1. ELENA optics issues Pavel Belochitskii

2. Part I: linear optics 23/11/2015Meeing on ELENA commissioning2

3. Choice of extraction energy Extraction energy E kin =100 keV allows to increase significantly an amount of captured antiprotons (~30%) If go to lower energy, one meets strong limitations imposed by:  IBS (Intra Beam Scattering)  transverse space charge limitations (incoherent tune shift)  very high vacuum required  difficult to manufacture foil thinner than 1µm If go to higher energy:  smaller number of antiprotons due to thicker degrader foil  difficult to equipe extraction lines with electrostatic elements (high voltage) 23/11/2015Meeing on ELENA commissioning3

4. Preliminary choice of some of the main parameters Come from experiments:  bunch length must not exceed 300 nsec, or 1.3 m (twice of trap length)  The transverse beam sizes must be around 1 mm (±1σ) -> set requirements to beam emittance at extraction and to beta function values at the focal point (end of transfer line to experiment)  The momentum spread of extracted beam should be small enough to fit requirements of experiments and to avoid problems with beam transport in electrostatic beam lines 23/11/2015Meeing on ELENA commissioning4

5. Requirements to lattice which come from layout constraints Ring must be compact, C= 30.4m (1/6 of AD). This is the minimal length to put required equipment in, and the maximal length to fit properly inside of AD hall Two extractions from ELENA must be prepared to provide all experiments with beam The orientations of the injection section and the extraction sections have to help relaxing requirements to the injection and the extraction equipment Two dedicated straight section have to be prepared, for electron cooling (4.5 m minimum) and for beam injection The extraction needs less space due to low beam energy of 100 keV and will be done from standard sections The hexagonal ring compared with the rectangular ring, is much better both from the point of view of making easy injection in and extraction from ELENA ring and using the space available in AD hall in the optimal way Crane should have access to areas where heavy modules will be installed 23/11/2015Meeing on ELENA commissioning5

6. ELENA in AD hall 23/11/2015Meeing on ELENA commissioning6

7. Requirements to lattice which come from accelerator physics betatron tunes must be chosen carefully to provide the maximal space in a tune diagram free from the low order resonances. This will allow operating with the nominal direct space charge tune shift ΔQ = 0.1 or even bigger values, resulting in higher number of antiprotons possible in one bunch The beta function values in the cooling section should not be too small, otherwise tails in beam distribution will never being cooled They should not be too big as well, otherwise optics distortion by electron cooler will be essential The vertical beta function value in bending magnet should be modest (cheaper magnets) The maximal beta function values should be modest (cheaper equipment for given acceptance) It is desirable to avoid too small beta function values to limit IBS 23/11/2015Meeing on ELENA commissioning7

8. ELENA optics: choice of the bending magnet parameters Longer magnet makes smaller contribution to the beam focusing in the ring and easy optics adjustment. Shorter magnet allows operate at very low extraction energy 100 keV with magnetic field not too small Shorter magnets provide more space for other equipment placement, which is very critical for ELENA ring Compromised value of bending length 0.97 m and magnetic field at extraction energy 493 G have been chosen By varying the edge angle at the entrance and exit of bending magnet one can make focusing stronger or weaker in one or another plane The gap value of 76 mm was chosen to provide fast pumping from magnets and allow installation of bake out equipment 23/11/2015Meeing on ELENA commissioning8

9. Choice of the working point Tunes should allow to operate with maximal incoherent tune shift due to space charge which is critical in ELENA at extraction energy The working point is chosen near main diagonal Q x - Q y = integer, providing big area in tune diagram free from the most dangerous resonances The following working point placements have been studied: a) 1.5<Q x,y <2 near Q x - Q y = 0, b) 1<Q x <1.5, 2<Q y <2.5 near Q x - Q y =-1, and c) 2<Q x <2.5, 1<Q y <1.5 near Q x - Q y =1 The drawback of variant a) 1.5 4m in electron cooler The c) variant with tunes 2<Q x <2.5, 1<Q y <1.5 has been chosen 23/11/2015Meeing on ELENA commissioning9

10. Tunes diagram ELENA WP has been chosen: Provide good margins for incoherent tune shift due to space charge -> the area near main diagonal has been chosen Twiss function values in the centre of electron cooling section should be favourable for fast cooling speed Both geometrical and dynamic acceptances should be big enough to keep all the particles from AD until extraction Chromaticity correction should be reasonable to avoid too strong sextupoles 23/11/2015Meeing on ELENA commissioning10

11. Possible lattice configurations with machine periodicity of two (difficulties with beam extraction) 23/11/2015Meeing on ELENA commissioning11

12. Possible lattice configurations with periodicity of two (beam extraction is possible) 23/11/2015Meeing on ELENA commissioning12

