EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH... 6 I Cf /QCKA/ /ll M7$L+~O Dm 3 MJ 9% V/f 5 CERN AT/94-06 (DI) LHC Note 265 Local Power Distribution from Particle Losses in the LHC Inner Triplet Magnet Q1 A. Morsch ABSTRACT A full simulation of the energy deposition caused by particles produced in inelastic events was performed for the most critical region of the LHC low-b collision optics, the outer end of Q1. One finds that for the nominal luminosity of 1034 cm 2s 1 the power density reaches a maximum of 2.7 mwc1n 3 in the central super conducting cables of the first shell. This shell is the most sensitive since there the magnetic field strength reaches its maximum. CERN LIBRHRIES. sawzvq I\\ \\\\ \\\\I\\\ \\ \\ \ \\\li\\\ \ \l \\ \\I\ F B GEEB5E Results presented ut the 1993 Workshop on LHC Technology Chamonix 11-15 October 1993 Geneva, Switzerland 25 March 1994 OCR Output
OCR Output1. Introduction [U In a previous report, it was established that at LHC particles from inelastic pp-interactions cause irradiances in the order of 100 mwcm 2 on the inner surfaces of the outer end of Q1 (the first quadrupole of the inner triplet of the LHC collision optics) and the outer end of D1 (the first separation magnet). Considering elementary properties of particle showers initiated by particles with energies in the order of 1 TeV the resulting power density in the super conducting coils was estimated to be in the order of 10 mw cm 3. Since the quench limit of current super conducting coils lies around 10 mw cm 3, particle losses from inelastic interactions could jeopardise the performance of the LHC low [3 collision optics at highest luminosities. The previous estimations could not take into account the effect of the magnetic field in the material and it was decided to perform a full shower simulation for the critically hot regions. The restriction of these simulations to a reasonably small area makes it possible to calculate the average power density for volumes which correspond in the transverse direction to fractions of the dimensions of the super conducting cables. The results for Q1 for which a complete technical design concept including the magnetic field map is available [2] will be presented in this report. Note that the standard LHC luminosity is now fixed to the value Lg= 10 cm 2s 1 and the beam energy to 7 TeV [3]. In the previous report we used 1.65 1034 cm 2s 1 and 7.7 TeV and hence, all power values have to be scaled, in a very good approximation, by a factor 0.55; rate values by a factor 0.61. 2. Shower Simulation For the shower simulation the FLUKA (FLUctuating I<Askade) code [4] was used, which can, in contrast to other programs, follow all the components of a hadronic cascade in a single run using either analogue or biased sampling techniques or both. The runs were performed with the EIv[F (ElectroMagnetic Fluka) option which activates full electron / photon transport. In the following we describe the most important input specifications for the FLUKA run. Geometry In Fig. 1, the geometrical set up of Q1 as defined to FLUKA is sketched. The main simplification with respect to the actual magnet design is the replacement of the detailed cable arrangement of the coil by a homogenous shell. Defining the complex cable arrangement to FLUKA would mean to introduce a large number of material boundaries. This considerably increases the running time and the probability of program 'crashes'. Such an effort is not justified by the expected increase in accuracy. The coil material was defined as a mixture of Cu and NbTi with the volume ratio Cu/NbTi=1.3 according to the present cable design specifications. OCR Output
It is assumed that the quadrupole is situated in an even intersection region, because there the expected irradiation is highest [U Energy Threshold Particles are tracked down to a kinetic energy of 10 MeV. Beam Particles A sample of charged tracks from 104 inelastic pp-interactions (inelastic non-diffractive and single diffractive) at *}s= 7 TeV was generated using PYTI-IIA 5.6 [5]. From this sample those tracks were selected, which hit the inner surface of Q1 within a region of 1.6 m before its outer end. These are the tracks which can contribute to the energy deposition in the outer end of Q1. The subsample contains 6300 tracks and was used as the input to FLUKA. 3. Results The inner surface of Q1 is irradiated by a total of 32 W out of which 25 W are absorbed in the cold mass of the magnet. Less than 1 W leave the magnet radially and 6 W leave the endcaps. 3.1 Local Power Distributions The energy deposition as simulated by FLUKA was scored in bins which have been matched in the r plane to the dimensions of the super conducting cables: 9 mm bins in the radial direction corresponding to the cable height and 2.1 bins in corresponding to the cable width of the first shell. For the longitudinal direction a bin-size of 40 cm was chosen. To obtain the power density in the material, the energy deposition is normalised to the production rate. In Figs. 2a-e, the power distribution at the end of Q1 is presented as a function of in five radial slices corresponding to the beam pipe and the four cable shells. One observes that the peaked structure of the irradiance around the 0, 90, 180, 270 symmetry directions is preserved: in the first shell 50% of the power contained in intervals around the symmetry axis and 80 % in i32 regions. The highest power density is reached in the beam pipe (3 mwcm 3). The highest density (2.7 mwcm 3) inside the coils is reached in the central (with respect to 0 ) cables of the inner shell which is the most critical because there the magnetic field strength is highest. Outside the six innermost cables of the first shell the power density is lower than 1mWcm 3, nowhere the density is lower than 0.2 mwcm 3. In the 2nd to 4th shells which are less critical the maximum power densities amount to ~1 mwcm OCR Output
