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Clement Hines
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1 CAN WE PREDICT LUMINOSITY? F Antniu, M Hstettler', G Iadarla, S Papadpulu', Y Papaphilippu, D Pellegrinil, G Trad, 1CERN, Geneva, Switzerland, 2University f Liverpl, UK Abstract In these prceedings, a luminsity mdel based n the main cmpnents (intrabeam scattering, synchrtrn radiatin, elastic scattering and luminsity burn-il) respnsible fr the LHC luminsity evlutin, is cmpared with data frm the 2016 Run f LHC Based 011 a bunch-bybunch and fill-by-fill analysis, the data are cmpared t the mdel predictins and pssible surces f luminsity degradatin are discussed The impact f the degradatin mechanisms n the integrated luminsity is als presented with synchrtrn radiatin [9, 10] The transverse emittance and bunch length evlutin were then fully parameterized with respect t the initial beam parameters and the time, using multi-parametric fit functins Finally the cmbined ellect at any plane can be calculated thrugh: (16, E (10'A dr dr dt 185+ = flen, N130, Ext), 6w, (Tm, 611) (2) where (It the time interval fr which the calculatin is perfrmed and En the energy The prcedure is described in mre details in [2] INTRODUCTION The cntributin frm the prtn-prtn cllisins elastic The perfrmance f a cllider is best described by the luminsity (integrated ver time) which, in general, is given scattering t the transverse emittance grwth [4,5], is als included, based n: _ by [l]: 0): 27rrr(\(t)(ry(t) Hg, W dew i at )W = Nebxaﬁrezlriy>Mum) n17fi rvl([)n2(z), (1) where m, the number f clliding bunches fret the rev- lutin frequency, Nl g the number f particles per bunch fr each beam and n the rms hrizntal and vertical beam sizes at the cllisin pint Due t the crssing angle at cllisin (I) and the fact that the beta functin varies rapidly arund the interactin pint (1P), a gemetric factr fg((r,(t),,8*) and the hurglass effect reductin factr W(0,,,8*) shuld be cnsidered, Where (rs and,8 are the rms bunch length and the beta functin in the interactin pint (1P) cllisin (assuming rund ptics) respectively Althugh luminsity is a macrscpic indicatr f glbal cllider perfrmance, the bserved bunch-by-bunch (bbb) variatins in the transverse and lngitudinal emittances and in current, impacts its evlutin and finally the integrated luminsity per fill A bbb mdel was develped based n the three main mechanisms f luminsity degradatin in the LHC [2]: intrabeam scattering (IBS) synchrtrn radiatin (3) where NIP is the number f interactin pints, 01, the elastic crss sectin and <63» is the rms prtn-prtn scattering angle The emittance evlutin alng the ﬁll can then be estimated, fr any time interval fr which the bunch current Nb (_) «a variatin is small, using the differential equatin: dt d [BS+SR dz Plastic The main mechanism f the bunch intensity degradatin during cllisins is the luminsity burn-011, causing the bunch current decay due t the cllisins themselves The burn-ﬂ' decay time is given by: Trim : NM) klou mi 5 ( ) (SR) and luminsity burn ff Here, the mdel is cmpared with the LHC beam data frm the 2016 Run where N,,(, is the initial bunch intensity, [0 the initial luminsity, k the number f interactin pints and (rm, is the MODEL DESCRIPTION as shwn in Fig 1 [ll] At 65 TeV (rm, z 110 mb, 0 3; a 30 mb and (ring; 2 80 mb [ll] In the case f the The emittance evlutin f the beams in the LHC during the Flat Bttm (FB), the ramp and the ﬁrst part f the Flat Tp (FT) (befre the squeeze) is dminated by the intrabeam scattering (IBS) eﬂ ect [3] During cllisins a cmbinatin f ell ects including burn-ff, lbs, beam-beam, nise, etc, cause emittance blw up and/r particle lsses [4] Based n the assumptin that 188 and Synchrtrn Radiatin (SR) are the dminant effects fr the emittance evlutin during c]lisins, the evlutin f different injected beam parameters (transverse emittances (6,), bunch length (0')), bunch current (N[,) were calculated using the ibs rutine f MADX prtn-prtn ttal crss sectin and is energy depended LHC with very small beta functins at the interactin pints, nly the inelastic part f the prtn-prtn cllisins is expected t cntribute t the burn-ll' lsses, while the elastic part is causing transverse emittance blw up described by eq eq (3) [6] The bunch current evlutin can then be calculated thrugh: Nb : IVZ)O/(1 + I/Tnm')- (6) Cmbining equatins eq (1), eq (2), eq (3), eq (4), eq (5) and eq (6) and iterating in small time-steps (such that 125

