Differentiable optimization for eddy current parameter fitting

Joint optimization of time constants

Joint optimization using JAX

Equal weights

More weight on orbit

A lot more weight on orbit

Validation

Summary

$C_{\text{orbit}}=1,C_{\text{conv}}=1$

$C_{\text{orbit}}=2,C_{\text{conv}}=1$

$C_{\text{orbit}}=5,C_{\text{conv}}=1$

model	train_loss	train_orbit_loss	train_conv_loss	val_loss	val_orbit_loss	val_conv_loss	tau1	tau2	tau3	c1	c2	c3	orbit_weight	conv_weight
1-exp	0.11438	0.05425	0.06013	0.16533	0.05426	0.11106	0.96662	nan	nan	-2.75497	nan	nan	1	1
2-exp	0.03314	0.02423	0.00891	0.06507	0.02423	0.04083	0.56577	10.02299	nan	-3.83201	-0.93112	nan	1	1
3-exp	0.02820	0.02036	0.00784	0.04356	0.02036	0.02320	0.35746	1.71219	12.20504	-6.04847	-0.59914	-0.77219	1	1
1-exp	0.16169	0.04279	0.07611	0.05955	0.04279	0.01676	1.20598	nan	nan	-2.12960	nan	nan	2	1
2-exp	0.05344	0.02126	0.01092	0.05262	0.02126	0.03135	0.30667	2.83066	nan	-8.69259	-0.94475	nan	2	1
3-exp	0.04855	0.02035	0.00785	0.04429	0.02035	0.02393	0.36330	1.68360	12.05574	-5.88719	-0.58616	-0.78355	2	1
1-exp	0.28182	0.03913	0.08615	0.04757	0.03913	0.00844	1.42345	nan	nan	-1.81053	nan	nan	5	1
2-exp	0.11632	0.02078	0.01244	0.06808	0.02078	0.04730	0.33473	2.65647	nan	-7.33028	-0.92294	nan	5	1
3-exp	0.10962	0.02035	0.00787	0.04527	0.02035	0.02492	0.37574	1.68594	11.89791	-5.61501	-0.55273	-0.79442	5	1

Eddy current decay on orbit as modeled

As observed in the Eddy current modeling and fit.

Analytical Eddy Current compensation

On Friday the LINAC3 source ran out of ions and had to go into 12 h oven re-fill. The consequence was no beam for physics. But we could do a proton MD at 26 GeV with LHC cycles.
We had two MD5 cycles (26 GeV MD cycles) with different cycles before…one with very low energy flattop and one LHC 450 GeV.
Anton’s model can predict the B-train within 0.1 G on these plateaus (very good news!!). I turns out however that these are not the fields the beam sees in the machine. And the difference is eddy current effects…

If we cannot model these we cannot remove MD1. But modelling should still be doabel with beam measurements. We know the field changes versus radial position changes and we can model radial position changes as function of previous Bdot and time etc…

We need an MD for this system identification during the commissioning and then we can put all this together.

We will do something similar for the quads, where first we have to have the dipole decay component already removed.

https://cds.cern.ch/record/1014025/files/ab-note-2007-009.pdf https://cds.cern.ch/record/702648/files/sl-note-2001-013.pdf

• Investigate eddy current compensation using beam-based measurements. [completion:: 2025-02-20]