For the LHC parameters at a 850 ma current limit (Lg: 2.62 1034 cm 2s and ~}s=7.3 TeV) the peak value is 7.2 mwcm 3. The tune shift limit is reached at Lg: 3.62 1034 cm 2s l corresponding to an initial current of 1.1 A [6]. In this case the peak power density amounts to 10 mwcm 3, which is equal to the estimated quench limit for super conducting coils produced with today s technology. In Fig. 3, the radial distribution of the power is shown for the two central cables (-2.1 < qi < 2.1 ). Note that the first bin corresponds to the beam pipe; the bin size is not equal to the thickness of the pipe, but the power density has been adequately scaled. In the same figure, we show for comparison the power distribution which would result if no magnetic field were present in the material (dashed line). The effect of the magnetic field is to smear out the energy in the radial direction. Thereby the peak density is reduced by approximately a factor 4. In fact, the previous estimadons, which could not take into account the effect of the magnetic field, differ from the present results approximately by the same factor. 3.2 Model Dependence In order to get a feeling for the model dependence of the results, the irradiance values for Q1 are compared to the values obtained using two other Monte Carlo generators for inelastic non-diffractive interactions: ISAIET [7] and DTUTET. [8] For Q1 the differences are less then 7%. 4. Conclusions For the most critical region of the LHC low B collision optics, the outer end of Q1, a full simulation of the energy deposition from inelastic events was performed. Assuming a luminosity of 1034 cm 2s 1 and a centre of mass energy of ~}s=7 TeV, Q1 is irradiated by a total power of 32 W out of which 25 W are absorbed in the cold mass of the magnet. Plotting the power distribution at the outer end of the magnet one finds, that within the coils the power density reaches a maximum of 2.7 mwcm 3 ( 7.2 mwcm 3 for the LHC parameters at the 850 ma cmrent limit and 10 mw cm 3 at the tune shift limit) in the innermost cables of the first shell. This shell is the most critical, since the magnetic field strength reaches there its maximum of ~ 8 T. Only outside the six innermost cables of each pole the power density is below 1 mwcm 3 and nowhere in the first shell the power density is below 0.2 mwcm 3. In the 2nd to 4th shells which are less critical the maximum power densities amount to ~l mwcm Assuming that the quench limit for super conducting coils produced with today s technology lies around 10 mwcm 3 it is possible that the irradiation OCR Output
from particles produced in inelastic ppdnteractions limits the LHC luminosity before the tune-shift limit is reached. The power density produced by particle losses must be considered as an important parameter in the optimisation of the inner triplet. Acknowledgements I am grateful for fruitful conversations with K. Eggert, R. Ostojic, K. Potter, and G. R. Stevenson. References [1] K. Eggert and A. Morsch, 'Particle Losses in the LHC Interaction Regions', CERN AT/93 17 (DI) and LHC Note 229. [2] R. Ostojic, T.M. Taylor, and G.A. Kirby, Design and Construction ofa One Meter Model ofthe 70 mm Aperture Quadrupole for the LHC Low-B Insertion', Preprint presented at the 13th International Conference on Magnet Technology, Victoria, Canada (1993). R. Ostojic private communication. [3] The LHC Study Group, LHC: The Large Hadron Collider Accelerator Project', CERN AC/93-O3 (LHC). [4] P.A. Aarnio, A. Fasso, ].-H. Mohring, ]. Ranft, P.R. Sala, G.R. Stevenson, and ].M. Zazula, 'FLUKA: Hadronic Benchmarks and Applications'. K. Potter and G.R. Stevenson private communications. [5] H.-U. Bengtson and T. Sjostrand, Computer Physics Commim. 46 (1987) 43. [6] W. Herr, Private Communication. [71 F. Paige et al., ISA]`ET Monte Carlo, BNL 38034 (1986). [sl ]. Ranft, K. Hahn, 'DTLUET 88, CERN TIS-RP 218. OCR Output
Figure Captions: Fig. 1 Geometry of the low-b Quadrupole Q1 as defined to FLUIQA. Fig. 2 Azimuths distribution of the power density at the end of Q1: (a) Beam ipe, (b) lst cable shell, (c) 2nd cable shell, (d) 3rd cable shell and (e) 4th cable shell. Fig. 3 Radial distribution of the power density for the two innermost cables. Solid line: with magnetic field (realistic) and dashed line: no magnetic field in the material, for comparison. OCR Output
OCR OutputOCR OutputOCR OutputOCR Outputth magnetic field - - - without magnetic field 14 EJ 10 12 F`! 4 10 12 14 r(cm) Fig.3