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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 Cartesian reference system.

SBEND

is a sector bending magnet. Its pole faces meet at the centre of curvature of the curved reference system.

They are defined by the commands:

SBEND,TYPE=string,APERTURE=real-vector,L=real,ANGLE=real,
      K0=real,K1=real,K2=real,K3=real,K0s=real,K1S=real,K2S=real,K3S=real
      E1=real,E2=real,H1=real,H2=real,HGAP=real,FINT=real;
RBEND,TYPE=string,APERTURE=real-vector,L=real,ANGLE=real,
      K0=real,K1=real,K2=real,K3=real,K0S=real,K1S=real,K2S=real,K3S=real,
      E1=real,E2=real,H1=real,H2=real,HGAP=real,FINT=real;

For both types, the following attributes are permitted:

L

The length of the magnet (default: 0 m). For a rectangular magnet the length is measured along a straight line, while for a sector magnet it is the arc length of the reference orbit. A thin dipole is described with length zero. In this case all fields are the integrated fields.

ANGLE

The geometric bend angle (default: 0 rad). It is this attribute only which determines the geometry of the magnet. A positive bend angle bends the reference axis to the right, i.e. towards negative $x$ values.

K0

The normal dipole component $K_0=\frac{1}{B \rho}B_y$. If this value is not given, it is taken as ANGLE/L. A positive value bends positive particles to the right (towards negative $x$).

K0S

The skew dipole component $K_{0s}=\frac{1}{B \rho}B_x$. The default is $0 \mathrm{m}^{-2}$. The component is positive for a bend up.

K1

The normal quadrupole component $K_1=\frac{1}{B \rho}\frac{\partial B_y}{\partial x}$. The default is $0 \mathrm{m}^{-2}$. The component is positive, if $B_y$ is positive on the positive $x$-axis. This implies horizontal focusing of positively charged particles which travel in positive $s$ direction.

K1S

The skew quadrupole component $K_{1s}=\frac{1}{B \rho}\frac{\partial B_x}{\partial x}$. The default is $0 \mathrm{m}^{-2}$. The component is negative, if $B_x$ is positive on the positive $x$-axis.

K2

The normal sextupole component $K_2=\frac{1}{B \rho}\frac{\partial^2 B_y}{\partial x^2}$. The default is $0 \mathrm{m}^{-3}$. The component is positive, if $B_y$ is positive on the positive $x$-axis.

K2S

The skew sextupole component $K_{2s}=\frac{1}{B \rho}\frac{\partial^2 B_x}{\partial x^2}$. The default is $0 \mathrm{m}^{-3}$. The component is negative, if $B_x$ is positive on the positive $x$-axis.

K3

The normal sextupole component $K_3=\frac{1}{B \rho}\frac{\partial^3 B_y}{\partial x^3}$. The default is $0 \mathrm{m}^{-4}$. The component is positive, if $B_y$ is positive on the positive $x$-axis.

K3S

The skew sextupole component $K_{3s}=\frac{1}{B \rho}\frac{\partial^3 B_x}{\partial x^3}$. The default is $0 \mathrm{m}^{-4}$. The component is negative, if $B_x$ is positive on the positive $x$-axis.

E1

The rotation angle for the entrance pole face (default: 0 rad).

E2

The rotation angle for the exit pole face (default: 0 rad).

H1

The curvature of the entrance pole face (default: $0 \mathrm{m}^{-1}$).

H2

The curvature of the exit pole face (default: $0~\mathrm{m}^{-1}$). 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.

Note trhat the following is misleading: the FINT and HGAP attributes are defined but their effects have not been implemented (JMJ 24/10/2001).

FINT

The field integral (default =0).

HGAP

The half gap of the magnet (default: 0 m).

The pole face rotation angles are referred to the magnet model for a RBEND and SBEND respectively. The quantities FINT and HGAP specify the finite extent of the fringe fields as defined in SLAC-75 as follows:

$$\mathtt{FINT} = \int_0^\infty{\frac{B_y(s) (B_0 - B_y(s))}{B_0^2 g}}ds,\qquad \mathtt{HGAP} = 2 g.$$

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:

Typical 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

A reasonable average value for FINT is 0.5. All thes dipole examples have the same bend angle:

BR:RBEND,L=5.5,ANGLE=+0.001;       // Deflection to the right
BR:RBEND,L=5.5,K0=+0.001/5.5;      // Deflection to the right
                                   // This magnet has a straight reference
BL:SBEND,L=5.5,ANGLE=-0.001;       // Deflection to the left
BL:SBEND,L=5.5,K0=-0.001/5.5;      // Deflection to the left
                                   // This magnet has a straight reference

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