occurs in the extended region of an output cone, while the bunching of the spent electron beam is responsible for the excitation of this mode. The influence of some additional factors such as reflections of both modes from the output window, electron velocity spread, and magnetic field profile was studied numerically. It was shown that reflections, mode transformation, and velocity spread can enhance the effect of an abrupt power increase and reduce the starting current of the operating mode. The discovered after-cavity interaction can be either useful for a power increase at the HOAM operation of the frequency-tunable gyrotron or harmful for high cyclotron harmonic operation due to an expansion of the zone of fundamental cyclotron resonance mode excitation.

     

A Two-dimensional Theory of Noise Emission from Thermionic Cathodes†

A two-dimensional theory of noise emission from magnetically shielded thermionic cathodes is presented. The radial and axial components of noise velocity and current are derived for the ‘ equipotential’ region in the immediate vicinity of the cathode. It is shown that the transverse components, often neglected in one-dimensional theories, are in fact orders of magnitude larger than the axial components. Use of high magnetic field normal to the cathode suppresses the transverse components resulting in greatly reduced noise of the beam     

A Nonlinear Finite-Element Leaky-Waveguide Solver

A novel hybrid finite-element method for the analysis of leaky-waveguide structures is presented. The possibly radiating structure is enclosed within a fictitious circular contour-C in order to truncate the infinite solution domain. The field in the unbounded domain, outside contour-C, is expressed as a superposition of transverse electric and magnetic modes. Their radial dependence is expressed in terms of Hankel functions, which satisfy the radiation condition at infinity. The bounded area is discretized using hybrid node/edge elements for an accurate and efficient handling of the electric field vector wave equation. The transparency of the fictitious contour is ensured by enforcing the field continuity conditions according to the principles of a vector Dirichlet-to-Neumann mapping. The whole procedure yields a nonlinear eigenvalue problem for the complex axial propagation constant (beta). The nonlinearity is due to the appearance of beta within the argument of the Hankel functions. The final nonlinear problem is solved by employing a matrix Regula-Falsi algorithm. Initial guesses for the Regula-Falsi algorithm and a fast estimation of the eigenvalues spectrum are provided by a linear formulation based on a second-order approximation (beta/k_o)² Lt 1. The proposed method is validated against published numerical and experimental results for both leaky and surface wave modes.     

同轴腔电子回旋微波激射器电子效率的研究

通过非线性模拟计算同轴腔电子回旋微波激射器的电子效率,结果与德国卡尔斯鲁研究中心研制的同轴腔电子回旋微波激射振荡器的实验效率比较吻合,进而通过提高初始横纵向速率比和引入坡度磁场,使器件的电子效率从26.7%提高到34.6%.这种效率放大的物理机制是:坡度磁场改变了相对论电子的运动条件,有效地改善了波束互作用过程中电子的群聚状态,从而提高了电子束的换能效率.     

含有部分填充等离子体柱的螺旋线混合模的理论分析

导出了含有部分填充等离子体柱的螺旋线中混合模的色散方程,计算出混合模的色散曲线并由此探讨了混合模的形成条件。研究了约束磁场对轴向电场的径向分布的影响。在低约束磁场下轴向电场的径向分布显示场与电子束的耦合显著增强,无聚焦磁场时存在着沿等离子体柱面传播的 TG模。     

Radiation from a spherical aperature antenna immersed in a compressible plasma

The exterior boundary-value problem for a sphere immersed in a compressible plasma medium is solved. The model is a perfectly conducting sphere excited by an aperture, in its surface, which has a specified distribution of the tangential electric field. The configuration is such that Maxwell's equations, when combined with the continuum theory of fluid dynamics, are separable. The sheath at the interface with the plasma is characterized by an absorptive boundary condition which assumes a linear relationship between the pressure and the mean velocity of the electrons. It is shown that the TM (transverse magnetic) waves are coupled with the electroacoustic waves, while the TE (transverse electric) waves are decoupled. Some numerical results are presented which show, in quantitative manner, the relative fraction of the total power which is radiated in the form of electroacoustic waves.     

Electron motion in a helically perturbed magnetic field

Exact solutions have been obtained for the equations of an electron subjected to a transverse rotating magnetic field superimposed on a homogeneous axial magnetic field. The solutions show that complete transfer of the axial energy into transverse energy is possible for a range of values of the injection velocity and the transverse magnetic field.     

