radiative recombination of bare nuclei and ions in electron cooling system a.v. philippov, a.b....

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’11),

September 12–16, 2011, Alushta, Ukraine

A.V. Philippov, Workshop on Beam Cooling and Related Topics (COOL’11), September 12–16, 2011, Alushta, Ukraine 2/22

OUTLINE

Introduction1 Analysis of experimental data of radiative recombination (RR) rates

for bare nuclei2 Analysis of experimental data of RR rates for intermediate charge

state of ions3 RR beam lifetime and cooling timeConclusion

A.V. Philippov, Workshop on Beam Cooling and Related Topics (COOL’11), September 12–16, 2011, 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: Au32+, Au33+, Au43+, Au51+, Au61+, Au68+ and Au69+ during their acceleration in the Booster and the beam lifetime of the gold bare nuclei Au79+ in NICA.


1 0 5 1 0 4 0 .0 0 1 0 .0 1 0 .1 1 1 00 .1

0 .5

1 .0

5 .0

1 0 .0

5 0 .0

E , e V

Rec

ombi

natio

nra

te,1

08

cm3 s

e H e 2 H e 1 Z U2 Z He

2

e C 6 C 5 Z U2 Z C

2

e N 7 N 6 Z U2 Z N

2

e N e 10 N e 9 Z U2 Z Ne

2

e U 92 U 91 e U 92 U 91

1 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. 46. 1923. P. 836.], black solid line — R. Schuch [Phys. Rev. А. V. 45. N. 11. 1992. P. 7894-7905.].

Black dashed line is the fit of the formula above.

Fitted

Fitted1 1

1

1

8

3 8

,

,Ry

.

Z Z Z Z

Z Z

E f E

E bf E a

E


1 ANALYSIS OF EXPERIMENTAL DATA OF RR RATES FOR BARE NUCLEI(Contnd)

1 0 5 1 0 4 0 .0 0 1 0 .0 1 0 .1 1 1 00 .1

0 .5

1 .0

5 .0

1 0 .0

5 0 .0

E , e V

Rec

ombi

natio

nra

te,1

08

cm3 s

e S i14 S i13 Z U2 Z Si

2

e C l17 C l16 Z U2 Z Cl

2

e A r18 A r17 Z U2 Z Ar

2

e B i83 B i82 Z U2 Z Bi

2

e U 92 U 91 e U 92 U 91

RR rates vs. the electron relative energy ΔE, experiments: TSR, CRYRING, ESR. Red solid line — theoretical models of H.A. Kramers [Phil. Mag. V. 46. 1923. P. 836.], black solid line — R. Schuch [Phys. Rev. А. V. 45. N. 11. 1992. P. 7894-7905.].

Black dashed line is the fit of the formula above.

Fitted

Fitted1 1

1

1

8

3 8

,

,Ry

.

Z Z Z Z

Z Z

E f E

E bf E a

E



RR rates vs. magnetic field strength B, experiment: ESR. [M. Steck, et al. EPJ D. 15. 2001. P. 145-154.]

1 0 5 1 0 4 0 .0 0 1 0 .0 1 0 .1 1 1 00 .1

0 .5

1 .0

5 .0

1 0 .0

5 0 .0

E , e V

Rec

ombi

natio

nra

te,1

08

cm3 s

80 m T84 m T94 m T104.2 m Ta 1.0a 0.7a 0.4a 0.2

RR spectra of U92+ measured at 4 different magnetic guiding field strengths.

Fitted

Fitted1 1

1

1

8

3 8

,

,Ry

.

Z Z Z Z

Z Z

E f E

E bf E a

E



RR rates vs. transverse electron temperature T experiment: ESR.[M. Steck. NIM A. 2004. V. 532. P. 427-432.]

clearing voltage

2 2 2

12

cathode

cathode

V cmcm s ,

Gs

VV cm ,

cm

g cm seV ,

Erg eV

10 cm, 1.6 10 Erg eV,

,

0.2 eV.

d

e d

dB

B

d

EV

B

UE

l

m VT

k

l k

T T T

T


1 ANALYSIS OF EXPERIMENTAL DATA OF RR RATES FOR BARE NUCLEI[M. Bell and J.S. Bell. Particle Accelerators. 1982. V. 12. P. 49-52.][M. Steck. NIM A. 2004. V. 532. P. 427-432.] (Contnd)

RR rates vs. transverse electron temperature T experiment: ESR (Bell & Bell comparison). RR spectra of U92+ measured for a different drift temperature Td, emRed dashed line — Maxwell, blue dashed line — flattened.

