LUMINOSITY MODELING FOR THE LHC ) $QWRQLRX * $UGXLQL 0 +RVWHWWOHU * ,DGDUROD 63DSDGRSRXORX < 3DSDSKLOLSSRX G. Papotti, G. Trad, CERN, Geneva, Switzerland Abstract In this paper, a luminosity model based on the three main components responsible for the LHC luminosity degradation (intrabeam scattering, synchrotron radiation and luminosity burn-off), is compared with data from RunII. Based on a Fill-by-Fill analysis and observations, additional sources of luminosity degradation will be discussed. Finally, the model is used for luminosity performance projections for the 2016 LHC parameters. INTRODUCTION The performance of a collider is best described by the luminosity (integrated over time) which, in general, is given by [1]: L(t) = n b f rev N 1 (t)N 2 (t) 2πσ x (t)σ y (t) HF g , (1) where n b the number of colliding bunches, f rev the revo- lution frequency, N 1,2 the number of particles per bunch for each beam and σ x,y the rms horizontal and vertical beam sizes at the collision point. Due to the crossing an- gle at collision φ and the fact that the beta function varies rapidly around the interaction point (IP), a geometric fac- tor F g (σ s (t),β ∗ ) and the hourglass effect reduction factor H (σ s ,β ∗ ) should be considered, where σ s and β ∗ are the rms bunch length and the beta function at collision (assum- ing round optics) respectively. Although luminosity is a macroscopic indicator of global collider performance, the observed bunch-by-bunch (bbb) variations in the transverse and longitudinal emittances and in current, impacts its evolution and finally the integrated luminosity per fill. A bbb model was developed based on the three main mechanisms of luminosity degradation in the LHC [2]: intrabeam scattering (IBS), synchrotron radiation (SR) and luminosity burn-off. Here, the model is compared with 2015 RunII data. Finally, luminosity predictions based on the 2016 LHC beam parameters are presented. MODEL DESCRIPTION The emittance evolution of the beams in the LHC during the Flat Bottom (FB), the ramp and the first part of the Flat Top (FT) (before the squeeze) is dominated by the intrabeam scattering (IBS) effect [3]. During collisions a combination of effects including burn-off, IBS, beam-beam, noise, etc., cause emittance blow up and/or particle losses [4]. Based on the assumption that IBS and Synchrotron Radiation (SR) are the dominant effects for the emittance evolution during collisions, the evolution of different injected beam param- eters (transverse emittances, bunch length, bunch current) were calculated using the “ibs” routine of MADX with synchrotron radiation [5, 6]. The transverse emittance and bunch length evolution was then fully parameterized with respect to initial beam parameters and the time, using simple fit functions. Finally the combined effect in any plane can be calculated through a single parametric function: [ x (t), y (t),σ s (t)] = f (En, N b (t 0 ), x (t 0 ), y (t 0 ),σ s (t 0 ), t−t 0 ), (2) where t − t 0 the time interval for which we need to calculate the effect. The procedure is described in more details in [2]. The main mechanism of the bunch intensity degradation during collisions is the luminosity burn-off, causing the bunch current decay due to the collisions themselves. The burn-off decay time is given by: τ nuc = N b0 kL 0 σ tot , (3) where N b0 is the initial bunch intensity, L 0 the initial lumi- nosity, k the number of interaction points and σ tot is the proton-proton total cross section and is energy depented as shown in Fig. 1 [7]. At 6.5 TeV σ tot ≈ 110 mb. The bunch current evolution can then be calculated through N b = N b0 /(1 + t/τ nuc ). Figure 1: Dependences of total, inelastic and elastic cross- sections on the scattering energy √ s [7]. Combining equations 1, 2 and 3 and iterating in small time-steps (such that the current variation in each time-step is relatively small) can give us a self-consistent calculation of the beam parameters, and thus the luminosity evolution in time. 2012 VERSUS 2015 LUMINOSITY EVOLUTION In 2015 LHC ran at a record beam energy of 6.5 TeV/beam and a relaxed beam configuration with lower bunch intensity, and brightness with respect to 2012 and a relaxed β ∗ = 80 cm, resulting in lower peak luminosity and long luminosity lifetimes with respect to RunI. A com- parison between the luminosity evolution of two fills of 77 LUMINOSITY MODELING FOR THE LHC ) $QWRQLRX * $UGXLQL 0 +RVWHWWOHU * ,DGDUROD 63DSDGRSRXORX < 3DSDSKLOLSSRX G. Papotti, G. Trad, CERN, Geneva, Switzerland Abstract In this paper, a luminosity model based on the three main components responsible for the LHC luminosity degradation (intrabeam scattering, synchrotron radiation and luminosity burn-off), is compared with data from RunII. Based on a Fill-by-Fill analysis and observations, additional sources of luminosity degradation will be discussed. Finally, the model is used for luminosity performance projections for the 2016 LHC parameters. INTRODUCTION The performance of a collider is best described by the luminosity (integrated over time) which, in general, is given by [1]: L(t) = n b f rev N 1 (t)N 2 (t) 2πσ x (t)σ y (t) HF g , (1) where n b the number of colliding bunches, f rev the revo- lution frequency, N 1,2 the number of particles per bunch for each beam and σ x,y the rms horizontal and vertical beam sizes at the collision point. Due to the crossing an- gle at collision φ and the fact that the beta function varies rapidly around the interaction point (IP), a geometric fac- tor F g (σ s (t),β ∗ ) and the hourglass effect reduction factor H (σ s ,β ∗ ) should be considered, where σ s and β ∗ are the rms bunch length and the beta function at collision (assum- ing round optics) respectively. Although luminosity is a macroscopic indicator of global collider performance, the observed bunch-by-bunch (bbb) variations in the transverse and longitudinal emittances and in current, impacts its evolution and finally the integrated luminosity per fill. A bbb model was developed based on the three main mechanisms of luminosity degradation in the LHC [2]: intrabeam scattering (IBS), synchrotron radiation (SR) and luminosity burn-off. Here, the model is compared with 2015 RunII data. Finally, luminosity predictions based on the 2016 LHC beam parameters are presented. MODEL DESCRIPTION The emittance evolution of the beams in the LHC during the Flat Bottom (FB), the ramp and the first part of the Flat Top (FT) (before the squeeze) is dominated by the intrabeam scattering (IBS) effect [3]. During collisions a combination of effects including burn-off, IBS, beam-beam, noise, etc., cause emittance blow up and/or particle losses [4]. Based on the assumption that IBS and Synchrotron Radiation (SR) are the dominant effects for the emittance evolution during collisions, the evolution of different injected beam param- eters (transverse emittances, bunch length, bunch current) were calculated using the “ibs” routine of MADX with synchrotron radiation [5, 6]. The transverse emittance and bunch length evolution was then fully parameterized with respect to initial beam parameters and the time, using simple fit functions. Finally the combined effect in any plane can be calculated through a single parametric function: [ x (t), y (t),σ s (t)] = f (En, N b (t 0 ), x (t 0 ), y (t 0 ),σ s (t 0 ), t−t 0 ), (2) where t − t 0 the time interval for which we need to calculate the effect. The procedure is described in more details in [2]. The main mechanism of the bunch intensity degradation during collisions is the luminosity burn-off, causing the bunch current decay due to the collisions themselves. The burn-off decay time is given by: τ nuc = N b0 kL 0 σ tot , (3) where N b0 is the initial bunch intensity, L 0 the initial lumi- nosity, k the number of interaction points and σ tot is the proton-proton total cross section and is energy depented as shown in Fig. 1 [7]. At 6.5 TeV σ tot ≈ 110 mb. The bunch current evolution can then be calculated through N b = N b0 /(1 + t/τ nuc ). Figure 1: Dependences of total, inelastic and elastic cross- sections on the scattering energy √ s [7]. Combining equations 1, 2 and 3 and iterating in small time-steps (such that the current variation in each time-step is relatively small) can give us a self-consistent calculation of the beam parameters, and thus the luminosity evolution in time. 2012 VERSUS 2015 LUMINOSITY EVOLUTION In 2015 LHC ran at a record beam energy of 6.5 TeV/beam and a relaxed beam configuration with lower bunch intensity, and brightness with respect to 2012 and a relaxed β ∗ = 80 cm, resulting in lower peak luminosity and long luminosity lifetimes with respect to RunI. A com- parison between the luminosity evolution of two fills of 77 LUMINOSITY MODELING FOR THE LHC F. Antoniou, G. Arduini, M. Hostettler, G. Iadarola, S.Papadopoulou, Y. Papaphilippou, G. Papotti, G. Trad, CERN, Geneva, Switzerland