Circular modes, beam adapters, and their applications in beam optics

Abstract

In the optics of charged particle beams, circular transverse modes can be introduced; they provide an adequate basis for rotation-invariant transformations. A group of these transformations is shown to be identical to a group of the canonical angular momentum preserving mappings. These mappings and the circular modes are parametrized similar to the Courant-Snyder forms for the conventional uncoupled, or planar, case. The planar-to-circular and reverse transformers (beam adapters) are introduced in terms of the circular and planar modes; their implementation on the basis of skew quadrupole blocks is described. Various kinds of matching for beams, adapters and solenoids are considered. Applications of the planar-to-circular, circular-to-planar and circular-to-circular transformers are discussed. A range of applications includes round beams at the interaction region of circular colliders, flat beams for linear colliders, relativistic electron cooling, and ionization cooling.

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

“…[6,7]. The analyses in these papers are based on new sets of canonical variables -the guiding center variables in [6] and the coordinates for circular modes in [7].…”

Final cooling

“…would naturally have an expectation value of Within solenoidal focusing, Burov et al [10,11] have noted that a more natural choice of coordinates would be the circular modes -labeled cyclotron and drift modes. The cyclotron mode coordinates are:…”

“…Over several periods of energy loss and reacceleration, one obtains a small-emittance in cyclotron mode without damping in drift mode, and a large ratio of those emittances, which are identified with ε -and ε + in ref. [11] (A factor of ~10 is readily obtained in simulations.) These modes are rotated into x and y coordinates by round-to-flat beam optics.…”

Three-dimensional analysis of wakefields generated by flat electron beams in planar dielectric-loaded structures

“…This limit case can be practically reached by using structures with large aspect ratios (L x ) L y ) driven by flat electron beams with their transverse horizontal emittance much smaller than the vertical one " x ( " y . Flat beams can be produced in photoinjectors by using a roundto-flat beam transformation [36,37]. In such a scheme, a beam with large angular momentum is produced in a photoinjector [38].…”