The decay of the allowed multipoles in the Large Hadron Collider (LHC) dipoles is expected to perturb the beam stability during the particle injection. The decay amplitude is largely affected by the powering history of the magnet and is particularly dependent on the pre-cycle flat-top current and duration as well as the pre-injection preparation duration. With possible prospects of having different genres of cycles during the LHC operation, the powering history effect must be taken into account in the Field Description Model for the LHC and must hence be corrected during machine operation. This paper presents the results of the modelling of this phenomenon

Bottura, L

Micallef, J

Sammut, N

Sanfilippo, S

CERN Document Server

1 CERN, Accelerator Technology Department, Geneva, Switzerland2  University of Malta, MaltaEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHEuropean Laboratory for Particle PhysicsTHE DEPENDENCE OF THE FIELD DECAY ON THE POWERING HISTORYOF THE LHC SUPERCONDUCTING DIPOLE MAGNETSN. Sammut1, L. Bottura1, J. Micallef2, S. Sanfilippo1The decay of the allowed multipoles in the Large Hadron Collider (LHC) dipoles is expected to perturbthe beam stability during the particle injection. The decay amplitude is largely affected by the poweringhistory of the magnet and is particularly dependent on the pre-cycle flat-top current and duration as wellas the pre-injection preparation duration. With possible prospects of having different genres of cyclesduring the LHC operation, the powering history effect must be taken into account in the FieldDescription Model for the LHC and must hence be corrected during machine operation. This paperpresents the results of the modelling of this phenomenon.Presented at the Tenth European Particle Accelerator Conference (EPAC'06)26-30 June 2006, Edinburgh, UKGeneva, Large Hadron Collider ProjectCERNCH - 1211 Geneva 23SwitzerlandLHC Project Report 956 Abstract4 August 2006THE DEPENDENCE OF THE FIELD DECAY ON THE POWERING HISTORY OF THE LHC SUPERCONDUCTING DIPOLE MAGNETS* N. Sammut#, L. Bottura, S. Sanfilippo, CERN, Geneva, Switzerland J. Micallef, University of Malta, MaltaAbstract The decay of the allowed multipoles in the Large Hadron Collider (LHC) dipoles is expected to perturb the beam stability during the particle injection.  The decay amplitude is largely affected by the powering history of the magnet and is particularly dependent on the pre-cycle flat-top current and duration as well as the pre-injection preparation duration. With possible prospects of having different genres of cycles during the LHC operation, the powering history effect must be taken into account in the Field Description Model for the LHC and must hence be corrected during machine operation. This paper presents the results of the modelling of this phenomenon.   INTRODUCTION The Large Hadron Collider (LHC) at CERN can only be controlled adequately if the main magnetic field and its harmonics are known to the required accuracy. Unfortunately, a control system solely based on measurements of beam perturbations produced by the field inhomogeneities may be too demanding for the instruments available. Therefore, in order to reduce the burden on the beam-based feedback, a feed-forward system will be used to predict the behaviour of the field errors during the machine cycle. This feed-forward system is known as the Field Description for the LHC (FIDEL) [1]. The latter is primarily based on a field model which separates the effects that together contribute to the total field in a magnet aperture.  One of the main error components that largely affects the field during the injection plateau is the systematic decay of the allowed harmonics. It has now been established that this phenomenon is mostly a consequence of field changes in the strands caused by current redistribution in the superconducting cables [2], [3]. Unless the small changes of the local magnetic field are overwhelmed by a change in the transport current, they affect the magnetisation of the filaments in the strands causing it to decrease. This therefore results in a net magnetisation decrease in the aperture i.e. a field decay. As described in [4], the decay drift can be modelled well enough with a double exponential function of the type:    ( ) ( ) ⎟⎟⎠⎞⎜⎜⎝⎛−−+⎟⎟⎠⎞⎜⎜⎝⎛−=Δ−−−−τττ 9111,,,injinj ttttinj ededdtt   (1)   which is a direct consequence of current diffusion through the cable.  