In an axially symmetric magnetic field, charged particles move along the axis and rotate around the axis at the same time. Accordingly, the transverse motion can be decomposed into two parts, the focusing movement and the rotation of the meridian plane, and the 4-dimensional transfer matrix can be expressed as the product of a focusing matrix and two rotation matrices. The overall transfer matrix is re-derived in this article with the rotation matrices and the focusing matrix. Then the corresponding sigma matrix is given to further estimate the beam emittance extracted from electron cyclotron resonance ion source. The second moment of the beam distribution function is discussed in detail.%带电粒子在轴对称磁场中一边沿着对称轴向前运动,一边绕对称轴旋转.所以横向运动可以分解为两部分:聚焦运动和子午面的旋转.因此,4维横向传输矩阵可以表示为聚焦矩阵和旋转矩阵的乘积.用旋转矩阵和聚焦矩阵重新推导了总的传输矩阵.然后给出了相应的相椭圆系数矩阵来进一步估算从ECR离子源引出束流的发射度.详细地讨论了束流分布函数的二次矩.
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