13. chosen optics: main features Two dedicated straight sections, one for electron cooling and other one for injection Periodicity of 2 (cooler off) or 1 (cooler on) Three quadrupole families to control tunes and optics functions in cooler section Edge angle in bending magnets to balance focusing between two planes Two sextupole families to control chromaticity Two skew quadrupole to control linear coupling in machine BPMs and correctors to control orbit in machine 23/11/2015Meeing on ELENA commissioning13

14. Lattice functions (Q x,y =2.30/1.30) 23/11/2015Meeing on ELENA commissioning14

15. Lattice main parameters 23/11/2015Meeing on ELENA commissioning15 Q x / Q y β x /β y /D x, m (cooler) β x /β y /D x, m (max) K1, m -2 K2, m -2 E 1 =E 2, degrees α 2.3 / 1.32.1/2.2/1.511.8/6.6/1.72.3/-1.2/0.7224/-45170.26

16. Chromaticity correction In all lattices it is difficult to find places suitable for placement of focusing sextupole (β x >>β y, decent D x value) and defocussing (β y >>β x, decent D x value) sextupoles Places for sextupoles have to be foreseen during the linear optics design 23/11/2015Meeing on ELENA commissioning16

17. 23/11/2015Meeing on ELENA commissioning17 Electron cooler schematic layout and main parameters Drift section length l c, m1.0 Beam cooled at momentum, MeV/c35 & 13.7 Electron beam current I e, mA5 & 2 Cathode voltage at 35 MeV/c and 13.7 MeV/c, V355 & 55 Nominal/maximal magnetic field in solenoid, G100÷200 Electron beam radius at 35 MeV/c and 13.7 MeV/c, mm25

18. Effect of electron cooler solenoid on optics Linear coupling is created by cooler solenoid of length l msol with magnetic field B msol, it is compensated by two compensating solenoids of length l comp with magnetic field B comp = 0.5·B msol · l msol / l comp placed on each side of cooler Focusing done by solenioids produces tune shifts For the nominal field B msol =100 G they are δQ x =18·10 -4 and δQ y =19·10 -4. The tune shifts due to compensated solenoids are δQ x =32·10 -4 and δQ y =33·10 -4. Totally, for the nominal field in the main solenoid, the tune shifts at extraction energy are δQ x =50·10 -4 and δQ y =52·10 -4. For the field in main solenoid B msol =200 G the tune shifts are δQ x =0.020 and δQ y =0.021 23/11/2015Meeing on ELENA commissioning18

19. Effect of electron beam of cooler on optics The electron beam of ELENA cooler makes extra defocusing (in both planes) on ring optics. The tune shifts are given by Effect is more pronounced at extraction energy 100 keV (β=1.46·10 -2, γ=1), the classical proton radius r 0 =1.5410 -18 m, the cooling length l 0 =1.0 m, =β 0 (1+ l 0 3 /(12β 0 )), beta function values in the centre of the cooler β x,0 =2.1 m, β y,0 =2.2 m and the electron beam current I e =2 mA tunes shifts are ΔQ x,y = -0.012 Effects of cooler on optics (due to solenoidal fields and due to electron beam) have opposite sign and partly compensate each other These effect break periodicity of 2, but optics perturbation is weak 23/11/2015Meeing on ELENA commissioning19

20. Effect of electron beam of cooler on optics 23/11/2015Meeing on ELENA commissioning20

21. Coupling due to errors and its compensation The tilt errors in quadrupole alignment δφ and the vertical orbit offset in sextupoles δy produce linear coupling in ELENA, which can be estimated in terms of coupling vectors C ± as For δφ rms =0.65·10 -3 and y rms =2·10 -3 m and given beta function values, normalized quadrupole strengths K1=(∂B y / ∂x)/Bρ and sextupole strengths K1=(∂ 2 B y / ∂x 2 )/Bρ, multiplied by their lengths, and assuming no correlation between their strength and phases one finds one finds that C ± (r.m.s., quadrupoles)=0.9·10 -3, and C ± (r.m.s.,sextupoles)=5.1·10 -3, resulting in C ± (total)=5.1·10 -3 23/11/2015Meeing on ELENA commissioning21

22. Coupling due to errors and its compensation Experience from AD: extra coupling might come from stray fields Way of compensation: two skew quadrupoles used, properly separated in phase advance (very difficult in ELENA ring) Fair margins in amplitude foreseen Only the difference resonance Q x - Q y = 1 will be cared, the WP is well distanced from the sum coupling resonance and it is neglected 23/11/2015Meeing on ELENA commissioning22

23. Orbit excursion due to errors Various sources contribute to orbit excursion: quadrupole misalignments, bending magnet field and tilt errors, cooler solenoid and compensating solenoids tilt errors, stray fields from various sources, earth field No detailed simulations with ensemble of the rings with randomly distributed errors have been performed yet, instead simple estimations based on reasonable assumptions of error values have been done The r.m.s. deviations have been found: x r.m.s. ≈1.3 mm and y r.m.s. ≈ 0.9 mm and the maximal values are expected twice bigger 23/11/2015Meeing on ELENA commissioning23

