Tracks through a TM110mode (deflecting) rf cavity with all magnetic and electric field components. NOT
RECOMMENDED—See below.
Parallel capable? : yes
GPU capable? : no
Backtracking 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 timedependent elements) 

VOLTAGE_WAVEFORM  STRING  NULL  <filename>=<x>+<y> form specification of input file giving voltage waveform factor vs time 

VOLTAGE_PERIODIC  short  0  If nonzero, voltage waveform is periodic with period given by time span. 

ALIGN_WAVEFORMS  short  0  If nonzero, 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 nonnegative, pass on which to start modeling cavity. 

END_PASS  long  1  If nonnegative, pass on which to end modeling cavity. 

GROUP  string  NULL  Optionally used to assign an element to a group, with a userdefined 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
 (137) 
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
 (138) 
and (using CGS units)
 (139) 
For a cylindrical cavity, the function Ψ for the m = 1 aximuthal mode is
 (140) 
where k = x_{11}∕R, x_{11} is the first zero of J_{1}(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
 (141) 
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
The Lorentz force on an electron is F = eE_{z}ẑ  ec ×, giving
 (152) 
Hence, for ωt = 0 and E_{0} > 0 we have F_{x} > 0. This explains our choice of sign and phase convention above. Indeed, owing to the factor of 2, we have a peak deflection of eE_{0}L∕E, where L is the cavity length and E the beam energy. Thus, if V = E_{0}L 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