1. 1 NICA Collider: status and further steps O.S. Kozlov LHEP, JINR, Dubna for the NICA team Machine Advisory Committee, JINR, Dubna, October 19-20, 2015

2. 2 1.Collider optics and parameters 2.Instabilities in collider 3.Correction systems of the rings 4.Dynamic Aperture estimation 5.Multipole corrector parameters 6.Collider optics: further steps Contents

3. 3 1. Collider general parameters Circumference, m503.04 Number of bunches2 Rms bunch length, m0.6 Beta-function at IP, m0.35 Betatron tunes, Qx / Qy9.44 / 9.44 Chromaticity, Q’x / Q’y-33 / -28 Ring acceptance,  mm  mrad 40 Long. acceptance,  p/p  0.010 Gamma-transition,  tr 7.088 Ion energy, GeV/u1.03.04.5 Ion number per bunch2.0∙10 8 2.4∙10 9 2.3∙10 9 Rms  p/p, 10 -3 0.551.151.5 Rms beam emittance, hor/vert, (unnormalized),  mm  mrad 1.1/ 0.95 1.1/ 0.85 1.1/ 0.75 Luminosity, cm  2 s  1 0.6∙10 25 1.0∙10 27 IBS growth time, sec1604601800 Tune shift,  Q total =  Q SC +2  -0.050-0.037-0.011

4. 4 1. Collider Optics Periodic Cell Lcell=11.96m Ldip=1.94m Bmax=1.8T Lquad=0.46m Gmax=23T/m Lcorr=0.30m (dipole, quadrole, sextupole, octupole windings)

5. 5 1. Collider Optics Optics for both beams (Half of the Ring).  L(Triplet-IP)=5.25m Dy not compensated

6. 6 1.2. Collider Ring scheme & Layout, Ion Mode

7. 7 Stochastic cooling systems layout in collider SC system parameters: W=2  4 GHz, P= up to 500 W amplifier, L_pickup=2m

8. 8 2. Specification of the instabilities in NICA collider Sidorin,Zenkevich

9. 9 2. Specification of the instabilities in NICA collider Sidorin,Zenkevich

10. 10 3.1. Dipole correction: Closed Orbit Correction Error Type R.m.s. value Dipole magnets: Relative field error,  (BL)/(BL) 0.0005 Longitudinal displacement,  S 0.5 mm Transverse displacement,  Y 0.5 mm Roll error,  0.5 mrad Quadrupole magnets:Transverse displacement,  X/  Y 0.10/0.10 mm Magnet alignment tolerances realized by geodetic system and relative dipole guiding field tolerance

11. 11 C.O. Distortion Statistics for N=100 random orbits Horizontal orbit [mm]: X min X max -17.4 18.1 5.7 Vertical orbit [mm]: Y min Y max -19.1 14.6 5.6 2.1. Closed Orbit Correction Maximal/minimal horizontal/vertical pickup readings before/after correction

12. 12 Required maximal values of horizontal/vertical corrector strength. Horizontal orbit [mm]: X min X max -0.55 0.49 0.12 Vertical orbit [mm]: Y min Y max -0.53 0.62 0.13 Maximal corrector strenght:  max X/Y [mr] 0.30 / 0.30 Max. number of used correctors 25 Correction Quality X/Y 33/30 C.O. Correction Algorithm - MICADO C.O. Correction Statistics for required r.m.s residual orbit=0.1 mm 2.1. Closed Orbit Correction

13. 13 3.2. Quadrupole correction of tune  Nominal Betatron Tunes Qx/Qy=9.44  9.46 require for effective Stochastic Cooling in Energy range 3  4.5 GeV/u;  Qx/Qy=9.10 – second possible working point: Ecool up to 3GeV/u, larger DA;  Collider correction range: Qx/Qy=9.10  9.46 ;  Main collider quadrupoles: Imax=11kA  Trim quadrupoles families in long straights used for tune correction together with another matching conditions: Imax=1kA Tune diagram up to 7 th resonance order

14. 14 3.2. Quadrupole correction of tune Tuning of the ring with trim quadrupoles (an example for 1 half of the straight section).

15. 15 3.3. Skew quadrupole corrections: Coupling Sources of X/Y coupling in collider:  Solenoids: MPD: Bs=0.5T, Leff=5.8m; ECool: Bs=0.2T, Leff=6.0m  Quadrupoles random roll:  =0.1mrad expected Solenoid effects:  Tune Shifts  X/Y Coupling, but  x   y MPD[ + ], ECool [ - ] 4 Skew Quadrupole Families K 1 [m -2 ]: -0.0209, +0.0048, +0.0068, +0.0176 Gmax=0.3[T/m] L SQ =0.3m Correction @ Ek=1GeV/u :  Tune Shifts: min +/-0.01, max +/- 0.03  Coupling: correction of 2 nearest resonances Qx-Qy=0, Qx+Qy=19 by skew quads (or solenoids).

