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
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.
PHASE_NOISE_GROUP		long	0	Group number for phase noise.

A simple traveling or standing wave deflecting RF cavity.

Parameter Name	Units	Type	Default	Description
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

$$B = B_0 \hat{y} \cos \omega t$$ (61)

The corresponding electric field is obtained from Faraday's law (MKS units)

$$\left(\nabla \times \vec{E}\right)_y = - \frac{\partial \vec{B}}{\partial y}.$$ (62)

Assuming $E_x = E_y = 0$, we have

$$E_z = B_0 \omega x \sin \omega t.$$ (63)

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

$$\Delta p_x = \frac{q B_0 \Delta L}{m c} \cos \omega t$$ (64)

$$\Delta p_y = 0$$ (65)

$$\Delta p_z = \frac{q B_0 \omega x \Delta L}{m c^2} \sin\omega t$$ (66)

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

$$\Delta p_x = \frac{q V}{m c^2} \cos \omega t$$ (67)

$$\Delta p_y = 0$$ (68)

$$\Delta p_z = \frac{q V}{m c^2} k x \sin\omega t,$$ (69)

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.