10.98 SHRFDF—Simulation through space harmonics of zero length deflecting cavity.

Simulation through space harmonics of zero length deflecting cavity.
Parallel capable? : yes
GPU capable? : no
Back-tracking capable? : no






Parameter Name UnitsType Default

Description






FACTOR double1

A factor by which to multiply all components.






TILT RADdouble0.0

rotation about longitudinal axis






PERIOD_LENGTHM double0.0

cavity period length, or cell length






PERIOD_PHASE RADdouble0.0

cavity period phase advance, or so-called working mode






V0 V double0.0

effective voltage of space harmonic n=0






V1 V double0.0

effective voltage of space harmonic n=1






V2 V double0.0

effective voltage of space harmonic n=2






V3 V double0.0

effective voltage of space harmonic n=3






V4 V double0.0

effective voltage of space harmonic n=4






V5 V double0.0

effective voltage of space harmonic n=5






V6 V double0.0

effective voltage of space harmonic n=6






V7 V double0.0

effective voltage of space harmonic n=7






V8 V double0.0

effective voltage of space harmonic n=8






V9 V double0.0

effective voltage of space harmonic n=9






PHASE0 HZ double0.0

Phase of space harmonic n=0






PHASE1 HZ double0.0

Phase of space harmonic n=1






PHASE2 HZ double0.0

Phase of space harmonic n=2






PHASE3 HZ double0.0

Phase of space harmonic n=3






PHASE4 HZ double0.0

Phase of space harmonic n=4






PHASE5 HZ double0.0

Phase of space harmonic n=5






PHASE6 HZ double0.0

Phase of space harmonic n=6






PHASE7 HZ double0.0

Phase of space harmonic n=7






SHRFDF continued

Simulation through space harmonics of zero length deflecting cavity.






Parameter Name UnitsType Default

Description






PHASE8 HZ double0.0

Phase of space harmonic n=8






PHASE9 HZ double0.0

Phase of space harmonic n=9






PHASE_REFERENCE long 0

phase reference number (to link with other time-dependent elements)






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 element simulates an rf deflector with specified space harmonic parameters (voltage, phase). The thin kicks from the fundamental deflecting mode are the same as for the element RFDF. The thin kicks from the space harmonics (n 1) are [55]

            ∂(H--H0)-
ΔPx   =   -   ∂x
      =   ∑∞ - qV ⋅sin(k z + ϕ ) ⋅(1α  + 1-α3 ⋅(3x2 + y2))
          n=1    n      n     n    2 n   16 n
(156)

ΔPz   =   - ∂(H∂-zH0)-
          ∞∑
      =      - q Vn ⋅kn ⋅cos(knz + ϕn)⋅(12αn ⋅x + 116α3n ⋅(x2 + y2) ⋅x)
          n=1
(157)

The wave numbers kn and αn are listed below.

     φ  + 2πn
kn = -0-------
        d
(158)

α2n + k2n = k20
(159)

where kn is wave number of nth space harmonic, n an integer number, φ0 the phase advance per cavity period, d the cavity period length, αn the wave number in the radial direction, m wave number (per 2π) in the angular direction.

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