EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
Bending Magnets
Two different type keywords are recognised for bending magnets,
they are distinguished only by the reference system used:
- RBEND is a rectangular bending magnet.
It has parallel pole faces and is based on a curved
rbend reference system;
its length is the straight length as in the Figure but
internally the arc length is being used.
- to define an RBEND with the arc length as length (straight line
shorter than input - for compatibility with MAD8 version up to
version 8.23.06 including), the option RBARC=FALSE has to be set.
- SBEND is a sector bending magnet.
Its pole faces meet at the centre of curvature of the curved
sbend reference system.
They are defined by the commands:
SBEND, L=real,ANGLE=real,TILT=real,K0=real,K0S=real,K1=real,E1=real,E2=real,
FINT=real,FINTX=real,HGAP=real,K2=real,H1=real,H2=real;
RBEND, L=real,ANGLE=real,TILT=real,K0=real,K0S=real,K1=real,E1=real,E2=real,
FINT=real,FINTX=real,HGAP=real,K2=real,H1=real,H2=real;
For both types,
the following first-order attributes are permitted:
- L:
The length of the magnet (default: 0 m).
For a rectangular magnet the length is measured along a straight line
as in the Figure (internally the arc length is used), while for a
sector magnet it is the arc length of the reference orbit.
To define an RBEND with the arc length (shorter straight length),
the option RBARC=FALSE has to be set.
- ANGLE:
The bend angle (default: 0 rad).
A positive bend angle represents a bend to the right,
i.e. towards negative x values.
- TILT:
The roll angle about the longitudinal axis (default: 0 rad,
i.e. a horizontal bend). A positive angle represents a clockwise
rotation. A TILT=pi/2 turns a horizontal into a vertical bend, i.e. a
positive bend ANGLE denotes a deflection down.
Please note that contrary to MAD8 one has to
specify the desired TILT angle, otherwise it is taken as 0 rad. This
was needed to avoid the confusion in MAD8 about the actual meaning of
the TILT attribute for various elements.
- Please take note that K0 and K0s are left in
the data base but are no longer used for the MAP of the bends (but see
below for what K0 is being used), instead ANGLE and TILT
are used exclusively. We believe that this will allow for a clearer
and unambiguous definition, in particular in view of the upcoming
integration of MAD-X with PTC which will allow a more general
definition of bends. However, it is required to
specify k0 to assign RELATIVE field errors to a bending magnet since
k0 is used for the normalization and NOT the ANGLE. (see
EFCOMP).
- K1:
The quadrupole coefficient
K1 = (1 / B rho) (del By / del x).
The default is 0 m-2.
A positive quadrupole strength implies horizontal focussing
of positively charged particles.
- E1:
The rotation angle for the entrance pole face
(default: 0 rad).
- E2:
The rotation angle for the exit pole face
(default: 0 rad).
- FINT:
The field integral whose default value is 0.
- FINTX:
Allows (FINTX > 0)to set FINT at the element exit different from its entry
value. In particular useful to switch it off (FINTX=0).
- HGAP:
The half gap of the magnet (default: 0 m).
The pole face rotation angles are referred to the magnet model for
rectangular bend and
sector bend respectively.
The quantities FINT and HGAP specify
the finite extent of the fringe fields as defined in
[SLAC-75]
There they are defined as follows:
The default values of zero corresponds to the hard-edge approximation,
i.e. a rectangular field distribution.
For other approximations, enter the correct value of the half gap,
and one of the following values for FINT:
Linear Field drop-off 1/6
Clamped "Rogowski" fringing field 0.4
Unclamped "Rogowski" fringing field 0.7
"Square-edged" non-saturating magnet 0.45
Entering the keyword FINT alone sets the integral to 0.5.
This is a reasonable average of the above values.
The following second-order attributes are permitted:
- K2:
The sextupole coefficient
K2 = (1 / B rho) (del2 By / del x2).
- H1:
The curvature of the entrance pole face (default: 0 m-1).
- H2:
The curvature of the exit pole face (default: 0 m-1).
A positive pole face curvature induces a negative sextupole component;
i.e. for positive H1 and H2
the centres of curvature of the pole faces are placed inside the magnet.
Examples:
BR: RBEND,L=5.5,ANGLE=+0.001; // Deflection to the right
BD: SBEND,L=5.5,K0S=+0.001/5.5; // Deflection up
BL: SBEND,L=5.5,K0=-0.001/5.5; // Deflection to the left
BU: SBEND,L=5.5,K0S=-0.001; // Deflection down
hansg,
frs,
August 28, 2003