Abstract In this paper, a luminosity model based on the three main components responsible for the LHC luminosity degradation (intrabeam scattering, synchrotron radiation and luminosity burn—off), is compared with data from RunII. Based on a Fill—by—Fill analysis and observations, additional sources of luminosity degradation will be discussed. Finally, the model is used for luminosity performance projections for the 2016 LHC parameters. INTRODUCTION The performance of a collider is best described by the luminosity (integrated over time) which, in general, is given by [l]: ’117fr0\'Nl(t)N2(r) at) : 2nm<r>m<r> W9? , (1) where m, the number of colliding bunches, f,“ the revo— lution frequency, N12 the number of particles per bunch for each beam and 0-“. the rms horizontal and vertical beam sizes at the collision point. Due to the crossing an— gle at collision ¢ and the fact that the beta function varies rapidly around the interaction point (1P), a geometric fac— tor fl(o-5(t),,8*) and the hourglass effect reduction factor “Hm-5,6”) should be considered, where a", and [3* are the rms bunch length and the beta function at collision (assum— ing round optics) respectively. Although luminosity is a macroscopic indicator of global collider performance, the observed bunch—by—bunch (bbb) variations in the transverse and longitudinal emittances and in current, impacts its evolution and finally the integrated luminosity per fill. A bbb model was developed based on the three main mechanisms of luminosity degradation in the LHC [2]: intrabeam scattering (IBS), synchrotron radiation (SR) and luminosity burn—off. Here, the model is compared with 2015 RunII data. Finally, luminosity predictions based on the 2016 LHC beam parameters are presented. MODEL DESCRIPTION The emittance evolution of the beams in the LHC during the Flat Bottom (FB), the ramp and the first part of the Flat Top (FT) (before the squeeze) is dominated by the intrabeam scattering (IBS) effect [3]. During collisions a combination of effects including burn—off, IBS, beam—beam, noise, etc., cause emittance blow up and/or particle losses [4]. Based on the assumption that IBS and Synchrotron Radiation (SR) are the dominant effects for the emittance evolution during collisions, the evolution of different injected beam param— eters (transverse emittances, bunch length, bunch current) were calculated using the “ibs” routine of MADX with synchrotron radiation [5,6]. The transverse emittance and bunch length evolution was then fully parameterized with respect to initial beam parameters and the time, using simple fit functions. Finally the combined effect in any plane can be calculated through a single parametric function: [EX(Z)7 EyU)» 0-50)] : f(En, NbUO), 6X(t0)7 $00), 0—500), t_tO)a (2) where t— to the time interval for which we need to calculate the effect. The procedure is described in more details in [2]. The main mechanism of the bunch intensity degradation during collisions is the luminosity burn—off, causing the bunch current decay due to the collisions themselves. The burn—off decay time is given by: Tlmr : NbO , (3) kLOO-I‘ol where Nbo is the initial bunch intensity, L0 the initial lumi— nosity, k the number of interaction points and mg, is the proton—proton total cross section and is energy depented as shown in Fig. 1 [7]. At 6.5 TeV 0-,,” z 110 mb. The bunch current evolution can then be calculated through Nb : NbO/(1+t/Tmlc)- E ‘ 51 E. 140 . ATLAS ,[ D - TOTEM . 120 . Lower energy pp . » Lower energy and cosmic ray pp T ‘ 100 Cosmic rays ‘ — COMPETE Rflpliu 13.1 - L88|n[s} + amn‘m . i 10 10,1 103 104 [5 [GeV] Figure 1: Dependences of total, inelastic and elastic cross— sections on the scattering energy x/E [7]. Combining equations 1, 2 and 3 and iterating in small time—steps (such that the current variation in each time—step is relatively small) can give us a self—consistent calculation of the beam parameters, and thus the luminosity evolution in time. 2012 VERSUS 2015 LUMINOSITY EVOLUTION In 2015 LHC ran at a record beam energy of 6.5 TeV/beam and a relaxed beam configuration with lower bunch intensity, and brightness with respect to 2012 and a relaxed [3* = 80 cm, resulting in lower peak luminosity and long luminosity lifetimes with respect to RunI. A com— parison between the luminosity evolution of two fills of 77 LUMINOSITY MODELING FOR THE LHC ) $QWRQLRX * $UGXLQL 0 +RVWHWWOHU * ,DGDUROD 63DSDGRSRXORX < 3DSDSKLOLSSRX G. Papotti, G. Trad, CERN, Geneva, Switzerland Abstract In this paper, a luminosity model based on the three main components responsible for the LHC luminosity degradation (intrabeam scattering, synchrotron radiation and luminosity burn-off), is compared with data from RunII. Based on a Fill-by-Fill analysis and observations, additional sources of luminosity degradation will be discussed. Finally, the model is used for luminosity performance projections for the 2016 LHC parameters. INTRODUCTION The performance of a collider is best described by the luminosity (integrated over time) which, in general, is given by [1]: L(t) = n b f rev N 1 (t)N 2 (t) 2πσ x (t)σ y (t) HF g , (1) where n b the number of colliding bunches, f rev the revo- lution frequency, N 1,2 the number of particles per bunch for each beam and σ x,y the rms horizontal and vertical beam sizes at the collision point. Due to the crossing an- gle at collision φ and the fact that the beta function varies rapidly around the interaction point (IP), a geometric fac- tor F g (σ s (t),β ∗ ) and the hourglass effect reduction factor H (σ s ,β ∗ ) should be considered, where σ s and β ∗ are the rms bunch length and the beta function at collision (assum- ing round optics) respectively. Although luminosity is a macroscopic indicator of global collider performance, the observed bunch-by-bunch (bbb) variations in the transverse and longitudinal emittances and in current, impacts its evolution and finally the integrated luminosity per fill. A bbb model was developed based on the three main mechanisms of luminosity degradation in the LHC [2]: intrabeam scattering (IBS), synchrotron radiation (SR) and luminosity burn-off. Here, the model is compared with 2015 RunII data. Finally, luminosity predictions based on the 2016 LHC beam parameters are presented. MODEL DESCRIPTION The emittance evolution of the beams in the LHC during the Flat Bottom (FB), the ramp and the first part of the Flat Top (FT) (before the squeeze) is dominated by the intrabeam scattering (IBS) effect [3]. During collisions a combination of effects including burn-off, IBS, beam-beam, noise, etc., cause emittance blow up and/or particle losses [4]. Based on the assumption that IBS and Synchrotron Radiation (SR) are the dominant effects for the emittance evolution during collisions, the evolution of different injected beam param- eters (transverse emittances, bunch length, bunch current) were calculated using the “ibs” routine of MADX with synchrotron radiation [5, 6]. The transverse emittance and bunch length evolution was then fully parameterized with respect to initial beam parameters and the time, using simple fit functions. Finally the combined effect in any plane can be calculated through a single parametric function: [ x (t), y (t),σ s (t)] = f (En, N b (t 0 ), x (t 0 ), y (t 0 ),σ s (t 0 ), t−t 0 ), (2) where t − t 0 the time interval for which we need to calculate the effect. The procedure is described in more details in [2]. The main mechanism of the bunch intensity degradation during collisions is the luminosity burn-off, causing the bunch current decay due to the collisions themselves. The burn-off decay time is given by: τ nuc = N b0 kL 0 σ tot , (3) where N b0 is the initial bunch intensity, L 0 the initial lumi- nosity, k the number of interaction points and σ tot is the proton-proton total cross section and is energy depented as shown in Fig. 1 [7]. At 6.5 TeV σ tot ≈ 110 mb. The bunch current evolution can then be calculated through N b = N b0 /(1 + t/τ nuc ). Figure 1: Dependences of total, inelastic and elastic cross- sections on the scattering energy √ s [7]. Combining equations 1, 2 and 3 and iterating in small time-steps (such that the current variation in each time-step is relatively small) can give us a self-consistent calculation of the beam parameters, and thus the luminosity evolution in time. 2012 VERSUS 2015 LUMINOSITY EVOLUTION In 2015 LHC ran at a record beam energy of 6.5 TeV/beam and a relaxed beam configuration with lower bunch intensity, and brightness with respect to 2012 and a relaxed β ∗ = 80 cm, resulting in lower peak luminosity and long luminosity lifetimes with respect to RunI. A com- parison between the luminosity evolution of two fills of 77 LUMINOSITY MODELING FOR THE LHC ) $QWRQLRX * $UGXLQL 0 +RVWHWWOHU * ,DGDUROD 63DSDGRSRXORX < 