Definitions

Fig. 2 An expanded lattice contains a set of branches (not necessarily in an array) and each branch holds an ordered array of lattice elements.

• Branch: Contains an ordered list of lattice elements that can be tracked through. A branch can describe such things as a storage ring or Linac.

• Branch expansion: The process, starting from the root BeamLine of a branch, of constructing the ordered list of lattice elements contained in that branch.

• Element: See Lattice element.

• Lattice: The outermost structure that holds a set of branches and can be used to define an entire accelerator complex.

• Lattice expansion: This includes branch expansion along with connecting branches together via Fork elements, expression evaluations, and floor position and reference species and energy calculation.

• Root BeamLine: A BeamLine that is used as the basis for creating a branch.

• Root branch: A branch that is specified in a Lattice structure. Non-root branches are branches that are formed due to the presence of Fork elements.

• Lattice element: Basic building block of a lattice most often representing something physical like a quadrupole magnet or an RF cavity.

Lattice Elements

The basic building block used to describe an accelerator is the lattice element. Typically, a lattice element is something physical like a bending magnet or an electrostatic quadrupole, or a diffracting crystal. Further details here.

Lattice Branches

A lattice branch holds an ordered array of lattice elements that gives the sequence of elements to be tracked through. A branch can represent something like a storage ring, transfer line or Linac. In the simplest case, a program can track through the elements one element at a time. However, lattice elements may overlap which will naturally complicate tracking.

Lattices

A lattice is the root structure holding the information about a machine. A machine may be as simple as a line of elements (like the elements of a Linac) or as complicated as an entire accelerator complex with multiple storage rings, Linacs, transfer lines, etc.

Essentially a lattice has an array of branches with each branch describing part of the machine. Branches can be interconnected to form a unified whole. Branches can be interconnected using Fork elements. This is used to simulate forking beamlines such as a connections to a transfer line, dump line, or an X-ray beamline.

Besides branches, a lattice will hold information like details of any support girders that are present and multipass information in the case where elements are transversed multiple times as in an ERL or in opposite directions as in a colliding beam machine.

Root branch

The branch from which other branches fork but is not forked to by any other branch is called a root branch. A lattice may contain multiple root branches. For example, a pair of intersecting storage rings will generally have two root branches, one for each ring.

Lattice Expansion

An important concept is lattice expansion and branch expansion. Branch expansion is the process, starting from the root BeamLine of a branch, of constructing the ordered list of lattice elements contained in that branch. Lattice expansion involves branch expansion along with things like calculating the reference energy for all elements.