COD 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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