任意时间分布电子束与单间隙微波腔的非线性自洽过程研究

将电子束作为激励源，根据Maxwell方程和电子受到的洛伦兹力，给出了描述工作模式在电 子束作用下的激励方程和电子束电子在工作模式作用下的运动方程（即微波谐振腔中电子束 与微波场相互作用的自洽方程组）.根据该自洽方程组，进一步研究了任意时间分布电子束 与单间隙微波腔的相互作用.通过分析微波腔中电子束与微波作用的线性和非线性过程，给 出了电子束调制深度、微波腔作用间隙对微波输出功率的影响.最后从理论上给出了影响微 波输出功率的综合物理参量. 关键词： 微波腔 模式 自洽方程 单间隙微波腔     

Electric field measurements and computational modeling at ultrahigh-field MRI

While magnetic resonance images essentially contain a map of the both circularly polarized components of the RF transverse magnetic fields (B(1) field), the thermal heat and electromagnetic power deposition is generated by the associated electric fields. Measurement of electric field distributions/intensities across a sample yields an indirect indication of possible cause of heating within the sample and potentially enables the detection of "hot spots," which can be present within inhomogeneous radiofrequency (RF) fields, such as the case with magnetic resonance imaging at high field strength. As a result, establishing a valid technique for direct measurements of the electric field and its correlation, obtained using computational electromagnetics, is essential in assessing (1) the safety of the RF coil designs and (2) the validity of the calculations. In this work, a probe was built and used to measure the transverse electric field (E(1) field) distributions within an empty 8 T (tuned to 340 MHz) RF head coil and within a saline water phantom loaded in the same coil. The measured E(1) field distributions were favorably compared to the distributions obtained utilizing a finite difference time domain in-house package.     

微波谐振腔中电子与微波作用的非稳态过程研究

在微波腔中微波场影响电子的运动,同时电子束作为电流源也产生辐射,影响微波场,这种相互作用包含线性和非线性过程。根据Maxwell理论,微波腔中的实际微波场可以按微波腔的模式展开,而且不同模式与电子束之间的相互作用不同。将电子束作为激励源,根据Maxwell方程和电子受到的洛伦兹力,建立不同模式在电子束作用下的激励方程和电子束电子在不同模式作用下的运动方程（即微波谐振腔中电子束与微波场相互作用的自洽方程组）,并由此进一步分析一维情况下单间隙微波腔中微波建场、辐射场呈指数增长和饱和等非稳态作用过程,该过程涉及到电子束与微波作用的线性和非线性过程。     

Higher-order frequency dependence of radiofrequency penetration in planar,cylindrical, and spherical models

In the last few years, solutions for radiofrequency penetration in various homogeneous geometric shapes have been presented. As imaging is pushed to very high fields, including those available in small-bore units, some further understanding of the effects of relative permittivity, ϵ_r, and conductivity, σ, is required. To this end, we compare the RF field and power deposition out to fourth order in frequency, ω, for planar, cylindrical, and spherical shapes. The expected reduced power deposition as conductivity increases is easily described. Further, modifications to the equations for the spherical model resulting from several errors in the literature are given. Even for high fields, the expressions also reveal that for physiologic values of a and ϵ, the higher-order term in ω⁴ can become small, leaving the usual first-order functional dependence on w, a, e, and geometry and, hence, a near-uniform RF penetration.     

微波谐振腔中电子与微波作用的非稳态过程研究

 在微波腔中微波场影响电子的运动，同时电子束作为电流源也产生辐射，影响微波场，这种相互作用包含线性和非线性过程。根据Maxwell理论，微波腔中的实际微波场可以按微波腔的模式展开，而且不同模式与电子束之间的相互作用不同。将电子束作为激励源，根据Maxwell方程和电子受到的洛伦兹力，建立不同模式在电子束作用下的激励方程和电子束电子在不同模式作用下的运动方程（即微波谐振腔中电子束与微波场相互作用的自洽方程组），并由此进一步分析一维情况下单间隙微波腔中微波建场、辐射场呈指数增长和饱和等非稳态作用过程，该过程涉及到电子束与微波作用的线性和非线性过程。     

Hydrodynamic analogies between the equations of classical hydrodynamics and electrodynamics in electrochemistry

