RADIATIVE RECOMBINATION OF BARE NUCLEI AND IONS IN ELECTRON COOLING SYSTEM. A.V. Philippov, A.B. Kuznetsov, I.N. Meshkov
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1 RADIATIVE RECOMBINATION OF BARE NUCLEI AND IONS IN ELECTRON COOLING SYSTEM A.V. Philippov A.B. Kuznetsov I.N. Meshkov Veksler and Baldin Laboratory of High Energy Physics Joint Institute for Nuclear Research Dubna Russia Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine
2 OUTLINE Introduction Analysis of experimental data of radiative recombination (RR) rates for bare nuclei Analysis of experimental data of RR rates for intermediate charge state of ions 3 RR beam lifetime and cooling time Conclusion A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine /
3 INTRODUCTION Review of experimental results and their comparison with theoretical approaches is presented in this talk. We consider two essential cases for NICA: Recombination of bare gold nuclei in the NICA cooling system Recombination of intermediate charge state of gold ions in the Booster cooling system. Based on these comparisons we evaluated the contribution of the RR losses of intermediate charge state of gold ions: Au 3+ Au 33+ Au 43+ Au 5+ Au 6+ Au 68+ and Au 69+ during their acceleration in the Booster and the beam lifetime of the gold bare nuclei Au 79+ in NICA. A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 3/
4 ANALYSIS OF EXPERIMENTAL DATA OF RR RATES FOR BARE NUCLEI RR rates vs. the electron relative energy ΔE experiments: TSR CRYRING ESR. Red solid line theoretical models of H.A. Kramers [Phil. Mag. V P. 836.] black solid line R. Schuch [Phys. Rev. А. V. 45. N P ]. Fitted 50.0 Z Z Z Z E f E Recombination rate 0-8 cm 3 s e - +He + ØHe + + ÿz U Z He e - +C 6+ ØC 5+ + ÿz U Z C e - +N 7+ ØN 6+ + ÿz U Z N e - +Ne 0 + ØNe 9+ + ÿz U Z Ne e - +U 9 + ØU e - +U 9 + ØU Black dashed line is the fit of the formula above DE ev A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 4/ f E a Eb Ry E. Fitted 3 8 ZZ 8
5 ANALYSIS OF EXPERIMENTAL DATA OF RR RATES FOR BARE NUCLEI (Contnd) RR rates vs. the electron relative energy ΔE experiments: TSR CRYRING ESR. Red solid line theoretical models of H.A. Kramers [Phil. Mag. V P. 836.] black solid line R. Schuch [Phys. Rev. А. V. 45. N P ]. Fitted 50.0 Z Z Z Z E f E Recombination rate 0-8 cm 3 s e - +Si 4 + ØSi ÿz U Z Si e - +Cl 7 + ØCl ÿz U Z Cl e - +Ar 8 + ØAr ÿz U Z Ar e - +Bi 83 + ØBi ÿz U Z Bi e - +U 9 + ØU e - +U 9 + ØU Black dashed line is the fit of the formula above DE ev A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 5/ f E a Eb Ry E. Fitted 3 8 ZZ 8
6 ANALYSIS OF EXPERIMENTAL DATA OF RR RATES FOR BARE NUCLEI (Contnd) RR rates vs. magnetic field strength B experiment: ESR. [M. Steck et al. EPJ D P ] Recombination rate 0-8 cm 3 s mt 84 mt 94 mt 04. mt a=.0 a=0.7 a=0.4 a=0. Fitted ZZ RR spectra of U 9+ measured at 4 different magnetic guiding field strengths DE ev A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 6/ Z Z E f E f E a Eb Ry E. Fitted 3 8 ZZ 8
7 ANALYSIS OF EXPERIMENTAL DATA OF RR RATES FOR BARE NUCLEI (Contnd) RR rates vs. transverse electron temperature T experiment: ESR. [M. Steck. NIM A V. 53. P ] EVcm Vd cm s B Gs l T E d U clearing voltage Vcm k 0 cm kb.6 0 Erg ev cathode cm cathode V me g V cm s d ev Erg ev d B T T T T l 0. ev. A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 7/
8 ANALYSIS OF EXPERIMENTAL DATA OF RR RATES FOR BARE NUCLEI (Contnd) RR rates vs. transverse electron temperature T experiment: ESR. [M. Steck. NIM A V. 53. P ]. Case B=96 mt. Recombination rate 0 - s - Recombination rate 0 - s - Recombination rate 0 - s T ev 96 mt R NICA T ev Recombination rate 0 - s b T0. ESR a T ev ESR U NICA enica 0.4 NICAZAu ESR neesr Recombination rate 0 - s T ev a R Ry b Z n Top curve (right slope) Bottom curve (left slope) T ev A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 8/ R ESR.
