Assuming the flip-coil measures integrated field strength (Database
----------
"BACT" units, kG-m), the following relationships hold:
BACT = Cb*E*KMOD*LEFF (kG-m)
where
Cb = "magnetic rigidity" constant = 33.35640952 (kG-m/GeV)
E = energy (GeV)
KMOD = Database KMOD value (bend angle (in radians) per unit length,
1/m)
LEFF = Database LEFF value (effective magnet length, m)
The dipole deflection is:
delta theta (RAD) = 3e7 * dipolestrength(kG.m)
--------------------------
ENERGY (eV)
delta theta (RAD) = dipolestrength (kG.m)
_________________________
Cb * ENERGY (GeV)
About Quadrupoles:
BACT is "length integrated transverse gradient" in units of
kG*m/m or just kG.
BACT = g (transverse gradient, kG/m) * leff (m)
KMOD = g ("transverse gradient")
_____________________________
Brho
where Brho is Cb*Energy
KMOD can be thought of as 1/focal length
per unit magnet length. Has units of 1/m^2
BDES->KMOD:
KMOD = g = BDES
______ ______________________
Brho leff*Cb*energy
KMOD->BDES:
BDES = KMOD * (leff*Cb*Energy)
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Now the time honored technique to measure beta function at a quad by spinning
the quad strength and looking at dnu/dB:
Assimilating Sand's Chapter 2 about the guide field, I use EQ. 2.102 together
with the notions of KMOD, BACT for quad, and Cb above to convince myself that:
Beta = 4*pi*Cb*Energy * ( dnu/dB)
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I recently struggled with the formulation of how to determine quad alignment
by looking at the slope of a downstream position monitor vs. quad strength.
Let's say we are interested in measuring the vertical offset in a
quadrupole. Scan the quadrupole and sample the BACT and some BPM downstream.
Fit the result to a line (Y axis as vertical position monitor readout, X
axis as quadrupole strength). The information is in the fitted slope.
Here's the formula:
R34 is the RMATRIX value between
slope; dY R34*Yoffs quad angle and BPM position.
----- = --------------
dBACT Energy * Cb Yoffs is the beam position in
the quad which we try to measure.
dY/dBACT we get from the fit
described above.
BE CAREFUL ABOUT THE UNITS!
Energy is beam energy.
Cb is "magnetic rigidity" as per
above.
If you want the proof, you wrote it up
here
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