In high current linear accelerators there may be instability in the coherent lateral motion of the particles caused by the electrostatic image of the beam. Appropriate placement of focusing magnetic lenses (the type normally employed to prevent symmetric radial expansion of the beam) can be used to control the lateral motion. Criteria for stability are derived.

1.
For a discussion of images in circular accelerators see L. J. Laslett, “On Intensity Limitations Imposed by Transverse Space‐Charge Effects in Circular Particle Accelerators,” Proc. 1963 Brookhaven Summer Study Program, Brookhaven Nat. Lab. Rep., BNL‐7534 (1963), pp. 324–367.
2.
L. J. Laslett, “Digital Computations of Image‐Field Coefficients for Extended and Off‐Center Beams in an Alternating‐Gradient Synchrotron,” University of California, Lawrence Radiation Laboratory Rep. UCID‐10162 (1966).
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N. W. Hetherington and C. H. Woods, “The Effects of Space Charge and Relativity on the Shapes of Charged‐Particle Beams,” University of California, Lawrence Radiation Lab. Rep. UCRL‐6010 (1960).
5.
J. W. Beal, “Beam Trajectories under the Influence of Self‐Fields and External Focussing Elements,” University of California, Lawrence Radiation Lab. Rep. UCRL‐14194 (1965).
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© 1970 The American Institute of Physics.
1970
The American Institute of Physics
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