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Evolution of an off-axis probe beam in EMMA. Shinji Machida ASTeC/STFC/RAL 29 April, 2008 http://www.astec.ac.uk/intbeams/users /machida/doc/nufact/ffag/machida20080429.pdf & ppt. Problem to be discussed (1) chromaticity. Nonscaling FFAG has finite chromaticity.

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Evolution of an off-axis probe beam in EMMA

Shinji Machida

ASTeC/STFC/RAL

29 April, 2008

http://www.astec.ac.uk/intbeams/users

/machida/doc/nufact/ffag/machida20080429.pdf & ppt

Problem to be discussed (1)chromaticity

• Nonscaling FFAG has finite chromaticity.

• There is no synchrotron oscillations.

• Phase advance depends on momentum and its difference will be accumulated.

• From the figure above, average chromaticity is roughly 10.

• Take two particles with momentum difference of 1%, phase difference (/2) after 10 turns becomes 1.

Problem to be discussed (2)what does that means?

• As long as a beam is injected on-axis, the different phase advance is almost invisible.

• Once a beam is injected off-axis, smearing in phase space should appear.

• Phase difference of 2 after 10 turns means that a probe beam will be spread out completely in azimuthal direction.

y’

y’

dp>0

on-axis

off-axis

dp=0

dp<0

y

y

Simulation results (1)momentum spread

• Use the following parameters

• a=1/6, b=1/4

• Gaussian with a cut at 2 sigma

• Acceleration with 10 turns

Figure shows dp/p of a few % during acceleration.

black: on-axis

red: off-axis in vertical with 1  mm rad (normalized)

Simulation results (2)phase space evolution (z,pz)

• A beam is initially displaced in vertical direction with 1  mm rad.

• In 3 turns, a probe beam becomes a ring.

• Chromaticity is large at low momentum.

Simulation results (3)configuration space evolution (s-longitudinal,z-vertical)

• A beam is initially displaced in vertical direction with 1  mm rad.

• Correlation among longitudinal position, (momentum,) and vertical position is manifest.

Simulation results (4)summary

• A probe beam injected off-axis quickly smears out and becomes a ring with a radius of the off-set amplitude.

• This is a process which can not be restored at extraction.

• With a limited aperture only for a probe beam emittance, diagnostic line after extraction just sees a fraction of a probe beam.

• We should design diagnostic line either

• for only on-axis beam with tomography measurement, or

• for off-axis large beam as well but give up tomography if it is hard to install.

• We may not have to scan the whole phase space at injection. As long as the amplitude ( m rad) of the off-set is the same, probe beams end up with the same ring in phase space.

• However, with machine errors, it is in fact difficult to know the amplitude at injection. It is useful to have some flexibilities to scan phase space.

• We also need to show that a probe beam becomes a ring in the fastest acceleration case.