Tracks through a TM110-mode (deflecting) rf cavity with all magnetic and electric field components. NOT
RECOMMENDED—See below.
Parallel capable? : yes
GPU capable? : no
Back-tracking capable? : no
| Parameter Name | Units | Type | Default | Description |
| 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 | peak deflecting voltage |
| PHASE_REFERENCE | long | 0 | phase reference number (to link with other time-dependent elements) |
|
| VOLTAGE_WAVEFORM | STRING | NULL | <filename>=<x>+<y> form specification of input file giving voltage waveform factor vs time |
|
| VOLTAGE_PERIODIC | short | 0 | If non-zero, voltage waveform is periodic with period given by time span. |
|
| ALIGN_WAVEFORMS | short | 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. |
|
| 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. |
|
| 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 |
|
NB: Although this element is correct insofar as it uses the fields for a pure TM110 mode, it is recommended that the RFDF element be used instead. In a real deflecting cavity with entrance and exit tubes, the deflecting mode is a hybrid TE/TM mode, in which the deflection has no dependence on the radial coordinate.
To derive the field expansion, we start with some results from Jackson[17], section 8.7. The longitudinal electric field for a TM mode is just
|
| (147) |
where p is an integer, d is the length of the cavity, and we use cylindrical coordinates (ρ,ϕ,z). The factor of -2i represents a choice of sign and phase convention. We are interested in the TM110 mode, so we set p = 0. In this case, we have
 | (148) |
and (using CGS units)
 | (149) |
For a cylindrical cavity, the function Ψ for the m = 1 aximuthal mode is
 | (150) |
where k = x11∕R, x11 is the first zero of J1(x), and R is the cavity radius. We don’t need to know the cavity radius, since k = ω∕c, where ω is the resonant frequency. By choosing cosϕ for the aximuthal dependence, we’ll get a magnetic field primarily in the vertical direction.
In MKS units, the magnetic field is
 | (151) |
Using mathematica, we expanded these expressions to sixth order in k * ρ. Here, we present only the expressions to second order. Taking the real parts only, we now have
can be computed easily 
The Lorentz force on an electron is F = -eEzẑ - ec
×
, giving
 | (162) |
Hence, for ωt = 0 and E0 > 0 we have Fx > 0. This explains our choice of sign and phase convention above. Indeed, owing to the factor of 2, we have a peak deflection of eE0L∕E, where L is the cavity length and E the beam energy. Thus, if V = E0L is specified in volts, and the beam energy expressed in electron volts, the deflection is simply the ratio of the two. As a result, we’ve chosen to parametrize the deflection strength simply by referring to the “deflecting voltage,” V .
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.
RFTMEZ0