Round-to-flat transformation of angular-momentum-dominated beams

Abstract

A study of round-to-flat configurations, and vice versa, of angular-momentum-dominated beams is presented. The beam propagation in an axial magnetic field is described in terms of the familiar Courant-Snyder formalism by using a rotating coordinate system. The discussion of the beam transformation is based on the general properties of a cylindrically symmetric beam matrix and the existence of two invariants for a symplectic transformation in 4D phase space.

Twiss parameters and beam matrix formulation of generalized Courant–Snyder theory for coupled transverse beam dynamics

“…͑32͒ is valid because wЈw T = ww TЈ . We can readily show that ͱ det͑͒ = ⑀ Ќ 2 , as expected, and the volume enclosed by a 4D rms hyperellipsoid is V 4D = ͑ 2 / 2͒ ͱ det͑͒ = ͑ 2 / 2͒⑀ Ќ 2 , and the so-called trace invariant 18 is calculated to be…”

Beam envelope calculations in general linear coupled lattices

“…[2][3][4] Interestingly, one of the recent trends in the beam physics community is to introduce coupling elements between two planes intentionally for sophisticated beam manipulations. [5][6][7][8][9] Several ideas have been proposed to generalize the original CS theory for the systematic beam dynamics description of such coupled systems with as much similarity as possible to the original CS theory. 6,10,11 In recent papers, 12,13 the dynamics of charged particles in general linear coupled lattices has been formulated in terms of a generalized CS theory, which extends the original CS theory to the fully coupled cases.…”

Concept for controlled transverse emittance transfer within a linac ion beam

“…Rigorous analysis of coupled four-dimensional transverse beam dynamics can be found in [6][7][8][9]. This section is concluded in providing eidetic justification for the beam line elements, which a round to flat transformation should include.…”

“…(39) of [9] assuming an angular momentum dominated beam. The final rms emittances agree also well to the eigenemittances as evaluation of Eq.…”