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next planned revision: 2009-11 |
An injection is where the bunches begin their movement into the machine. They traverse the injection only once.
Since a crossing connects the two rings in two ways, it has points in common with the segment that would normally be in that sector.
The most difficult point to compute is the point where the line from outside crosses the polygon of the segment that would be there. It requires finding the equations for two straight lines and solving them for their intersection point. The entire algebra is given in the figure. For ease of writing these formulae, the radii of the ring have been called r and R instead of RII and RIO.
Note that the solution relies on point O being on line segment DE and that this depends on the slope angle ß. This angle must therefore be chosen within a fairly narrow range.
There are two paths through an injection segment but one of them is identical to that of the corresponding normal segment. The path through the injection line itself is a single straight line that by convention is a whole number (cNrInjectionSections, chosen to be 3) times the length of an average section.