2 E 140 ATLAS c _ TOTEM 1 20 Lwer energy pp ' A Lwer energy and csmic ray pp 100- Csmic rays s} 60» 4; COMPETE Rl2u 131» Lash-(s) aratn ts) 20} ' :Mgrma ] 10 \s [GeV] Figure 1: Dependences f ttal, inelastic and elastic crsssectins n the scattering energy \/ [11] the current variatin in each tirne step is relatively small) prvides a self-cnsistent calculatin f the beam parameters, and thus the luminsity evlutin in time The infrastructure allws the user t select the mdel r the data fr each specific parameter in a transparent manner Fur different mdes are defined and will be used in the next: 1 Pure mdel: I ::-'r {in}! i :: Mira; FULL"; H1 FrL'HDI? Figure 2: Hrizntal (tp) and vertical (bttm) emittance evlutin frm injectin t stable beams fr all the high intensity fills f 2016 Thse are fills crrespnding t the time perid frm June t Octber 2016 In rder t apply the mdel, the bunch by bunch transverse emittances, bunch lengths and bunch intensities are required The bunch by bunch luminsity data are als needed fr cmparisn Fr this, the fllwing datasets have been used: 0 Initial values f bunch intensities, emittances and bunch length taken frm the data 0 Mdel iteratin t cmpute intensity, emittance, bunch length and luminsity evlutin 2 EmpiricalBlwUpBurnOfI: 0 Transverse emittance evlutin taken frm the data 0 Mdel iteratin t cmpute bunch intensity, bunch length and luminsity evlutin 3 lbsempiricallsses: Intensity evlutin taken frm the data 0 Mdel iteratin t cmpute emittance, bunch length and luminsity evlutin 4 EmpiricalBlwUpEmp'rricalLsses: Intensity and emittance evlutin taken frm the data 0 Mdel iteratin t cmpute luminsity evlutin DATA ANALYSIS In 2016, the LHC perated with a center f mass energy f 13 TeV and similar beam parameters as in 2015, but with a lwer E f 40 cm (in 2015,8*=80 cm), resulting in a significant increase in the integrated luminsity; in 2015 the LHC delivered t CMS an integrated luminsity f 42 fi)"1 while in fb-l [7] Fr the analysis that fllws all the fills f the prductin perid f 2016, after the intensity ramp-up were analyzed 0 The bunch-by-bunch intensity sharing is measured by the Fast Beam Current Transfrmer (FBCT) The bunch-by-bunch emittance measurements fr bth beams and bth planes frm the synchrtrn radiatin telescpes (BSRT) The bunch-by-bunch bunch lengths as measured by the beam quality mnitr (BQM) The bunch-by bunch luminsity data as published frm ATLAS and CMS (Massi files) A mre detailed descriptin is presented in [8] EMITTANCE EVOLUTION FROM INJECTION TO SABLE BEAMS Figure 2 shws the average hrizntal (tp) and vertical (bttm) emittance, fr all the prductin fills f 2016 at different time in the LHC cycle The emittance at injectin is shwn in blue, at the beginning f the ramp in green, at the end f the ramp in red and at the beginning f stable beams in cyan The errr-bars crrespnd t the ne standard deviatin ver all the bunches Here nly the data frm beam 1 are shwn, hwever, the situatin is very similar fr beam 2 as well At the beginning f the year standard beams were injected in the LHC, with the average injected hrizntal/vertical emittance fluctuating arund 28/25,um rad and arriving at the beginning f stable beams arund 35/29,um rad With the intrductin f the BCMS beam prductin scheme, the emittance was gradually decreased t 16/15 rim-rad at injectin and 25/20 rim-rad at the beginning f stable beams It is interesting t ntice 126