24. Orbit excursion due to stray fields and earth field in AD hall The systematic measurements of magnetic field in AD hall in place of ELENA location have been performed, its amplitude doesn’t exceed 0.5 G in any point Its effect in ELENA was simulated with MADX program. It was assumed that massive conductive equipment like magnets protects beam well from the stray fields. At the non-protected places the value of the magnetic field was assumed 0.5 G everywhere. For purely vertical field the maximal horizontal orbit excursion is x max =4.2 mm and the r.m.s. excursion x r.m.s =2.0 mm. After correction with 8 correctors it is reduced down to maximal value x max =1.4 mm and r.m.s. excursion x r.m.s. =0.5 mm. For the same situation in the vertical plane y max =8.4 mm and excursion y r.m.s. =5.5 mm. After correction the orbit excursion was reduced down to values of y max =1.2 mm and y r.m.s. =0.5 mm 23/11/2015Meeing on ELENA commissioning24

25. Orbit correction scheme The choice of number and positions of combined (DHV) orbit correctors and beam position monitors (BPM) in the ELENA ring is dictated mainly by ring layout. Two orbit correctors with BPM’s integrated inside are placed at each side of two dedicated straight sections. Other 4 sections have 4 orbit corrector and 6 BPM’s integrated into quadrupoles. Thus totally 10 BPM’s and 8 correctors are foreseen for orbit correction Two horizontal coils are integrated into electron cooler to correct orbit distortion created by toroid kicks. Together with other two combined correctors on each side of section they will be used for making local horizontal orbit bump around cooler for the best alignment antiproton beam w.r.t. electron beam, hence for fast cooling. Two small vertical coils will be integrated into cooler for making local vertical orbit bump around cooler, together with the same two combined correctors on each side of cooler section. In a similar way two correctors with two integrated BPM’s are placed at the sides of the injection section. Together with using them for an orbit correction they will help to minimize the trajectory and the angle offsets for injected beam, hence reducing its emittance blow up. 23/11/2015Meeing on ELENA commissioning25

26. AD beam at extraction: the horizontal emittance in 2011 and 2012 23/11/2015Meeing on ELENA commissioning26

27. AD beam at extraction: the vertical emittance in 2011 and 2012 23/11/2015Meeing on ELENA commissioning27

28. ELENA acceptance and apertures The ELENA acceptances are defined as big as A x,y =75 π mm mrad in both planes The relatively big value was chosen for the reasons:  To avoid beam losses during deceleration from injection energy down to first plateau, where the beam emittance is at its maximal value. The electron cooling is applied for the first time  To keep tails in beam transverse distribution often generated in AD which sometimes may include 10% to30% of total intensity  To take into account emittance blow up appeared after beam transfer from AD to ELENA With beta function values at electron cooler β x,y ≈2 m the beam size for maximal emittance is σ x,y =(75·2) 1/2 ≈12.5 mm which is fits in the electron beam radius of 25 mm The apertures are defined according the formula 23/11/2015Meeing on ELENA commissioning28

29. ELENA cycle Injection of a bunched beam followed by deceleration Beam cooling at intermediate momentum to counteract beam emittances and momentum spread blow up Deceleration down to extraction energy, beam cooling, bunching at harmonic h=4, then compression to provide required bunch length and fast extraction The final goal is delivering to experiments beam 1.3m long with 1σ~1mm 23/11/2015Meeing on ELENA commissioning29

30. ELENA performance limitation due to space charge Most important for bunched beam and a low energies, especially right before extraction Here r p =1.54·10 -18 m, the ring circumference C=30.4m, factors G T =1÷2 and G L =1÷2 depend on transverse and longitudinal beam distributions, 60% of deceleration efficiency assumed (3·10 7 antiprotons injected into ELENA, 1.8·10 7 antiprotons decelerated down to 100 keV) 4 bunches extracted the bunch intensity is N b =0.45·10 7 (basic scenario) 23/11/2015Meeing on ELENA commissioning30

