Root-mean-square emittance of multiple beam systems

Abstract

A general expression for the rms emittance of a multiple beam system is unambiguously derived. The emittances for rectangular and circular arrays of identical beamlets are analyzed and expressed in terms of quantities associated with the beamlet distribution and the array geometry. A few examples relevant to actual experiments are included.

Structured electron beams from nano-engineered cathodes

“…It should be pointed out that in the limit where both f and m approach infinity, the geometric factors G R,r,r and G R,h,r converge to the same asymptotic limit of a 2 /3, which only depend on the size of the emitting area; this is in agreement with Ref. [12]. Thus the rms transverse emittance ε NC is approximated as…”

“…An example of a 5 × 5-array distribution at the 200-nm downstream of the cathode surface appears in Fig 2. In parallel, and to validate the simulations of dynamics associated with large arrays of nano-emitters, it is useful to extend the formalism developed in Ref. [12], and explore the variation of the array emittance given the array geometry and single-emitter Courant-Snyder and emittance beam properties. In Ref.…”

Numerical simulations of early-stage dynamics of electron bunches emitted from plasmonic photocathodes

“…This new distribution is then used as a starting distribution in an RF gun and the corresponding dynamics simulated with the fast PIC program Astra [9]. To date our efforts have focused on transversely imaging the cathode-array structure downstream of an accelerator beamline with 4 × 4 transfer matrix R. Given the Courant-Snyder parameters [for the horizontal plane (α x,1 , β x,1 )] associated to a single beamlet (formed from a nanohole) along with the parameters computed of the entire beam (α x , β x ) we found a general relationship that ensure single-particle imaging in the horizontal plane to be [10] single-beamlet emittance [11]. The latter set of equations respectively force (i) each beamlet to be at a waist (we assume all the beamlets have identical parameters) and (ii) the entire beam to be collimated.…”

A General Slice Moment Decomposition of RMS Beam Emittance

“…We demonstrate that the square of the projected emittance can be decomposed as the sum of four contributions, each with a distinct geometrical interpretation in terms of the slice beam moments. Fragments of a treatment along these lines can be found in various forms in the literature [5]- [9]. The purpose of this paper is to consolidate these results in the form of a general and carefully presented mathematical treatment, with proofs of some nontrivial features included.…”