Hi,
I'm using an RFDF to streak bunches.
The zero-cross phase of RFDF i obtain by setting phase=90, whereas for zero-cross phase of RFCW i set phase = 0. Is this difference intentional?
Also, is the definition of voltage the same as RFCW. With RFCW if i have a cavity 1m long and run on crest, then my bunch gains energy by VOLTAGE eV. Does this hold for the deflecting mode - i.e. if I use the same RF frequency but this time in deflecting mode, will the "peak field" in the cavity have the same value as for the accelerating mode?
Pete
RF deflecting cavity
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michael_borland
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Re: RF deflecting cavity
Pete,
Sorry for the confusion. In both cases, we have Ez proportional to sin(phase). In the case of RFCA and RFCW, this means the accelerating field (which is what you care about) peaks for phase=90 deg. For the deflecting cavities, the deflection comes from the magnetic field, so it is shifted by 90 degrees.
For RFDF, the model is similar to that used in Cornacchia and Emma, PRSTAB 084001 (2002). The change in slope is e*V/E*cos(phase). There is also a small longitudinal field. Strictly speaking, the transverse deflection of the particles should not change the overall momentum, since it is nominally accomplished by a magnetic field. However, in a real cavity the mode is not really a pure TM mode but has TE components, so the right calculation is unclear. As a result, I just treat the deflection as if it was done by an electric field. The error is second order.
For RFTM110, the dynamics is done correctly, but the cavity model is a pure TM110 mode, which doesn't exist in a cavity with beam pipes. The result is that the deflection varies with radial position, which is not true in a real deflecting cavity.
--Michael
Sorry for the confusion. In both cases, we have Ez proportional to sin(phase). In the case of RFCA and RFCW, this means the accelerating field (which is what you care about) peaks for phase=90 deg. For the deflecting cavities, the deflection comes from the magnetic field, so it is shifted by 90 degrees.
For RFDF, the model is similar to that used in Cornacchia and Emma, PRSTAB 084001 (2002). The change in slope is e*V/E*cos(phase). There is also a small longitudinal field. Strictly speaking, the transverse deflection of the particles should not change the overall momentum, since it is nominally accomplished by a magnetic field. However, in a real cavity the mode is not really a pure TM mode but has TE components, so the right calculation is unclear. As a result, I just treat the deflection as if it was done by an electric field. The error is second order.
For RFTM110, the dynamics is done correctly, but the cavity model is a pure TM110 mode, which doesn't exist in a cavity with beam pipes. The result is that the deflection varies with radial position, which is not true in a real deflecting cavity.
--Michael