HQ01 field quality study update F. Borgnolutti, G. Chlachidze, J. DiMarco, H. Felice, P. Ferracin, M. Marchevsky, G.L. Sabbi, E. Todesco, X. Wang HiLumi WP3 meeting on HQ test results August 2, 2012

Measurement accuracy (probe resolution) Topics Measurement accuracy (probe resolution) Coil block positioning tolerance Static behavior Main field reproducibility Geometric and iron saturation Dynamic behavior Eddy current effect and Rc Multipole decay as a result of low Rc 8/2/2012

Measurement accuracy Plateau of measured multipoles = probe resolution. 250 mm long probe: 0.006 units at 14 kA at probe radius (21.55 mm). 8/2/2012 10-26-2011

Resolution at Rref = 40 mm Scaling from Rref = 21.55 mm to 40 mm. Target resolution based on CM18 discussion: 0.1 units or better System meets the minimum requirement up to n = 6 100 mm 250 mm n 880 A 14 kA s/n* 3 0.014 0.015 7.0 0.010 9.6 4 0.026 0.027 3.8 0.019 5.2 5 0.047 0.051 2.0 0.036 2.8 6 0.088 0.094 1.1 0.066 1.5 7 0.163 0.174 0.6 0.123 0.8 8 0.303 0.323 0.3 0.228 0.229 0.4 9 0.563 0.600 0.2 0.423 0.425 10 1.045 1.114 0.1 0.785 0.788 (*) s/n ratios calculated assuming 0.1 units harmonic amplitude. FNAL working on a new probe. A factor of ~12.5 increase in resolution for n = 6 with the same radius. 8/2/2012 10-26-2011

Coil block positioning tolerance Harmonics measured at 12 kA using the 100 mm probe at 3 axial locations. Averaged from up- and down-ramps. Match measured σ with the one calculated for random block displacements. Uncertainty on σ is 50% with measurements at 3 locations. Will decrease to 25% with 9 locations (requires ~ 1 m long straight section). Rref = 21.55 mm Best fit obtained with displacement σ=29.6 µm TQC/TQS coil block positioning σ: 36 µm – 64 µm. [Borgnolutti et al., IEEE TAS 19(3), p.1100, 2009] Comparable to the level of current LHC IR quads and main dipoles. 8/2/2012

Main field reproducibility Two measurements from each probe. Each measurement = Precycle (to 10 kA) + 1 machine cycle (to 14 kA), 10 A/s. Normalized TF (two meas. shown) σ (b2) of measurements from the same probe σ < 10 units below 6 kA (mainly related to “spikes” – much lower at 1.9K) σ < 2.4 units up to 14 kA (may decrease with larger statistics) Target: < 1 unit at 7 TeV. [E. Todesco, CM18 presentation, Indico] 8/2/2012

Geometric component and iron saturation Rref = 40 mm Geometric: 12.025 T/m/kA at 2 kA. Iron saturation at 14 kA: -5.8% with respect to geometric value. Some discrepancy between measurement and calculation Need to incorporate as-built coil geometry and changes due to cool-down and excitation. Discrepancy changes slope at 10 kA – possibly more than one source. Iron properties? Other? 8/2/2012 10-26-2011

Static b6 Shift the calculation with +4.5 units to match the measurement between 4 – 8 kA. Calculation for nominal geometry at warm. Some discrepancy between measurement and calculation Δ = -1.5 units at 14 kA corresponds to ~ 90 µm outward displacement of two mid-plane blocks under Lorentz forces. ANSYS shows ~ 30 µm. 8/2/2012

Dynamic effect Inter-strand eddy current dominates the dynamic effect. Dynamic field error scales with ramp rate. Decay time constant on the order of 10 s. Raw data (static+dynamic component) After subtracting static effect 8/2/2012

Calculation of Rc from sensitivity matrix Solve a linear system: e = Sg. e: field error vector; S: sensitivity matrix; g: conductance vector (g = 1/Rc). Sensitivity factors computed from roxie Using field errors measured at 10 kA, 40 A/s. Assuming uniform Rc in block/layer to reduce the number of unknowns. Unique and physical solution not always available. B2 B6 B2 and B6 1=2=3=4 0.40 0.14 - 4=∞ 1= 2 0.29 3 0.33 Field error Block Rc (µΩ) Results suggest Rc ~ 0.1 – 0.4 μΩ. 8/2/2012 10-26-2011

Inverse calculation of Rc Based on method originated from SSC and LHC. [Ogitsu et al., Particle Accelerators, 57, p. 215, 1997; Wolf et al., IEEE TAS 7(2), p. 797, 1997.] Goal: to match measured field error of B2 and B6. Error < 3.1% between measured and calculated field errors. Rc lower in outer layer (0.2 – 0.22 µΩ). 8/2/2012

Inverse calculation to match full error vector 5 8 7 9 Rc ~ 0.1 – 0.4 µΩ. Error < 5% between calculated and measured dynamic field component. Consistent with 0.33 µΩ measured Rc on an HQ prototype cable. [Collings et al., IEEE TAS 21(3), p. 2367, 2011.] Top-bottom asymmetry in Rc (two different cables). Low Rc accompanied by high AC loss. To compare with loss measurement and quench behavior. 8/2/2012 10-26-2011

Multipole decay at different current levels Strong exponential decay in multipoles with τ ranges from 25 to 55 s. The decay of inter-strand eddy current due to low Rc. Rref = 40 mm τ estimated ~ 40 s at 10 kA based on Rc of 0.3 µΩ in block 3 with quadrupole symmetry. [A. P. Verweij, Ph.D. thesis, 1995] Expectation with 20 µΩ Rc: τ reduces to the order of 0.1 s and negligible decay. 8/2/2012

Conclusions Current probe meets the minimum resolution requirement up to n = 6. New probe being developed to improve accuracy at the same radius. Plan to develop larger radius probes and anti-cryostats for future test. Coil block positioning error s ~ 30 μm at 12 kA, comparable to current IR quads and LHC main dipoles. Main field reproducibility at 14 kA (80% of SSL at 4.4 K) is < 2 units. May improve with larger statistics. Target is < 1 unit at 7 TeV. Harmonics as function of current are in general agreement with calculations. Further analysis is in progress to understand differences up to 0.6% (TF) and 1.5 units (b6). Rc between 0.1 – 0.4 μΩ obtained from direct and inverse calculations. Consistent with 0.33 μΩ measured on an HQ01 prototype cable. Responsible for large eddy current effect and multipole decay. Cored cable was introduced in second generation coils. 8/2/2012