Transcript Development of high-resolution halo

Kakuri-I Meeting, 09-DEC-2003, RCNP
Feasibility Study of the Polarized 6Li ion Source
9-DEC-2003
A. Tamii
Research Center for Nuclear Physics, Osaka Univ., Japan
1
Contents
1.
Physics Motivation
2.
Overview of the Polarized 6Li Ion Source
3.
Simulation of the Depolarization of 6Li in the ECR
Ionizer
4.
Feasibility Test Plan
2
Physics Motivation
• Study of the nuclear structure by the (6Li, 6He) Reaction
– Selective excitation of DT=1, DS=1
– Tensor analyzing power at 0°
→ Selectivity for the 0-,1-, and 2- states
– High resolution measurement by dispersion matching
⇔(d,2He), (p,n)
• Study of the nuclear structure by the (6Li, 6Li*(0+, T=1; 3.56MeV))
Reaction
– Selective excitation of DT=1, DS=1 and DTz=0
= Isovector M1 transition
– Tensor analyzing power at 0°
→ Selectivity for the 0-,1-, and 2- states
⇔(d,dS=0)
3
• Study of the reaction mechanism of composite particle
– Elastic Scattering, inelastic scattering, (6Li, 6He)
Reaction
(diff. cross section and analyzing power)
• Study of the break up mechanism of 6Li with a polarized
beam
• Study of the spin structure of 6Li
⇔ 3-body calculation
4
Development of Polarized 6Li ion Sources at
Other Laboratories.
• Max Plank Institute, Heidelberg, Germany
Optical Pumping + Surface Ionizer (+ Charge Exchange+Tandem)
6Li1+:
20-30mA
• Florida State University, USA
Optical Pumping + Surface Ionizer (+ Charge Exchange+Tandem+LINAC)
• Daresbury, UK
Stern-Gerlach+RF + Surface Ionizer (+ Charge Exchange+Tandem)
• Wisconsin, USA
Stern-Gerlach+RF (+ Cs-Beam-Bombard+Tandem)
6Li0+:
3×1015, 6Li1-: 0.18mA
• Saturne, France
Optical Pumping + Surface Ionizer (+ EBIS+Accum. Ring+Synchrotron)
20-35mA
6Li3+: 7×108 particles/spill
Pzz = 70% at 187.5 keV/A
6Li1+:
5
Plan of the polarized 6Li ion source (I)
Optical
Li Oven Pumping
RF
Pol.
(Transition
)Meas.
ECR 14.5 or 18 GHz
Ionizer
6
Li 3+
6
Li 0+
Analyzer
Laser
s+-pol.
Laser
s+-pol.
Faraday
Cup
AVF
Cyclotron
6
Plan of the polarized 6Li ion source (II)
F=3/2
2p1/2
F=3/2
F=1/2
2S1/2
-3/2
-1/2
1/2
3/2
Level Diagram of a6Li atom
20-30mA
Pol. 80-90%
6Li1+:
7
Simulation of the Depolarization in the ECR Ionizer
(extension of the simulation by Prof. M. Tanaka)
• Fractions and polarizations of escaped ions are calculated by assuming the initial
conditions, transition rates, and magnetic-substate transition matrix.
• The rate equations are analytically solved.
l2*→2, D2*→2
2+
l2→1, D2→1
Li
l2→escape
l1→2, D1→2
Escape
l2→3, D2→3
l3→2, D3→2
6
Li 3+
l3→escape
l2→2*, D2→2*
1→
2*
D
→
2*
,
l1*→1, D1*→1
l1
l1→1*, D1→1*
0→
1*
D
→
1*
,
l0
l0→escape
l1→escape
Escape
6
1*
→
Li
1+
D2
Escape
6
,
l1→0, D1→0
Li 2+*
1*
l0→1, D0→1
6
l 2→
0*
→
D1
Li
,
0+
Li 1+*
0*
6
6
l 1→
l0*→0, D0*→0
Li 0+*
l0→0*, D0→0*
6
Escape
li→j: Transition Rate from
i to j [s-1]
Di→j: Transition Matrix of Magnetic Substates from
i to j (0≦Dji ≦1)
8
Assumption of the Plasma Condition
The following plasma condition is assumed according to the empirical analysis of
the laser abraded Al ion intensities from a 14.5 GHz ECR ionizer (SHIVA).
YAG Laser: 10nsec,
100-250mJ
(M. Imanaka, PhD thesis, Univ. of Tsukuba)
Buffer Gas: Oxygen
RF Power: 250 W
Neutral Oxygen Gas Density (ngas): 1.44×1010 cm-3
Electron Density (ne): 2.23×1011 cm-3
Electron Temperature (Te) : 582 eV
Ion Temperature (Ti) : 5 eV
Charge Exchage Rate: Muller and Saltzborn
Confinement time of Al: t i 
i
imax
ne, Te, tc, Ti are fitted to the data.
t c for the i+ ions, tc=10msec
7+
1.5
beam intensity [a.u.]
Ionization Rate: Voronov’s empirical Fit
-3
ne=2.23(±0.06)e11[ cm ]
T e=582(±46)[ eV]
τc=9.1(±0.5)[ ms]
T i =5[ eV]
-3
ngas=1.44e10[ cm ]
6+
3+
1
4+
8+
0.5
9+
0
0
0.01
0.02
time [s]
0.03
9
Magnetic-Substate Transition Matrix (1/2)
(according to the calc. of 3He by M. Tanaka and Y. Plis)
•
The wave functions Yi(t) of the electron-nucleus system in a magnetic field system are written as a linear
conbination of |IJ> states as
YI (0)   1
1
1
(1    ) cos   
(1    )
2
2
1
 x
3
 