1 0 6 1 0 5 1 0 4 0 .0 0 1 0 .0 1 0 .1 10 .0 1

0 .0 2

0 .0 5

0 .1 0

0 .2 0

0 .5 0

1 .0 0

T d , e V

Rec

ombi

natio

nra

te,1

02

s1

96 m T98.2 m T100.5 m T102.8 m T105 m TB ell & B ell , M axw ellB ell & B ell , F lattened

2Maxwell,RR 2 3 2

31 0 1 2 2

2Flattened,RR 2 3 2 2

31 0 1 2

832 4ln ,

2 33 3

232 5ln ln 2 .

2 63 3

BZ Z

e

BZ Z

e

k TZ Rya Z Ry

m T T Z Ry

k TZ Rya Z Ry

m T T Z Ry

cathode cathode, 0.2 eVdT T T T




1 0 6 1 0 5 1 0 4 0 .0 0 1 0 .0 1 0 .1 10 .0 1

0 .0 2

0 .0 5

0 .1 0

0 .2 0

0 .5 0

1 .0 0

T d , e V

Rec

ombi

natio

nra

te,1

02

s1

96 m T98.2 m T100.5 m TB ell & B ell , M axw ellB ell & B ell , F lattened

2Maxwell,RR 2 3 2

31 0 1 2 2


31 0 1 2

832 4ln ,

2 33 3

232 5ln ln 2 .

2 63 3

BZ Z

e

BZ Z

e

k TZ Rya Z Ry

m T T Z Ry

k TZ Rya Z Ry

m T T Z Ry





1 0 6 1 0 5 1 0 4 0 .0 0 1 0 .0 1 0 .1 10 .0 1

0 .0 2

0 .0 5

0 .1 0

0 .2 0

0 .5 0

1 .0 0

T d , e V

Rec

ombi

natio

nra

te,1

02

s1

98.2 m T102.8 m T105 m TB ell & B ell , M axw ellB ell & B ell , F lattened

2Maxwell,RR 2 3 2

31 0 1 2 2


31 0 1 2

832 4ln ,

2 33 3

232 5ln ln 2 .

2 63 3

BZ Z

e

BZ Z

e

k TZ Rya Z Ry

m T T Z Ry

k TZ Rya Z Ry

m T T Z Ry



2 ANALYSIS OF EXPERIMENTAL DATA OF RR RATESFOR INTERMEDIATE CHARGE STATE OF IONS

1 0 5 1 0 4 0 .0 0 1 0 .0 1 0 .1 1 1 00 .1

0 .5

1 .0

5 .0

1 0 .0

5 0 .0

E , e V

Rec

ombi

natio

nra

te,1

08

cm3 s

e U 28 U 27 e U 92 U 91

RR spectra of U28+ measured at ESR. [A. Müller et al. Phys. Scr. 1991. V. T37. P. 62-65.]

Black line is the fit of the formula above.

Fitted

Fitted1 1

1

1

8

3 8

,

,Ry

.

Z Z Z Z

Z Z

E f E

E bf E a

E


2 ANALYSIS OF EXPERIMENTAL DATA OF RR RATESFOR INTERMEDIATE CHARGE STATE OF IONS (Contnd)

RR rates vs. electron shell structure, experiments: ESR, LEAR, SIS18

1 5 2 0 2 5 3 01 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

E le c t ro n n u m b e r in io n , N e

Rec

ombi

natio

nra

te,1

08

cm3 s A u, ES R

P b, ES RP b, LEA RB i, S IS 18U , ES R

Complete shellPb54+[Ar]4s23d8

One electron missingPb53+[Ar]4s13d10

Complete shellPb52+[Ar]4s23d10

Complete shellAu63+[Ne]3s23p4

U76+[Ne]3s23p4

Bi67+[Ne]3s23p4

Pb66+[Ne]3s23p4

One electron missingPb65+[Ne]3s23p5

Bi66+[Ne]3s23p5

Au62+[Ne]3s23p5

U75+[Ne]3s23p5

One electron missingBi64+[Ar]4s1

Au60+[Ar]4s1

Pb63+[Ar]4s1


2 ANALYSIS OF EXPERIMENTAL DATA OF RR RATESFOR INTERMEDIATE CHARGE STATE OF IONS (Contnd)

RR rates vs. electron shell structure, experiments: LEAR (Pb52+, 53+, 54+), ESR (Au25+), TSR (Au49+, 50+, 51+). Au49+ and Pb52+ — [Ar]4s23d10,Au50+ and Pb53+ — [Ar]4s13d10, Au51+ and Pb54+ — [Ar]4s23d8.

1 0 5 1 0 4 0 .0 0 1 0 .0 1 0 .1 1 1 00 .0 1

0 .1

1

1 0

1 0 0

1 0 0 0

E , e V

Rec

ombi

natio

nra

te,1

08

cm3 s e A u 25 A u24

e A u 49 A u48 e A u 50 A u49 e A u 51 A u50

e P b52 P b51 Z Au2 Z Pb

2


2


2

e A u 50 A u 51 e A u 79 A u 78

Black solid and dashed lines are the fit of the formula above.