3 Eh?" I r x E ; t T_ _ _ e,7 ' _ -, f :~ -( I L ' -' 7 <1 1' s ; 3 («raw ' A H emr H - Eml v Iv _ ' l r - t,1-_,r'- \ - 3 s- ' w: - A, (r ',, -, ' K 4 I ~' - 4 )\ ' - a ;-' my 1 l 1" ll 7,, e Figure 4: Hrizntal (tp) and vertical (bttm) emittance evlutin frm injectin t stable beams fr all the high intensity ﬁlls f 2016 t understand further this ell ect, the average peak luminsity fr all the fills was calculated thrugh eq (1) using the measured bunch parameters (transverse emittances bunch Figure 3: Average bunch intensity (red) and average bunch emittance (H: blue, V: green) fr beam 1 (tp) and beam 2 (bttm) at the beginning f Stable Beams fr the physics ﬁlls in 20l 6 the large emittance blw up (deﬁned as / 6W 1) frm injectin t stable beams, f the rder f 25/16 % in the ﬁrst part and 55/33 % after the transitin t BCMS This is induced mainly during the Ramp where the intrabeam scattering effect fr the range f bunch parameters f 2016 can explain nly a small fractin f it; fr an injected transverse emittance f 15 pmrad and bunch intensity f lel l a hrizntal emittance blw up f 13 % frm injectin t stable beams is expected due t ibs and nly 3 % f it is induced during the ramp while n effect is expected in the vertical plane The average bunch intensity in the LHC fr 2016 was kept in similar levels as in 2015 Mre speciﬁcally, fr the ﬁrst part f the year the average bunch intensity was Nb ~ 12 X 10'1 while later went dwn t N), ~11><10, with negligible lsses alng the cycle (frm injectin t stable beams) Figure 3 shws the evlutin f the average bunch intensity (red), hrizntal (blue) and vertical (green) emittance values at the beginning f stable beams alng the year, fr beaml 1 (tp) and beam 2 (bttm) LUMINOSITY IMBALANCE ALONG THE YEAR Due t the fact that the experiments f ATLAS and CMS have a dill erent crssing plane (vertical fr ATLAS and hrizntal fr CMS) and the hrizntal and vertical emittances are nt equal during cllisins, an imbalance in the lumins- ity delivered t the tw experiments was bserved Aiming intensity, bunch length) at the beginning f stable beams, fr bth ATLAS and CMS This calculated peak luminsity was then cmpared t the average measured peak luminsity prvided by the experiments and the results are shwn in the tp part f l ig 4 The calculated values are shwn in crsses while the measured nes in circles The results fr ATLAS are shwn in blue while fr CMS in red The bttm plt f ﬁg 4 shws the luminsity imbalance (deﬁned as (LC/us ATLAS )/- \TLA5) between the tw experiments using the same marker cnventin as in the tp ne During the ﬁrst part f the year, befre the transitin t BCMS beams, very gd agreement between the calculated and measured peak luminsities is bserved After the transitin t BCMS, even thugh the calculated and measured imbalance agrees well, the abslute values start t diverge In the third part, n the ther hand, after the crssing angle reductin, a disagreement is bserved bth in abslute values and in imbalance It is imprtant t ntice here that a recalibratin f the BSRT system was perfrmed befre the transitin t BCMS and befre the crssing angle change The impact f the calibratin factrs in these bservatins is currently under scrutiny In rder t better understand the bserved imbalance between ATLAS and CMS, an experiment was perfrmed where 4 bunches with different pile up density (r brightness) were brught t cllisin and the crssing angle was gradually reduced t 0 pm-rad as shwn in ﬁg 5 In the left part f the ﬁgure the evlutin f the pile-up density f the 4 bunches is presented while in the right the imbalance between ATLAS and CMS At the beginning f the ﬁll, a 5-8% gemetric etlect is bserved higher fr the higher bright ness bunches At the end f the ﬁll where the crssing angle was reduced t 0, a 5% imbalance is still bserved, even thugh fr zer crssing angle theretically the tw experiments shuld nt see any difference Further investigatin is in prgress in rder t understand this bservatins 127

