Abstract
The force between two moving point charges, because of its inverse square law singularity, cannot be applied directly in the numerical simulation of bunch dynamics; radiative effects make this especially true for short bunches being deflected by magnets. This paper describes a formalism circumventing this restriction in which the basic ingredient is the total force on a point charge comoving with a longitudinally aligned, uniformly charged string. Bunch evolution can then be treated using direct particle-to-particle, intrabeam scattering, with no need for an intermediate, particle-in-cell, step. Electric and magnetic fields do not appear individually in the theory. Since the basic formulas are both exact (in paraxial approximation) and fully relativistic, they are applicable to beams of all particle types and all energies. But the theory is expected to be especially useful for calculating the emittance growth of the ultrashort electron bunches of current interest for energy recovery linacs and free-electron lasers. The theory subsumes coherent synchrotron radiation and centrifugal space charge force. Renormalized, on-axis, longitudinal field components are in excellent agreement with values from Saldin et al. [DESY Report No. DESY-TESLA-FEL-96-14, 1995; Nucl. Instrum. Methods Phys. Res., Sect. A 417, 158 (1998).]
Highlights
The electric and magnetic forces between two point charges are proportional to the inverse square of their separation distance
Until a brief discussion in a later section, it is left open whether L is matched to the actual bunch length or is purely artificial
The main content of this paper is closed-form expressions for the force on a point charge due to a comoving charged string. They are intended to form the basis of treatments of space charge effects as direct ‘‘intrabeam scattering’’ with no need for charge distribution tallying followed by field solving
Summary
The electric and magnetic forces between two point charges are proportional to the inverse square of their separation distance. A later paper by Geloni et al [14] discusses the off-axis problem, for vertical, but not radial, offsets Another feature of the present paper is that it shows how the renormalization procedure (which leaves ordinary space charge in field-free regions unaccounted for) can be avoided. Though this paper is not ‘‘string theory’’ as that term is currently understood, the use of the recently fancy noun ‘‘string’’ is not entirely inappropriate because, as in elementary-particle theory, the spurious (or at least nonelectromagnetic) self-force of a string is less divergent (only logarithmic) than is the self-force of a point charge Though this may still leave a renormalization process necessary, the sensitivity of the procedure is greatly reduced by the gentler divergence. The paper begins with the easiest part of the calculation—the self-force of a straight charged string in field-free space
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