It is shown that the use of equations of hydrodynamics of an incompressible and compressible fluid gives similar results for a number of experimental data from the field of classical electrodynamics used in electrochemistry. The analogue of electric current in wires is a stream that creates around itself a flow of a fluid. The analogue of electric field is the acceleration of a flow, whereas the analogue of magnetic induction is the frequency of a rotational motion of the fluid. Ampere’s law in hydrodynamics describes the interaction of flows with real bodies in terms of the Zhukovsky equation. The power laws in the fluid are similar, with some distinctions, to Maxwell equations. The expansion of the equations of conservation of momentum and mass in a series in perturbations leads to wave equations also similar to the Maxwell equations for the propagation of electromagnetic waves.     

Effects of coil dimensions and field polarization on RF heating inside a head phantom

Deterioration of radiofrequency (RF) inhomogeneity with increasing static magnetic field in magnetic resonance imaging (MRI) is one of the fundamental challenges preventing their clinical rendition and posing safety hazards. Variation in RF coil designs could help redistribute RF energy absorption over the imaged object. This work is intended to determine experimentally the difference in RF heating produced within a human head phantom by in situ measurement of RF inhomogeneity as a function of coil design utilized at 8 T. The heating patterns of 1/4 wavelength (long) and 1/8 wavelength 11-cm (short) transverse electromagnetic (TEM) coils loaded with a homogeneous human head phantom at 340 MHz were evaluated. In addition, different transmit/receive (T/R) configurations were used in search for the possibility of "hot-spot" formation. Fluoroptic thermometry was used to measure temperatures in multiple positions in a head phantom made of ground turkey breast for RF powers corresponding to a specific absorption rate (SAR) of 4.0 W/kg for 10 min. Numerical simulations were performed to study the general RF power deposition patterns in phantoms at 340 MHz including the effects of field polarization. The temperature increases varied from 0 to 0.8 degrees C for the long RF coil, while the short RF coil produced a maximum temperature change of 0.5 degrees C. Similar to ultra high-field electromagnetic simulations, these measurements revealed low peripheral and high deep-tissue heating at 8 T. The findings indicated that the largest temperature changes for both cases were less than 1 degrees C. While these results showed an increase in localized heating due to RF pulses at 8 T, they highlight that RF inhomogeneity could be redistributed using different RF coil designs through which the hot spots could be made cooler.     

平面横电磁波模的初值问题

经典理论所描述的电场和磁场处处同相的平面电磁波模并不存在.Maxwell方程组的解依赖于 电磁场的初始值或边界条件,根据不同的初始条件解得的平面电磁波模是不同的.结果表明 ,平面电磁波是横波,在不同的位置,由变化的电场激发的磁场或由变化的磁场激发的电场 振幅不同,电场与磁场的相位差也不同. 关键词： Maxwell方程组 最优微分方程 初始条件 平面电磁波     

FDTD方法分析高功率微波对大气的电离与击穿

 应用麦克斯韦方程和电子流体方程,利用时域有限差分方法(FDTD)计算模拟了高功率微波(HPM)对大气的电离与击穿;该方法用瞬时电场代替等效电场,时刻更新大气电离击穿过程中的电离频率和碰撞频率,消除了近似解析法未考虑大气电离击穿过程中电场幅度衰减而引起的误差,计算得到击穿阈值大小随海拔高度的变化趋势与文献所得的变化趋势相吻合,其值略大于近似解析解;并通过仿真计算分析了HPM脉冲幅值、脉宽以及海拔高度等参数对大气击穿的影响。     

FDTD方法分析高功率微波对大气的电离与击穿

应用麦克斯韦方程和电子流体方程,利用时域有限差分方法(FDTD)计算模拟了高功率微波(HPM)对大气的电离与击穿;该方法用瞬时电场代替等效电场,时刻更新大气电离击穿过程中的电离频率和碰撞频率,消除了近似解析法未考虑大气电离击穿过程中电场幅度衰减而引起的误差,计算得到击穿阈值大小随海拔高度的变化趋势与文献所得的变化趋势相吻合,其值略大于近似解析解;并通过仿真计算分析了HPM脉冲幅值、脉宽以及海拔高度等参数对大气击穿的影响。     