Fitted

Fitted1 1

1

1

8

3 8

,

,Ry

.

Z Z Z Z

Z Z

E f E

E bf E a

E


3 RR BEAM LIFETIME AND COOLING TIME

RR beam lifetime in lab frame:

We use well known Parkhomchuk formula for cooling time in lab frame:

All the units in CGS; q, Z — ion charge and nuclear number; mu, me— unit of mass, electron mass; γ, β — Lorenz factor, beta; max, min — impact parameter; L — electron Larmor radius; V, V|| — , || ion velocity; Veff — electron effective velocity; B — magnetic field angular spread; B — magnetic field in Gs; ΔE — electron energy shift in eV; , — beta-function, emittance; lcool, cool — length, relative length of cooling section; kB=1.6·10−12 Erg/eV — Boltzmann constant; e — electron charge; c — speed of light.

1 RRRR RR Fitted1 cool

1 1 12

1 1, , .Z Z eZ Z

Z Z Z Z Z ZZ Z

ndn dn

n dt n dt

1 2cool 2coolcool cool

3 22 2 2 2eff

22 2max min cool

max min2min 0

30 e

4, , ln ,

1, , , ,

, , 10 ,

Z e e Z eeZ e Z e Z e Z e

u e

L e BZ e L

BL e e

e

n m e Z

Am m V V V

l m ce k TV V

k EV m qB mVm

V c V c V c V

2

ff 0 .BB

e

k EV

m


3 RR BEAM LIFETIME AND COOLING TIME (Contnd)

Estimation of gold ions beam losses in Booster.

1 0 5 1 0 4 0 .0 0 1 0 .0 1 0 .1 1 1 00 .0 1

0 .1

1

1 0

1 0 0

E , e V

Rec

ombi

natio

nra

telo

sses

,

A u 25 , A u 32 , A u50

A u 15 , A u 51 , A u79

Black solid and dashed lines are the fit of the formula above.

Fitted

Fitted1 1

1

1

8

3 8

,

,Ry

.

Z Z Z Z

Z Z

E f E

E bf E a

E



Estimation of bare gold nucleus beam lifetime at NICA: Ie=1 A, re=1 cm, T/T||=0.2/5·10−3 eV, B=0.1 T. Intrabeam scattering (IBS) time (τIBS) — black dashed line. The optimal electron energy shift in between of two black dashed lines (0.05 and 2 eV).

1 0 4 0 .0 0 1 0 .0 1 0 .1 1 1 0 1 0 01

1 0

1 0 0

1 0 0 0

1 0 4

E , e V

Bea

mlif

etim

e,s

RR cool 1 G eVuRR cool 3.5 G eVuRR cool 4.5 G eVu τIBS(1 GeV/u)=1300 s



Estimation of bare gold nucleus beam lifetime at NICA vs. transverse temperature: Ie=1 A, re=1 cm, B=0.1 T. Based on ESR experiment noted above.


CONCLUSION

The RR process of gold bare nuclei in NICA cooling system can be suppressed by two methods:

– by choosing of optimal relative electron energy shift ΔE between ions and electrons beam,

– and by an artificial increase the transverse temperature T of the electron beam.

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.


REFERENCES

[1] Concept of NICA Collider. JINR. 2010.[2] H.A. Kramers. Phil. Mag. V. 46. 1923. P. 836.[3] М. Pajek and R. Schuch. Phys. Rev. А. V. 45. N. 11. 1992. P. 7894-7905.[4] M. Bell and J.S. Bell. Particle Accelerators. 1982. V. 12. P. 49-52. (and

references therein for table).[5] W. Shi et al. Euro. Phys. J. D. 15. 2001. P. 145-154.[6] A. Hoffknecht et al. Phys. Rev. А. 2000. V. 63. 012702.[7] O. Uwira et al. Hyperfine Interaction. 1997. V. 108. P. 167-175.[8] A. Hoffknecht et al. Phys. Scr. 2001. V. T92. P. 402-405.[9] W. Spies et al. Hyperfine Interactions. 1998. V. 114. P. 237-243.[10] R. Schuch et al. Acta Physica Polonica B. 1996. V. 27. N. 1-2. P.

307-322.[11] L. Andersen et al. Phys. Rev. Lett. 1990. V. 64. P. 729-732.[12] G.I. Budker et al. Proceedings of the V All-Union Meeting on

Accelerators of Charged Particles 6. P. 236-240.[13] A. Müller et al. Phys. Scr. 1991. V. T37. P. 62-65.[14] A. Wolf et al. NIMA. 2000. V. 441. P. 183-190. / A. Hoffknecht et

al. HYINT. 1998. V. 114. P. 257-261.[15] S. Baird et al. Phys. Lett. B. V. 361. Iss. 1-4. 1995. P. 184-186.


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radiative recombination of bare nuclei and ions in electron cooling system a.v. philippov, a.b....

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