Abstract An analysis is presented of the evolution of a narrow ion beam, produced for instance by an electrospray source, in ambient pressure air. To minimize beam broadening, an intense axial electric field E is externally imposed. Still, radial beam broadening due to the ionic diffusivity D and space charge must be accounted for. Ignoring axial contributions of diffusion and space charge, a simple second order partial differential equation is obtained for the space charge induced field. In the planar problem, this field is governed by Burgers's equation, which is exactly solvable via the Cole-Hopf transformation. The axisymmetric problem is not similarly tractable by any familiar transformation, but may be reduced to an ordinary differential equation in terms of a similarity variable, yielding the complete beam structure under all regimes of interest. The beam broadening effect of space charge is governed by the ratio between the beam current I and the group 2 π e 0 D E , where e 0 is the permittivity of the gas.

中文翻译：

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空间电荷和扩散对轴对称离子束的扩展

摘要 分析了窄离子束的演化，例如由电喷雾源在环境压力空气中产生。为了最大限度地减少光束展宽，外部施加了一个强烈的轴向电场 E。尽管如此，必须考虑由于离子扩散系数 D 和空间电荷而导致的径向束变宽。忽略扩散和空间电荷的轴向贡献，得到空间电荷感应场的简单二阶偏微分方程。在平面问题中，该场由 Burgers 方程控制，该方程可通过 Cole-Hopf 变换精确求解。轴对称问题不能通过任何熟悉的变换同样处理，但可以根据相似变量简化为常微分方程，在所有感兴趣的状态下产生完整的梁结构。空间电荷的电子束展宽效应由电子束电流 I 与族 2 π e 0 DE 之间的比率控制，其中 e 0 是气体的介电常数。