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Accelerator Physics at the Tevatron Collider pp 187–258Cite as

Emittance Growth and Beam Loss

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

Abstract

A wide range of diffusion and beam loss mechanisms were studied during the Tevatron Run II commissioning and operations. Many of them were well known [Coulomb scattering, residual gas and intrabeam scattering (IBS)] but required substantial studies and deeper theoretical insights because of unique experimental conditions and beam parameters.

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Notes

  1. 1.

    This case describes well the beam lifetime in an electron synchrotron when the horizontal beam emittance is set by equilibrium between synchrotron radiation (SR) damping and diffusion due to SR. The vertical emittance is much smaller and therefore the beam loss due to diffusion in vertical plane is negligible. It makes the problem being single dimensional.

  2. 2.

    Actually this condition is satisfied for all circular accelerators build to this time with exception of LEP presenting a weakly relativistic case.

  3. 3.

    Note that at this point we consider only variations of f related to the scattering. Effects of betatron motion will be accounted at the next stage of calculations.

  4. 4.

    Method of the integration can be found below in the computation of similar integral for intra-beam scattering [see details further down Eq. (6.80)]. Note also that the Kernel (6.66) can be used without δ-function [like in Eq. (6.65)] in alternative form of integro-differential equation: \( \partial f/\partial t-\lambda \partial (If)/\partial I={\displaystyle {\int}_0^{I_b}W\left(I,{I}^{\prime}\right)\left(f\left({I}^{\prime },t\right)-f\left(I,t\right)\right)d{I}^{\prime }} \).

  5. 5.

    For rectangular distribution with total bunch length ϕ tot (n(ϕ) = 1/ϕ tot within bunch) and linear RF one obtains \( {\displaystyle \operatorname{}{\widehat{p}}^2n\left(\phi \right) d\psi}=2\pi \omega I/{\phi}_{\mathrm{tot}} \), and, consequently, \( {D}_{\left|\right|}(I)=\tilde{A}{L}_{\mathrm{c}}/{\phi}_{\mathrm{tot}} \).

  6. 6.

    Here we choose alternative form of Eq. (6.61).

  7. 7.

    It implies that the emittance growth rate is sufficiently small which is true in hadron colliders and storage rings.

  8. 8.

    Note that by definition the spectral density used in measurements is 4π larger than the spectral density used in Sect. 6.2.3.

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Authors and Affiliations

  1. Accelerator Physics Center, Fermi National Accelerator Laboratory, MS341, 500, Batavia, IL, 60510, USA

    R. Carrigan, V. Lebedev, N. Mokhov, S. Nagaitsev, V. Shiltsev, G. Stancari, D. Still & A. Valishev

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  1. R. Carrigan
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  2. V. Lebedev
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  3. N. Mokhov
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  4. S. Nagaitsev
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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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Carrigan, R. et al. (2014). Emittance Growth and Beam Loss. 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_6

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