Booster Corrector Coordinate System

1
Booster Corrector Coordinate System

2
General

• Requirement
• All corrector packages will be wired with the
  same polarity, and this is the polarity that the
  MTF will use
• Conventions
• Generic convention (a la Syphers and Edwards)
• For normal elements, at y0, positive currents
  give positive coefficients for
• Skew elements rotated half a pole
  counterclockwise from normal elements (as seen
  from beam)
• Determined by beam behavior
• Traditionally by effect in horizontal plane

3
Convention

• A positive current for each elements will do
  the following
• Follow traditional convention between normal and
  skew elements
• Rotate skew quadrupole 45 degrees
  counterclockwise
• Rotate skew sextupole 30 degrees counterclockwise

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Dipoles (beam view)
Horizontal dipole
Vertical dipole
B
B

• Bend outward (x)
• Same as now (2006)
• Same as generic

• Bend upward (y)
• Opposite now (2006)
• Opposite generic

• Normal dipole
• ByB1
• B1 is positive

• Skew dipole
• BxA1
• A1 is negative

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Normal Quads
By
Normal
x

• Opposite generic
• Same as now (2006)
• Positive horizontal tune change
• Negative vertical tune change

• Normal quad (A20)
• _at_y0
• ByB2x/Rref
• B2 is negative

6
Skew Quads
Skew
x
Bx

• Skew quad (B20)
• _at_y0
• BxA2x/Rref
• A2 is positive

• Opposite generic
• Same as now (2006)
• Positive horizontal tune change
• Negative vertical tune change

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Normal Sextupole
Normal
x
By

• Normal Sext. (A30)
• _at_y0
• ByB3(x/Rref)2
• B3 is negative

• Opposite generic
• Same as now (2006)
• Positive horizontal chromaticity
• Negative vertical chromaticity

8
Sextupole
Bx
y
Skew

• Skew Sext. (B30)
• _at_x0
• Bx-A3(y/Rref)2
• A3 is positive

• Opposite generic
• Same as now (2006)
• Positive horizontal chromaticity
• Negative vertical chromaticity

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Formalism Used By Technical Division
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Analysis Remarks (Tech. Div.)

• Analysis registers the field angle as the
  closest south pole.
• Field coefficients need to be rotated into the
  proper coordinate system as defined in Table 1.
• Which one you grab depends on where the rotation
  starts (as well as the magnet and its powering
  convention).
• trickier as the magnet multi-polarity gets higher
• in this case, the magnitude of the rotation is
  pretty clear, the sign less so
• GV used the probe simulation to arrive at the
  sign (amplitude checks as well)
• The rotations applied are given in Table 1.

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Summary (Tech. Div.)
Table 1