10.84 RFDF—A simple traveling or standing wave deflecting RF cavity.

A simple traveling or standing wave deflecting RF cavity.
Parallel capable? : yes
GPU capable? : no
Back-tracking capable? : no






Parameter Name UnitsType Default

Description






L M double 0.0

length






PHASE DEGdouble 0.0

phase






TILT RADdouble 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*(xˆ
2  -yˆ
2
)/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 short 0

If nonzero, then cavity is standing wave.






VOLTAGE_WAVEFORM STRINGNULL

<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 DEGdouble 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 DEGdouble 0.0

Rms noise level for phase linked to group.






VOLTAGE_NOISE_GROUP long 0

Group number for voltage noise.






RFDF continued

A simple traveling or standing wave deflecting RF cavity.






Parameter Name UnitsType 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 short 0

If non-zero, calculations involving matrices assume this element is a drift space.






DX M double0.0

misalignment






DY M double0.0

misalignment






DZ M double0.0

misalignment






MAGNETIC_DEFLECTION short 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 = B0 ˆycosωt
(128)

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

(      )      ( ∂B⃗)
 ∇  × ⃗E   = -   ---   .
         y       ∂t  y
(129)

Assuming Ex = Ey = 0, we have

Ez =  B0ωx sin ωt.
(130)

The change in momenta (in units of mc) in passing through a slice of length ΔL is

Δp    =   qB0ΔL--cosωt                               (131)
   x        mc
Δpy   =   0                                          (132)
          qB0ωx ΔL
 Δpz  =   -----2----sin ωt                            (133)
             mc

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

          qV
Δpx  =   ---2 cos ωt                               (134)
         mc
Δpy  =   0                                         (135)
         -qV-
Δpz  =   mc2 kx sin ωt,                             (136)
where k = ω∕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.

RFMODE