31. Intensity limit due to space charge Example 1, coasting beam at extraction momentum pc=13.7 MeV/c:  For the beam intensity N=1.8·10 7 and emittances ε x =ε Y =4π mm mrad the tune shift is equal to ΔQ=-0.010. For the high intensity extracted beam in AD N=3.6·10 7 and perfect deceleration efficiency of 100% the tune shift value is still low, ΔQ=-0.020. Example 2, bunched beam at the end of deceleration (pc=13.7 MeV/c):  For intensity N=1.8·10 7 and for beam which occupies 1/3 of the ring, have emittances ε x,y =15π mm mrad and is more dense at its centre (the coefficients G T and G L are equal to 2) the tune shift is equal to ΔQ= -0.032. For the better deceleration efficiency in ELENA of 80% it goes up to ΔQ= -0.044. Example 3, bunched beam before extraction (pc=13.7 MeV/c):  For intensity N=1.8·10 7 distributed in 4 bunches, emittances ε x,y =4π mm mrad and the bunch length l b =1.3 m the tune shift value is ΔQ=-0.121. The coefficients G T and G L are equal to 2. By use of RF system with double harmonics (h=4 and h=8) one can flatten the longitudinal beam distribution making tunes shift smaller in about 25% resulting in ΔQ=-0.096. 23/11/2015Meeing on ELENA commissioning31

32. Operation with tune shift ΔQ>0.1 is on demand Operation with experiments number ready for taking a beam smaller than 4 is likely due to  Limited human resources in AD experiments- > difficult to run 24 h / 7days, at least 3 teams required to run continuously  Human limitations: weekends, vacations  Experiment’s time is used not only for taking a beam (collecting data), but for many kind of other work (change/repair equipment, filling in liquid helium, meetings, discussions etc.) One of the users can be AD / ELENA team for MD’s but this must be schedule properly High deceleration efficiency in ELENA (more than 60%) may be achieved Intensity in AD is higher than average (3.5·10 7 is often the case) 23/11/2015Meeing on ELENA commissioning32

33. IBS in ELENA: ramps Calculated with BETACOOL (comparison with M.Martini program shows very small differences) Negligible effect on first ramp Small at the beginning of second ramp 1/τ x =0.020 s, 1/τ y =-0.009 s, and 1/τ l =0.146 s (N=1.8·10 7, ε x,y =5π mm mrad, Δp/p=1·10 -3, bunch length equal to1/3 of the ring ) Small at the end of second ramp 1/τ x =0.019 s, 1/τ y =-0.002 s, and 1/τ l =0.018s (N=1.8·10 7, ε x,y =15π mm mrad, Δp/p=3·10 -3, bunch length equal to1/3 of the ring ) The effect on momentum spread depends on ramp duration and sensitive to momentum cooling at 35 MeV/c For Δp/p=5·10 -4 after cooling at 35 MeV/c the momentum spread blow up become essential 1/τ l =1.037 s 23/11/2015Meeing on ELENA commissioning33

34. IBS in ELENA: plateaus Set limit on ultimate emittances and momentum spread at the end of electron cooling ) For intensity N=1.8·10 7, emittances ε x,y =4π mm mrad, momentum spread Δp/p=1·10 -3 at the beginning of bunch compression the longitudinal blow up rate is fast 1/τ l =6.02 s. At the end of bunch compression (≈50 msec later) transverse blow ups are fast, and longitudinal is slow 1/τ x =3.1 s, 1/τ y =1.8 s, and 1/τ l =-0.094 s In case of fast extraction no essential increase of beam sizes observed 23/11/2015Meeing on ELENA commissioning34

35. Part II: optics studies by tracking 23/11/2015Meeing on ELENA commissioning35

36. More knowledge of ELENA optics with tracking studies Compare optics properties for working points near diagonal Q x -Q y =1, with tunes 2<Q x <2.5, 1<Q y <1.5 Which is the dynamic aperture of ELENA ring at injection, and before first electron cooling (where we need maximal acceptance), is it bigger than geometrical acceptance? Which is the dynamic aperture at the last cooling plateau (with kinetic energy E-mc 2 =100 keV), where the coupling due to solenoidal field of cooler and compensating solenoids is maximal and space charge limita? How much the dynamic aperture depends on cooler magnetic field value? Which are transverse geometrical acceptances with nonlinear effects taking into account 23/11/2015Meeing on ELENA commissioning36

37. How we perform tracking studies of ELENA optics MADX+PTC Elements included: bending magnets, quadrupoles, sextupoles, sometimes multipoles. Normally RF cavity is off (ELENA beam has small momentum spread throughout all the cycle) Mathematica based post tracking analysis Typical number of turns is 5000, smaller number gives phase portraits not completed, especially in case of simultaneous action of few resonances Fair number of turns are required as well for FFT analysis: good resolution and reproducible peak amplitudes help in post tracking analysis Particles with the same initial angle have been set for tracking, all initial x- coordinates are equal to initial y-coordinates, their amplitude varied from 1 mm to 31 mm, which corresponds to emittance about 200 π mm mrad (compare with 75 π mm mrad typical geometrical acceptance) 23/11/2015Meeing on ELENA commissioning37

