EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

Bending Magnets

Two different type keywords are recognised for bending magnets, they are distinguished by the reference system used:

• SBEND is a sector bending magnet. The planes of the pole faces intersect at the centre of curvature of the curved sbend reference system.

• RBEND is a rectangular bending magnet. The pole faces are parallel. The reference system is the curved rbend reference system;

Bending magnets are defined by the commands:

label: SBEND, L=real, ANGLE=real, TILT=real,
              K0=real, K1=real, K2=real,
              E1=real, E2=real, FINT=real,FINTX=real, 
              HGAP=real, H1=real, H2=real,
              THICK = logical;

label: RBEND, L=real, ANGLE=real, TILT=real, 
              K0=real, K1=real, K2=real,
              E1=real, E2=real, FINT=real, FINTX=real, 
              HGAP=real, H1=real, H2=real, 
              ADD_ANGLE={array_of_max_5_angles},
              THICK = logical;

• L: The length of the magnet (default: 0 m).
  For sector bends the declared length is the arc length of the reference orbit.
  For rectangular bends the declared length is normally the length of a straight line joining the entry and exit points, as in the Figure.
  Internally MAD-X only uses the arc length of the reference orbit for both bend types.

  In order to define RBEND's with a declared length equal to the arc length of the reference orbit, the option RBARC must be previously set to FALSE in MAD-X with Option, RBARC= false;

• ANGLE: The bend angle (default: 0 rad).
  A positive bend angle represents a bend to the right, i.e. towards negative x values.

• ADD_ANGLE: An array of (maximum 5) bending angles for multiple passes. See add_pass option of the sequence command.
  This is only allowed for RBEND elements and is ignored for SBEND elements.

• TILT: The roll angle about the longitudinal axis (Default: 0 rad, i.e. a horizontal bend).
  A positive angle represents a clockwise rotation.
  An attribute TILT=pi/2 turns a horizontal bend into a vertical bend, and a positive ANGLE then denotes a downwards deflection.
  

• K1: The quadrupole coefficient (Default: 0 m^-2).
  K₁ = (1 / B rho) (del B_y / del x).
  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).
  The pole face rotation angles are referred to the magnet model for rectangular bend and sector bend respectively.
  E1 and E2 are positive if they reduce the length of the side of the bend that is further away from the centre of curvature.
  E1 and E2 must be specified as positive to give an SBEND parallel faces, ie turning it into an RBEND.
  E1 and E2 must be negative to give an RBEND faces whose planes intersect at the centrer of curvature, ie turning it into an SBEND.

• FINT: The fringe field integral at the entrance and exit of the bend. (Default: 0).
• FINTX: If defined and positive, the fringe field integral at the exit of the element, overriding FINT for the exit. (Default: =FINT)
  This allows to set different firnge field integrals at entrance (FINT) and exit (FINTX) of the element.
• HGAP: The half gap of the magnet. (Default: 0 m).

• K2: The sextupole coefficient (Default: 0 m^-3)
  K₂ = (1 / B rho) (del² B_y / 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.

• K0: OBSOLETE
  Please take note that K₀ and K_0s are left in the data base but are no longer used for the map of the bends, instead ANGLE and TILT are used exclusively.
  However, specifying K0 is required in order to be able to assign RELATIVE field errors to a bending magnet because K0 is used for the normalization instead of the ANGLE. (see EFCOMP).
  With K₀ = (1 / B rho) B_y, one gets K0 = ANGLE / arclength.

• THICK: If this logical flag is set to true the bending magnet will be tracked through as a thick-element, instead of being converted into thin-lenses.
  (Default: false)

Fringe fields:
The quantities FINT and HGAP specify the finite extent of the fringe fields as defined in [SLAC-75]:

The default values of zero correspond 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

Note also that the possibility to specify both FINT and FINTX allows one to set different values at entrance and exit of a bend element.
This can be particularly useful to set the fringe field integral to zero on one side only, e.g. when slicing a dipole.

Examples:

// rectangular horizontal dipole deflecting to the right
BR: RBEND, L=5.5, ANGLE=+0.001;    

// sector vertical dipole deflecting downwards
BD: SBEND, L=5.5, ANGLE=+0.001, TILT=pi/2; 

// sector horiziontal dipole deflecting to the left
BL: SBEND, L=5.5, ANGLE=+0.001, TILT=pi;   

// rectangular vertical dipole deflecting upwards
BU: RBEND, L=5.5, ANGLE=+0.001, TILT=-pi/2;