Coherent effects in the ionization loss of ultrarelativistic electron ensembles (bunches) are studied on the basis of perturbation theory of quantum mechanics. These effects originate from the interference of the electrons’ proper electric fields with each other. General expressions for the ionization loss in this case, as well as their applicability conditions, are derived. It is shown that for ensembles of sufficiently small spatial size, achievable in modern accelerator facilities, the discussed effects lead to an increase of the ionization loss by several orders of magnitude compared to the result predicted by the Bethe-Bloch formula. In this case, the effective mean ionization potentials of the atomic shells depend not only on the structure of the atomic levels, but on the ensemble form factors as well. The numerical calculations are made for hydrogen atoms, taking into account the density effect in the ionization loss. The ionization loss due to resonant excitation and ionization of atoms by ensembles with periodical modulation of the particle density (realized at free-electron lasers) is investigated.

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相对论电子集合由于原子的相干激发和电离而导致的能量损失

基于量子力学的微扰理论，研究了超相对论电子团（束）的电离损失的相干效应。这些影响源于电子固有电场的相互干扰。推导了这种情况下电离损失的一般表达式及其适用条件。结果表明，对于现代加速器设施中可实现的足够小空间大小的合奏，与Bethe-Bloch公式所预测的结果相比，所讨论的效果导致电离损失增加了几个数量级。在这种情况下，原子壳的有效平均电离势不仅取决于原子能级的结构，而且还取决于整体形状因子。考虑到电离损失中的密度效应，对氢原子进行了数值计算。研究了由于共振激发和原子电离与粒子密度的周期性调制（在自由电子激光器上实现）的合奏而导致的电离损失。