9 ANALYSIS OF EXPERIMENTAL DATA OF RR RATES FOR BARE NUCLEI [M. Bell and J.S. Bell. Particle Accelerators. 98. V.. P ] [M. Steck. NIM A V. 53. P ] (Contnd) RR rates vs. transverse electron temperature T experiment: ESR (Bell & Bell comparison). RR spectra of U 9+ measured for a different drift temperature T d e mred dashed line Maxwell blue dashed line flattened..000 T T d Tcathode T cathode 0.eV Recombination rate 0 - s MaxwellRR 3 3 8k B Z Ry 4 T 3 ZZ a0 Z Ry ln 3 3 mt e T 3 Z Ry FlattenedRR 3 3 k B Z Ry 5 T 3 ZZ a0 Z Ry ln ln. 3 3 mt e T 6 Z Ry 96 mt 98. mt 00.5 mt 0.8 mt 05 mt Bell & Bell Maxwell Bell & Bell Flattened T ev A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 9/
10 ANALYSIS OF EXPERIMENTAL DATA OF RR RATES FOR BARE NUCLEI [M. Bell and J.S. Bell. Particle Accelerators. 98. V.. P ] [M. Steck. NIM A V. 53. P ] (Contnd) RR rates vs. transverse electron temperature T experiment: ESR (Bell & Bell comparison). RR spectra of U 9+ measured for a different drift temperature T d e mred dashed line Maxwell blue dashed line flattened..000 T T d Tcathode T cathode 0.eV Recombination rate 0 - s MaxwellRR 3 3 8k B Z Ry 4 T 3 ZZ a0 Z Ry ln 3 3 mt e T 3 Z Ry FlattenedRR 3 3 k B Z Ry 5 T 3 ZZ a0 Z Ry ln ln. 3 3 mt e T 6 Z Ry 96 mt 98. mt 00.5 mt Bell & Bell Maxwell Bell & Bell Flattened T ev A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 0/
11 ANALYSIS OF EXPERIMENTAL DATA OF RR RATES FOR BARE NUCLEI [M. Bell and J.S. Bell. Particle Accelerators. 98. V.. P ] [M. Steck. NIM A V. 53. P ] (Contnd) RR rates vs. transverse electron temperature T experiment: ESR (Bell & Bell comparison). RR spectra of U 9+ measured for a different drift temperature T d e mred dashed line Maxwell blue dashed line flattened..000 T T d Tcathode T cathode 0.eV Recombination rate 0 - s MaxwellRR 3 3 8k B Z Ry 4 T 3 ZZ a0 Z Ry ln 3 3 mt e T 3 Z Ry FlattenedRR 3 3 k B Z Ry 5 T 3 ZZ a0 Z Ry ln ln. 3 3 mt e T 6 Z Ry 98. mt 0.8 mt 05 mt Bell & Bell Maxwell Bell & Bell Flattened T ev A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine /
12 ANALYSIS OF EXPERIMENTAL DATA OF RR RATES FOR INTERMEDIATE CHARGE STATE OF IONS RR spectra of U 8+ measured at ESR. [A. Müller et al. Phys. Scr. 99. V. T37. P ] Recombination rate 0-8 cm 3 s e - +U 8 + ØU e - +U 9 + ØU Fitted ZZ Black line is the fit of the formula above DE ev A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine / Z Z E f E f E a Eb Ry E. Fitted 3 8 ZZ 8
13 ANALYSIS OF EXPERIMENTAL DATA OF RR RATES FOR INTERMEDIATE CHARGE STATE OF IONS (Contnd) RR rates vs. electron shell structure experiments: ESR LEAR SIS8. Recombination rate 0-8 cm 3 s Complete shell Au 63+ [Ne]3s 3p 4 U 76+ [Ne]3s 3p 4 Bi 67+ [Ne]3s 3p 4 Pb 66+ [Ne]3s 3p 4 One electron missing Bi 64+ [Ar]4s Au 60+ [Ar]4s Pb 63+ [Ar]4s One electron missing Pb 65+ [Ne]3s 3p 5 Bi 66+ [Ne]3s 3p 5 Au 6+ [Ne]3s 3p 5 U 75+ [Ne]3s 3p 5 Au ESR Pb ESR Pb LEAR Bi SIS8 U ESR Complete shell 30 Pb Electron number in ion N 54+ [Ar]4s 3d 8 e One electron missing Pb 53+ [Ar]4s 3d 0 Complete shell Pb 5+ [Ar]4s 3d 0 A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 3/
14 ANALYSIS OF EXPERIMENTAL DATA OF RR RATES FOR INTERMEDIATE CHARGE STATE OF IONS (Contnd) RR rates vs. electron shell structure experiments: LEAR (Pb ) ESR (Au 5+ ) TSR (Au ). Au 49+ and Pb 5+ [Ar]4s 3d 0 Au 50+ and Pb 53+ [Ar]4s 3d 0 Au 5+ and Pb 54+ [Ar]4s 3d 8. Recombination rate 0-8 cm 3 s e - +Au 50 + ØAu e - +Au 79 + ØAu e - +Pb 5 + ØPb ÿz Au Z Pb e - +Pb 53 + ØPb ÿz Au Z Pb e - +Pb 54 + ØPb ÿz Au Fitted e - +Au 5 Z + Z ØAu 4 Z + Z E f E + e - +Au 49 + ØAu Eb f Ea e - +Au 50 + ØAu Ry e - +Au 5 + ØAuFitte 50 + d+ 3 8 E. ZZ Black solid and dashed lines are the fit of the formula above. 0.0 Z Pb DE ev A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 4/