38. How we interpret output from tracking studies of ELENA optics Hamiltonian formalism with normalized variables x/(β x ) 1/2, p x (β x ) 1/2, y/(β y ) 1/2, p y (β x ) 1/2 is used In the case of linear motion H=constant (Courant-Snyders invariant written with action-angle variables and eliminated revolution frequency) and the phase space trajectories are circles In the simple case of one resonance nQ x -mQ y =p dominated there is invariant nI x +mI y =const, here I x,y is an action variable, n,m are integers and p is the order of resonance In case of two resonances which can produce similar effects on phase space (i.e. Q x -Q y =1 and 2Q x -2Q y =2) the extra help to make a true choice could come from FFT analysis 23/11/2015Meeing on ELENA commissioning38

39. Which nonlinear effects are included into simulation? Nonlinearities due to ring sextupoles (used to compensate chromaticity) Nonlinearities of bending magnets Nonlinearities from electron cooler caused by toroid field, penetrating into ring (not performed yet) 23/11/2015Meeing on ELENA commissioning39

40. Starting point for run: machine with zero chromaticities (Q x,y =2.21/1.23, sextupoles on) Horizontal (top) and vertical (bottom) phase space in normalized coordinates for beam of momentum 35 MeV/c (left) and 13.7 MeV/c (right) Strong distortions of trajectories, especially at 13.7 MeV/c Particles with initial coordinate more than 16 mm are lost (dynamic aperture about 50 π mm mrad) 35 MeV/c: beam emittances are at their maximal values-> requirements to dynamic aperture are strong 13.7 MeV/c: beam emittances are modest, small dynamic aperture accepted 23/11/2015Meeing on ELENA commissioning40

41. Starting point for run: machine with zero chromaticities (Q x,y =2.21/1.23, sextupoles on) Horizontal and vertical invariants for beam with momentum 35 MeV/c (left) and 13.7 MeV/c (right) Strong coupling between horizontal and vertical motion, especially for x=16 mm particle Coupling is a bit stronger at 13.7 MeV/c (the range of action variation is a bit bigger) 23/11/2015Meeing on ELENA commissioning41

42. FFT is useful to get more info from tracking Complicated picture for identifying peaks in FFT with resonances At small amplitudes (1mm to 11 mm) horizontal and vertical modes are well separated, but this is not the case at 16 mm (modes are coupled with tune values different from that for 1 mm to 11 mm) One finds that in vertical plane two main peaks are at the same frequencies as shown in FFT for horizontal plane (by other words, there is no pure horizontal or vertical motion) At 35 MeV/c plot is very similar to this one, with exception that main modes are slightly different due to weaker coupling 23/11/2015Meeing on ELENA commissioning42

43. First impressions (or could we use this set for beam deceleration) The blow up of beam emittance due to nonlinearities from sextupoles and bending magnets is quite visible resulting in ineffective use of geometrical acceptance of ELENA. If possible, this WP should be avoided for beam deceleration at the first ramp and first beam cooling After the first cooling at intermediate plateau particles have small transverse amplitudes, and nonlinearities are less harmful -> no beam losses are expected Yet particles with bigger amplitude experience influence of nonlinear forces which could cause slow cooling. This will result in enhancing beam tails that worth to avoid Could we reduce nonlinearities? 23/11/2015Meeing on ELENA commissioning43

44. Nonlinearities from sextupoles 4 chromaticity sextupoles in ELENA, strengths depend on working point The maximal momentum spread in ELENA beam is achieved at the end of the first ramp right before the first cooling at 35÷40 MeV/c and is equal to Δp/p=1.4·10 -3. For 95% of the beam the tune shift due to chromaticity sextupoles will be within ΔQ x,y =1.4·10 -3 ξ x,y. For the WPs of ELENA optics which are above 4 th order resonances (their tunes are Q x,y =2.30/1.30 and Q x,y =2.46/1.46) chromaticity values ξ x,y ≤3 result in maximal tune spread value during cycle ΔQ x,y ≤ 5·10 -3. For the WP of ELENA optics which are below 4 th order resonances (Q x,y =2.21/1.21) chromaticities ξ x,y ≤4.6 result in maximal tune spread value during cycle ΔQ x,y ≤ 7·10 -3 Due to small momentum spread nonlinearities coming from sextupoles can be significantly reduced by operating with chromaticity compensated partly or completely non compensated. 23/11/2015Meeing on ELENA commissioning44

45. Sextupoles off, distortions reduced (no toroid fields included yet) No lost particles, acceptances are much bigger, yet fair phase space distortions Tiny difference between 35 MeV/c and 13.7 MeV/c Horizontal plane -> Vertical plane -> 23/11/2015Meeing on ELENA commissioning45

46. With sextupoles off no more coupled modes, and resonances are weaker Ring sextupoles on Ring sextupoles off 23/11/2015Meeing on ELENA commissioning46

