Field Model for the Multipoles Factory FQWG, 17/3/2004 S.Amet, L.Deniau, M.Haverkamp, L.Larsson, T.Pieloni, S.Sanfilippo, M. Schneider, R. Wolf, G.Ambrosio (+), P.Bauer (+) and many other contributors from AT-MTM presented by L.Bottura (+) Fermilab, TD

Salvific Magnetic Reference … or usine-a-gaz wasting resources ? (LE, private communication, Chamonix XIII, 2004) a key to the successful ramp management at the LHC… ora pro nobis

Overview A description of the field dynamics in the LHC MB’s and MQ’s: the Field Model:  general decomposition in error components  static errors (geometric, persistent, saturation)  decay and snap-back Error sources  extrapolation errors  magnet life-long instabilities  modelling errors  measurement errors Expected results  uncertainty on settings at injection and flat-top  uncertainty on ramp correction (work in progress)

The field model complex harmonic coefficient C n in MB’s and MQ’s depends on  time t  current I  ram-rate dI/dt  temperature T  powering history I(-t) simple fits based on physical models or empiric relations (tested against measurements)

Components in the field model general decomposition in error sources  geometric  DC magnetization from persistent currents  iron saturation  decay at injection  snap-back at acceleration  coil deformation at high field  coupling currents  residual magnetization smaller values smaller variability smaller uncertainty higher values higher variability higher uncertainty

Geometric multipoles important at all field levels absolute field is linear in current, normalised field is constant measured in warm conditions (can be extrapolated from industry data)

Persistent currents mostly important at low field (but present throughout) proportional to the magnetization M proportional to J c assume that the Jc(B) scaling is maintained (geometry and B distribution effects are condensed in fitting exponents  and  ) add T dependence

Iron saturation important at high field only associated with details of iron geometry (shape of inner contour, slits, holes, …) no “theoretical” expression available, apart for the general shape of the saturation curve (sigmoid) take a convenient fit to the experimental data

Decay appears during constant current excitation associated with current redistribution in the superconducting cables result of a complex interaction: current redistribution  local field  magnetization  bore field assume that the dynamics follows that of current diffusion

Powering history effects average effect of powering history has an uncertainty due to limited sampling (2 % of production ?) 2 magnets3 magnets

Powering history dependence main parameters:  flat-top current  flat-top duration  waiting time before injection  (injection duration) t FT t injection t preparation I FT I t

Snap-back first few tens of mT in the acceleration ramp, after injection pendant to decay: magnetization changes are swept away by background field result of a complex interaction: current ramp  background field  magnetization  bore field magnet family invariant found by serendipity

Look at the data the right way… fit of the b3 hysteresis baseline hysteresis baseline subtracted b3 snap-back singled out exponential fit

Same magnet, different cycles  b 3 and  I change for different cycles… … and they correlate !

An invariant for snap-back !?! great ! the correlation plot holds for many magnets of the same family

Coil deformation coil deforms under Lorentz loads at high field the displacement of the strands is proportional to the electromagnetic force this effect is small (order of 0.1 … 0.2 units of b3)

Coupling currents important during the ramp eddy currents flow resistively among superconducting filaments in strands and superconducting strands in cables these currents couple the superconducting filaments and strands contribution is proportional to dB/dt and constant in B (neglect magnetoresistivity effects) this effect is small (order of 0.1… 0.2 units of b3)

Residual magnetization important at very low field (e.g. warm measurements) iron (or other magnetic parts) maintain a magnetization after powering at high field very small values, broadly unknown origin, useful to adapt fits (especially for the transfer function)

W/C extrapolation errors 30 % cold measured (realistic ?) uncertainty estimated on a sector (50 magnets) take best result (lowest uncertainty) for the estimate, from W/C extrapolation

Magnet stability at long term coil geometry changes during the magnet life  settling and ratcheting of the composite formed by cables, wedges and insulations geometric multipoles change systematic effect observed only on allowed multipoles

Modelling errors deviation of local fit from average  for magnets completely measured the fit residual can be decreased at will  for magnets not completely measured the model may be not appropriate/sufficient/adapted uncertainty on decay and SB produced by  LHC powering cycle different from the one measured and modelled 6 TeV vs. 7 TeV expected and unexpected waiting times temperature changes …

Modelling of Decay scaling Analytical model accurate to ≈20 % Neural network accurate to ≈ 5 % the model of the average has an uncertainty

Uncertainty from model assume model is accurate to 20 % of effect add uncertainty on average due to limited sample  so far 2 % of the population has been characterised (partially)  assume 20 magnets till the end of the production NOTE: this is obviously a good reason to have extra magnets on the benches at LHC start-up and after

Uncertainty from measurements assume coil radius is known to within 50  m  sensitivity to harmonic of order n scales as the radius to the n-th power  error on the harmonics  n is proportional to n  Radius add uncertainty from measurement r.m.s.

Uncertainty on settings injection uncertainty on b1 is the same at injection and flat-top uncertainty on a1 does not contain the effect of changes of magnet roll uncertainty on b3 and b5 at injection significantly larger than at flat-top

Summary of estimates A comment: seems pretty damn good to me, there must be something wrong…

Work in progress (by KW-14) verify model vs. measured magnets (L. Deniau, V. Granata, N. Sammut) hardware concept for reference magnets (M. Buzio, A. Masi) data fusion concept (L. Deniau) experience at HERA, Tevatron, RHIC (L. Bottura) plan and cost estimate (L. Bottura) scope of the review, panel, participants, to be discussed at the next FQWG