15 3 RR BEAM LIFETIME AND COOLING TIME RR beam lifetime in lab frame: RR RR dn Z dnz ZZ necool RR Fitted ZZ ZZ ZZ nz dt nz dt. We use well known Parkhomchuk formula for cooling time in lab frame: cool cool Zene cool cool 4m e ez Ze Ze Ze 3 Ze Ze Am u me V V Veff ln l e m c k T Ze max min L cool e B max V V min L min L V0 me kbe V qb me me V c V c V 0 c V 3 B 0 eff BV0. me All the units in CGS; q Z ion charge and nuclear number; m u m e unit of mass electron mass; γ β Lorenz factor beta; max min impact parameter; L electron Larmor radius; V V ion velocity; V eff electron effective velocity; B magnetic field angular spread; B magnetic field in Gs; ΔE electron energy shift in ev; beta-function emittance; l cool cool length relative length of cooling section; k B =.6 0 Erg/eV Boltzmann constant; e electron charge; c speed of light. k E A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 5/
16 3 RR BEAM LIFETIME AND COOLING TIME (Contnd) Estimation of gold ions beam losses in Booster. Recombination rate losses % Au 5 + Au 3 + Au 50 + Au 5 + Au 5 + Au 79 + Fitted ZZ Black solid and dashed lines are the fit of the formula above DE ev A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 6/ Z Z E f E f E a Eb Ry E. Fitted 3 8 ZZ 8
17 3 RR BEAM LIFETIME AND COOLING TIME (Contnd) Estimation of bare gold nucleus beam lifetime at NICA: I e = A r e = cm T /T =0./5 0 3 ev B=0. T. Intrabeam scattering (IBS) time (τ IBS ) black dashed line. Beam lifetime 0 4 s RR cool ü GeVu RR cool ü 3.5 GeVu RR cool ü 4.5 GeVu τ IBS ( GeV/u)=300 s DE ev A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 7/
18 3 RR BEAM LIFETIME AND COOLING TIME (Contnd) Estimation of bare gold nucleus beam lifetime at NICA vs. transverse temperature: I e = A r e = cm B=0. T. Beam lifetime 0 4 s RR cool Bell & Bell ü GeVu RR cool Bell & Bell ü 3.5 GeVu RR cool Bell & Bell ü 4.5 GeVu τ IBS ( GeV/u)=300 s T ev A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 8/
19 CONCLUSION The RR process of gold bare nuclei in NICA cooling system can be suppressed in two methods: by choosing of optimal relative electron energy shift between ions and electrons beam and by an artificial increase the transverse temperature of the electron beam (more preferable). In order to suppress the RR process of intermediate gold ions charge state in the Booster cooling system during ions accumulation is required to avoided when using the ions with electron shell configuration which have one electron missing. A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 9/
20 CONCLUSION (Contnd) Beam lifetime 0 4 s RR cool Bell & Bell ü GeVu RR cool Bell & Bell ü 3.5 GeVu RR cool Bell & Bell ü 4.5 GeVu T ev Beam lifetime 0 4 s RR cool ü GeVu RR cool ü 3.5 GeVu RR cool ü 4.5 GeVu DEeV A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine 0/
21 REFERENCES [] I.N. Meshkov et al. Status of NICA Project These Proceedings. MOIO0. [] H.A. Kramers. Phil. Mag. V P [3] М. Pajek and R. Schuch. Phys. Rev. А. V. 45. N P [4] M. Bell and J.S. Bell. Particle Accelerators. 98. V.. P (and references therein for table). [5] W. Shi et al. Euro. Phys. J. D P [6] A. Hoffknecht et al. Phys. Rev. А V [7] O. Uwira et al. Hyperfine Interaction V. 08. P [8] A. Hoffknecht et al. Phys. Scr. 00. V. T9. P [9] W. Spies et al. Hyperfine Interactions V. 4. P [0] R. Schuch et al. Acta Physica Polonica B V. 7. N. -. P [] L. Andersen et al. Phys. Rev. Lett V. 64. P [] A. Müller et al. Phys. Scr. 99. V. T37. P [3] A. Wolf et al. NIMA V. 44. P / A. Hoffknecht et al. HYINT V. 4. P [4] S. Baird et al. Phys. Lett. B. V. 36. Iss P [5] I. Meshkov. Ion Recombination in Electron Coolers. Working meeting. 4 March 0. CERN. Geneva. Private communication. [6] P. Beller et al. NIM A V. 53. P [7] V.V. Parkhomchuk A.N. Skrinskii. Phys. Usp V. 43. Num. 5. P A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine /
22 Thank you for your attention! A.V. Philippov Workshop on Beam Cooling and Related Topics (COOL ) September 6 0 Alushta Ukraine /
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