We calculate exact two-dimensional analytic expressions for the electric and magnetic fields and their potentials generated by a linear beam of relativistic charged particles between infinite ideally conducting planes and ferromagnetic poles. We use the method of summing an infinite sequence of fields of linear image charges and image currents to obtain solutions and also calculate the density distribution of the electric charge on the conductor surface induced by the charged particle beam. We obtain new formulas for the linear approximation of the fields near the beam and discuss the mathematical features of the exact solutions and the applicability constraints for the linear approximations.

中文翻译：

---

平行平面之间带电粒子的相对论束的场：通过图像方法获得的精确二维解

我们计算了电场和磁场的精确二维解析表达式及其由无限理想导电平面和铁磁极之间的线性相对论带电粒子束产生的电势。我们使用线性镜像电荷场和镜像电流场的无限序列求和的方法来获得解，并计算带电粒子束在导体表面上感应的电荷密度分布。我们获得了光束附近场的线性近似的新公式，并讨论了精确解的数学特征和线性近似的适用性约束。