Label: RFMULTIPOLE, VOLT=real, LAG=real,
HARMON=integer, FREQ=real,
LRAD=real, TILT=real,
KNL:={k0nl, k1nl, k2nl, ... }, ! Normal coefficients
KSL:={k0sl, k1sl, k2sl, ... }, ! Skew coefficients
PNL:={p0n, p1n, p2n, ... }, ! Normal phases [2pi]
PSL:={p0s, p1s, p2s, ... }; ! Skew phases [2pi]
A RFMULTIPOLE is a thin-lens element which
exhibits the properties of an RF-cavity and of a magnet of
arbitrary order oscillating the a certain frequency:
- L: The length of the rfmultipole (DEFAULT: 0 m)
- LAG: The phase lag [2pi] (DEFAULT: 0)
- FREQ: The frequency [MHz] (no DEFAULT). Note that if the RF
frequency is not given, it is computed from the harmonic
number and the revolution frequency f0 as before. However, for
accelerating structures this makes no sense, and the frequency
is mandatory.
- HARMON: The harmonic number h (no DEFAULT). Only if the
frequency is not given.
- LRAD: A fictitious length, which was originally just used to
compute synchrotron radiation effects. A non-zero LRAD in
conjunction with the OPTION thin_foc set to a true logical
value takes into account of the weak focussing of bending
magnets.
- TILT: The roll angle about the longitudinal axis (default: 0
rad). A positive angle represents a clockwise rotation of the
multipole element.
Please note that contrary to MAD8 one has to specify the
desired TILT angle, otherwise it is taken as 0 rad. We
believe that the MAD8 concept of having individual TILT
values for each component and on top with default values
led to considerable confusion and allowed for excessive
and unphysical freedom. Instead, in MAD-X the KNL/KSL
components can be considered as the normal or skew
multipole components of the magnet on the bench, while the
TILT attribute can be considered as an tilt alignment
error in the machine.
- KNL: The normal rfmultipole coefficients from order zero to
the maximum; the parameters are positional, therefore zeros
must be filled in for components that do not exist. Example of
a thin-lens sextupole: ms:rfmultipole, knl:={0, 0, k2l};
- KSL: The skew rfmultipole coefficients from order zero to
the maximum; the parameters are positional, therefore zeros
must be filled in for components that do not exist. Example of
a thin-lens skew octupole:
ms: rfmultipole, ksl:={0, 0, 0, k3sl};
Both KNL and KSL may be specified for the same
multipole.
- VOLT: The peak RF voltage (DEFAULT: 0 MV). The effect of the
cavity is
- delta(E) = VOLT * sin(2 pi * (LAG - HARMON * f0 t)).
- PNL: The phase for each normal rfmultipole coefficients from
order zero to the maximum; the parameters are positional,
therefore zeros must be filled in for components that do not
exist.
- PSL: The phase for each skew rfmultipole coefficients from
order zero to the maximum; the parameters are positional,
therefore zeros must be filled in for components that do not
exist.
A rfmultipole requires the particle energy (ENERGY) and the
particle charge (CHARGE) to be set by a BEAM command before any
calculations are performed. Notice that, contrary to the regular
multipole where the dipole component has no effect on the
reference orbit, an RF-Multipole that includes a dipole component
bends also the reference orbit.