Numerical solution of integral equations

Stallmann, Friedmann W.

doi:10.1007/bf02165120

Cited by 9 publications

(2 citation statements)

References 5 publications

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“…This is analogous to results obtained by Franklin and others [7,8]. (Previously, a deterministic approach had been taken k by many people [9,10,11,12,13].) This specific form of the solution is found convenient in the later determination of the wind velocity.…”

Section: Dnsupporting

confidence: 82%

Remote Determination of the Profiles of the Atmospheric Structure Constants and Wind Velocity along a Line-of-Sight Path by a Statistical Inversion Procedure

Heneghan¹,

Ishimaru²

1973

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Section: Dnsupporting

confidence: 82%

Remote Determination of the Profiles of the Atmospheric Structure Constants and Wind Velocity along a Line-of-Sight Path by a Statistical Inversion Procedure

Heneghan¹,

Ishimaru²

1973

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“…Equation 5allows us to calculate the longitudinal bunch profile knowing the distribution of synchrotron amplitudes. Conversely, if we are given the bunch profile, we can extract gˆτ by numerically solving an integral equation [12]. In addition, as the synchrotron amplitudes are related to the synchrotron frequencies by Eq.…”

Section: Longitudinal Bunch Profilementioning

confidence: 99%

Estimation of longitudinal bunch characteristics in the LHC using Schottky-based diagnostics

Lasocha

Alves

2020

Phys. Rev. Accel. Beams

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The Large Hadron Collider (LHC) Schottky monitors have been designed to measure various parameters of relevance to beam quality, namely tune, momentum spread, and chromaticity. In this work, we present how this instrument can be used to estimate longitudinal bunch characteristics, such as longitudinal bunch profile or synchrotron frequency distribution. Under the assumption of bunched beams with no intrabunch coherent motion, we start by deriving the relation between the distribution of synchrotron amplitudes within the bunch population and the longitudinal bunch profile from probabilistic principles. Subsequently, we fit the cumulative power density of acquired Schottky spectra with the underlying distribution of synchrotron amplitudes. Finally, the result of this fit is used to reconstruct the bunch profile using the derived model. The results obtained with this method are verified by comparison with longitudinal profile measurements from the LHC wall current monitors.

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The beam wave case and remote sensing

Ishimaru¹

1978

Topics in Applied Physics

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Numerical solution of integral equations

Cited by 9 publications

References 5 publications

Remote Determination of the Profiles of the Atmospheric Structure Constants and Wind Velocity along a Line-of-Sight Path by a Statistical Inversion Procedure

Remote Determination of the Profiles of the Atmospheric Structure Constants and Wind Velocity along a Line-of-Sight Path by a Statistical Inversion Procedure

Estimation of longitudinal bunch characteristics in the LHC using Schottky-based diagnostics

The beam wave case and remote sensing

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