感应电压叠加器次级非轴对称磁绝缘物理模型和数值分析

Theoretical Model and Numerical Analysis of Nonaxisymmetrical Magnetic Insulation in the Secondary Side of Induction Voltage Adders

针对感应腔注入电流非均匀分布引起的感应电压叠加器次级非轴对称磁绝缘问题,在磁绝缘经典层流理论基础上,通过引入角向非均匀分布的模数,将经典一维轴对称磁绝缘Creedon理论推广至两维（r,θ）平面,建立了圆柱坐标系下二维层流物理模型,推导了磁绝缘电参数（电磁场、空间电子密度、电子鞘层等）与相对论因子γ（r,θ）的关系。当给定边界条件（阴极磁感应强度角向分布）时,数值求解物理模型,获得了感应电压叠加器次级非轴对称磁绝缘电参数的二维分布。当感应电压叠加器次级阴极磁感应强度满足余弦分布时,磁绝缘电子鞘层边界近似呈高斯分布。在靠近馈入点的角向位置,由于磁感应强度较大,电子鞘层较薄,磁绝缘电子密度较大。阳极磁感应强度分布均匀性优于阴极,且两者相位相差180°,数值分析结果与RITS-3装置实验结果基本相符。建立的物理模型和分析方法可用于长距离磁绝缘线内筒偏心等非轴对称磁绝缘问题。

By introducing a parameter defined as an azimuthal mode number, the classical Creedon theory is generalized to two-dimensional situations, to describe the nonaxisymmetrical magnetic insulation caused by azimuthally asymmetrical distributions of feed currents within cavity in induction voltage adders（IVA）. A two-dimension Creedon model is developed, and the relationship of electrical parameters of the magnetic insulation（i.e., electric filed, magnetic flux density, electron density, and electron sheath edge） depending on the relativistic factor, γ（r, θ）, is derived. Given some boundary conditions, e.g., the azimuthal distributions of magnetic flux density on the cathode, the physical model is numerically solved, and the two-dimensional distribution of characteristics of the nonaxisymmetrical magnetic insulation of IVA is acquired. It is found that, as the magnetic flux density on the cathode satisfies the cosine distribution, the azimuthal distributions of electron sheath edges approximate the Gauss function. At the azimuthal positions close to injection points, the thickness of the electron sheath is much thinner due to the stronger magnetic flux density, whereas the electron density is lower. The azimuthal uniformity of the magnetic flux density on the anode is much better than that of cathode, and the phase between them is about 180°, which are in agreement with the experiments on the RITS-3 facility. In addition, the physical model and numerical solutions presented in this paper are capable of describing the nonaxisymmetrical magnetic insulation caused by the off-center of inner electrodes in the long magnetically insulated transmission lines（MITL）.