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RFDF

A simple traveling or standing wave deflecting RF cavity.
Parallel capable? : yes
Parameter Name Units Type Default Description
L $M$ double 0.0 length
PHASE $DEG$ double 0.0 phase
TILT $RAD$ double 0.0 rotation about longitudinal axis
FREQUENCY $HZ$ double 2856000000 frequency
VOLTAGE $V$ double 0.0 voltage
FSE   double 0.0 Fractional Strength Error
B2   double 0.0 Normalized sextupole strength, kick=(1+b2*(x2-y2)/2)...
TIME_OFFSET $S$ double 0.0 time offset (adds to phase)
N_KICKS   long 0 number of kicks (0=autoscale)
PHASE_REFERENCE   long 0 phase reference number (to link with other time-dependent elements)
STANDING_WAVE   long 0 If nonzero, then cavity is standing wave.
VOLTAGE_WAVEFORM   STRING NULL $<$filename$>$=$<$x$>$+$<$y$>$ form specification of input file giving voltage waveform factor vs time
VOLTAGE_PERIODIC   long 0 If non-zero, voltage waveform is periodic with period given by time span.
ALIGN_WAVEFORMS   long 0 If non-zero, waveforms' t=0 is aligned with first bunch arrival time.
VOLTAGE_NOISE   double 0.0 Rms fractional noise level for voltage.
PHASE_NOISE $DEG$ double 0.0 Rms noise level for phase.
GROUP_VOLTAGE_NOISE   double 0.0 Rms fractional noise level for voltage linked to group.
GROUP_PHASE_NOISE $DEG$ double 0.0 Rms noise level for phase linked to group.
VOLTAGE_NOISE_GROUP   long 0 Group number for voltage noise.

A simple traveling or standing wave deflecting RF cavity.
Parameter Name Units Type Default Description
PHASE_NOISE_GROUP   long 0 Group number for phase noise.
START_PASS   long -1 If non-negative, pass on which to start modeling cavity.
END_PASS   long -1 If non-negative, pass on which to end modeling cavity.
DRIFT_MATRIX   long 0 If non-zero, calculations involving matrices assume this element is a drift space.
DX $M$ double 0.0 misalignment
DY $M$ double 0.0 misalignment
DZ $M$ double 0.0 misalignment
MAGNETIC_DEFLECTION   long 0 If non-zero, deflection is assumed to be performed by a magnetic field, rather than electric field (default).
GROUP   string NULL Optionally used to assign an element to a group, with a user-defined name. Group names will appear in the parameter output file in the column ElementGroup





This cavity provides a transverse deflection that is constant as a function of transverse coordinates. It is probably the best model for a real cavity, because real cavities contain a mixture of TM- and TE-like modes that result in a uniform deflection.

For simplicity of use, the deflection is specified as a voltage, even though it originates in a magnetic field. The magnetic field is

\begin{displaymath}
B = B_0 \hat{y} \cos \omega t
\end{displaymath} (68)

The corresponding electric field is obtained from Faraday's law (MKS units)
\begin{displaymath}
\left(\nabla \times \vec{E}\right)_y = - \frac{\partial \vec{B}}{\partial y}.
\end{displaymath} (69)

Assuming $E_x = E_y = 0$, we have
\begin{displaymath}
E_z = B_0 \omega x \sin \omega t.
\end{displaymath} (70)

The change in momenta (in units of $m c$) in passing through a slice of length $\Delta L$ is

$\displaystyle \Delta p_x$ $\textstyle =$ $\displaystyle \frac{q B_0 \Delta L}{m c} \cos \omega t$ (71)
$\displaystyle \Delta p_y$ $\textstyle =$ $\displaystyle 0$ (72)
$\displaystyle \Delta p_z$ $\textstyle =$ $\displaystyle \frac{q B_0 \omega x \Delta L}{m c^2} \sin\omega t$ (73)

If we want to think in terms of a deflecting voltage, we can re-write this as

$\displaystyle \Delta p_x$ $\textstyle =$ $\displaystyle \frac{q V}{m c^2} \cos \omega t$ (74)
$\displaystyle \Delta p_y$ $\textstyle =$ $\displaystyle 0$ (75)
$\displaystyle \Delta p_z$ $\textstyle =$ $\displaystyle \frac{q V}{m c^2} k x \sin\omega t,$ (76)

where $k = \omega/c$.





Explanation of $<$filename$>$=$<$x$>$+$<$y$>$ format: Several elements in elegant make use of data from external files to provide input waveforms. The external files are SDDS files, which may have many columns. In order to provide a convenient way to specify both the filename and the columns to use, we frequently employ $<$filename$>$=$<$x$>$+$<$y$>$ format for the parameter value. For example, if the parameter value is waveform.sdds=t+A, then it means that columns t and A will be taken from file waveform.sdds. The first column is always the independent variable (e.g., time, position, or frequency), while the second column is the dependent quantity.


next up previous
Next: RFMODE Up: Element Dictionary Previous: RFCW
Robert Soliday 2014-06-26