2
1 x  x2
3
B
x
Bc : criticalmagneticfield
Bc
sin   
YII (0)  sin    0  cos    1
YIII (0)  sin    1  cos    0
YIV (0)   1
YV (0)   cos    1  sin    0
YVI (0)   cos    0  sin    1
•
The time revolution of the |↓+1> state is
 1 t  cos   YII (t )  sin   YIV (t )
 cos   YII (0) exp(iEIIt )  sin   YIV (0) exp(iEIVt )
 cos   sin    0  cos    1 exp(iEIIt )
 sin    cos    0  sin    1 exp(iEIVt )
•
The probability to find |↓+1> and its time average (after sufficient time) is
P(t )  cos2   exp(iEIIt )  sin 2   exp(iEIVt )
2
 cos4    sin 4    2 cos2   sin 2   cosEII  EIV t 
P  cos4    sin 4   
1
(1   2 )
2
10
Magnetic-Substate Transition Matrix (2/2)
•
By similar calculations we obtain










•
1

1
 1 '  
1   2

2
0 '  
 
 1 '


 1 ' 
 
0 '  

 1 '  
1
1   2

2





1
1   2
2

1
1   2
2



1
1   2
2
1


1
1   2
2





 1
0
 1
 1
0
 1










We are not interested in the electron spin.
In the case that the orientation of the electron spin is random at t=0, by taking the average for the initial
state and sum for the final state concerning the electron spin, we obtain





•











1
2 
1  
2

1
1   2
2


1
2
 3  
 1 '  4

1
0 '    1   2

4
 1 '  
0






1
1   2
4

1
2   2   2
4
1
1   2
4




  1 
2 
1   0 


 1 
3   2 

0

1
4
1
4




When x=5/3, the matrix is
Ddep
0 
 0.955 0.045


  0.045 0.871 0.083
 0
0.083 0.917

11
Critical Magnetic Field
Calc. by H. Okamura
12
Depolarization due to the electron spin resonance (ESR) effect
We take SHIVA as a model case.
If micro-wave with a power of 250W is applied in a (non-resonating) cylinder with a diameter of 72mm.
W
 2.0 1010 J/cm3
r 2c
B1  m0u  0.16Gauss
u
The thickness of the ESR region is
DR  4.0mm at R  5.0cm (in axial direction)
DR  0.9mm at R  1.9cm (in radial direction)
The effective thickness averaged for isotropic ion velocity distribution and averaged half-length between the ECR
points are
4.0  0.9  2 1 
2R 
 1  ln
  12 mm
3
2
DR 
1 5.0  1.9  2
R
 1.5 cm
2
3
L
The spin rotation angle of the electron calculated with random-walk approximation is
L
v
  D  N   e B1 
v
t i  6.2 102 rad  3.6
R
The nuclear depolarization is caused by the hyper-fine coupling between the electron and the nucleus.
Hence depolarization is negligible. Note that the calculation depends on the assumed plasma parameters.
13
Depolarization due to the inhomogeneous magnetic field
The T1 relaxation is calculated by the following formula by Schearer et al., Phys. Rev. 139 (1965) A1398.
1 2 v 2  H y 



