The effects of the RHIC E-lenses magnetic structure layout on the proton beam trajectory Page: 4 of 5
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Figure 2: Layout of Two Electron Lenses. Top: top view,
bottom: side view.
In addition to these constraints, the two lenses should
have a different magnetic polarity (SN-NS or NS-SN) and
therefore, locally compensate each other for both linear
coupling and spin effects. Furthermore, the central line of
the solenoids GSB_Y, CSB_Y, CSB_B, and GSB_B,
located, respectively, at -490 cm, -145 cm, 145 cm, and
490 cm have a 30 degree angle to the directions of proton-
beam transport. This configuration will induce dipole,
quadrupole, and skew dipole and quadrupole components
when the proton beam passes through the two e-lenses
The multipole magnetic field components in Fig. 3
generated by e-lens are analyzed and compared by
Fourier fit method via Opera.
In cylindrical coordinates, we can express the radial
and azimuthal components of magnetic field B in the
Br (r, 0) = co1(b, sin(nO) + a, cos (n0)) (1)
B (r, 0) = Z1 (b sin(n0) - a, cos(n0)) (2)
Where b, is the amplitudes of the 2n pole normal term
and a, is the amplitudes of 2n pole skew term in the
The multipole magnetic field, B0 can be computed on a
reference radius Rref at different longitudinal positions
and fitted as Fourier series. Then, according to formula
(2), the coefficients of this Fourier series are the multipole
magnetic field components. The reference radius Rref =
NoFmur Dipole -NO3 H mQuadrupole -skew Fipole -skewQuadpoe
Figure 3: High-Order Magnetic Field Components.
SINGLE-PASS TRAJECTORIES OF THE
PROTON BEAM TRACKED BY OPERA
The dipole component field of the two electron lenses
can deflect the trajectories of protons. To verify this effect
and find a method to correct it, we tracked, by Opera, the
centroid of the blue proton beam as it passed through
these two electron lenses.
In our simulation, the blue proton beam starts from
-900 cm with eight different initial vertical angles; the
horizontal angle is set to zero. The energy of the proton
beam is 250 GeV, and the Lorentz factor is 266.
Figure 4 reveals that the blue proton beam has the same
angle before and after the two electron lenses. However,
within them, the blue proton beam is deflected. If its
initial angle is about 100 grad, the blue proton beams'
trajectories within the two electron lenses can be set to be
parallel to the Z-axis.
00 -700.0 500.0 3000 -1000 1000 3000 5000 7000 9000
Figure 4: Proton Beam's Vertical Trajectories in Electron
-1 OE- 0 -700.0 -5000 -3000 -1000 1000 3000
500.0 700z0 9000
Figure 5: Proton Beam's Horizontal Trajectories in
Figure 5 plots the blue proton beam's horizontal
trajectories. After passing through the two electron lenses,
it exhibits a shift of about 0.01 cm in horizontal plane. In
horizontal plane, because the blue proton beam passes
first through the yellow 5 mm E-lens, it is deflected by
the fringe field of the yellow E-lens by about 0.009 cm;
this value is much greater than the change in the beam's
position caused by the fringe field of the blue e-lens,
which is less than 0.001 cm.
CLOSED ORBIT CALCULATION WITH
To include the e-lenses elements lattice in the RHIC
lattice, these elements, such as the transverse field of GSB
0 004 0--
e - ~ M -
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Gu, X.; Pikin, A.; Luo, Y.; Okamura, M.; Fischer, W.; Gupta, R. et al. The effects of the RHIC E-lenses magnetic structure layout on the proton beam trajectory, article, March 28, 2011; United States. (https://digital.library.unt.edu/ark:/67531/metadc847186/m1/4/: accessed March 23, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.