4 Figure 5: Left: Evlutin f the pile-up density f the 4 bunches with different brightness Right: Luminsity imbalance between ATLAS and CMS The crssing angles is gradually reduced and at the end the bunches are clliding with zer crssing angle LUMINOSITY EVOLUTION Figure 8: Average emittance grwth per fill as predicted by the mdel (green) and measured (blue) bth in the hrizntal (tp) and vertical (bttm) planes Figure 6: Luminsity evlutin cmparisn between the pure mdel (green) and measurements (gray) ity evlutin using the pure" mdel is verestimated with respect t the measurement The same bservatin is valid fr the luminsity evlutin f all the fills f the year and cnsequently fr the evlutin f the bunch-by-bunch transverse emittanccs, bunch length and bunch intensity as well Instead if we use the empirical emittance evlutin frm the BSRT data, and reiterate the mdel in rder t cmpute the predictin f the bunch length, bunch intensity and luminsity evlutin the agreement becmes much better, as shwn in fig 7 Eventually using bth the empirical emittance and bunch intensity evlutin, the luminsity evlutin is very well reprduced Fr the example fill, already by using nly the empirical emittance blw up the luminsity evlutin is very well predicted, shwing that the main surce f the luminsity degradatin fr this particular case is an extra emittance blw up mechanism Hwever, fr ther fills nt nly extra emittance blw up but als extra lsses were bserved In this respect, a statistical apprach was adpted in rder t understand the behavir f the luminsity evlutin and degradatin mechanisms ver the year EXTRA EMITTANCE BLOW UP Figure 7: Luminsity evlutin cmpaiisn between the mdel using the empirical emittance evlutin ( Empin cal- BlwUpBurnOfl" ) (green) and measurements (gray) In rder t validate the luminsity mdel and identify pssible surces f luminsity degradatin in 2016, the mdel was applied bunch-by-bunch t all the prductin fills f 2016, under dill erent assumptins as described in sectin Mdel descriptin Figure 6 (tp) shws the cmparisn f the average luminsity evlutin as measured by the experiments (gray) and cmputed by the pure mdel (green) f a typical fill f 2016 (fill 5198) The predicted lumins- In rder t understand the behavir f the extra emittance blw up alng the year the average expected emittance grwth per fill frm the mdel was cmpared t the measured ne and the results are shwn in fig 8 The mdel predictin is shwn in green while the BSRT measurements are shwn in blue The results fr bth hfizntal (tp) and vertical (bttm) planes are shwn The errr-bars indicate the ne standard deviatin ver all the bunches per fill It is interesting t ntice a cnstant difference between the mdel predictin and the measurements, which seem t be independent n the bunch brightness Bth planes shw an extra emittance blw up f arund 005/1/11/ I1, with respect t the mdel Analysis is in prgress t understand further the mechanism that induces this extra emittance blw up 128

5 Figure 10: Average nrmalized lsses ver the ﬁrst hur in Figure 9: Tp: Instantaneus beam lss rate nrmalized t the luminsity fr all the physics ﬁlls f 2016 Each clr represents a dill'erent ﬁll Bttm: The average and the ne standard deviatin interval ver all the ﬁlls EXTRA LOSSES As discussed earlier, extra beam lsses n tp f luminsity burn ff lsses, were bserved fr mst f the 2016 physics ﬁlls In rder t have a better understanding f the effect, the instantaneus lss rate nrmalized t the luminsity was calculated bunch by bunch fr all ﬁlls and the average ell ect ver all the bunches per ﬁll is shwn in ﬁg 9 The results fr beam 1 are shw n the left while the results fr beam 2 n the light In the case f burn ll dminated lsses, this shuld reveal the value fr the inelastic crss sectin f the prtn-prtn cllisins (thus ~ )) Hw- ever, this is nt the case and a similar trend is bserved fr all the ﬁlls, fr bth beams; fast lsses ccur during the ﬁrst 2 3 h in stable beams, while later the lsses becme bum ff dminated The effect is mre prnunced fr beam I than beam 2 In the tp plts f ﬁg 9 each clr crrespnds t a dill erent ﬁll, while in the bttm ne the