47. Nonlinearities from bending magnets Nonlinear fields at the edges of bending magnet, which are strong due to big curvature ρ=0.927 m. Effect of this field can be significantly reduced by proper shimming at both ends of each magnet Making a scan for the optimal value of sextupolar component in bending magnet (with a particle tracking, by minimizing energy exchange between horizontal and vertical invariants), one finds K2·L=0.3165 m -2, here K2=(1/Bρ)(∂ 2 B y /∂x 2 ) Let’s try run machine with compensated chromaticities (to minimize space in tune diagram occupied by beam) 23/11/2015Meeing on ELENA commissioning47

48. Sextupoles off, sextupolar field in bending magnets is compensated No compensation of sextupolar fields in bending magnets In each bending magnet thin sextupole lenses are placed at both ends 23/11/2015Meeing on ELENA commissioning48

49. Sextupoles off, sextupolar field in bending magnets is compensated Ring sextupoles off, no compensation of sextupolar fields in bending magnets. Coupling resonances, especially Q x -Q y =1 contribute a lot to emittance blow up Ring sextupoles off, in each bending magnet thin sextupole lens placed at both sides. Weak coupling resonance(s), emittance blow up in the horizontal plane mainly due to the second order resonance 2Q x =4 23/11/2015Meeing on ELENA commissioning49

50. Sextupoles off, sextupolar field in bending magnet is compensated Ring sextupoles off, no compensation of sextupolar fields in bending magnets. Coupling resonances of 3 rd and 4 th order are visible Ring sextupoles off, in each bending magnet thin sextupole lens placed at both sides. The only visible resonance is 2Q x =4.Tune dependence on amplitude is very small 23/11/2015Meeing on ELENA commissioning50

51. Do we need excellent compensation of nonlinearities in ELENA? Laslett tune shift caused by space charge is the main intensity limitation in ELENA. It is imposed for bunched beam right before extraction The conservative value of ΔQ=0.1 is accepted With 60% of deceleration efficiency 1.8·10 7 pbars are available for physics but they should be splitted into 4 bunches to fit ΔQ≤0.1 condition, resulting in 4.5·10 6 pbars at best delivered to one experiment If most of the resonances especially third order ones will be suppressed, there is a good chance to increase ΔQ up to ~0.18 (either below 4 th order resonances or above them) resulting in ~8.1·10 6 pbars in one bunch In this case 3 or even 2 experiments can take a beam sharing full ELENA intensity. This makes ELENA operation much more flexible 23/11/2015Meeing on ELENA commissioning51

52. Sextupoles on for compensation of 50% of chromaticity, sextupolar field in bending magnet is compensated by shims Ring sextupoles off, in each bending magnet thin sextupole lens placed at each side. Top: horizontal plane, bottom: vertical plane Ring sextupoles on, chromaticities reduced in 50%, in each bending magnet thin sextupole lens placed at both sides horizontal plane -> vertical plane -> 23/11/2015Meeing on ELENA commissioning52

53. Sextupoles on for compensation of 50% of chromaticity, sextupolar field in bending magnet is compensated by shims Ring sextupoles on, natural chromaticities reduced in50%, in each bending magnet thin sextupole lens placed at both sides Ring sextupoles off, in each bending magnet thin sextupole lens placed at each side. No coupling resonances, only 2Q x =4 resonance signatures are observed 23/11/2015Meeing on ELENA commissioning53

54. Sextupoles on for compensation of 50% of chromaticity, sextupolar field in bending magnet is compensated by shims Ring sextupoles on, natural chromaticities reduced in 50%, in each bending magnet thin sextupole lens placed at both sides Ring sextupoles off, in each bending magnet thin sextupole lens placed at both sides 23/11/2015Meeing on ELENA commissioning54

55. Let’s look at working points above (space charge driven) 4 th order resonances Two more WPs have been checked, Q x =2.38, Q y =1.35 (just above 3 rd order resonance) and Q x =2.44, Q y =1.46 23/11/2015Meeing on ELENA commissioning55

56. Working points comparison: Q x =2.44, Q y =1.46 (right) versus Q x =2.21, Q y =1.23 (left) Q x =2.21,Q y =1.23, no sext compensation in BM: maximal amplitude for particle to survive is 16mm, the (dynamic) acceptance about 50 π mm mrad Q x =2.44,Q y =1.46, no sext compensation in BM: all particles survive, the (dynamic) acceptance more than 190 π mm mrad 23/11/2015Meeing on ELENA commissioning56

57. Working points comparison: Q x =2.44, Q y =1.46 (right) versus Q x =2.21, Q y =1.23 (left) 23/11/2015Meeing on ELENA commissioning57

58. Working points comparison: Q x =2.44, Q y =1.46 (right) versus Q x =2.21, Q y =1.23 (left) The main difference between two WPs: Much stronger coupling for Q x =2.21, Q y =1.23 Extra modes (w.r.t. main mode) are weaker for Q x =2.44, Q y =1.46 main modes are decoupled no signature of 3 rd order coupling resonance Q x -2Q y =0 is visible Smaller number of resonances 23/11/2015Meeing on ELENA commissioning58