T 1 3  I2t c H 04  y 
2
For ions by putting the following numbers we obtain
 I  3.94107 rad / s / T
t c  1.2 106 sec
v  1.3 106 sec
H 0  0.5 T
H y
y
T1  4.5 msec for ions
 0.15T / cm
For neutral lithium atoms, by putting the numbers we obtain
 I  3.94107 rad / s / T
t c  3.7 105 sec
v  9.7 104 sec
H 0  0.5 T
H y
y
T1  6.3 for neutral atoms
 0.3T / cm
The T1 relaxation time for ions has large depolarization effect when we consider the confinement time of 6Li3+
(1 msec) and should be carefully taken care of.
14
Ionization Rate by Electron Impact
Voronov’s empirical fit
6
Li i
G.S. Voronov, Atom. Data and Nucl. Data Tables 65 (1997)1.
1  PU 1/ 2 K U
 i i 1  ve  A
U e
X U
I
U i
Te
cm3s-1
3.26×10-9 cm3s-1
6Li2+→ 6Li3+: 7.53×10-10 cm3s-1
ii 1  ii 1ne
ne: 2.23×1011 cm-3
li+1,i [cm3s-1]
A, P, X, K: Fitting Parameters
6Li1+→ 6Li2+:
Li i+1
10-6
Te: Electron Temperature
4.52×10-8
6
[cm3s 1 ]
Ii: Ionization Energy
6Li0+→ 6Li1+:
li+1,i
10-7
6Li 0+→6Li 1+
10-8
6Li 1+→6Li 2+
6Li 2+→6Li 3+
-9
10
582 eV
10-10
1
10
100
1000
10000
Te [eV]
15
Charge Exchange Reaction Rate with the Neutral Gas
Muller and Saltzborn Empirical Fit
6
A. Muller and E. Saltzborn, Phys. Lett. A62 (1977) 391.
Li i-1
li-1,i
6
Li i
2.76
  1.431012 i1.17 I gas
[cm2 ]
 2.76
 i i 1  vi  3.15106 i1.17 I gas
Ti
Ai
[cm3s 1 ]
Igas: Ionization Energy of the Neutral Gas (Oxygen: 13.6 eV)
Ti: Ion Temperature (5 eV)
Ai: Ion Mass in AMU
6Li1+→ 6Li0+:
2.14×10-9 cm3s-1
6Li2+→ 6Li1+: 4.81×10-9 cm3s-1
6Li3+→ 6Li2+: 7.72×10-9 cm3s-1
ii1   ii1ngas
ngas: 1.44×1010 cm-3
16
Atomic Excitation Rate by Electron Impact (1/2)
•
6Li0+→ 6Li0+* 2s→2p
(including cascade)
6
Li i*
D. Leep and A. Gallagher, Phys. Rev. A 10 (1974) 1082.
 ~ 3.5a02  3.11016 [cm2 ] at Te ~ 600eV
ve  4.5 107 [cm3s1 ]
00*  ve ne
li * i
a factor of ~10 larger than the ionization rate coefficient 6Li i
•
6Li1+→ 6Li1+* 1s→2p
assume that a factor of ~5 larger than the ionization rate
coefficient
ve  1.6 108 [cm3s1 ] 11*  ve ne
17
Atomic Excitation Rate by Electron Impact (2/2)
•
6Li2+→ 6Li2+* 1s→2p
Fisher et al., Phys. Rev. A 55 (1997) 329.
6
Li i*
Empirical fit of 1s→2p excitation cross sections of hydrogen-like atoms
 ~ 1.0a02 Zi4  1.11018 [cm2 ] at Te ~ 550eV
ve  1.6 109 [cm3s1 ] 22*  ve ne
Summing up transitions 1s→2,…,6 and taking the Boltzmann distribution
ve  1.82109 [cm3s1 ]
li * i
6
Li i
a factor of ~2 larger than the ionization rate coefficient
18
Confinement Time of The Ions
• It is very difficult to estimate the confinement time of ions in an
ECR plasma.
If we assume (M.Imanaka, PhD Thesis; Shirkov, CERN/PS 94-13 )
t i  i Ai
and scale the value of t3+=2.3msec, which was fitted to
the Al data,
6
Li i
li
escape
t 1  0.33[ms]
t 2  0.66[ms]
t 3  0.99[ms]
i  t i1
19
Other processes
Inelastic Ionization and Radiative Capture Processes
In the present calculation, these processes has no (or negligible) effect.
6
Li i-1*
6
*i
1
D
i+
l i-
1*
i
Li i+1*
*i
li
-1
+
1*
i
Di
6
Li i
20
Summary of the Processes in the ECR Ionizer
Escape
6.9E+01, 1
Escape Feeded
6
Li 2+
Escape
1.7E+02, 1
1.1E+02, Ddep
6
Li 3+
1.0E+03, 1
100%, 1
Li 1+
7.3E+02, Ddep
1.5E+03, 1
3.1E+01, 1
6
Li 2+*
3.0E+03, 1
100%, 1
Li 0+
~0
6
1.0E+04, 1
6
100%, Ddep
Li 1+*
4.1E+02, 1
6
3.6E+03, 1
Li 0+*
1.0E+05, 1
6
Escape
21
Summary of the Processes in the ECR Ionizer
Escape
Li 2+*
Escape Feeded
19.1%, 1
3.2%, 1
6
Li 2+
Escape
7.9%, 1
9.9%, Ddep
6
Li 3+
90.1%, 1
Li 1+
9.9%, Ddep
69.8%, 1
48.9%, 1
0.4%, 1
6
40.8%, 1
Li 0+
~0
6
9.1%, 1
6
100%, Ddep
Li 1+*
100%, 1
6
100%, 1
Li 0+*
90.9%, 1
6
Escape
22
Results of the simulation
The result of the simulation is
P3 ,escape
 0.0165 0.0010 0.0000


