Michele Martino TE-EPC Status Update of Power Converter Precision & Accuracy Performance: Noise Michele Martino TE-EPC 88th WP2 Meeting – CERN 6/R-012 – 21/03/2017

? ∆𝐵 𝐵 = ∆𝐼 𝐼 Final goal of the study Beam physics constraints are usually specified in terms of ∆𝐵 𝐵 Power Converters conversely are specified in terms of electrical quantities Usually/mostly in terms of current ∆𝑰 𝑰 Assuming ∆𝐵 𝐵 = ∆𝑰 𝑰 “seems” safe but it can be costly as it might lead to over-specification!! M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Model of PC output to magnetic field two regimes: current control (<0.1 Hz): voltage control (>0.1 Hz): with current ripple (Power converter specifications) voltage ripple (Power converter specifications) transfer function of the load (circuit) seen by the power converter transfer function from the input current of the magnet to the magnetic field (assumed constant) transfer function of the cold bore, absorber, beam screen etc., TVacuum ≤1 (not taken into account) M. Giovannozzi - HL-LHC Circuit Review - 21-23 March 2016

Model of PC output to magnetic field two regimes: current control ( <𝑓 0 ): voltage control ( >𝑓 0 ): with current ripple (Power converter specifications) voltage ripple (Power converter specifications) transfer function of the load (circuit) seen by the power converter 𝐼 𝑓 = 𝑉(𝑓) 𝑅 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 +2𝜋𝑖∙ 𝐿 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 (𝑓)∙𝑓 transfer function from the input current of the magnet to the magnetic field (assumed constant) transfer function of the cold bore, absorber, beam screen etc., TVacuum ≤1 (not taken into account) M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Model of PC output to magnetic field B Current control ( 𝑓<𝑓 0 ) 𝑓 0 is a design parameter and can be chosen conveniently (with limitations) For SC magnets (large L, small R) 𝑓 0 is not going to be chosen above a few Hertz In this regime both 𝑇 𝑣𝑎𝑐𝑢𝑢𝑚 (𝑓)≅1 and 𝑇 𝐼𝑡𝑜𝐵 (𝑓)≅𝑐𝑜𝑛𝑠𝑡 are deemed to hold true! ∆𝐵 𝐵 = ∆𝐵 𝑏𝑒𝑎𝑚 𝐵 𝑛𝑜𝑚 𝑏𝑒𝑎𝑚 = 𝑩 𝒃𝒆𝒂𝒎 (𝒇) 𝑩 𝒏𝒐𝒎 𝒃𝒆𝒂𝒎 ≅ 𝑰 𝒄𝒊𝒓𝒄𝒖𝒊𝒕 𝒇 𝑰 𝒏𝒐𝒎 𝒄𝒊𝒓𝒄𝒖𝒊𝒕 = ∆𝐼 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝐼 𝑛𝑜𝑚 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 = ∆𝐼 𝐼 M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Model of PC output to magnetic field B Voltage control ( 𝑓>𝑓 0 ) this regime requires a more accurate modelling and experimental validation as neither assumption might be justified! 𝑇 𝑣𝑎𝑐𝑢𝑢𝑚 (𝑓) depends entirely on material properties and geometry of cold bore, absorber, beam screen and temperature! Many phenomena might be at play for the 𝑇 𝐼𝑡𝑜𝐵 𝑓 : Eddy currents (and other “losses”) Superconductive material AC behaviour (type II) M. Martino TE-EPC - WP2 Meeting - 21/03/2017

𝐿=𝐿(𝑓): existing results for LHC 1085 Quadrupole No DC bias Dramatic effect due to the Beam Screen Small signal excitation 𝑇 𝑣𝑎𝑐𝑢𝑢𝑚 𝑓 ? Courtesy TE-MSC C. Giloux - 2009 M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Modelling the phenomenon : assumptions 𝑖 𝐷𝐶𝐶𝑇 𝑖 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 𝑖 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 = 𝑍 // 𝑍 // +𝑠 𝐿 𝐷𝐶 𝑖 𝐷𝐶𝐶𝑇 𝑖 𝑍 // 𝐿 𝑒𝑞 𝐿 𝑒𝑞 = 𝐿 𝐷𝐶 1+𝑠 𝐿 𝐷𝐶 𝑍 // 𝑖 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 = 𝑅 // 𝑅 // +𝑠 𝐿 𝐷𝐶 𝑖 𝐷𝐶𝐶𝑇 = 1 1+𝑠 𝐿 𝐷𝐶 𝑅 // 𝑖 𝐷𝐶𝐶𝑇 If 𝑍 // is a resistance 𝑅 // then (In this case active power losses would have a component ∝ 𝑓 2 ) In any reasonable case 𝑖 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 is a “low pass” version of 𝑖 𝐷𝐶𝐶𝑇 M. Martino TE-EPC - WP2 Meeting - 21/03/2017