59. Q x =2.44, Q y =1.46 (right) versus Q x =2.21, Q y =1.23 (left): sextupolar compensation in BM included Sextupoles run at reduced amplitude (chromaticity is partly compensated) Sextupoles run at full amplitude (chromaticity is compensated) High WP is better in view of nonlinearities 23/11/2015Meeing on ELENA commissioning59

60. Both WPs above third order resonance: Q x =2.44, Q y =1.46 versus Q x =2.38, Q y =1.35 (sextupolar compensation in BM included) Very similar plots… … with tiny preference of Q x =2.44, Q y =1.46 w.r.t. Q x =2.38, Q y =1.35 23/11/2015Meeing on ELENA commissioning60

61. Working point comparison The higher working points (above third order resonance(s)) have smaller nonlinearities w.r.t. low working points (below 4rt order resonance) The difference between Q x =2.44, Q y =1.46 and Q x =2.38, Q y =1.35 looks insignificant In addition to that, the geometrical acceptance (i.e. defined by apertures of equipment modules of ELENA ring) is the best for Q x =2.3, Q y =1.3, a bit worth for w.r.t. Q x =2.46, Q y =1.46, and more worth for Q x =2.23, Q y =1.23 Yet other important issues like IBS lifetime and electron cooling rates have to be taking into account as well … and nonlinearities from toroids have to be taken into account as well 23/11/2015Meeing on ELENA commissioning61

62. Does one find a significant difference at 35 MeV/c with electron cooler solenoid at 200 G compared with 100 G? Bsol=100 G, 35 MeV/c, Q x =2.38, Q y =1.35 Ring sextupoles on to set chromaticity to zero Bsol=200 G, 35 MeV/c, Q x =2.38, Q y =1.35 Ring sextupoles on to set chromaticity to zero Only small difference was found at 35 MeV/c, no toroids yet included into simulation 23/11/2015Meeing on ELENA commissioning62

63. Does one find a significant difference at 13.7 MeV/c with electron cooler solenoid at 200 G compared with 100 G? Bsol=100 G, 13.7 MeV/c, Q x =2.38, Q y =1.35 Ring sextupoles on Bsol=200 G, 13.7 MeV/c, Q x =2.38, Q y =1.35 Ring sextupoles on, more distortions More difference phase space distortions is visible at 13.7 MeV/c between cooler at 100 G and at 200 G, but this is for particles with big amplitude which is not the case at extraction energy 23/11/2015Meeing on ELENA commissioning63

64. Does one find a significant difference at 13.7 MeV/c with electron cooler solenoid at 200 G compared with 100 G? Bsol=200 G, 13.7 MeV/c, Q x =2.38, Q y =1.35 Ring sextupoles on, fair difference in resonance excitation The difference is well visible, and might be stronger when effects of electron cooler will be included (to be continued) 23/11/2015Meeing on ELENA commissioning64 Bsol=100 G, 13.7 MeV/c, Q x =2.38, Q y =1.35 Ring sextupoles on

65. 13.7 MeV/c, cooler solenoid at 200 G, ring sextupoles off Bsol=100 G, 13.7 MeV/c, Q x =2.38, Q y =1.35 Ring sextupoles off Bsol=200 G, 13.7 MeV/c, Q x =2.38, Q y =1.35 Ring sextupoles off 23/11/2015Meeing on ELENA commissioning65

66. Electron cooler solenoid at 200 G vs at 100 G: summary The effect of solenoid field is more pronounced at low momenta At 35 MeV/c, Bsol=200 G, and with sextupoles in machine the effect is still small at 16mm, which corresponds to beam emittance about 55 π mm mrad. It is more pronounced at 21mm (ε≈100 π mm rad), but this value is bigger than the geometrical acceptance of machine At 13.7 MeV/c the effect is stronger, but after the first cooling at 35 MeV/c beam emittance is much smaller, and no essential effect is expected as well In addition to the factor of reduced beam emittances at 13.7 MeV/c, one can as well switch ring sextupoles off because tune spread due to non zero chromaticity is negligible because of very small momentum spread On the contrary (w.r.t. faster electron cooling) side the toroid field will produce stronger dipole kick, which even being compensated, make the maximal orbit distortion twice bigger At the same time nonlinear toroid field is much stronger, and machine acceptance can drop (to be investigated) 23/11/2015Meeing on ELENA commissioning66

67. How close is the optics model to real bending magnet: magnetic measurements of pre-series bending magnet Measurements of optics properties of manufactured magnet -> relative variation of ∫Bdl is within 2·10 -4 w.r.t. OPERA model of magnet with excluded quadrupole component. Good agreement of magnet model and manufactured magnet! Courtesy by Daniel Schoerling 23/11/2015Meeing on ELENA commissioning67

