Abstract
We report a universal beam envelope equation that governs the transverse linear dynamics of high-intensity and high-brightness relativistic beams under constant acceleration in axisymmetric linear accelerators. This dimensionless and almost parameter-free nonlinear equation is useful for understanding scaling properties and for investigating nonlinear behaviors that are beyond analytical analysis. Particularly, we explore emittance compensation in high-brightness beams evolving from the space-charge regime to the thermal-emittance regime, a transition that commonly occurs during acceleration but is not well studied. A new formula is given for correctly computing the rms bunch emittance from slice envelopes, which is different from the commonly used quadratic sum of the thermal emittance and the rms emittance in the envelope phase space.
Highlights
This paper deals with transverse linear beam dynamics during acceleration of space-charge-dominated highbrightness relativistic beams in axisymmetric accelerators
A major difficulty is due to the repulsive Coulomb forces that tend to blow up high-density electron bunches at low energy
Because of cancellation between the Coulomb force and the self-magnetic force of a bunch moving at high velocity, the space-charge forces are inversely proportional to the square of the beam energy and are less harmful at high energy
Summary
This paper deals with transverse linear beam dynamics during acceleration of space-charge-dominated highbrightness relativistic beams in axisymmetric accelerators. A key advance in rf photoinjector development is the recovery of the initial emittance with proper focusing, a technique known as emittance compensation [1,2] This critical process is governed by the nonlinear envelope equation addressed shortly. For spacecharge-dominated beams, the invariant envelope is analogous to Brillouin flow for nonaccelerating beams, where focusing and defocusing forces are balanced to produce a stable beam This theory successfully revealed a matching condition for a space-charge-dominated beam at the entrance of a linac. It is inadequate for emittance compensation inside an injector where the beam is far from equilibrium and there is no well-defined invariant envelope. The correct account of thermal-emittance effect becomes important as a beam comes out of the space-charge-dominated regime in a linac
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