All calculations are based on six-dimensional transfer matrices. Three distinct menus are available namely: View , View 4D and Space Charge. The functions of the View menu are meant to be used when the motion is uncoupled. However, note that while the initial lattice functions (at the beamline upstream end) are assumed to be uncoupled, no additional assumption is made about coupling. Internally, the code propagates the so-called Edwards-Teng lattice functions. The downstream beam sizes, beta-functions and dispersions are correctly computed regardless of any coupling introduced by the elements in the beamline.
The initial beam phase space is determined by
In ring mode, computations will obviously be correct only when the overall one-turn transfer matrix contains no coupling entries. Because full six-dimensional matrix calculations are always performed, the dispersions, betatron beam envelopes and the momentum compaction factor will be calculated correctly even when the lattice is strongly coupled. When beta-functions are computed from the View Menu, a message box will will inform the user in the event coupling exceeds an a-priori specified threshold. The latter can be changed from the View|Control menu.
The functions in the View 4D (and Space Charge as well) menu make no assumptions about coupling and should be preferred when dealing with X-Y coupled lattices. An extension of the standard Twiss parameter formalism is used (see Coupled XY coupled lattice treatment).
Lattice functions for periodic lattices are determined using 2x2 matrices for each plane; obviously both the dispersion and the beta-functions determined in this manner will not be correct if coupling is present in the overall transfer matrix.
The program accounts for adiabatic damping due to acceleration (linear or electrostatic accelerator case). The beam emittance decreases in inverse proportion to the relativistic factor, $ \beta\gamma $. In contrast, the determinant of the transfer matrix is equal to one even in presence of acceleration so as to eliminate dependence of the beta-functions on the beam energy. Using these conventions, the beta function, $\beta$, and the beam size, $a$, are related by the following equation $$ a = \sqrt{ \epsilon_{in}\beta_F \frac{\beta_{in}\gamma_{in}}{\beta\gamma} }$$ where $\epsilon_{in}$ is the initial beam emittance, and $ \beta_{in} $, $ \gamma_{in} $ and $ \beta $, $ \gamma $ are respectively the initial and final relativistic factors.