𝐿=𝐿(𝑓): existing results for LHC 1085 Quadrupole With Beam Screen With Beam Screen M. Martino TE-EPC - WP2 Meeting - 21/03/2017

𝐿=𝐿(𝑓): existing results for LHC 1085 Quadrupole With Beam Screen With Beam Screen Good fit up to 1kHz  M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Results for MQXFS3: No DC @ WARM -3dB @ 150Hz Good fit up to 3kHz  M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Results for MQXFS3: No DC @ COLD -3dB @ 50Hz Very good fit up to 3kHz  M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Beam Screen Simulations : Q1 Approximation: ⊥ B-field infinitely long thin cylinder 𝑆𝐸≅ 1+ 1 2 𝜇 𝑟 −1 2 𝜇 𝑟 𝜌 0 ∆+ 𝜌 0 2 𝜇 𝑟 ∆ 𝛾 2 Shielding Efficiency ∆ thickness 𝛾≅ 1+𝑗 𝛿 𝜎 conductivity 𝑃 perimeter 𝑆𝐸≅ 1+𝑗 𝑃 2 𝜇 0 ∆𝜎𝑓 Single pole approximation: 1st pole accurate to ±10% M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Beam Screen Simulations HL-LHC: Q1 @ 80K -20dB @ <150 Hz M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Beam Screen Simulations HL-LHC: Q2 @ 80K -20dB @ <300 Hz M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Beam Screen Simulations HL-LHC: D1 @ 80K -20dB @ <350 Hz M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Beam Screen Simulations HL-LHC: D2 @ 20K -20dB @ <120 Hz M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Beam Screen Simulations LHC: Dipole @ 20K -20dB @ 200 Hz M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Beam Screen Simulations LHC: Quadrupole @ 20K -20dB @ <500 Hz BS acts like as a 1st order (at least) low pass 50Hz bandwidth! M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Estimation of Noise LHC MQFA.A12 𝑖 𝐷𝐶𝐶𝑇 sampled at 1kS/s (including measurement noise) M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Estimation of Noise LHC MQFA.A12 𝑖 𝐷𝐶𝐶𝑇 filtered by a 1st order low pass with 50Hz bandwidth M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Conclusions Beam Screen represents the major contribution of power losses due to eddy currents but the magnet itself dissipates some! These effects can be electrically modelled as parallel impedances to the “ideal” superconducting magnet modelled as 𝐿 𝐷𝐶 ! Both effects imply that the current that produces the useful magnetic induction field 𝑖 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 is a low pass version of 𝑖 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 Measurements, magnetic and electrical, are needed to confirm the model and assess the final impact on useful magnetic field hopefully in April 2017 for MQXFS5 and summer with Beam Screen HL-LHC Beam Screens will introduce more than 20dB attenuation at 300Hz - for LHC Quadrupoles this is just a bit less (simulations) M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Thank you for your attention Credits to: Miguel Cerqueira Bastos WP6B, Riccardo de Maria WP2, Lorenzo Bortot WP7, Marco Morrone WP12 M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Back-up slides M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Time domain behaviour 𝑍(𝑠)=𝑠 𝜆 𝑠 + 𝜆 𝐿 𝐷𝐶 𝐷𝐶 =𝑠 𝑍 (𝑠) 𝑍(𝑠)=𝑠 𝜆 𝑠 + 𝜆 𝐿 𝐷𝐶 𝐷𝐶 =𝑠 𝑍 (𝑠) 𝐴(𝑠)= 1 𝑠 𝐿 𝐷𝐶 + 1 𝜆 𝑠 ℎ 𝐴 (𝑡)= 1 𝐿 𝐷𝐶 1 𝑡 + 1 𝜆 𝜋𝑡 1(𝑡) ℎ 𝑧 (𝑡)=𝜆 1 𝜋𝑡 − 𝜆 𝐿 𝐷𝐶 erfcx 𝜆 𝐿 𝐷𝐶 𝑡 ⁡ 1(𝑡) 𝑖(𝑡)= ℎ 𝐴 𝑡 ∗𝑣(𝑡) 𝑣(𝑡)= ℎ 𝑧 (𝑡)∗ 𝑑 𝑑𝑡 𝑖(𝑡) M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Magnetic flux “seen” by the circuit 𝐿 𝑑𝑐 is the “apparent” or “secant” inductance 𝜙 𝑛𝑜𝑚 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 = 𝐿 𝑑𝑐 ( 𝑖 𝑛𝑜𝑚 )𝑖 𝑛𝑜𝑚 𝜙 𝑛𝑜𝑚 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 is assumed directly due to 𝐵 𝑛𝑜𝑚 𝑏𝑒𝑎𝑚 (DC operation at nominal current) For a simplified circuit with resistive cables we can “always” write : 𝑣 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑡 =𝑅 𝑖 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑡 + 𝑑 𝜙 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑑𝑡 𝑣 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 =𝑅 𝑖 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 +𝑗2𝜋𝑓 𝜙 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 (𝑓) 𝜙 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 (𝑓)= 𝐿 𝑎𝑐 (𝑓) 𝑖 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 (𝑓) 𝐿 𝑎𝑐 (𝑓) is such that 𝐿 𝑎𝑐 0 = 𝐿 𝑑𝑐 (at 𝑖 𝑛𝑜𝑚 ) 𝜙 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 = 𝑣 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 𝑅 𝐿 𝑎𝑐 (𝑓) +𝑗2𝜋𝑓 𝜙 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 = 𝑣 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 𝑅 𝐿 𝑎𝑐 (𝑓)+𝑗2𝜋𝑓 ≤ 𝑣 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 2𝜋𝑓 ∆𝜙 𝜙 = 𝜙 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 𝜙 𝑛𝑜𝑚 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 = 𝜙 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 𝐿 𝑑𝑐 𝑖 𝑛𝑜𝑚 ≤ 𝑣 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 2𝜋𝑓 𝐿 𝑑𝑐 𝑖 𝑛𝑜𝑚 M. Martino TE-EPC - WP2 Meeting - 21/03/2017

