Elements/MULT

MULT †

A magnet with multipoles. Note that the reference plane is defined so that the skew quadrupole component becomes zero. It can have a nonzero ANGLE to express a combined funtion bending magnet with multipoles. Note that the definition of the multipoles with nonzero ANGLE is very special The current version does not allow nonzero ANGLE inside a solenoid or with acceleration. Also the fringe field and emittance calculation are not installed properly for nonzero ANGLE.

AE1

The absolute face angle at the entrance. The effective face angle is E1 * ANGLE + AE1, and a positive angle at the entrance corresponds to a surface with dx/ds > 0.

AE2

The absolute face-angle at the exit to the bending angle. The effective face angle is E2 * ANGLE + AE2, and a positive angle at the exit corresponds to a surface with dx/ds < 0.

ANGLE

bending angle The bending angle. If positive, it bends the orbit in x-s plane toward negative-x-direction. ANGLE determines the geometry of the beam line, while K0 represents a dipole kick on top of the bending angle given by ANGLE, i.e., the total deflection of the beam is given of ANGLE + K0.

DISFRIN

If nonzero, the nonlinear maxwellian fringe is suppressed. The effects of DISFRIN and FRINGE are summarized as

                   DISFRIN=0                   DISFRIN<>0
             Nonlinear      Linear       Nonlinear     Linear
FRINGE=0    entr & exit      none          none         none
FRINGE=1       entr          entr          none         entr
FRINGE=2       exit          exit          none         exit
FRINGE=3    entr & exit   entr & exit      none      entr & exit

DISRAD: If nonzero, the synchrotron radiation in the particle-tracking is inhibited.
DPHI: elative phase offset. The stable synchrotron phase above the transition is near PHI = 0. The acceleration is given as
where ts is the equilibrium time determined by the valance between the acceleration and the radiation loss around the ring. DPHI is not taken into account to determine the design mementum p0(s).

E1: The ratio of the face-angle at the entrance to the bending angle. The effective face angle is E1 * ANGLE + AE1, and a positive angle at the entrance corresponds to a surface with dx/ds > 0. For example, a symmetrically-placed rectangular magnet has E1 = 0.5 and E2 = 0.5.

E2: The ratio of the face-angle at the exit to the bending angle. The effective face angle is E2 * ANGLE + AE2, and a positive angle at the exit corresponds to a surface with dx/ds < 0. For example, a symmetrically-placed rectangular magnet has E1 = 0.5 and E2 = 0.5.

F1,F2: F1 and F2 are parameters to characterize the slope of the field at the edges defined as:

with
where s0 is the location of the edge where the effective length is defined, and K1_0 is the nominal value of K1, given by the keyword K1. The effects only in the first ordef of K1 is taken into account.

FREQ: Rf frequency. If this keyword is nonzero, the keyword HARM is ignored. The acceleration is given by
where ts is the equilibrium time determined by the valance between the acceleration and the radiation loss around the ring. (CAVI only) The non-relativistic corrections
are automatically added to V20 and V02, respectively. The Lorentz factor is evaluated as inverse of average of at the entrance and the exit.

FRINGE

The effects of the linear fringe (characterized by F1 and F2), and the nonlinear Mexwellian fringe are controled as:

                   DISFRIN=0                   DISFRIN<>0
             Nonlinear      Linear       Nonlinear     Linear
FRINGE=0    entr & exit      none          none         none
FRINGE=1       entr          entr          none         entr
FRINGE=2       exit          exit          none         exit
FRINGE=3    entr & exit   entr & exit      none      entr & exit

HARM: A harmonic number. This is valid only when FREQ is zero.

Kn (n=0-21): The normal 2(n+1)-pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means horizontal focusing.

L: Effective length.

misalignments

Misalignments of a MULT element are expressed by the keywords DX, DY, DZ, CHI1, CHI2, and ROTATE(=CHI3). They specify all misalignments of a rigid body, At the entrans of MULT, the coordinates of a particle are transformed as

\begin{pmatrix}

x \\ y \\ ds

\end{pmatrix}_{ 1}

\begin{pmatrix}

c3 & -s3  & 0 \\
s3 &  c3  & 0 \\
0  &  0   & 1

\end{pmatrix} \begin{pmatrix}

1  &  0   & 0   \\
0  & c2   & -s2 \\
0  & s2   & c2

\end{pmatrix} \begin{pmatrix}

c1 & 0   & -s1 \\
0  & 1   & 0   \\
s1 & 0   & c1

\end{pmatrix} \begin{pmatrix}

x-DX \\
y-DY \\
 -DZ

\end{pmatrix} }} , where c1 and s1 are Cos[CHI1] and Sin[CHI1], etc. The inverse is applied at the exit. Those misalignments are also valid within a solenoid. Other straight elements such as QUAD or THIN do not and will not have these full misalignment specifications, because they can be substituted by MULT. The geometry of the design orbit are determined by the saved values of CHI1, CHI2, and DZ, while the current values are used for DX, DY, and ROTATE.

multipole_with_nonzero_ANGLE: The multipoles in MULT with nonzero ANGLE are defined as

with
where . Actually the summation is truncated at n + k <= 21 in the current version. While this definition converges to the regular one for multipoles when ANGLE -> 0, K0 and K1 of MUILT are different from those of BEND.

PHI: Relative phase offset. The stable synchrotron phase above the transition is near PHI = 0. The acceleration is given as
where ts is the equilibrium time determined by the valance between the acceleration and the radiation loss around the ring.

RADIUS: Radius of the vacuum chamber. Effective when SPAC is ON.

SKn (n=0-21): The skew 2(n+1)-pole magnetic field component (times the length L).
where L is the length of the component. Positive sign means a horizontally focusing magnet rotated around z-axis by -90/(n+1) degree, i.e., ROTATE = (90/(n+1)) DEG.

VOLT: Accelerating peak voltage in Volt. The acceleration is given by
where ts is the equilibrium time determined by the valance between the acceleration and the radiation loss around the ring.

MULT †

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