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  • Open Access

Phase measurement for driven spin oscillations in a storage ring

N. Hempelmann et al. (JEDI Collaboration)
Phys. Rev. Accel. Beams 21, 042002 – Published 16 April 2018
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    Abstract

    This paper reports the first simultaneous measurement of the horizontal and vertical components of the polarization vector in a storage ring under the influence of a radio frequency (rf) solenoid. The experiments were performed at the Cooler Synchrotron COSY in Jülich using a vector polarized, bunched 0.97  GeV/c deuteron beam. Using the new spin feedback system, we set the initial phase difference between the solenoid field and the precession of the polarization vector to a predefined value. The feedback system was then switched off, allowing the phase difference to change over time, and the solenoid was switched on to rotate the polarization vector. We observed an oscillation of the vertical polarization component and the phase difference. The oscillations can be described using an analytical model. The results of this experiment also apply to other rf devices with horizontal magnetic fields, such as Wien filters. The precise manipulation of particle spins in storage rings is a prerequisite for measuring the electric dipole moment (EDM) of charged particles.

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    • Received 13 January 2018

    DOI:https://doi.org/10.1103/PhysRevAccelBeams.21.042002

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Accelerator/storage ring control systemsRadio frequency techniques
    1. Properties
    Polarization
    Accelerators & Beams

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    Vol. 21, Iss. 4 — April 2018

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    • Figure 1
      Figure 1

      Coordinate system used to describe the spin motion. The z-axis is defined by the nominal beam momentum, the y-axis points upward and the x-axis to the side. α is the angle between the polarization vector and the horizontal plane. α′ is the angle between the projection of the polarization vector onto the xy-plane and the x-axis. ϕspin is the phase of the spin rotation.

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    • Figure 2
      Figure 2

      Principle of the experiment. Δϕ can take any value in the shaded region. α is initially ±π/2. The first solenoid pulse tilts the polarization into the horizontal plane. The feedback system is then switched on to set a certain value of Δϕ. After that, the solenoid is switched on again at a lower amplitude and the feedback is switched off, leading to oscillations.

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    • Figure 3
      Figure 3

      Analytical solutions [Eq. (4)] for the on-resonance case q=0 and α0=0 as a function of nk for different values of Δϕ0.

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    • Figure 4
      Figure 4

      Analytical solutions [Eq. (4)] for the off-resonance case q=0.5. The other parameters are the same as in Fig. 3.

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    • Figure 5
      Figure 5

      Observation of bound oscillation of Δϕ around −π/2. The fit results correspond to k=(8.95±0.11)×10−7, q=0.250±0.027 and C=−0.934±0.013 at a χ2/NDF of 101.4/74.

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    • Figure 6
      Figure 6

      Observation of unbound oscillation of Δϕ. The fit results correspond to k=(8.51±0.58)×10−7, q=0.52±0.16 and C=0.205±0.087 at a χ2/NDF of 82.8/74.

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    • Figure 7
      Figure 7

      Representation of on-resonance (q=0, top) and off-resonance (q=0.5, bottom) solutions in the coordinate system defined in Eq. (7).

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    • Figure 8
      Figure 8

      Representation of the data and fits from Figs. 5 (black) and 6 (red) in the Cartesian coordinate system defined in Eq. (7). All points and curves lie on the unit sphere.

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