68. Quadrupolar component of pre-series bending magnet and optics model ∫K1·dl=-0.525 m -1, with proper interpretation of the measurements with “fluxmeter” this comes to ∫K1·dl=-0.638 m -1 seen by particle passed through the magnet. It looks smaller compared with K1·L=2·tan φ/ρ=0.660 m -1. Assuming the difference comes due to error in edge angle, one find φ=16.5° compared with design value of 17°. “Fluxmeter”: curved array of long coils courtesy by Lucio Fiscarelli 23/11/2015Meeing on ELENA commissioning68

69. Bending magnet used for tracking with MADX+PTC and bending magnet designed with OPERA: comparison Particles start at mid point of bending magnet to be tracked outside of with MADX or OPERA, end point is well away from magnet to take into account fringe field Tracking is performed within OPERA program (yellowish green), or with MADX+PTC (light green) The ellipse inclination is defined by focusing in bending magnet->the value of edge angle φ=16.45° was derived compared with φ=17° of magnet design (comes from ELENA lattice) 23/11/2015Meeing on ELENA commissioning69

70. How can we cope with 0.5° edge angle error in bending magnet? Design, FINT=17° FINT=16.45°After correction Q x /Q y 2.3 / 1.32.36 / 1.242.3 / 1.3 β x /β y /D x (max), m11.8/6.6/1.7311.4/7.4/1.6512.3/6.2/1.63 β x /β y /D x (cooler), m 2.12/2.30/1.501.75/2.13/1.372.11/2.47/1.34 K1, m -2 2.28/-1.21/0.72 2.20/-1.20/0.63 23/11/2015Meeing on ELENA commissioning70 Design, FINT=17° FINT=16.45°After correction Q x /Q y 2.23 / 1.232.30/1.162.23/1.23 β x /β y /D x (max), m15.0/9.3/1.7413.3/11.5/1.6213.8/8.8/1.76 β x /β y /D x (cooler), m 3.12/2.11/1.502.41/1.82/1.312.91/2.18/1.22 K1, m -2 1.95/-0.54/0.62 1.70/-0.43/0.57 Design, FINT=17° FINT=16.45°After correction Q x /Q y 2.46 / 1.462.54/1.422.46/1.46 β x /β y /D x (max), m14.8/4.5/1.4915.9/4.5/1.4515.8/4.6/1.85 β x /β y /D x (cooler), m 1.40/2.42/0.931.12/2.54/0.931.40/2.62/0.80 K1, m -2 3.28/-2.54/0.77 3.24/-2.58/0.67 With error in edge angle of each bending magnet of 0.5 an error in tunes up to ΔQ=0.08 may happen which is quite noticeable and important This will be immediately recognized with tune measurements It has to be confirmed with orbit response measurements Optics correction base on orbit response will be implemented

71. Summary of studies The biggest nonlinearities comes with sextupoles. Due to small momentum spread of beam from AD one can significantly reduce their strength yet keeping tune spread small right after injection. After the first cooling they can be switched off. The second source of nonlinearities are edge fields in bending magnets. They can be compensated by making a proper profile at magnet edges. This compensation was done during magnetic design of magnet. The measurements of pre-series magnet showed very good agreement between manufactured magnet and designed one, this was confirmed by tracking. The tune dependence on amplitude is small even for big emittances (less than 0.007 for all cases) and doesn't make a problems In lattices with higher working points (above third order resonance) nonlinearities are weaker compared with those below 4 th order resonance The coupling produced by solenoids of electron cooler is not a limiting factor at the parameters ELENA will operate within the model used up to, i.e. without toroids. 23/11/2015Meeing on ELENA commissioning71

72. Studies to be continued… The including of toroids into the model is a crucial part of investigation, it may reduce dynamic aperture significantly and impose a limit of magnetic field of cooler The proper solution of this task is to include a real field in cooler into model. By other words, one has to include the field map of cooler into tracking. The first attempt in this direction has been already done, but failed. Due to complexity of cooler the field “quality” was not o.k., which resulted in beam “heating”. Both the horizontal and vertical action variables W nx and W ny have been grown with time (number of turns). The “difficult points” in field map have been identified, it was found that they are related to fast variation in shielding shape, which requires special care. As result, one needs a field map of object with length of at least ±1.25 m long with a step of 3mm or less. As result, the 5000 turns tracking needs few days for run of one variant, compared with few seconds when using MADX+PTC model. One, probably, can split cooler into many pieces, and make a fit for the field of each slot with fields presented in a series of multipoles. In this case one can use MADX+PTC with huge gain of calculation speed and with simplectic model. Still the question how well this model represents real cooler field is an open issue. 23/11/2015Meeing on ELENA commissioning72

73. Thank you for attention! 23/11/2015Meeing on ELENA commissioning73