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Beam Optics and Orbits: Methods Used at the Tevatron Accelerators

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Accelerator Physics at the Tevatron Collider

Part of the book series: Particle Acceleration and Detection ((PARTICLE))

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Abstract

The success of the Tevatron Run II would not be possible without detailed work on the linear and nonlinear beam optics. The scope of optics work included all major stages: the optics design, optics measurements, and optics correction. Optics of all transport lines and rings was measured and corrected. This work resulted in a significant reduction of the emittance growth for beam transfers and increased the acceptances of the rings and transfer lines. The most spectacular improvements are related to the improvements of antiproton beam transport from the Accumulator to the Main Injector (MI) and optics improvements in Tevatron, Debuncher, and Accumulator. The electron cooler beam transport presented significant challenge for both the optics design and its commissioning.

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Notes

  1. 1.

    Note that in practical optics calculations the difference between particle angles and their canonical momenta does not usually exist because most optics codes compute transfer matrices between points where the longitudinal magnetic fields are equal to zero.

  2. 2.

    Equation (2.47) also demonstrates that if beta- and alpha-functions are chosen incorrectly, such that the value of the discriminant is negative, u becomes imaginary, thus redetermining the alpha-functions.

  3. 3.

    The Tevatron lattice is based on the detailed optics measurement and takes into account large coupling terms coming mainly from the skew-quadrupole components of the superconducting dipoles. If the coupling corrections are adjusted to minimize the tune split, the value of coupling parameter u varies along the lattice in the range of about [−0.002, 0.04].

  4. 4.

    The condition tr(q c T q c ) ≪ 1 also results in that |κ| ≪ 1. Actually, expressing both equations through the matrix elements, one obtains tr(q c T q c ) = a 2 + b 2 + c 2 + d 2 and κ ≡ det(q c ) = ad − bc. Obviously, |ad − bc| < a 2 + b 2 + c 2 + d 2.

  5. 5.

    Experience gained with the upgrade of electronics of Tevatron BPMs carried out in 2004 proved that before the upgrade the major contribution to variations of differential BPM response was related to imperfections of electronics. After the upgrade the spread of variations was reduced from ~10 to ~1 %. Contribution coming from nonlinearity of differential BPM response with coordinate related to the geometry of BPM was much smaller. The imperfection of electronics looks the most probable reason for variations of differential BPM response for the transfer line BPMs.

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Authors and Affiliations

  1. Fermi National Accelerator Laboratory, 500, Batavia, IL, 60510, USA

    V. Lebedev, V. Shiltsev & A. Valishev

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  1. V. Lebedev
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  2. V. Shiltsev
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  3. A. Valishev
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Correspondence to V. Lebedev .

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Editors and Affiliations

  1. Accelerator Division, Fermi National Accelerator Laboratory, Batavia, Illinois, USA

    Valery Lebedev

  2. Accelerator Physics Center, Fermi National Accelerator Laboratory, Batavia, Illinois, USA

    Vladimir Shiltsev

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Lebedev, V., Shiltsev, V., Valishev, A. (2014). Beam Optics and Orbits: Methods Used at the Tevatron Accelerators. In: Lebedev, V., Shiltsev, V. (eds) Accelerator Physics at the Tevatron Collider. Particle Acceleration and Detection. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0885-1_2

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