THE MAGNETIC MODEL OF THE LARGE HADRON COLLIDER B. Auchmann, L. Bottura, M. Buzio, L. Deniau, L. Fiscarelli, M. Giovannozzi, P. Hagen. M. Lamont, G. Montenero, G. Mueller, M. Pereira, S. Redaelli, V. Remondino, F. Schmidt, R.

Steinhagen, M. Strzelczyk, R. Tomas Garcia, E. Todesco, W. Venturini Delsolaro, L. Walckiers, J. Wenninger, R. Wolf, F. Zimmermann, CERN, Geneva, Switzerland.

Abstract The beam commissioning carried out in 2009 has

proved that we have a pretty good understanding of the behaviour of the relation field-current in the LHC magnets and of its reproducibility. In this paper we summarize the main issues of beam commissioning as far as the magnetic model is concerned. An outline of what can be expected in 2010, when the LHC will be pushed to 3.5 TeV, is also given.

INTRODUCTION During the three weeks of beam commissioning in

2009, the LHC has been operated at a maximum energy of 1.18 TeV. In a very short time circulating beams have been established, and then ramps to 1.18 TeV and collisions, both at injection and high energy, have been successfully tried [1]. During the last days of beam commissioning, the operation crew even managed to successfully squeeze [2] the beam at 1.18 TeV from 11 to 7 m in CMS!

In this paper we outline the main result of the beam commissioning as far as the magnetic model [3-5] is concerned. The first aim is to reconstruct from beam-based measurements an assessment of the precision of the model. The second one is to identify areas where the knowledge of the magnets is not sufficient for operation, and how to improve it.

Throughout the paper we will use two words coming from the slang of the magnet community: (i) by transfer function we indicate the ratio between the field generated by a magnet and the current flowing in its coils; (ii) most of the quantities are expressed as a relative value in units, one unit being 0.01%.

ORBIT How much strength of the arc orbit correctors did we use ?

The orbit correctors in the arc have a nominal current of 55 A. At the injection energy of 450 GeV they have been typically powered with less than 1 A (see Fig. 1). Applying a scaling factor, one expects a powering below 15 A at 7 TeV, i.e., we have nearly a factor 4 of margin. This is not completely correct since the powering at injection is so low that the magnet could behave in a non linear way (see Fig. 2, where magnetic measurements are shown). Therefore one should expect that the current to be used in the orbit correctors during ramp and at top energy will not be a simple scaling of the values used at injection. Anyway, the first results show that the orbit

correction is using only a small fraction of the budget available. This confirms the high homogeneity of the transfer function in the main dipoles and the good alignment of the main quadrupoles.

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Figure 1: Current used in orbit correctors MCB, on December 15 at 21.00.

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Figure 2: Measured transfer function of the orbit correctors, in block4 and in SM18.

Difference between sectors The eight sectors of the LHC arcs are powered with

slightly different currents which are tuned on the ground of the room temperature magnetic measurements. The difference in the transfer function of each arc reflects the tolerances of the magnet components and manufacturing. According to magnetic measurements, one has a 10 units peak to peak difference between the transfer function of the sectors. Due to a slight decrease of the transfer function during the production (of the order of less than 10 units [6]), sector 7-8, containing the magnets of the beginning of the production, has 6 units larger transfer function than average. This is compensated by using a 6

units smaller current in the sector (see Table 1). On the other hand, sectors 6-7 and 1-2 have 4 units lower transfer function, and they are powered with 4 units larger current (see Table 1). Beam measurements showed that using these settings, the peak to peak difference in the transfer function between sectors is reduced to 5 units in both beams. This is a valuable cross-check of the loop magnetic measurements – beam measurements (see Table 1).

Table 1: Current in the main dipoles, and difference between sectors transfer functions estimated through

beam measurements [7].

(A) (units) Sector Beam1 Beam2757.21 3.9 1 2 -2.3 -2.5757.05 1.8 2 3 0.9 -0.5756.92 0.1 3 4 2.4 2.5756.71 -2.7 4 5 0.2 -2.1756.91 0.0 5 6 -2.7 -1.5757.19 3.7 6 7 -1.2 -1.1756.47 -5.8 7 8 1.7 3.2756.83 -1.1 8 1 2.2 0.2

Current Measured (units)

Bumps around spectrometers Both Alice and LHCb have magnetic spectrometers

providing horizontal and vertical magnetic field respectively, that need to be compensated by means of three orbit correctors each (compensators belonging to four families: 2 MBXWT, 2 MBXWS, 1 MBXWH, 1 MBWMD). During operation in 2009, the non closure of the bump around the experiments was found to be larger than expected. Unfortunately, there is no possibility of finding a unique solution from beam measurements, since the problem is under-constrained. The possible errors [8] are of the order of 0.5 to 2 % (see Figure 3). This effect can be corrected and it has not been a severe limit to operation, but it would be worth to be investigated. Two issues have been pointed out. • The spectrometers are long magnets with a large

gap, hence generating a non uniform field with non-negligible stray field components. A mapping along the longitudinal axis is available. This could be included in the beam dynamics model.

