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Orbit Distortion calculated by tracking code (PTC). David Kelliher ASTEC/STFC/RAL 4 th November, 2007. Contents. PTC model of EMMA Orbit distortion calculated by PTC Correcting closed orbit distortion Correcting accelerated orbit distortion Local orbit correction. PTC model of EMMA.

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Orbit distortion calculated by tracking code ptc

Orbit Distortion calculated by tracking code (PTC)

David Kelliher

ASTEC/STFC/RAL

4th November, 2007


Contents
Contents

  • PTC model of EMMA

  • Orbit distortion calculated by PTC

  • Correcting closed orbit distortion

  • Correcting accelerated orbit distortion

  • Local orbit correction



P olymorphic t racking c ode
Polymorphic Tracking Code

  • PTC is a kick code, allowing symplectic integration through all accelerator elements

  • Inherently based on a map formalism

  • New subroutines were written to simulate acceleration in EMMA.

  • PTC_TWISS parameters calculated in the Ripken style.






Phase space with vertical misalignments
Phase space with vertical misalignments

Vertical alignment error standard deviation = 50 microns

120V/cavity assumed



Vertical distortion during acceleration
Vertical Distortion during acceleration

Cavities

rms = 2.4 mm

All elements

rms = 3.2 mm




Conclusions
Conclusions

  • PTC has been set up to model EMMA. The characteristic serpentine acceleration curve in longitudinal phase space is produced.

  • Accelerated orbit distortion is not noticeably influenced by integer tune resonances.

  • Orbit is distorted by quasi-random kicks instead.

  • Corrector strengths which reduce closed orbit distortion do not reduce accelerated orbit distortion, i.e. corrector magnets are not useful in reducing orbit distortion in non-scaling FFAGs with acceleration completed in few turns.

  • Amplification factor (rms of distortion/  misalignment) is of order 100.

  • To reduce orbit distortion (both vertical and horizontal), local correction of magnets is necessary.




Find optimal vertical corrector strengths to reduce closed orbit distortionLeast-Squares Minimisation method

For consistency, would like to replace

MADX TWISS with PTC_TWISS

Input Error (BPM data)

Vertical magnet misalignments

Apply a set of vertical corrector strengths from within some range

2 > target value

Calculate TWISS orbit at select energies

Calculate penalty function 2 - Given by the sum of vertical orbit distortion squared over select energies.

Output vertical orbit distortion at each energy

2 < target value

Use vertical corrector strengths over entire energy range



Correction of closed orbit in range 10 11 2 mev ptc twiss using corrector settings from madx
Correction of closed orbit in range 10-11.2 MeV orbit distortion(PTC_TWISS, using corrector settings from MADX)


Correction of accelerated orbit in range 10 11 2 mev ptc twiss using corrector settings from madx
Correction of accelerated orbit in range 10-11.2 MeV orbit distortion(PTC_TWISS, using corrector settings from MADX)



Correction of closed orbit in full energy range ptc twiss using corrector settings from madx
Correction of closed orbit in full energy range orbit distortion(PTC_TWISS, using corrector settings from MADX)


Correction of accelerated orbit over full energy range ptc twiss using corrector settings from madx
Correction of accelerated orbit over full energy range orbit distortion(PTC_TWISS, using corrector settings from MADX)

rms of vertical orbit distortion in both cases is 1.8 mm


Failure of harmonic correction
Failure of Harmonic Correction orbit distortion

  • Effect of kicker varies since the phase advance between the kicker and any point in the lattice changes as the momentum changes. Therefore, conventional harmonic correction of the error source with kickers is not possible in a nonscaling FFAG.



Introduction
Introduction orbit distortion

  • Already showed that corrector strengths which reduce closed orbit distortion do not in general significantly reduce “accelerated orbit” distortion.

  • This presentation: vary corrector strengths to see if accelerated orbit distortion can be reduced.

  • Only vertical orbit distortion due to magnet misalignments considered.


Method
Method orbit distortion

  • Vary first corrector strength, run PTC, calculate the orbit distortion rms over the full energy range, find minimum

  • Improve result by varying corrector strength about this minimum.

  • Repeat for each corrector and find the best one.

  • Keeping this optimal corrector, repeat the exercise for a second corrector.

  • Continue until 16 correctors used.


Scan for minimum orbit distortion
Scan for minimum orbit distortion orbit distortion

uncorrected orbit rms = 2.7mm


Adding more correctors
Adding more correctors orbit distortion


Correction with 1 kicker
Correction with 1 kicker orbit distortion

Vertical orbit distortion rms reduced from 2.67mm to 0.64mm


Dependence of distortion on initial conditions i
Dependence of distortion on initial conditions I orbit distortion

  • In general, the closed orbit co-ordinates at the injection momentum do not give optimal initial conditions. Starting the tracking at a momentum where the integer tune is close to integer results in relatively high orbit distortion.


Dependence of distortion on initial conditions ii
Dependence of distortion on initial conditions II orbit distortion

  • In general, the closed orbit co-ordinates at the injection momentum do not give optimal initial conditions. A scan over the initial phase space (x,x’,y,y’) allows the distortion to be reduced.


Optimise initial y y
Optimise initial (y,y’) orbit distortion

Vertical orbit distortion rms reduced from 2.67mm to 0.63mm


Conclusions1
Conclusions orbit distortion

  • Important to first establish initial conditions in (x,x’,y,y’) that best reduce the orbit distortion. In general this (x,x’,y,y’) will not be the same as the closed orbit at the injection energy.


Optimising the accelerated orbit distortion
Optimising the accelerated orbit distortion orbit distortion

  • For a given set of magnet misalignments, is it possible to calculate the optimal accelerated orbit – i.e. the orbit with the minimum orbit distortion rms over the momentum range?

  • How many vertical corrector magnets would be needed to kick the beam onto this optimal orbit? Introducing correctors magnets will change the optimal orbit itself.



Infer magnet misalignments from kicker strengths see my presentation may 14 th
Infer magnet misalignments from kicker strengths orbit distortion(see my presentation - May 14th)

  • Misalignment of quadrupole j can be expressed as a kick j

  • Orbit position measured at ideal BPM i is the sum of these kicks.

  • MADX CORRECT module finds the set of k that best restores target orbit.

  • Kickers are placed in the middle of divided magnets. Assume k j.


Calculate vertical misalignments at 10 mev no source of error other than vertical misalignments
Calculate vertical misalignments at 10 MeV orbit distortion(no source of error other than vertical misalignments)

rms error = 1.5 microns


Accuracy of vertical misalignment prediction (10-11 MeV) orbit distortion(no source of error other than vertical misalignments)


Future work
Future Work orbit distortion

  • Work with Etienne Forest to improve PTC modelling of EMMA (after this workshop)

  • Investigate if local correction of magnet misalignments is feasible.


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