  0.0010 0.0148 0.0017 P1 ,in
 0.0000 0.0017 0.0157


The polarization of escaped 3+ ions when we feed 1+ ions with pure magnetic substate
population is summarized as follows
Note that depolarization due to the inhomogeneous magnetic field is not included in the
Present calculation.
23
Result of the simulation
(parameter dependence)
Polarization of the extracted beam from the ECR ionizer is approximately expressed as
(initial polarization)×(vector/tensor polarization in the figure)× (depolarization by inhomogeneity in the figure)
Ionization efficiency in the ECR ionizer is expressed as
(efficiency of feeding ions/atoms into the plasma)×(1+ →3+ efficiency in the figure)×(extraction efficiency)
24
Feasibility Test Plan
• Study of confinement time and ionization efficiency of Li is planed by using
the 18GHz superconducting ECR ion source at RIKEN and the laser abration
method.
• Optimization of the plasma condition:
Mirror ratio, neutral gas density, RF power
• Development of the Li-oven, surface ionizer for testing the beam current.
• Laser pumping system for testing the polarization of the 6Li3+ beam
• Further simulation with more realistic parameters is required.
25
Test with 18GHz ECRIS at RIKEN
• Test of confinement time
and ionization efficiency of
Li3+ with the 18GHz ECRIS
at RIKEN is planned.
LiF target
Laser Abration by YAG
T. Nakagawa et al., Rev. Sci. Instrum. 73 (2002) 513.
26
Design of the Li ion source
• Estimation of the required power of the laser
Diode Laser SYSDL19-675 ~15mW at 671nm
On the average ~6 times of pumping is possible
• Design of the Li oven
from E. Steffens et al., NIM 143 (1977) 409
• Design of the surface ionizer
27