• The compensators have not been precycled in 2009. This could change the transfer functions of few percent, but only at low currents.

Two magnets (MBXWT and MBXWS) have been re-measured in fall 2009 [9], confirming the transfer function values at high current within few per mil (see Figure 5).

TUNE Trims at injection Using the nominal settings of dipoles and quadrupoles, the tunes agree with the nominal tunes within 0.1 (see

Table 2). This corresponds to having an absolute precision of 15 units in the ratio between quadrupole field and the dipole field at injection B2/B1, which is a rather remarkable result. Tune trims are done through MQTF and MQTD, i.e. two families of quadrupoles per beam. These magnets, which have a nominal current of 550 A, were used at injection with values below 5 A. A simple scaling suggests that at high field the magnets will be powered with less than 80 A, i.e., at 15% of nominal.

Figure 3: Correction in the Alice spectrometer transfer function needed to close the bump vs. current [8].

Figure 4: Correction in the MBWMD compensator

transfer function needed to close the bump vs. current [8].

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Figure 5: Measurements of MBXWS using stretched

wire in fall 2009 (SSW) compared toHall probe measurements used for the FiDeL model (dashed line).

Table 2: Tune trim and current in the tuning quadrupoles at the beginning of the 6th ramp [10].

T rim Beam1 Beam2dQh -0.02 -0.09dQv 0.05 0.01

QT D (A) 1.02 -0.29QT F (A) -0.34 -2.12

The two beams have the same tune within 0.1. The

MQT have a low hysteresis, and operation confirms that this is not a limiting factor for steering the tune. In Figure 6 we show the experiment where the trim was applied to increase and then reduce the horizontal tune by 0.1 [11]. The measured tunes went back exactly on the previous values, showing that the MQT hysteresis is negligible for tune trimming.

Figure 6: Tune trim applied on the horizontal plane

back and forward to estimate the impact of hysteresis.

Behaviour during ramp At the beginning of the ramp, i.e. during the snapback,

the tune is stable within 0.005 [10]; this implies that the tracking of the quadrupole over the dipole is stable within 1 unit. This impressive result confirms the magnetic measurements, showing that the decay (and associated snapback) of the main components of dipoles and quadrupoles are within one unit, i.e., negligible.

During the ramp up to 1.18 TeV one observes a tune drift, which has been corrected through the feed-forward and the feedback systems. The drift is clearly systematic, and is somewhat different in the two beams. The tune drifts of about -0.1 in the horizontal plane and of 0.02 in the vertical one. Beam 2 horizontal tune has a horizontal drift of half of what observed in Beam1. This translates into a capability of tracking B2/B1 within 15 units. Even though this drift has posed no problems to operation, it is worth to analyse the probable sources [12].

• Initially the drift is pretty parallel to the diagonal, i.e. both planes have the same drift,

which is the fingerprint of an error in tracking B2/B1. Then, the variation of the horizontal plane is different from the vertical one, suggesting that the source is not a wrong modelling of the dipole and quadrupole main components.

• A second source can be an uncorrected b3 plus an orbit offset. No orbit feedback has been used during the ramp, so this could be the effect of a constant error in the b3 tracking with a changing offset during the ramp, or a systematic misalignment of the spool pieces w.r.t. the dipoles [12].

• A wrong precycling of the MQWA, MQWB, MQXA and MQXB has been shown to have a large impact on tune at injection, and disappears during the ramp. This effect (see next sections) will be corrected in 2010: therefore these patterns are likely to be different for the next machine run.

Figure 5: Tune drift during ramps 5 and 6 reconstructed

from data of the feedback system [10] (red is Beam1, blue Beam2).

Figure 6: Tune drift during ramps 7 and 8 reconstructed

from data of the feedback system [10] (red is Beam1, blue Beam2).