From the circuit to the beam From 𝑣 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 , 𝐿 𝑑𝑐 and 𝑖 𝑛𝑜𝑚 we can easily estimate maximum ∆𝜙 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝜙 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 ∆𝐵 𝑏𝑒𝑎𝑚 𝐵 𝑏𝑒𝑎𝑚 = ∆𝜙 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝜙 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 ? ∆𝐵 𝐵 = 𝐵 𝑏𝑒𝑎𝑚 (𝑓) 𝐵 𝑛𝑜𝑚 𝑏𝑒𝑎𝑚 ≅ 𝑖 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 𝑖 𝑛𝑜𝑚 𝑓< 𝑓 0 𝑇 𝑣𝑎𝑐𝑢𝑢𝑚 𝑓 × 𝑇 𝑣→ 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 ′ 𝑓 × 𝑣 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 𝐿 𝑑𝑐 𝐼 𝑛𝑜𝑚 𝑓> 𝑓 0 𝑇 𝑣𝑎𝑐𝑢𝑢𝑚 𝑓 ≤𝑇 𝑣𝑎𝑐𝑢𝑢𝑚 0 =1 𝑇 𝑣 → 𝐵 =𝑠 𝑚 −2 𝑇 𝑣 → 𝐵 ′ =𝑠 M. Martino TE-EPC - WP2 Meeting - 21/03/2017

