COD Amplification Factor

 

Amplification Factor

 

Here Ax, y is the amplification factor for horizontal (x) and the vertical (y) plane, with the betatron tune values Qx,y normalised to bo the beta function at observation point, bi is the beta function at location of the ith  quadrupole; k is strength of a quadrupole of length l. The normalized amplification factors are 15.22, 8.89 for all quadrupoles in horizontal and vertical plane respectively and 1.03, 0.635 for dipole magnets in the respective planes.

 

Quadrupoles more sensitive to misalignment errors:

 

Old Octant   è QD, QF, QK1, Q5NW, Q7N, Q0B, Q6N2, Q1NW, Q5N ….

New Octant è QB4, QB3, QA3, QB2, QB4, QA2, QDLU ….

 

 

The different amplification factors can be considered to estimate the setting of power supply errors. These settings can be of static or dynamic. Herewith some calculations are carried out with different assumptions for power supply settings and residual orbits.

 

Horizontal and vertical dynamic rms orbits as a function of residual orbits and quadrupole strength setting errors in quadrupoles, sextupoles and dipole magnets.

 

Horizontal and vertical dynamic orbits (with average beta functions) at BPMs as a function of residual orbits and quadrupole strength setting errors in quadrupoles, sextupoles and dipole magnets.

 

Horizontal and vertical static orbits at BPMs as a function of misalignment and quadrupole strength setting errors in quadrupoles, sextupoles and dipole magnets.

 

Vertical spurious dispersion at BPMs as a function of misalignment and quadrupole strength setting errors in quadrupoles, sextupoles.

 

 

Vertical spurious dispersion at BPMs as a function of misalignment and quadrupole strength setting errors in quadrupoles, sextupoles.

 

Horizontal and vertical dynamic orbits (at various beta functions in insertion section) at BPMs as a function of residual orbits and quadrupole strength setting errors in quadrupoles, sextupoles and dipole magnets.

 

Beta beating and betatron tune variation as a function of static and dynamic quadrupole strength variation:

 

There are two kinds of dipole magnets in PETRA III, the CB dipole magnets (196 in numbers) in the old octant and CB1 dipole magnets (18 in numbers) in the new octant. These magnets are connected in series with two power supplies. Below the orbits errors are shown due to dipole angle setting errors for CB dipoles, while the total bending angle are fixed with 2p.

 

 

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