average ell ect ver all the ﬁlls and the ne standard deviatin interval are shwn The red slid line indicates the inelastic crss sectin limit f the 80 mb Figure 10 shws the average nrmalized lsses ver the lirst hur in stable beams, fr all the physics ﬁlls The results fr beam 1 are shwn in blue while fr beam 2 in red It is very interesting t ntice that the lsses behavir is very much all'ected by all the machine changes The highest lsses were bserved during the ﬁrst part f the year while during the middle part, the lsses were minimized, and fr beam 2 they were very clse t the burn-fl' limit Systematically fr bth these perids, beam 1 sull ered mre frm lsses than beam 2 After the crssing angle reductin, the lsses were again increased, hwever beam 1 and beam 2 behaved in a much mre similar way Anther very interesting bservatin is the fact that the lsses are minimized when the LIICb was perating in a psitive plarity, while they get maximized in the ppsite case Within the same plarity, the lsses are larger fr larger mmnn 1mm [:4 stable beams fr beam 1 (blue) and beam 2 (red) 1:; L hﬁ I M an» d'c-(x an WBunch ; ral-:5 n: 9" 4 Figure 11: Instantaneus lsses ver the ﬁrst hur in stable beams befre (tp) and after (bttm) the crssing angle reductin emittances which becme mre prnunced in the ﬁrst part f the run, with nminal beams and standard emittances (see ﬁg 3) It shuld be nted the impact f the tune ptimizatin n the lsses behavir A tune ptimizatin, based n the dynamic aperture studies presented in [13], has a psitive impact n the lsses behavir T summarize, the effects and machine cnditins that were bserved t have an impact n the lsses behavir are: the LHCb plarity, the emittance magnitude, the tune and the crssing angle reductin The impact f the beam-beam lng range ell ect is als under investigatin and sme ﬁrst bservatins are shwn in ﬁg 11 The clrbar in these plts shw the burnlll crrected lsses cmputed ver 10 minutes windws, expressed as percentage f the ttal intensity fr the ﬁrst hur in SB, befre (tp) and after (bttm) the crssing angle reductin The hrizntal axis shws the 25 ns bunch slt Darker clr indicates higher lsses In the tp plt, with the large crssing angle, the lsses are higher at the end f each train, which is a well knwn signature f the electrn clud effect On the ther hand after the reductin f the crssing angle, the situatin becmes different fr many trains where the highest lsses are bserved in the middle f the trains, which is a signature f the beam-beam lng range effect The ell ect is mre prnunced fr beam 1, where the extra lsses are higher, as discussed earlier It is thugh bserved fr beam 2 as well Further investigatin is in prgress in rder t quantify als frm simulatins the impact f the lng-range beam-beam effect n the luminsity lifetime [13] 129

6 AI LAS Lsses Enm mannp 3 1} \_ u 4 CMS Lsses fnt blw up be explained by the intrabeam scattering effect Arriving at stable beams a cmparisn between the peak luminsity as cmputed frm the measured bunch characteristics and as measured by the experiments f ATLAS and CMS was perfrmed Befre the transitin t the BCMS beams, very gd agreement is bserved bth in abslute value and in rati between the tw experiments After the transitin t BCMS a divergence start t appear, hwever the rati still agrees very well In the last part f the year, bth the abslute values and the rati disagree This discrepancy Figure 12: Integrated luminsity lss due t the extra lsses (blue) and due t the extra emittance blw up (green) fr the physics ﬁlls in 2016 IMPACT OF DEGRADATION MECHANISMS ON THE INTEGRATED LUMINOSITY The extra emittance blw up and the extra intensity lsses that were bserved during cllisins and discussed in the previus sectins cause a luminsity degradatin In rder t quantify this ell ect, the luminsity mdel was called under ditl erent assumptins fr each ﬁll and the integrated luminsity fr each case was cmputed after 3 h in stable beams Three different cases are cmpared: EmpiricalBlwUpBurnOff (2), IBSEmpiricalLsses (3) and Empiri- calblwuplsses (4) Case 4 is the ne which represents the real data The rati between (4) and (2) reveals the inte- grated luminsity lss due t the extra emittance blw up needs further investigatin; the impact f the calibratin f the BSRT instrument and the calibratin f the experiments are under scrutiny During cllisins, bth an extra emittance blw up and extra lsses, especially at the ﬁrst 2-3 h in stable beams are bserved Higher lsses were bserved fr standard beams with larger emittances while the minimum lsses were bserved fr the BCMS beams with small emittances A clear impact f the LIl plarity is bserved; higher lsses are bserved when the LHCb perates With negative plarity The lsses were then again increased after the crssing angle reductin A tune ptimizatin after this, had a clear psitive impact n the minimizatin f the lsses It is als interesting t ntice that after the crssing angle reductin, signatures f the lng-range beam-beam effect start t be present in the lsses patterns Finally, the impact f the degradatin mechanisms t the integrated luminsity ver the ﬁrst 3 h in stable beams was studied The impact f the extra emittance blw up is veiy smth alng the year, while the impact f the extra lsses varies depending n the changes taking place in the machine while the rati between (4) and (3) due t the extra lsses The results are presented in ﬁg 12 It is interesting t ntice that the evlutin f the integrated luminsity lss due t the emittance blw up (green) is rather smth alng the year On the ther hand the lss due t the extra lsses varies alng the year and it fllws the machine changes in the same way as the extra (n tp f burn-011) intensity lsses SUMMARY A luminsity mdel based n the main cmpnents respnsible fr the LHC luminsity degradatin (intrabeam scattering, synchrtrn radiatin, elastic scattering and lumi- nsity burn-ft) was applied t the LHC data frm the 2016 Run The mdel was applied bunch by bunch t all physics ﬁlls and under ditl erent assumptins The cmparisn between the mdel predictins and the measured evlutin f the bunch characteristics (intensity, hrizntal and vertical emittances and bunch length) and thus the luminsity led us t sme interesting cnclusins fr the perfrmance f the machine in 2016 At ﬁrst, the emittance evlutin frm injectin t stable beams was discussed An extra emittance blw up, cming mainly during the ramp, was present in all ﬁlls This cannt REFERENCES [l] W Herr and B Muratri, Cncept f Luminsity", CERN Acceleratr Schl: Intermediate Curse n Acceleratr Physics, Zeuthen, Germany, Sep 2003, pp36l 378 [2] F Antniu, G Arduini, Y Papaphilippu, G Paptti, TUPTY020, prc f IPAC 15, Richmnd, Virginia, USA (2015) [3] M Kuhn et al, Origins f transverse emittance blw-up during the LHC energy Ramp TUPROOIO, prc f IPAC' l4, Dre sden, Germany (2014) [4] M Lamnt and 0 Jhnsn, LHC beam and luminsity lifetimes revised, CERN-ACC , 2014 [5] T Garavaglia, Prtn-Prtn Scattering Cntributin t Emittance Grwth, Prceedings f the 1993 Particle Acceleratr Cnference [6] M Lamnt, Where d the prtns g [1", LBOC presenta- tin 2/2/2016 [7] LPC website: [8] M Hstettler et al, "Hw well d we knw ur beams? these prceedings [9] MADX website: 130

7 [10] [11] [121 [13] F Antniu and F Zimmermunn, Revisin f Intrabeum Scattering with Nn-Ultrarelativistic Cnectins and Vertical Dispersin fr MAD-X", CER1\' -ATS TOTEM Cllabratin et 211, Luminsity independent measurements f ttal elastic and inelastic crss-sectins at V7 = 7 TeV, Eurphys Lett 101 (2013) G Trad, Status f the Beam Prfile Measurements at the LHC these prceedings Y Papaphilippu ct 11 "Scenaris fr 2017 and 2018" these prceedings 131

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Collective effects in Beam Dynamics

Collective effects in Beam Dynamics Cllective effects in Beam Dynamics Givanni Ruml, Hannes Bartsik and Kevin Li USPAS, ne-week curse, 19-24 January, 2015 http://uspas.fnal.gv/index.shtml January 2015 USPAS lectures 2 Particle beam Nminal