3DSDSKLOLSSRX G. Papotti, G. Trad, CERN, Geneva, Switzerland Abstract In this paper, a luminosity model based on the three main components responsible for the LHC luminosity degradation (intrabeam scattering, synchrotron radiation and luminosity burn-off), is compared with data from RunII. Based on a Fill-by-Fill analysis and observations, additional sources of luminosity degradation will be discussed. Finally, the model is used for luminosity performance projections for the 2016 LHC parameters. INTRODUCTION The performance of a collider is best described by the luminosity (integrated over time) which, in general, is given by [1]: L(t) = n b f rev N 1 (t)N 2 (t) 2πσ x (t)σ y (t) HF g , (1) where n b the number of colliding bunches, f rev the revo- lution frequency, N 1,2 the number of particles per bunch for each beam and σ x,y the rms horizontal and vertical beam sizes at the collision point. Due to the crossing an- gle at collision φ and the fact that the beta function varies rapidly around the interaction point (IP), a geometric fac- tor F g (σ s (t),β ∗ ) and the hourglass effect reduction factor H (σ s ,β ∗ ) should be considered, where σ s and β ∗ are the rms bunch length and the beta function at collision (assum- ing round optics) respectively. Although luminosity is a macroscopic indicator of global collider performance, the observed bunch-by-bunch (bbb) variations in the transverse and longitudinal emittances and in current, impacts its evolution and finally the integrated luminosity per fill. A bbb model was developed based on the three main mechanisms of luminosity degradation in the LHC [2]: intrabeam scattering (IBS), synchrotron radiation (SR) and luminosity burn-off. Here, the model is compared with 2015 RunII data. Finally, luminosity predictions based on the 2016 LHC beam parameters are presented. MODEL DESCRIPTION The emittance evolution of the beams in the LHC during the Flat Bottom (FB), the ramp and the first part of the Flat Top (FT) (before the squeeze) is dominated by the intrabeam scattering (IBS) effect [3]. During collisions a combination of effects including burn-off, IBS, beam-beam, noise, etc., cause emittance blow up and/or particle losses [4]. Based on the assumption that IBS and Synchrotron Radiation (SR) are the dominant effects for the emittance evolution during collisions, the evolution of different injected beam param- eters (transverse emittances, bunch length, bunch current) were calculated using the “ibs” routine of MADX with synchrotron radiation [5, 6]. The transverse emittance and bunch length evolution was then fully parameterized with respect to initial beam parameters and the time, using simple fit functions. Finally the combined effect in any plane can be calculated through a single parametric function: [ x (t), y (t),σ s (t)] = f (En, N b (t 0 ), x (t 0 ), y (t 0 ),σ s (t 0 ), t−t 0 ), (2) where t − t 0 the time interval for which we need to calculate the effect. The procedure is described in more details in [2]. The main mechanism of the bunch intensity degradation during collisions is the luminosity burn-off, causing the bunch current decay due to the collisions themselves. The burn-off decay time is given by: τ nuc = N b0 kL 0 σ tot , (3) where N b0 is the initial bunch intensity, L 0 the initial lumi- nosity, k the number of interaction points and σ tot is the proton-proton total cross section and is energy depented as shown in Fig. 1 [7]. At 6.5 TeV σ tot ≈ 110 mb. The bunch current evolution can then be calculated through N b = N b0 /(1 + t/τ nuc ). Figure 1: Dependences of total, inelastic and elastic cross- sections on the scattering energy √ s [7]. Combining equations 1, 2 and 3 and iterating in small time-steps (such that the current variation in each time-step is relatively small) can give us a self-consistent calculation of the beam parameters, and thus the luminosity evolution in time. 2012 VERSUS 2015 LUMINOSITY EVOLUTION In 2015 LHC ran at a record beam energy of 6.5 TeV/beam and a relaxed beam configuration with lower bunch intensity, and brightness with respect to 2012 and a relaxed β ∗ = 80 cm, resulting in lower peak luminosity and long luminosity lifetimes with respect to RunI. A com- parison between the luminosity evolution of two fills of 77 LUMINOSITY MODELING FOR THE LHC F. Antoniou, G. Arduini, M. Hostettler, G. Iadarola, S.Papadopoulou, Y. Papaphilippou, G. Papotti, G. Trad, CERN, Geneva, Switzerland