Scattering by two-dimensional lossy, inhomogeneous dielectric andmagnetic cylinders using linear pyramid basis functions and pointmatching

A volume integral equation approach is used to calculate the scattering characteristics of lossy, inhomogeneous, arbitrarily shaped, two-dimensional dielectric and magnetic bodies. The scatterer is divided into triangular patches, which simulate curved and piecewise linear boundaries more closely than circular cylinder cells. Linear pyramid basis functions are employed to expand the unknown total electric field at the triangle nodes. The enforcement of the boundary conditions by point matching at the nodes converts the electric field integral equation to a matrix equation. Example cases are run and compared to previous moment methods and exact solutions, and this method shows good agreement. This method requires only one unknown per node in dielectric and magnetic material, which is a significant reduction in unknowns and matrix storage compared to traditional methods. By duality, this method can be used at either transverse electric or transverse magnetic polarization     

Axial slot antenna on dielectric-coated elliptic cylinder

The radiation properties of an axial slot antenna on a conducting elliptic cylinder with a homogeneous dielectric coating are investigated. In the dielectric coating and in the exterior free-space region the field is expanded in elliptic waves using the Mathieu functions. The Mathieu angular functions are employed as basis and testing functions to enforce the boundary conditions at the interface between the dielectric and the free-space regions. The equations of continuity at the boundary are solved by Galerkin's method. Numerical results are presented in graphical form for the transverse electric (TE) and transverse magnetic (TM) polarizations to illustrate the far-field radiation patterns, the gain versus coating thickness, and the aperture conductance versus coating thickness     

Transverse electric field effects on the electron transport properties of InP

In semiconductor devices such as field effect transistors (FETS) to assume that the electric field in the channel is one-dimensional is not valid for certain operating conditions. A Monte-Carlo method with a prescribed two-dimensional field distribution has been used to calculate the electron transport properties for InP when transverse field effects become important. For steady-state conditions the mean velocity, individual valley velocity and population fractions, and diffusion coefficient have been computed and the results compared with previous approaches to the problem. Transient effects have also been obtained along with the stratified velocity distribution.     

Acceleration of heavy ions in a thruster

The acceleration of heavy ions in a Hall thruster is analyzed. The numerical solutions to the 1D hydrodynamic equations that describe the three-component system (neutral particles, electrons, and ions) are obtained. The conditions for the collisionless motion of ions, ion acceleration in the presence of the self-consistent electric field, and electron diffusion across the magnetic field are considered. The self-consistent field is calculated using the Poisson equation. The absence of singularity in the case when the ion velocity coincides with the velocity of ion sound is demonstrated. The critical magnetic field above which the propagation of ion beam is impossible is determined.     

Hollow-beam focusing with electrostatic and periodic magnetic fields

A new method of focusing a hollow cylindrical electron beam is presented. The focusing system consists of a cylindrical center conductor inside the beam, a cylindrical outer conductor enclosing the beam, and a series of periodic magnets outside the tube. A radial electrostatic field between the conductors provides an outward force on the electrons. The periodic magnetic field produces an inward force on the electrons. The inward and outward forces can be adjusted to provide a balance of all the forces acting on the electrons at both boundaries of the beam by choosing the electric and magnetic fields properly. An approximate analysis has been made and is presented which gives necessary design information. A number of curves are presented which are useful in designing focusing systems of this type. Experimental results on a beam tester show that current transmission of over 90 per cent for perveance up to 11 micropervs can be obtained readily. The adjustments are not critical and the performance is very stable.     

Evaluation of electron temperature in transverse and axial magnetic fields in an arc plasma by diffusion voltage measurement

The diffusion voltage in a mercury arc plasma has been measured for arc currents from 2.5 A to 5 A in transverse and axial magnetic fields from zero to 1.1 kG. Assuming the radial distribution of charged particles proposed by Ghosal et al, (1978) and utilizing the method of Sen et al. (1983), the ratio of electron temperatures with and without a magnetic field has been evaluated. It becomes a maximum in an axial field and then decreases, whereas it shows a minimum in a transverse field and then increases. An expression for the ratio of the electron temperature with and without a field has been deduced that explains these results. Quantitative agreement between experiment and theory is fairly satisfactory.     

一种新型的中性原子交流电磁囚禁

提出了一种新型的冷原子强场seeking态磁势阱 ,利用的是原子在交变四极场中受到的梯度力。计算结果表明通过选择合适的参数 ,可以控制势阱在轴向和径向的势阱深度。在得到一个径向势阱深度达 0 6mK ,纵向深度为 0 5mK的交流磁势阱 ,可以将温度为～ 10 0 μK的冷原子囚禁在径向 1mm ,纵向 4mm的范围内。如果撤消轴向囚禁 ,还可以获得一个径向囚禁深度为 1 8mK ,能将温度为～ 10 0 μK的冷原子囚禁在径向 5 0 μm范围内的新型磁导管。