Hysteresis Compensation

Paper outline

3 min read

Introduction

  • Why are hysteresis and eddy currents a problem
    • Multi-cycling machine
    • Reduced flexibility in cycle combinations
    • Energy savings
      • Restrictions with economy modes
      • Quantify energy savings
    • Half-hearted mitigation MD1
  • EPA project & Hysteresis compensation work package description
  • Timeline
  • Short summary of paper, why on dipole and not on quadrupole → B-Train

Observations / Background

SPS is a multi-cycling machine

  • SPS has different clients, and accelerates beams with different properties and
  • Cycles are organized in supercycles
  • Changing supercycles cause change in hysteresis loops, with different remnant fields, especially when magnets are ramped to non-linear saturation domain. → Differnent resulting beam parameters depending on previous magnetic cycle
  • Tight scheduling with fast ramps up and down do not allow eddy current to decay, which couple with hysteresis
  • Dynamic economy, MD1

Figure: Supercycle composition a) SPS supercycle SFTPRO-MD1-SFTPRO-MD1, SFTPRO - ZERO - LHCPILOT - MD1, … SFTPRO1-MD1-SFTPRO-MD1 b) Difference w.r.t. a reference c) Difference w.r.t. a piecewise linear function fitted to the magnetic field response

High-precision field control for slow extraction

  • Discuss significance for SFTPRO due to very sensitive slow extraction
    • Effects of a few gauss relevant at flat top for spill stabilization
    • Accuracy of 0.1 Gauss required for flat bottom
    • Cite Francesco’s paper
    • Example plots

Existing methods for high-precision field control

  • Main dipole fields are measured in real time at 200 kHz
  • B-Train feedback to power converters, missing in higher order magnets
  • We use attempt pilot project using main dipoles due to existence of online measurement system

Figure: Discrete function fit to magnetic field response, and residual field on I vs

Prediction and feed-forward correction of magnetic fields with neural networks

Feed-forward correction principle

  • Dynamic magnetic field prediction with time series forecasting methods: what, how
    • Build a transfer function from using neural networks
  • Model choice, PINN, transformer

Methodology for data collection.

  • Special case for MBIs with reference magnet system and B-Train.
  • Lab measurements with vacuum chamber
  • Challenges with noise and drift correction
  • Data preparation Figure: Demonstration of compensation method a) LHC - MD1 - SFTPRO with timeline of when prediction, trim and start cycle Show which variables are used b) Diagram with trim hierarchy

Training neural network

  • Training and evaluation, model choice

Results and limitations

  • Usage of compensation method presented in previous section
  • First results and current limitations
    • Success for flat top on SFTPRO
    • Show several SFTPRO cycles overlayed with LHC in supercycle, raw and prediction, followed by plot of several SFTPRO right after supercycle change with raw and prediction
  • High precisions required on flat bottom, even higher precision required for flattening flat bottom
  • Trim needs to be sent at least 1.7s before cycle start, not a lot of time for prediction for heavy neural networks
  • Measurement drift in dipole field measurements a significant problem, as the drift is in the order of , marker presents significant problem in data accuracy
  • Measurements are noisy, almost in the order we are interested in
  • Measurements in the online SPS do not allow full mapping of hysteresis loops → lab measurements
  • For higher order magnets, and for dipoles we need high precision lab measurements and novel drift compensation methods

Figure: Eddy current correction at flat bottom on MD3, show inset with measured current, field, and radial position Figure: Hysteresis compensation of SFTPRO on flat top with changing supercycles, refer to Figure 1.

Conclusion

  • Feedforward correction a strong candidate for improving reproducibility of magnetic fields in a multi-cycling
  • Accuracy not there yet, but coming

Future

  • Lab measurements of higher order magnets
  • Improved models, potentially with PINN loss with transformers
  • Deployment in operations
  • New feedforward method required for higher order magnets.

Graph View