Abstract In this paper, a luminosity model based on the three main components responsible for the LHC luminosity degradation (intrabeam scattering, synchrotron radiation and luminosity burn—off), is compared with data from RunII. Based on a Fill—by—Fill analysis and observations, additional sources of luminosity degradation will be discussed. Finally, the model is used for luminosity performance projections for the 2016 LHC parameters. INTRODUCTION The performance of a collider is best described by the luminosity (integrated over time) which, in general, is given by [l]: ’117fr0\'Nl(t)N2(r) at) : 2nm<r>m<r> W9? , (1) where m, the number of colliding bunches, f,“ the revo— lution frequency, N12 the number of particles per bunch for each beam and 0-“. the rms horizontal and vertical beam sizes at the collision point. Due to the crossing an— gle at collision ¢ and the fact that the beta function varies rapidly around the interaction point (1P), a geometric fac— tor fl(o-5(t),,8*) and the hourglass effect reduction factor “Hm-5,6”) should be considered, where a", and [3* are the rms bunch length and the beta function at collision (assum— ing round optics) respectively. Although luminosity is a macroscopic indicator of global collider performance, the observed bunch—by—bunch (bbb) variations in the transverse and longitudinal emittances and in current, impacts its evolution and finally the integrated luminosity per fill. A bbb model was developed based on the three main mechanisms of luminosity degradation in the LHC [2]: intrabeam scattering (IBS), synchrotron radiation (SR) and luminosity burn—off. Here, the model is compared with 2015 RunII data. Finally, luminosity predictions based on the 2016 LHC beam parameters are presented. MODEL DESCRIPTION The emittance evolution of the beams in the LHC during the Flat Bottom (FB), the ramp and the first part of the Flat Top (FT) (before the squeeze) is dominated by the intrabeam scattering (IBS) effect [3]. During collisions a combination of effects including burn—off, IBS, beam—beam, noise, etc., cause emittance blow up and/or particle losses [4]. Based on the assumption that IBS and Synchrotron Radiation (SR) are the dominant effects for the emittance evolution during collisions, the evolution of different injected beam param— eters (transverse emittances, bunch length, bunch current) were calculated using the “ibs” routine of MADX with synchrotron radiation [5,6]. The transverse emittance and bunch length evolution was then fully parameterized with respect to initial beam parameters and the time, using simple fit functions. Finally the combined effect in any plane can be calculated through a single parametric function: [EX(Z)7 EyU)» 0-50)] : f(En, NbUO), 6X(t0)7 $00), 0—500), t_tO)a (2) where t— to the time interval for which we need to calculate the effect. The procedure is described in more details in [2]. The main mechanism of the bunch intensity degradation during collisions is the luminosity burn—off, causing the bunch current decay due to the collisions themselves. The burn—off decay time is given by: Tlmr : NbO , (3) kLOO-I‘ol where Nbo is the initial bunch intensity, L0 the initial lumi— nosity, k the number of interaction points and mg, is the proton—proton total cross section and is energy depented as shown in Fig. 1 [7]. At 6.5 TeV 0-,,” z 110 mb. The bunch current evolution can then be calculated through Nb : NbO/(1+t/Tmlc)- E ‘ 51 E. 140 . ATLAS ,[ D - TOTEM . 120 . Lower energy pp . » Lower energy and cosmic ray pp T ‘ 100 Cosmic rays ‘ — COMPETE Rflpliu 13.1 - L88|n[s} + amn‘m . i 10 10,1 103 104 [5 [GeV] Figure 1: Dependences of total, inelastic and elastic cross— sections on the scattering energy x/E [7]. Combining equations 1, 2 and 3 and iterating in small time—steps (such that the current variation in each time—step is relatively small) can give us a self—consistent calculation of the beam parameters, and thus the luminosity evolution in time. 2012 VERSUS 2015 LUMINOSITY EVOLUTION In 2015 LHC ran at a record beam energy of 6.5 TeV/beam and a relaxed beam configuration with lower bunch intensity, and brightness with respect to 2012 and a relaxed [3* = 80 cm, resulting in lower peak luminosity and long luminosity lifetimes with respect to RunI. A com— parison between the luminosity evolution of two fills of 77 LUMINOSITY MODELING FOR THE LHC