EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

Local Reference Systems

Reference System for Straight Beam Elements

• Drift space,
• Quadrupole,
• Sextupole,
• Octupole,
• Solenoid,
• CRABCAVITY,
• RF cavity,
• Electrostatic separator,
• Closed orbit corrector,
• Beam position monitor.

A rotation of the element about the S-axis has no effect on R and S, since the rotations of the reference system before and after the element cancel.

Figure 1: Reference System for Straight Beam Elements

Reference System for Bending Magnets

where alphais the bend angle. A positive bend angle represents a bend to the right, i.e. towards negative x values. For sector bending magnets, the bend radius is given by rho, and for rectangular bending magnets it has the value

rho = L / 2 sin(alpha/2).

If the magnet is rotated about the s-axis by an angle psi, R and S are transformed by

R* = T R, S* = T S T^-1.

where T is the orthogonal rotation matrix

The special value psi = pi/2 represents a bend down.

Figure 2: Reference System for Rectangular Bends; The signs of the pole-face rotations are positive as shown.

Figure 3: Reference System for Sector Bends; The signs of the pole-face rotations are positive as shown.

Elements which do not Change the Local Reference