From the circuit to the beam 𝑇 𝑣→ 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 ′ 𝑓 = 𝑇 𝜙 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 → 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 (𝑓) 𝑇 𝜙 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 → 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 (0) 1 𝑅 𝐿 𝑎𝑐 𝑓 +𝑗2𝜋𝑓 ≤ 𝑇 𝑣→ 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 ′′ 𝑓 2𝜋𝑓 ∆𝐵 𝐵 = 𝐵 𝑏𝑒𝑎𝑚 (𝑓) 𝐵 𝑛𝑜𝑚 𝑏𝑒𝑎𝑚 ≅ 𝑖 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 𝑖 𝑛𝑜𝑚 𝑓< 𝑓 0 𝑇 𝑣𝑎𝑐𝑢𝑢𝑚 𝑓 × 𝑇′ 𝑣→ 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 ′ 𝑓 × 𝑣 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 2𝜋𝑓𝐿 𝑑𝑐 𝑖 𝑛𝑜𝑚 𝑓> 𝑓 0 EPC + MSC will measure 𝑣 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 , 𝑖 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 , 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 (𝑓) and ideally 𝐵 𝑏𝑒𝑎𝑚 (𝑓) We will then estimate 𝑇′ 𝑣→ 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 ′ 𝑓 and ideally 𝑇 𝑣𝑎𝑐𝑢𝑢𝑚 𝑓 M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Existing results NC: Integrated Gradient / Current Vacuum chamber ∆𝐵 𝐵 ≪ ∆𝐼 𝐼 No DC bias Very small excitation current Courtesy TE-MSC-MM Buzio et al. 2014 M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Minutes of the last meeting Michele showed the expected stability of power converters of Class 1 and Class 2. Measured data, although limited, shows that Class 1 power converters are stable below 2 ppm p-p at 6 Hz and below 1 ppm at 0.1 Hz. The regulation frequency has been set to 0.5 Hz, however it could be increased up to 5 Hz (with some limitations) if needed since the sampling frequency is done at 10 Hz. The yearly stability has been measured and quantified in offset (about +-2 ppm) and gain (-7 to -2 ppm). Gain and offset are calibrated through dedicated measurements once or twice a year. Continuous online monitoring is not currently possible. At frequency above 10 Hz (e.g. 1 kHz), measurements are dominated by noise of the equipment and it would be complicated to use AC probes. For class 2 PC the stability is < 2 ppm (in 1h) and the noise is < 2 ppm (p-p 0.1 Hz BW) and 6 ppm (p-p 6 Hz BW). Gianluigi commented that for high frequency we could concentrate on 600 Hz and 300 Hz frequencies since they are the ones at which the noise impact the most the simulations. Massimo reminded that J-P. Burnet offered the possibility to bring the noise of 50Hz lines and multipoles below any specified value. Action: M. Cerqueira, M. Giovannozzi and R. Tomas will follow-up on the subject in separate ad-hoc meeting. M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Minutes of last meeting A discussion touching AC magnetic modelling and simulation followed. Miguel asked whether there are important changes in the differential inductance with the frequency. Stephan replied that about 4% has been reported in the literature. Complete simulations of AC magnet and beam screen response would be too complicated, however separate simulations of a magnet and the cold bore and beam could be performed (already quench stress simulation have been performed). It would be relatively easy to measure AC response without beam screen with an anti-cryostat in SM18 on a single dipole (a first opportunity may come in about 3 months). A measurement with beam screen would imply building the appropriate cryogenic infrastructure. In order to make AC measurement a special coil has to be built, but this is relatively straightforward. Lucio and Stephan will see what the possibilities are. The measurements could be used to benchmark simulation that could be then extended to new magnets. Gianluigi asked whether Thyristor or switching power converter will be used. Miguel replied that this has not been decided yet. The EPC expert could provide a more realistic noise spectrum. Riccardo reminded the present discontinuity from current regulation regime and voltage noise dominated regime. Gianluigi asked to Stephan whether the field quality degradation due to the beam screen could be simulated, Stephan replied he will enquire with Susana and Ezio. M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Proposed Measurement in SM18 M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Measurement Design RPHFA.SM18.RM.H converter seems the best fit in terms of both DC range and BW RPHFA.SM18.RM.H to run in Voltage mode at different DC levels + frequency sweep Additional (DC)CT might be needed since RPHFA.SM18.RM.H’s DCCT is rated 13kA 𝑣 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑡 , 𝑖 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑡 , 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 (𝑡) (and/or 𝐵 𝑏𝑒𝑎𝑚 (𝑡) ) synchronously acquired Acquisition with NI PXI-4462 24bit programmable gain setting 4-ch (up to 200 kS/s) Sine-fit post-processing to extract amplitude and phase of: 𝑣 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 , 𝑖 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 , 𝐵 𝑚𝑎𝑔𝑛𝑒𝑡 (𝑓) (and/or 𝐵 𝑏𝑒𝑎𝑚 (𝑓) ) M. Martino TE-EPC - WP2 Meeting - 21/03/2017

Q1-Q2a-Q2b-Q3 HL-LHC example ∆𝜙 𝜙 ≤ 𝑣 𝑐𝑖𝑟𝑐𝑢𝑖𝑡 𝑓 2𝜋𝑓 𝐿 𝑑𝑐 𝑖 𝑛𝑜𝑚 ∆𝜙 𝜙 ≤ 2 10𝑚 𝑉 𝑟𝑚𝑠 2𝜋 300 𝐻𝑧 255 𝑚𝐻 16.5𝑘𝐴 =1.78× 10 −9 =1.78 𝑝𝑝𝑏 M. Martino TE-EPC - WP2 Meeting - 21/03/2017