Rotation, SROTATION, YROTATION

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

Coordinate Transformations

YROTATION: Rotation About the Vertical Axis

label: YROTATION,TYPE=name,ANGLE=real;

The element YROTATION rotates the straight reference system about the vertical (y) axis. YROTATION has no effect on the beam, but it causes the beam to be referred to the new coordinate system

x₂=x₁cos(theta)-s₁sin(theta), y₂=x₁sin(theta)+s₁cos(theta),

It has one real attribute:

ANGLE: The rotation angle theta (default: 0 rad). It must be a small angle, i.e. an angle comparable to the transverse angles of the orbit.

A positive angle means that the new reference system is rotated clockwise about the local y-axis with respect to the old system.

Example:

KINK: YROTATION,ANGLE=0.0001;

SROTATION: Rotation Around the Longitudinal Axis

label: SROTATION,ANGLE=real;

The element SROTATION rotates the straight reference system about the longitudinal (s) axis. SROTATION has no effect on the beam, but it causes the beam to be referred to the new coordinate system

x₂=x₁cos(psi)-y₁sin(psi), y₂=x₁sin(psi)+y₁cos(psi),

It has one real attribute:

ANGLE: The rotation angle psi (default: 0 rad)

A positive angle means that the new reference system is rotated clockwise about the s-axis with respect to the old system.

Example:

ROLL1: SROTATION,ANGLE=PI/2.;
ROLL2: SROTATION,ANGLE=-PI/2.;
HBEND: SBEND,L=6.0,ANGLE=0.01;
VBEND: LINE=(ROLL1,HBEND,ROLL2);

The above is a way to represent a bend down in the vertical plane, it could be defined more simply by

VBEND: SBEND,L=6.0,K0S=0.01/6;

hansg, June 17, 2002