CHROMATICITY Trims at injection

Chromaticity has been trimmed at injection typically by 10-15 units [10]. This corresponds to an absolute precision of the b3 correction in the dipoles of 0.2-0.3 units. This is about a factor 3 larger of the precision of the measurement system, i.e., it is a pretty good result for an early stage of the beam commissioning, but in principle there should be some room for improvement. This also includes the decay of b3, since we inject the beam when the decay has already fully taken place (typically a few hours after establishing the injection currents).

Behaviour during ramp At the end of the ramp the chromaticity has lowered by

3-15 units (see Table 3). This corresponds to tracking the b3 in the main dipole within 0.3 units. Also in this case the result is encouraging, but there is room for improvement. There are known uncorrected effects that influence chromaticity during ramp. • According to the recent measurements carried out

in fall 2009 and winter 2009-2010, we believe that there are 0.2 units of uncorrected b3 (see next section). This gives about 8 units in horizontal and -8 units in the vertical chromaticity, i.e. justifying the horizontal drift but doubling the vertical one.

Table 3: Chromaticity change during the ramp to 1.18 TeV [10].

ΔQ'H ΔQ'Vramp4 B1 -6.3 -14.7ramp5 B1 -2.7 -13.2ramp6 B1 -3.0 -10.8ramp6 B2 -9.2 -8.1

BETA BEATING Beta beating has been measured a few times at injection energy and once at 1.18 TeV. The first measurement has been done without precycling. Data show that one has a very poor reproducibility if the precycling is not carried out (see Figure 7). On the other hand, if the magnet precycling is carried out, the beta beating is reproducible within a few percent (see Figure 8). A beta beating of 20-40% is observed in both planes at injection ([13], see Figure 8). The measurement at 1.18 TeV gives a beta beating within 20%, i.e. within specifications (see Figure 9). Optics simulations suggest that there are imperfections in the interaction regions quadrupole of the order of a few percent in the MQWA, and a half percent in the triplets, that disappear during the ramp [13]. Relevant sources of beta beating have been identified by the end of January 2010 [13] as a wrong precycling

strategy (see next sections), placing the MQXA and MQXB around IR1 and IR5, and the MQWA around IR3 and IR7 on the wrong branch of the hysteresis. The effect is particularly relevant for the MQWA, whose transfer function is 4% larger on the ascending branch of the hysteresis (see Figure 10). For the MQXA and MQXB, based on the magnetic measurements, the wrong precycling should give a about 0.5% lower transfer function at injection. This is in good agreement with what foreseen on the ground of beta beating measurements. The lack of precycling for the MQTLH (Q6 in IR3 and IR7) should not have a large impact since the magnetization is low.

Figure 7: Reproducibility of beta beating measurement

at 450 GeV, with and without precycling [13].

Figure 8: Reproducibility of beta beating measurement at 450 GeV in two runs with precycling [13].

ESTIMATES FOR RAMP AT 3.5 TEV At the beginning of the ramp some field component rapidly (within 10-50 A) snapback to their original values before the beginning of the decay. The effect is negligible for the dipole and quadrupole main components. The largest effect is on the first order harmonic in the dipoles, i.e. b3. At the end of the prototype phase, the amplitude of the average snapback in the dipoles was estimated at about 2.5 units [3,4]. Successive measurements showed that the precycle ramp rate was a relevant parameter.

Since during the series tests this parameter was fixed at 50 A/s to speed up measurements instead of 10 A/s, the decay to be expected was much lower, i.e. about 1 unit [5]. Having a precycle at much lower currents (i.e. 2 kA instead of 11.8 kA) further reduces the snapback amplitude [5].

Figure 9: Beta beating measurement at 450 and at 1180

GeV [12].

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Figure 10: Transfer function of the MQWA versus current measured on the ascending and descending hysteresis branch [14]. Two equations have been proposed to model this effect [4] [5]; they give similar results at 11.8 kA, but rather different values at 2 kA, ranging from 0.1 to 0.3 units (see Figure 10). In 2009, the [4] version has been implemented. Magnetic measurements carried out in winter 2009-2010 has shown that the [5] model reveals to be more precise (see Figure 11). Therefore we expect that during 2009 about 0.2 units of b3 were not corrected at the beginning of the ramp. The same model foresees a snapback for 2010 of 0.5-0.6 units, i.e. about the double of what we had at 2 kA in 2009.