大面积NBI 射频离子源电气参数设计分析

为探究射频离子源驱动器线圈电气参数对射频放电的影响,主要进行了射频离子源等离子体激发的物理分析,并计算了射频电源的频率选择与线圈放电电流、线圈匝间电压以及放电气压之间的关系,设计了射频离子源驱动器的主要参数。研制的射频离子源驱动器装置,成功获得氢等离子体射频放电。实验结果和理论计算结果符合很好。     

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为探究射频离子源驱动器线圈电气参数对射频放电的影响,主要进行了射频离子源等离子体激发的物理分析,并计算了射频电源的频率选择与线圈放电电流、线圈匝间电压以及放电气压之间的关系,设计了射频离子源驱动器的主要参数。研制的射频离子源驱动器装置,成功获得氢等离子体射频放电。实验结果和理论计算结果符合很好。     

大学生对麦克斯韦方程组的理解研究

本研究通过收集麦克斯韦方程组概念测试题的课堂讨论录音及书面回答,获得物理专业大学生对麦克斯韦方程组的错误理解,总结出学生常见的错误概念为不清楚方程式来源、对电场和磁场的相互关系理解有误、将电场和磁场进行不恰当类比、不能正确理解平行板间电磁场的来源、对感生电场和位移电流理解不到位等,对此提出有针对性的教学建议,为电磁学教学提供参考.     

Electric Field in a Gravitational Field

The potential of a static electric charge located in a Schwarzschild gravitational field is given by Linet. The expressions for the field lines derived from this potential are calculated by numerical integration and drawn for different locations of the static charge in the gravitational field. The field lines calculated for a charge located very close to the central mass can be compared to those calculated by Hanni–Ruffini. Maxwell equations are used to analyze the dynamics of the falling electric field in a gravitational field.     

Incompressible Einstein–Maxwell fluids with specified electric fields

The Einstein–Maxwell equations describing static charged spheres with uniform density and variable electric field intensity are studied. The special case of constant electric field is also studied. The evolution of the model is governed by a hypergeometric differential equation which has a general solution in terms of special functions. Several classes of exact solutions are identified which may be considered as charged generalizations of the incompressible Schwarzschild interior model. An analysis of the physical features is undertaken for the uniform case. It is demonstrated that uniform density spheres with constant electric field intensity are not realizable with isotropic pressures. This highlights the necessity of studying the criteria for physical admissability of gravitating spheres in general relativity which are solutions to the Einstein–Maxwell equations.     

高通鸟笼线圈激发螺旋波等离子体特性研究

研制了高通鸟笼线圈,使用氩气作为工质气体对射频天线的工作性能进行了初步评估。利用COMSOL5.4模拟出了鸟笼天线在13.56MHz的工作频率下,电场和磁场呈线性极化分布。对鸟笼线圈进行了电路结构解剖,推导出了其谐振频率计算公式。利用热耦合红外测温仪测试了正常工作状态下的鸟笼线圈外表温度明显低于传统射频天线,电容器最高温度仅65.8°。使用光谱仪对螺旋波等离子体放电光谱特性进行诊断。通过朗缪尔探针诊断了不同压强和磁场强度下螺旋波等离子体密度,在1.0Pa、600Gs、射频功率700W条件下等离子体密度达到1.62×10¹⁸m^-3。诊断了正向功率和反向功率对应的等离子体密度,其与磁滞现象变化趋势雷同。测试了螺旋波等离子体的径向密度分布,其在轴心处密度达到最高。探究了无磁场条件下等离子体特性,其密度值不会发生大幅度跃迁,纵向磁场是引发螺旋波等离子体放电的关键因素,低压条件下有利于得到更低的电子温度,最低达到2.67eV。表明鸟笼线圈低热耗、高馈入的特性使其在激发大体积的高密度螺旋波等离子体方面具有明显优势,可以投入到下一阶段氢气螺旋波等离子体的激...     

