10.63 MODRF—A first-order matrix RF cavity with exact phase dependence, plus optional amplitude and phase modulation.

A first-order matrix RF cavity with exact phase dependence, plus optional amplitude and phase modulation.
Parallel capable? : yes
GPU capable? : no
Back-tracking capable? : no






Parameter Name UnitsType Default

Description






L M double 0.0

length






VOLT V double 0.0

nominal voltage






PHASE DEGdouble 0.0

nominal phase






FREQ Hz double 500000000

nominal frequency






Q double 0.0

cavity Q






PHASE_REFERENCE long 0

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






AMMAG double 0.0

magnitude of amplitude modulation (fraction value)






AMPHASE DEGdouble 0.0

phase of amplitude modulation






AMFREQ Hz double 0.0

frequency of amplitude modulation






AMDECAY 1∕s double 0.0

exponential decay rate of amplitude modulation






PMMAG DEGdouble 0.0

magnitude of phase modulation






PMPHASE DEGdouble 0.0

phase of phase modulation






PMFREQ Hz double 0.0

frequency of phase modulation






PMDECAY 1∕s double 0.0

exponential decay rate of phase modulation






FIDUCIAL STRINGNULL

mode for determining fiducial arrival time (light, tmean, first, pmaximum)






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 is very similar to the RFCA element, except that the amplitude and phase of the cavity can be modulated.

The phase convention is as follows, assuming a positive rf voltage: PHASE=90 is the crest for acceleration. PHASE=180 is the stable phase for a storage ring above transition without energy losses.

The element works by first computing the fidicial arrival time t. Using this, the effective voltage is computed using the amplitude modulation parameters, according to

                                       
Ve = V0(1 + Aam sin (ωam t+ ϕam )exp(- αamt))
(90)

where V 0 is the nominal cavity voltage VOLT, Aam is AMMAG, ωam is the angular frequency corresponding to AMFREQ, ϕam is the amplitude modulation phase corresponding to AMPHASE (converted from degrees to radians), and αam is AMDECAY.

The phase of the phase modulation is computed using

ϕpm = ωpm t+ Δ ϕpm,
(91)

where ωpm is the angular frequency corresponding to PMFREQ and Δϕpm is the phase offset corresponding to PMPHASE (converted from degrees to radians). The rf phase for the centroid is then computed using

ϕ = ω0t+  ϕ0 + Φm sin(ϕpm )exp(- αpm t),
(92)

where ω0 is the nominal rf angular frequency (corresponding to FREQ), ϕ0 corresponds to PHASE (converted to radians), Φm corresponds to PMMAG (converted to radians), and αpm corresponds to PMDECAY.

The effective instantaneous rf angular frequency is

ω = ω0 + ωpmΦm  cosϕpm.
(93)

Using all of the above, the voltage seen by a particle arriving at time t is then

V  = Vesin(ω(t- t)+ ϕ).
(94)

MONI