PRECYCLING ISSUES Missing precycles The following magnets have not been precycled in 2009: (i) the MQTLH in Q6, left and right of IR3 and IR7 and (ii) the spectrometers compensators MBXWT, MBXWS,

MBXWH, MBWMD. All the other magnets have been precycled according to prescriptions. This should have a relatively low impact, since the hysteresis of the MQTLH is small, and the compensators were used at high currents, where the precycling strategy has no influence.

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Figure 11: Expected amplitude of the b3 snapback

versus precycle current: scaled measurements (markers) and models present in Refs. [4] and [5].

Lowest precycle current By the end of January 2010 it has been found [14] that the minimum current used in the precycle is sometimes larger than the injection current. This implies that the magnet at injection is still on the descending branch of the hysteresis. This effect is present in MQWA, MQXA, MQXB, MBXW (see Table 4). These wrong settings have been corrected in February 2010. Table 4: Minimum precycle current and injection current

– in red values that have been corrected in 2010.

MagnetMin. precycle current (2009)

Min. precycle current (2010) Inj. Current

MB 350/500 350/500 757MQY 100 100 130

MQM 4.5 K 100 100 130MQM 1.9 K 100 100 130

MBX 200 200 345MBRC 200 100 284/385MBRS 200 200 353MBRB 200 200 395

MQ 350 350 686MQXA 400 200.1 408/452MQXB 700 350.2 700/776MBXW 18.1 18.1 43.7MBW 41.1 18.1 40.9

MQWA 35.1 20.1 35.3/38.0

Magnets with negative currents nominal settings Some magnets have a negative current as a nominal setting. This is the case for half of the MQTL and half of the MQWB. In this case the precycle should be first on negative currents, and then on positive to place the magnets on the descending branch of the hysteresis. On the other hand, in 2009 this effect has been not taken into

account. For the MQTL the impact is negligible, since the FiDeL model does not take magnetization into account. For the MQWB, which are powered with very low current and which have a relevant residual magnetization, the effect can be rather important. A down-up precycle has been implemented for MQWB with negative current settings.

CONCLUSIONS The beam commissioning experience of 2009 has shown that the reproducibility of the machine is well ensured if the precycling strategy is followed, and that the knowledge of the relation current.-magnetic field is in general very good. We quote the following issues, rated by order of relevance for beam operation. • The beta beating at injection is around 40% in some

sections of the machine. Even though this is a pretty impressive result for an early stage of commissioning, this is not yet within specifications. Inverse simulations suggest that some quadrupoles in the IR regions have a mismatch in the transfer function of the order of 1%. It has been recently found out that this could be partially due to a wrong precycling. On the other hand, the beta beating at 1.18 TeV is not far from the 20% specification, thus suggesting that the problems in the field model are at injection level, i.e. are related to the magnetization components. This is consistent with the hypothesis of a wrong precycling. With the revised precycles, we should expect a pretty different pattern of beta beating in 2010.

• The non closure of the bump around the spectrometer compensators is suggesting errors of the order of 1% either in the spectrometer or in the compensator transfer functions. Compensators have been measured again showing consistency with previous results within a few per mil. A more precise model of the spectrometers is being implemented to take into account of the variation of the field along the axis. Contrary to 2009, the compensators will be precycled in 2010; this could have some impact on the settings at low field, but not when the spectrometers are fully powered.

• There is a drift of chromaticity during the ramp which is not understood. A part of it is systematic for all ramps: this corresponds to about 0.3 units of uncorrected b3. According to measurements one should be able to track at least with a factor 3 higher precision (within 0.1 units). This drift could pose problems for operation. According to our best knowledge of the field model, in 2009 we had about

0.3 units of b3 snapback, and a correction of 0.1 units has been implemented.

• Tune: o There is a tune drift during the ramp (well after

the snapback) whose origin is not understood. The drift is systematic for all ramps, with a striking difference between beam1 and beam2. This does not pose problems for operation since the feedback system can cope with it easily.

o The tune steering is successful, showing that the hysteresis of the MQT is not an issue for operation. Small trims are necessary to obtain nominal tune.

o Due to the correction of the precycling for MQWA, MQXA and MQXB, it is likely that the tune trims and drifts during the ramp will be pretty different from 2009.

• Orbit correction has been successful, and the cell correctors are used with a pretty low current, suggesting a safety factor 4 at 7 TeV.

The ramp in 2010 will reach 3.5 TeV. The main change induced by this larger energy is that the precycle current will be higher, and this should double the b3 snapback from 0.3 to 0.6 units.

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