Aqueous flat cells perpendicular to the electric field for use in electron paramagnetic resonance spectroscopy

An analytic solution of the Maxwell equations for aqueous flat cells in rectangular TE(102) cavities has led to the prediction of significant (3-6 times) X-band EPR signal improvement over the standard flat cell for a new sample configuration consisting of many flat cells oriented perpendicular to the electric field nodal plane. Analytic full wave solutions in the presence of sample and wall losses have been obtained and numerically evaluated. Observation of the predicted fields led to a classification of three distinct types of sample loss mechanisms, which, in turn inspired sample designs that minimize each loss type. The resulting EPR signal enhancement is due to the presence and centering of a tangential electric field node within each individual sample region. Samples that saturate with the available RF magnetic field and those that do not are considered. Signal enhancement appears in both types. These observations, done for the TE(102) mode, carry over to the uniform field (UF) modes, a relatively new class of microwave cavities for use in EPR spectroscopy developed in this laboratory. Rectangular UF modes have an RF magnetic field magnitude that is uniform in a plane. Based on this analysis, a practical multiple flat-cell design is proposed.     

多晶硅表面陷阱坑形貌的光学性能模拟

采用COMSOL Multiphysics 3.5a有限元分析软件中的RF模块对3种硅片绒面的陷阱坑形貌(轻度腐蚀、正常腐蚀和过度腐蚀)的光学性能进行了数值模拟.通过求解麦克斯韦方程组和材料本构方程,获得了3种陷阱坑的表面电场z分量、表面磁场y分量和反射率的变化规律.结果表明:当波长为600 nm时,轻度腐蚀陷阱坑的表面电场z分量和表面磁场y分量的数值最小,反射率最高(约为35％);正常腐蚀陷阱坑的表面电场z分量和表面磁场y分量其次,反射率约为17％;过度腐蚀陷阱坑的表面电场z分量和表面磁场y分量的数值最大,反射率最低(约为10％).通过实验和模拟结果对比可知,模拟值和试验值的反射率变化趋势基本一致,两者吻合较好,可为实际生产和试验提供理论参考.     

The design of a body RF coil for low-field open MRI using pseudo electric dipole radiation and simulated annealing

The paper presents a new body RF coil design scheme for a low-field open MRI system. The RF coil is composed of four rectangular loops which are made of wide copper strips located near the surfaces of the bottom and top pole faces of the permanent magnet. The body RF coil has been designed by using the pseudo electric dipole radiation (PEDPR) method with the Metropolis algorithm. In the calculation of the RF fields via the finite difference time domain (FDTD) method, the computational time increases as the RF frequency becomes lower. Moreover, the computational process using the FDTD method takes a very long time when the RF coil is optimized. The optimization requires varying the configuration of the RF coil system and performing successive calculations of field strength and field homogeneity. When we perform these successive calculations, the computational time can be reduced by using the PEDPR method, where the segmented current elements of the RF coil are treated as pseudo electric dipole radiation sources. Because the RF coil is made of wide strips, the variation of the current density on the strip has been considered in the B₁-field calculation. For each configuration of the RF coil system, the current distribution is calculated via circuit analysis, where each copper strip is considered as a parallel combination of current element lines. The preliminary field calculation study by the FDTD method verifies both the circuit analysis method for the current distribution and the PEDPR method for the radiation field strength. The optimization of the RF coil configuration is performed by the Simulated Annealing (SA) process using the Metropolis algorithm. Simulations have been performed for a 10 MHz RF frequency. The optimized RF coil has four rectangular loops of 37 cm × 100 cm with 6.5 cm wide strips which are separated vertically 49 cm and horizontally center-to-center 63 cm. In the 25 cm diameter of spherical volume (DSV), the design results show a good field inhomogeneity of the B₁-field below 0.49 dB (5.8%).     

Towards a complete coil array

A complete RF coil system, as has been previously defined, is capable of generating any steady-state RF field, at the MR frequency, that is compatible with Maxwell's equations. A coil system is complete if it is capable of generating all basis vector fields in the multipole expansion of the electromagnetic fields. A complete coil system has the potential to reach the ultimate intrinsic signal-to-noise as an MRI receiver coil. It also offers maximum flexibility in tailoring the spatial RF field distribution as an excitation coil. Here, computer simulations have been performed on array coils employing composite coil elements, assuming the current loops are small and can be approximated by magnetic dipoles. We demonstrate that a coil array can be configured to approximate a truncated complete array coil and to generate the basis magnetic vector fields up to certain orders in the multipole expansion of the electromagnetic fields.