Compensation of the effects of a detector solenoid on the vertical beam orbit in a linear collider

This paper presents a method for compensating the vertical orbit change through the interaction region that arises when the beam enters the linear collider detector solenoid at a crossing angle. Such compensation is required because any deviation of the vertical orbit causes degradation of the beam size due to synchrotron radiation, and also because the nonzero total vertical angle causes rotation of the polarization vector of the bunch. Compensation is necessary to preserve the luminosity or to guarantee knowledge of the polarization at the interaction point. The most effective compensation is done locally with a special dipole coil arrangement incorporated into the detector (detector integrated dipole). The compensation is effective for both $e^{+}{e}^{-}$and $e^{-}{e}^{-}$beams, and the technique is compatible with transverse-coupling compensation either by the standard method, using skew quadrupoles, or by a more effective method using weak antisolenoids.

Figure 1

Illustration of $e^{+}{e}^{-}$ and $e^{-}{e}^{-}$ collisions in a detector solenoid field with sharp edges (schematically shown in the top plot) without (middle) and with (bottom) compensation of the IP angle by the detector integrated dipole and two external correctors. The model parameters are $L=3\mathrm{m}$, ${\theta }_c=10\mathrm{mrad}$, $B_0=5\mathrm{T}$, beam energy 250 GeV. The uncompensated vertical angle at the IP is approximately $45\mu \mathrm{rad}$. The compensation kicks are shown on the top plot by the blue arrows; they are located at $z=\pm 2\mathrm{m}$ and $z=\pm 5\mathrm{m}$ and their magnitudes are 75 and $30\mu \mathrm{rad}$. The IP is at $z=0\mathrm{m}$. Outgoing beams are shown by thick dashed curves.

Figure 2

Schematic of the silicon detector (SiD) with magnetic field lines calculated by ANSYS. The IP is at $z=0\mathrm{m}$.

Figure 3

Longitudinal and radial magnetic field in SiD calculated by ANSYS, without and with the weak antisolenoid which cancels the beam distortions produced by the detector solenoid. The red line shows the field with the antisolenoid parameters suggested in 1, and the green dot-dashed line shows the field with another configuration of the antisolenoids, optimized to reduce SR effects (see text). The radial field is at the nominal beam trajectory with half crossing angle ${\theta }_c=10\mathrm{mrad}$. Locations of the final doublet elements (quadrupoles QD0 and QF1, sextupole SD0, octupole OC0, and an optional dipole corrector BXMID) are also shown. The IP is at $z=0\mathrm{m}$.

Figure 4

Horizontal field strength on the beam axis of the SiD detector (top), and vertical beam orbits (bottom), in the absence of vertical IP angle compensation. The orbit calculated in the absence of any focusing elements is shown by a dashed line, and the orbit determined by tracking with DIMAD is shown by a solid line on the bottom plot. For the tracked beam, the IP beam coordinates are $x=0.65\mu \mathrm{m}$, $y=-18.5\mu \mathrm{m}$, $x^{\prime }=-0.21\mu \mathrm{rad}$, and $y^{\prime }=-104\mu \mathrm{rad}$. The beam size growth due to synchrotron radiation is $\Delta {\sigma }_y^{\mathrm{SR}}=0.31\mathrm{nm}$.

Figure 5

Illustration of IP angle compensation using only offsets of the final doublet quadrupoles. Horizontal field on the beam axis (top), beam orbit calculated by tracking (bottom). Contributions of the solenoid and FD quadrupoles are shown on the top plot separately. The beam size growth due to synchrotron radiation is $\Delta {\sigma }_y^{\mathrm{SR}}=5.2\mathrm{nm}$.

Figure 6

Horizontal field of the detector integrated dipole (DID) for the SiD detector. The DID strength is optimized to zero the IP vertical angle (blue line) or to minimize the SR vertical beam size growth (red line) in the case of bare SiD without antisolenoids.

Figure 7

Horizontal field on the beam axis (top) and the beam orbit (bottom). The IP angle has been compensated using DID and offsets of QD0 and QF1 quadrupoles. The orbit is determined by tracking. The beam size growth from synchrotron radiation is $\Delta {\sigma }_y^{\mathrm{SR}}=0.26\mathrm{nm}$.

Figure 8

Horizontal field on the beam axis (top) and beam orbit determined by tracking (bottom) in three cases: (i) bare SiD (no antisolenoid) and DID strength optimized to minimize SR beam size growth (blue thick line), $\Delta {\sigma }_y^{\mathrm{SR}}=0.034\mathrm{nm}$; (ii) SiD with antisolenoid (parameters from 1) (red line), $\Delta {\sigma }_y^{\mathrm{SR}}=0.83\mathrm{nm}$; (iii) SiD with antisolenoid optimized to minimize SR effects (green dash-dotted line), $\Delta {\sigma }_y^{\mathrm{SR}}=0.33\mathrm{nm}$. In the last two cases the IP angle is compensated by the DID, FD offsets, and BXMID without introducing any linear or second order dispersion.

Figure 9

Vertical angle at the IP (top) and the beam size growth due to synchrotron radiation (bottom), versus strength of the DID corrector, without antisolenoid (thick blue line), with the antisolenoid with parameters suggested in 1 (red line), and with the antisolenoid optimized to reduce the SR effects (green dash-dotted line).

Figure 10

Detector integrated dipole corrector. The top plot shows the actual arrangement of windings in one half of the corrector. The second half of the corrector is mirror symmetrical with respect to the solenoid center ($z=0$). The bottom plot shows a simplified model used for 3D field calculations with Tosca (Opera3D code) to evaluate the effect of iron in the SiD yoke on the dipole field. For ease in viewing the 3D model the solenoid coil and the top half of the SiD yoke are not shown. The arrows show the direction of the current. Except for a small deviation near the start of the end cap around $Z=\pm 3.2\mathrm{m}$ the horizontal field profile is very close to that assumed for the tracking studies shown in Fig. 6.