Generalized Kapchinskij-Vladimirskij Distribution and Beam Matrix for Phase-Space Manipulations of High-Intensity Beams

TL;DR

This paper generalizes the classical KV distribution to include coupling, energy variation, and emittance partition, providing new tools for designing and analyzing high-intensity beam manipulations in phase space.

Contribution

The authors extend the KV model to incorporate all linear coupling forces, energy changes, and emittance partitioning, enabling advanced phase-space manipulations.

Findings

The generalized KV model produces uniform density profiles.

Derived matrix envelope equations for the new model.

Provides theoretical tools for high-intensity beam design.

Abstract

In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution, formulated on the basis of the single-particle Courant-Snyder (CS) invariants, has served as a fundamental theoretical basis for the analyses of the equilibrium, stability, and transport properties of high-intensity beams for the past several decades. Recent applications of high-intensity beams, however, require beam phase-space manipulations by intentionally introducing strong coupling. In this Letter, we report the full generalization of the KV model by including all of the linear (both external and space-charge) coupling forces, beam energy variations, and arbitrary emittance partition, which all form essential elements for phase-space manipulations. The new generalized KV model yields spatially uniform density profiles and corresponding linear self-field forces as desired. The corresponding matrix envelope equations and beam matrix for the generalized KV model provide important new theoretical tools for the detailed design and analysis of high-intensity beam manipulations, for which previous theoretical models are not easily applicable.