F. Antoniou, G. Arduini, M. Hostettler, G. Iadarola, S.Papadopoulou, Y. Papaphilippou, G. Papotti, G. Trad, CERN, Geneva, Switzerland Abstract In this paper, a luminosity model based on the three main components responsible for the LHC luminosity degradation (intrabeam scattering, synchrotron radiation and luminosity burn-off), is compared with data from RunII. Based on a Fill-by-Fill analysis and observations, additional sources of luminosity degradation will be discussed. Finally, the model is used for luminosity performance projections for the 2016 LHC parameters. INTRODUCTION The performance of a collider is best described by the luminosity (integrated over time) which, in general, is given by [1]: _ nbfievNi(I)N2(t) at) _ 2n0'x(t)a'y(t) flf’ (1) where m, the number of colliding bunches, fm the revo- lution frequency, N1; the number of particles per bunch for each beam and o-X,y the rms horizontal and vertical beam sizes at the collision point. Due to the crossing an- gle at collision ¢ and the fact that the beta function varies rapidly around the interaction point (1P), a geometric fac- tor fl(o-S(t),fi*) and the hourglass effect reduction factor W(0’S,fi*) should be considered, where 0-, and 6* are the rms bunch length and the beta function at collision (assum- ing round optics) respectively. Although luminosity is a macroscopic indicator of global collider performance, the observed bunch—by-bunch (bbb) variations in the transverse and longitudinal emittances and in current, impacts its evolution and finally the integrated luminosity per fill. A bbb model was developed based on the three main mechanisms of luminosity degradation in the LHC [2]: intrabeam scattering (IBS), synchrotron radiation (SR) and luminosity bum-off. Here, the model is compared with 2015 RunII data. Finally, luminosity predictions based on the 2016 LHC beam parameters are presented. MODEL DESCRIPTION The emittance evolution of the beams in the LHC during the Flat Bottom (FB), the ramp and the first part of the Flat Top (FT) (before the squeeze) is dominated by the intrabeam scattering (IBS) effect [3]. During collisions a combination of effects including burn-off, IBS, beam-beam, noise, etc., cause emittance blow up and/or particle losses [4]. Based on the assumption that IBS and Synchrotron Radiation (SR) are the dominant effects for the emittance evolution during collisions, the evolution of different injected beam param- eters (transverse emittances, bunch length, bunch current) were calculated using the “ibs” routine of MADX with synchrotron radiation [5, 6]. The transverse emittance and bunch length evolution was then fully parameterized with respect to initial beam parameters and the time, using simple fit functions. Finally the combined effect in any plane can be calculated through a single parametric function: [€x(t)a 6y“)? 0-30)] : f(En, Nb([0), 6x00), Ey(t0)a 0-300), t_t0)7 (2) where t — to the time interval for which we need to calculate the effect. The procedure is described in more details in [2]. The main mechanism of the bunch intensity degradation during collisions is the luminosity burn—off, causing the bunch current decay due to the collisions themselves. The burn—off decay time is given by: NbO "MC : 7 3 T kLOO'tat ( ) where Nbo is the initial bunch intensity, L0 the initial lumi- nosity, k the number of interaction points and 0-,,” is the proton-proton total cross section and is energy depented as shown in Fig. 1 [7]. At 6.5 TeV 0,0, x 110 mb. The bunch current evolution can then be calculated through Nb : NbO/(1+t/Tnuc)' E ‘ Cl E. 140 . ATLAS ,[ D - TOTEM . 120 . Lower energy pp . » Lower energy and cosmic ray pp T ‘ 100 Cosmic rays ‘ — COMPETE Rflpliu 13.1 - I.88|n[s} + amn‘m . i 10 10" 103 10" 15 [GeV] Figure 1: Dependences of total, inelastic and elastic cross— sections on the scattering energy v} [7]. Combining equations 1, 2 and 3 and iterating in small time-steps (such that the current variation in each time—step is relatively small) can give us a self—consistent calculation of the beam parameters, and thus the luminosity evolution in time. 2012 VERSUS 2015 LUMINOSITY EVOLUTION In 2015 LHC ran at a record beam energy of 6.5 TeV/beam and a relaxed beam configuration with lower bunch intensity, and brightness with respect to 2012 and a relaxed 6* = 80 cm, resulting in lower peak luminosity and long luminosity lifetimes with respect to RunI. A com— parison between the luminosity evolution of two fills of 77