Correction of resonances driven by random errors
This presentation is the property of its rightful owner.
Sponsored Links
1 / 9

Correction of resonances driven by random errors PowerPoint PPT Presentation


  • 101 Views
  • Uploaded on
  • Presentation posted in: General

Correction of resonances driven by random errors. Previously, we successfully demonstrated that we can correct nonlinear resonance for high-intensity operation where space charge effects are important. All previous studies were done using lumped errors:

Download Presentation

Correction of resonances driven by random errors

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Correction of resonances driven by random errors

Correction of resonances driven by random errors

  • Previously, we successfully demonstrated that we can correct nonlinear resonance for high-intensity operation where space charge effects are important.

  • All previous studies were done using lumped errors:

  • Independent correction of sextupole and octupole resonances

  • Correction of skew resonance

  • Dynamic correction of several resonances which allows to reach low losses at high intensity.

    In June’03 we began to study resonance correction with resonances driven by random errors.


Lumped errors budget used in studies

Lumped errors budget used in studies

In resonance correction studies we assumed lumped b2=30 units and (b3,a3) = 60 units which corresponds to

  • 5 times stronger random sextupole errors than measured

  • 10 times stronger normal & skew octupole errors than measured

    With the present error budget coming just from arc dipoles and arc quadrupoles the dominant contribution comes from normal sextupole and normal octupole resonances – good correction.

    If the budget of skew octupole errors becomes factor of 5 stronger than the present - one will need skew octupole correctors.


Correction of sextupole resonances lumped errors w p 6 36 6 22 correction of 3qx 19 and 2qy qx 6

Correction of sextupole resonances (lumped errors):w.p. (6.36,6.22) - Correction of 3Qx=19 and 2Qy-Qx=6

N=0.6*10^14

blue – no errors

red – errors, no correction

green – errors, correction of 3Qx=19

% outside

Qy

Total emittance pi mm mrad

2Qy-Qx

3Qx

N=2*10^14

blue – no errors

grey – errors, no correction

green – errors, correction of 3Qx=19

pink – errors, simultaneous correction of 3Qx=19 and 2Qy-Qx=6 resonances

Qx


Correction of resonances driven by random errors

Correction of sextupole resonances (lumped errors):w.p. (6.4,6.3) - Correction of sum coupling resonance Qx+2Qy=19 and 3Qx=19 resonance

% outside

N=0.6*10^14

blue- no errors

red – errors, no correction

pink – errors, correction of Qx+2Qy=19

Total emittance pi mm mrad

N=2.0*10^14

blue- no errors

red- errors, no correction

green- errors, simultaneous corrections of

Qx+2Qy=19 and 3Qx=19 resonances

N=3.0*10^14

pink – errors, corrections of Qx+2Qy=19 and

3Qx=19 resonances

% outside


Correction of octupole resonance due to 10 units random b3 w p 6 4 6 3

Correction of octupole resonance due to 10 unitsrandom b3 (w.p. 6.4, 6.3)

We started by correcting octupole

resonance 4Qy=25 driven by random b3 of

10 units rms distributed over all magnets.

  • MAD lattices were constructed to have

    the same notation of magnets in both DYNA

    and UAL codes.

    2. Scripts to transfer errors from one code

    to another were written.

    3. Benchmarking tests were done to ensure

    that implementation is correct


Initial study

Initial study

  • Initial correction was not very good:

    At most reduction of factor of 2 in emittance growth was achieved.

    We then switched back to lumped errors and started detailed study of implementation of various multipoles in various elements (comparison of b3 in dipole vs. b3 in quadrupole, etc).

    No problems was found.

    It was then concluded that “not perfect” compensation is due the effect of other resonance bandwidth of which was big enough to play a role.

    We then switched to another w.p. to make sure that we have emittance growth only from a single resonance which we are correcting.


W p 6 36 6 22

w.p. (6.36,6.22)

3rd order resonances

excited by sextupole

errors

Random errors b2=5 units rms in all

magnets (dipoles and quads).

Total contribution is about factor of 5

bigger than expected based on measurements.

Correction of 3Qx=19 resonance.


Correction of b2 5 units rms

Correction of b2=5 units rms

Red- no correction

Green-correction


Remaining study

Remaining study

1. Perform Dynamic correction for all 3 major resonances

for this working points: 3Qx=19, 2Qx+2Qy=25 & 4Qx=25 driven by

random b2, b3 and a3.

2. Generate realistic loss models without correction based on available measured multipole:

  • As measured 2) factor of 2-5? Safety margin?

    3. Produce loss models with corresponding dynamics correction of major resonances for both w.p.


  • Login