Measurements have shown that the harmonic decay is not reproducible from cycle-to-cycle [4], [5]. The decay amplitude is strongly dependent on the magnet powering history. It has been shown in [6] that this dependence can be formulated by a composition of current imbalance redistributions from previous cycles which partially cancel. In the first approximation, these redistributions can be modelled in the same way as a charging-discharging L-R circuit.  POWERING HISTORY DEPENDENCE Studies performed on short LHC dipole models based on a single powering cycle [7] have shown that the decay amplitude is mostly dependent on the pre-cycle flat-top current IFT, flat-top duration tFT and the pre-injection plateau duration time tpreparation. The powering pre-cycle can therefore be characterised by these three parameters as shown in Figure 1. In practice, measurements have shown that the powering history of the magnet can be condensed into a single powering pre-cycle. quenchpre-cycle tpreparation preparation porch-dI/dt dI/dt tFT IFT current Ipreparation 760A injection porchparabolic acceleration starttime  Figure 1: Parameters affecting decay during injection MEASUREMENT PROCEDURE Powering history dependence measurements performed at cold on series dipole magnets were each preceded by a quench to erase all persistent currents. A pre-cycle with its parameters varied was then followed by an LHC cycle. A standard pre-cycle (IFT= 11850 A, tFT = 1000 s, tpreparation= 0 s) as used in series decay measurements was used as a reference.  When testing the influence of one parameter (e.g. the flat-top current) the second and third parameters (e.g. the flat-top duration and the pre-injection duration) were held constant at the value corresponding to the standard pre-cycle. The measurements were performed with the twin rotating coil system [8]. The IFT dependence was measured on 18 apertures, the tFT dependence was measured on 24 apertures and the tpreparation dependence was measured on 14 apertures.  *Work supported by CERN; # nicholas.sammut@cern.ch WEPLS104 Proceedings of EPAC 2006, Edinburgh, Scotland2622 07 Accelerator TechnologyT10 Superconducting Magnets1MATHEMATICAL FORMULATION The powering history dependence in the decay amplitude δn of the harmonic n can be modelled by:      ⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎝⎛−−=−−nEstdFTnEFTFTFTInnInnIstdIneEEeEEττδδ1010   (2)   ⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎝⎛−−=−−nTstdFTnTFTFTFTtnntnntstdtneTTeTTττδδ1010  (3)  ⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎝⎛++=−−nPstdnpreparationPnpreparationpreperationpreperatiotnntnntstdtnePPePPττδδ1010 (4) where δstd is the decay amplitude measured for a standard pre-cycle, i.e. with flat-top current equal to the nominal current of stdFTI = 11850 A, flat-top time stdFTt = 1000 s and pre-injection time stdnpreparatiot = 0 s. nEτ , nTτ and nPτ  are the time constants for the magnet memory for flat-top current, flat-top duration and pre-injection time respectively. nE0nE1 nT0 , nT1 , nP0  and nP1  are the fitting parameters. These three equations are a direct consequence of the assumption of exponential decay during constant current excitation, i.e. Eq 1, where only the longest time constant has been retained for simplicity. RESULTS The average dependence was obtained by first fitting Eq 2, 3 and 4 to the data. Figure 2 shows the measurement results of the b3 decay amplitude vs.  IFT  (top), tFT (middle) and tpreparation (bottom). Considering the average curves of the measurements, the importance of the three parameters can be determined for the main field and the harmonics being considered. The difference between the maximum and minimum value of the curves is shown in Table 1. This table therefore shows that the most important dependence is IFT since variations of this parameter cause the largest change. Table 1 also indicates that all the three parameter dependencies for b3 are important for modelling. The IFT and tpreparation dependence for b1 and b5 is relatively small and is comparable to the twin rotating coils measurement system uncertainty. For this reason we choose not to model these effects.    Table 1: The average effect of each powering history parameter on the allowed harmonics parameter b1 (units) b3 (units) b5 (units) IFT 0.9 1.29 0.21 tFT 0.02 0.46 0.03 tpreparation 0.49 0.6 0.02 00.511.522.533.53800 4800 5800 6800 7800 8800 9800 10800 11800IFT (A)delta b3 (units) 00.511.522.533.50 500 1000 1500 2000 2500 3000 3500 4000TFT (s)delta b3 (units) 00.511.522.533.50 200 400 600 800 1000 1200 1400 1600 1800 2000t-preinj (s)delta b3 (units) Figure 2: The effect of a variation of IFT (top), tFT (middle) and tpreparation (bottom) on the decay amplitude at the end of injection.  (bold black line is the average dependency) EXTRAPOLATION OF THE  PARAMETER SPACE Eqs. 2, 3 and 4 can be joined together to yield an equation that extrapolates the powering history dependence to a 3d parameter space: ⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎝⎛++⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎝⎛−−⎟⎟⎟⎟⎠⎞⎜⎜⎜⎜⎝⎛−−=−−−−−−nPstdnpreperationPstdnpreperationTstdFTnTFTnEstdFTnEFTtnntnntnntnnInnInnstdnePPePPeTTeTTeEEeEEττττττδδ101010101010  (5) The reference cycle is a pivot point that is common for all three powering history parameters. However, this pivot point has different values for the three parameters due to the limited sample of measurements taken. To homogenise the pivot point and to have a powering history prediction for the entire magnet population, a scaling law is used to scale the average curves of Figures 2. Eq. 5 is then used to fit the three scaled average curves to a 3-dimensional parameter space. The fit yields the parameters reported in Table 2. The corresponding surface plots are shown in Figure 3. For b3, the parameterization is found to produce an extrapolation with a maximum error of 0.15 units with a median error of 0.035 units. Proceedings of EPAC 2006, Edinburgh, Scotland WEPLS10407 Accelerator TechnologyT10 Superconducting Magnets262324000600080001000012000010002000300040000.511.522.5flat top current (A)flat top time (s)δn  4000600080001000012000050010001500200000.511.522.5flat top current (A)pre-inj time (s)δn 020004000050010001500200011.52flat top time (s)pre-inj time (s)δn  Figure 3: IFT vs. tFT (top), tpreparation vs. IFT (middle) tpreparation vs. tFT (bottom) CONCLUSION The decay amplitude dependence on the powering history of the LHC dipoles has been investigated by performing an extensive measurement program using rotating coils.  The measurements were focused on the pre-cycle flat-top current, the pre-cycle flat-top duration and pre-injection duration which are known to have the largest effect on the decay. A model was constructed to interpolate the results obtained. The model was then extended to a 3d parameter space to extrapolate the powering dependence to magnetic states that were not measured. The results of the extrapolation were very satisfactory since the maximum error between the 3d model and the data was only 0.15 units @17mm. This 3d model is therefore quite powerful and will provide a good extension to FIDEL.     Table 2: the fit parameters of the 3-dimensional  powering history dependence  Coefts b1 b3 b5 E0 -0.467 16.981 -0.7025 E1 -1.027 22.984 -1.0329 IFT τΕ 4.665 0.658 5.8430 T0 - 8.18 - T1 - 2.063 - tFT τΤ - 0.040 - P0 - -8.779 - P1 - 3.728 - tpreparation τP - 0.039 - population decay amplitude stdδ  0.986 2.004 -0.302 REFERENCES [1] N. Sammut, L. Bottura, J. Micallef “Mathematical Formulation to Predict the Harmonics of the Superconducting Large Hadron Collider”, Phys. Rev. ST Accel. Beams, 9, 012402, January 2006 [2] L. Krempasky, C. Schmidt, “Experimental Verification of ‘Supercurrents’ in Superconducting Cables Exposed to AC-fields”, Cryogenics 39 (1999) 23-33 [3]  R. Stiening, “A Possible Mechanism for Enhanced Persistent Current Sextupole Decay in SSC Dipoles,” SSC Report SSCL-359 (1991) [4]  A.K. Ghosh, K.E. Robins, W. Sampson, “Time Dependent Magnetization Effects in Superconducting Accelerator Magnets”, Proceedings to the 15th International Conference on High energy Accelerators, Vol. 2, 665-667, July 20-24, 1992  [5]  R.W. Hanft, B.C. Brown, D. A. Herrup, M. J. Lamm, A. D. McInturff, M.J. Syphers, “Studies of Time Dependence of Fields in Tevatron Superconducting Dipole Magnets”, IEEE Trans. Mag. Vol. 25, No. 2 (1989), 1647-1651 [6]  T. Schreiner, “Current Distribution Inside Rutherford-type Superconducting Cables and Impact on Performance of LHC dipoles”, Ph. D. thesis, Vienna University of Technology, 2002. [7] M. Haverkamp, “Decay and Snapback in Superconducting Accelerator Magnets”, Ph.D. Thesis, University of Twente, Netherlands, 2003 [8]  J. Billan et al. “Twin Rotating Coils for Cold Magnetic Measurements of 15 m Long LHC dipoles”, IEEE Trans. Appl. Supercond. 10, no.1, pp 1422-1426, Dec 1999 WEPLS104 Proceedings of EPAC 2006, Edinburgh, Scotland2624 07 Accelerator TechnologyT10 Superconducting Magnets3

The Dependence of the Field Decay on the Powering History of the LHC Superconducting Dipole Magnets

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