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Nonlinear chromaticity modelling and measurements - Episode III

CERN, FiDel meeting 30/8/11 . Nonlinear chromaticity modelling and measurements - Episode III. Outline: Model vs Measurements comparison Explaining the observed Q’’ MCO hysteresis MCD systematic misalignment Modelling the relative effect of the MO.

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Nonlinear chromaticity modelling and measurements - Episode III

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  1. CERN, FiDel meeting 30/8/11. Nonlinear chromaticity modelling and measurements - Episode III • Outline: • Model vs Measurements comparison • Explaining the observed Q’’ • MCO hysteresis • MCD systematic misalignment • Modelling the relative effect of the MO

  2. Comparison: model vs measurements Q’’ discrepancy Non-linear chromaticity was measured on 10 June & 2 July. B1/B2 measured 10 June, B2(x) data discounted as tune drifted. B2 only was measured on 2 July. Disagrees with predictions from the thick elements MAD-X / PTC model. Model is based on best available measurements of magnetic and alignment errors. Two explanations have been suggested for the Q’’ disagreement. Hysteresis of the MCO (octupolar spool pieces), and systematic misalignment of MCD (decupolar spool piece) w.r.t main dipole. CERN, FiDel 30/8/11. NL-chromaticity modelling & measurements. () show errors from polynomial fit

  3. Q’’ disagreement – MCO hysteresis CERN, FiDel 30/8/11. NL-chromaticity modelling & measurements. E. Todesco has provided an estimate of the MCO field taking account of hysteresis in the case of a pre-cycle. These errors have been applied to the model. Difference between observed NL-chroma and model without hysteresis errors is compared to the difference in predications of the two models: MCO hysteresis may explain a substantial fraction of the missing Q’’.

  4. Q’’ disagreement – systematic misalignment of MCD CERN, FiDel 30/8/11. NL-chromaticity modelling & measurements. Another potential source of observed Q’’ is systematic misalignment of MCD w.r.t main dipoles. Realistic maximum is |0.5mm| misalignment. Adding an additional -0.5mm & +0.5mm offset to the MCD in the x and y plane: Seems that effect of MCD misalignment is too small to explain the Q’’.

  5. MO (landau octupoles) in model CERN, FiDel 30/8/11. NL-chromaticity modelling & measurements. On 10 June measurments were made with landau octupoles powered nominally, then turned off. Model reproduces well the effect on Q’’ of the MOs. However change in Q’’’ is not predicted by the model.

  6. Conclusion CERN, FiDel 30/8/11. NL-chromaticity modelling & measurements. • Model Predictions and measurements of non-linear chromaticity do not agree (relative effect of spool pieces does agree well – see episode II) • Including the effect of hysteresis of MCOs in model can explain a significant fraction of the missing Q’’ • The effect of misaligning MCDs on the Q’’ is small • The relative effect of landau octupoles is reproduced well for Q’’, but disagrees for Q’’’ (under investigation).

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