16. 16 Q X / Q Y  Q X /  Q Y Unpertubed tunes 9.4352/ 9.4374 Difference resonance modes before correction 9.4257/ 9.4477-0.0100/+0.0100 Difference resonance modes after correction 9.4356/ 9.4378 +0.0004/+0.0004 Correction of 2 nearest coupling resonances with harmonics p=0, 19: Betatron tunes and tune Splits: 3.3. Skew quadrupole corrections: Coupling Qx-Qy=0 Qx+Qy=19

17. 17 3.3. Skew quadrupole corrections: Dy Dispersion functions: horizontal D x, vertical D y (before/after correction) Correction of the vertical dispersion D y could be provided by at least 2 additional skew quadrupole families located in arcs near maxima of D x -dispersion (8 correctors, G max = 1 T/m)

18. 18 3.4. Sextupole correction, Chromaticity of tune  Cancellation of sextupole nonlinearity influence on DA :   =180 0 between correctors of one family (F/D)  Sextupoles adjusted to minimaze tune variation: 4 families of sextupole correctors for second order chromaticity correction, Tune spread over the momentum acceptance ±4  p before (1) and after (2) correction  Natural chromaticities: Q’x=-33, Q’y=-28 (  Q’x,y~20 from 2 IPs)  Corrected chromaticities: Q’x=-1.5, Q’y=-1.5  Ncorr=24, G’max=150T/m^2

19. 19 3.5. System of Octupole correctors  Corrected (low) chromaticity could decrease higher order modes of beam instability and improve DA consequently beam lifetime;  Too low chromaticity can make the beam unstable due to weak head-tail instability ;  One way to compansate this effect is to introduce octupoles to create large amplitude dependent tune spread;  If the shifted coherent tunes due to wake fields is within incoherent betatron tune spread or synchrotron tunes all unstable higher mode can be damped by Landau damping;  Problems from octupoles: additional 2nd order chromaticity, reduction of DA 2. Introduction Amplitude dependent Tune Spread to compensate head-tail instability: 1. Compensation Amplitude dependent Tune Spread from Sextupoles: 2 families of Octupole correctors in arcs (Nf=Nd=10), Gmax=400T/m3.

20. X/Y DAs @ IP for Chrom. Correction Q’x,y=0: DAx=150pi, Day=18 0pi 20 (  B/B) 3,dip =4E-4 (E K = 1GeV/u) DAx = 140pi, DAy = 140pi No space charge 4. Dynamic Aperture

21. 21 4. Dynamic Aperture DA simulation with MAD-X code methods: 1.Thin lenses approximation – Symplectic integration of particle motion; 2. PTC - Polymorphic Tracking Code – Symplecticity + Space Charge. Conditions for calculations: RF cavities, Chromaticity sextupoles, Dipole nonlinearities (odd harmonics) ON N part =10 5 – max.number of particles: N turn =10 3  10 5 – number of turns. The long-term DA is evaluated by the Giovannozzi approach: where D  - asymptotic DA, b and k parameters are defined from dependency D(N). Results: Asymptotical DA for Q x,y =9.44/9.44 working point: D  =100  mm  mrad (PTC), 60  mm  mrad (tnin lens) > A x,y =40  mm  mrad

22. 22 4. Dynamic Aperture Zenkevich, Bolshakov Dynamic Aperture (PTC), “survival plot” Dynamic aperture, envelope (PTC). N part =10 5 – number of particles N turn =10 3 – number of turns

23. 23 4. Dynamic Aperture Dynamic aperture (PTC, thin-lens methods and approximations) vs number of turns N turn. N part =10 5 – max.number of particles N turn =10 5 – max.number of turns

24. 24 5. Multipole corrector Multipole Component Function Max. parameter of magnetic field Max. parameter of power supply [kA-turns] Number Dipole Closed orbit correction and control 0.15 Т8.040 Quadrupole Betatron tune correction 2.2 Т/m3.812 “Skew quadrupole Coupling compensation and vert. disp. correction 1.0 Т/m1.74; 8 Sextupole Chromaticity of tune control 150 Т/m 2 5.748 Octupole Second order corrections 400 Т/m 3 3.820 Set of multipole correcting elements for 1 ring

25. 25 6. Optimization of Collider optics and beam dynamics  Main quadrupoles (max 11kA) + Trim-Quadrupoles families (max 1kA) : betatron tunes correction in range Qx/Qy=9.1  9.46;  Introduction of additional skew quads families for Dy-correction near IP; Further considerations for optics and dynamics:   * variation at IP,  *=[0.35  1.0] m;  Resonances correction (various multipoles) ;  Systems of (scraper-collimator) for localization of particle losses with large amplitudes;  Further simulation of long term Dynamic Aperture with space charge, also taking into account fringe fields of the magnetic elements;  Checking of beam dynamics at working point Qx/Qy~9.1, and Qx  Qy.

26. 26 6.  * variation E K =1.0 GeV/u E K =3.0 GeV/u E K =4.5 GeV/u  * =0.35 m  max =190 m 2206002000  * =1.0 m  max =65 m 3009002500 Characteristic IBS growth times (sec), t X  t Y  t L (MAD-X, beam parameters – Table p.3)

27. 27 6. Fringe fields effect Zenkevich,Bolshakov preliminary results Dynamic Aperture (PTC tracking), N part =10 5, N turn =10 3, taking into account Final Focus Quadrupoles Fringe fields: (6 th, 10 th, 14 th order resonances excitation)  small DA Dynamic Aperture (PTC tracking) with Fringe field and MPD Solenoid Working point: Qx=9.34, Qy=9.32

28. 28 Thank you for your attention !

29. 29 1.2. Collider Ring scheme & Layout, Polarized Mode Polarization Control Polarization Control 2-nd Solenoid SS 1-st Solenoid SS SPD MPD