Evolution of an off axis probe beam in emma
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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

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Evolution of an off axis probe beam in emma

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

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

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

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

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

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

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.


Impacts on emma design

Impacts on EMMA design

  • 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.


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