Physics process in Cryog enic Gas Ion Cat...

Sivaji PurushothamanGSI, Darmstadt, Germany

Physics process in

Cryogenic Gas Ion Catcher

SMI 201021 - 24 April 2010, Stanford

Outline

• Gas catcher parameters

• Ion mobility

• Electron mobility

• Helium ion species

• Recombination coefficient

• Electric field shielding

• Recombination loss

• Experimental results

• Summary

Ion beam induced ionization

+

+

+

+

+

+

+

+

+

+

+

+

+ +++

+

+

+

++

+

-

-

-

-

--

-

-

-

-

-

--

-

-

-

--

-

-

-

-

-

-

-

Weakly ionized gas

High energy

ion beam

Helium gas

Electrons

-Neutral helium atoms

+Thermalized ions / Hen

+, n = 1, 2 , 3, 4 /metastables

Applied electric field

77 K

Cryogenic Gas Ion Catcher

parameters

1013 mbar @ 293 K

207.4 mbar @ 60 K

10 V cm-1

2.687 X 1019 cm-3

3.72 X 10-19 V cm2

3.72 X 10-2 Td

101.3 mbar @ 293 K

20.74mbar @ 60 K

100 V cm-1

2.687 X 1018 cm-3

3.72 X 10-17 V cm2

3.72 Td

Electric field (E)

Density (N)

E/N

Td=10-17 V cm2

Temperature

@

Pressure

Operating range : 4 X 10-2 Td to 4 Td

Ion transport parameters

!

µred = µN

N0

= µT0

P0

Pg

Tg

N = Gas density

Pg = gas pressure

P0 = 1013 mbar

T0 = 273 K

N0= 2.69 X 1019 cm -3

!

µ =vd

E

! = mobilityE = electric field

vd = drift velocity

When ions are in thermal equilibrium with neutrals

low applied electric field

!

µ =qD

kBTg

Nernst-Townsend-Einstein relation

kB = Boltzmann constant

Tg = gas temperature

q = charge of the ion

D = diffusion coefficient

Reduced mobility

!

rrms

= 2Dt

Radial diffusion

!

vd" E

Criterion for low-field behavior

!

m + M

mM

"

# $

%

& ' qE( << kBTg

B. L. Henson. Phys. Rev. A 15(4):1680, 1977

H.E. Revercomb and E.A. Mason, Anal. Chem. 47(1-2):970, 1975

d = sum of ion and neutral radii

!

E

N<< 3"

kBTg

e

#

$ %

&

' (

m

m + M

#

$ %

&

' (

12 d

2

z

qE! is the energy gained in a mean free path ! from the field E

kB= Boltzmann constantm = ion massM = neutral massq = electric charge of the particleTg= gas temperature

Field energy is smaller than the thermal energy

Low field mobility

kB= Boltzmann constantm = ion massM = neutral massq = electric charge of the particle

Tg= gas temperature

!

µ+ =3

16

2"

kBTg

#

$ %

&

' (

121

m+1

M

#

$ % &

' (

12 q

Ng)(1,1)

Tg( )

!

"(1,1)(Tg ) =

1

2 kBTg[ ]3

#2 $ % exp&#

kBTg

'

( ) )

*

+ , ,

0

-

. d#

!

" # = 1$ cos%[ ]0

&

' # (,%( )sin%d%

Average diffusion cross section

"= scattering angle

" = differential crossection for elastic scattering

momentum-transfer (diffusion) cross section

#= kinetic energy


High field mobility

kB= Boltzmann constantm = ion massM = neutral massq = electric charge of the particle

Tg= gas temperature

!

µ+ =3

16

2"

kBTeff

#

$ %

&

' (

121

m+1

M

#

$ % &

' (

12 q

Ng)(1,1)

Teff( )

!

"(1,1)(Teff ) =

1

2 kBTeff[ ]3

#2 $ % exp&#

kBTeff

'

( ) )

*

+ , ,

0

-

. d#

!

" # = 1$ cos%[ ]0

&

' # (,%( )sin%d%

Diffusion collision integral

"= scattering angle

" = differential crossection for elastic scattering

momentum-transfer (diffusion) cross section

#= kinetic energy


L. A. Viehland and E. A. Mason, J. Chem. Phys.,63(7):2913, 1975.

!

kBTeff =3

2kBTg +

1

2mvd

2Effective

temperature

Electron mobility in helium gas

G. Ramanan and G. R. Freeman, J. Chem. Phys., 93(5):3120, 1990.

J. L. Pack and A. V. Phelps, Phys. Rev., 121(3):798, 1961.

R. W. Crompton, M. T. Elford, and R. L. Jory, Aust. J. Phys., 20(4):369, 1967.

!N

[cm

-1 V

-1 s

-1]

E/N [Td]

vd [cm

s-1]

Helium ion species

T = 300 K & P < 1 mbar : He+ dominant

T < 120 K : He3+ is dominant

!

He2

++ 2He" He

3

++ He

!

He+

+ 2He" He2

++ Hefaster than

T = 300 K & P > 5 mbar : He2+ dominant

!

He+

+ 2He" He2

++ He

T < 200 K : He3+ Starts to form

!

He2

++ 2He" He

3

++ He

P. L. Patterson, J. Chem. Phys., 48(8):3625, 1968.

P. L. Patterson, Phys. Rev. A, , 2(4):1154, 1970

R. A. Gerber and M. A. Gusinow, Phys. Rev. A, , 2(4):1154, 1970

J. B. Gerardo and M. A. Gusinow, Phys. Rev. A, 3(1):255, 1971

Helium ions of concern

T = 77 K

E/N < 6 Td

He3+

E/N > 13 Td

He2+ and He+

H. Helm. J. Phys. B, 9(7):1171, 1976.

E/N > 13 Td He3+ are electrically heated and destroyed in collisions

Maximum E/N for CGIC ~ 4 Td

CGIC

E/N Maximum

Dominant He ion is He3+

i(H

e 2+)/

i(H

e3+)

E/N [Td]

Helium ion mobility at 77 K

H. Helm. J. Phys. B, 9(7):1171, 1976.

!re

d [c

m2 V

-1 s

-1]

E/N [Td]

Recombination coefficient

!

" ="2

+ N"3

N [cm-3] = Neutral density

$2 [cm3 s-1] = 2 body recombination coefficient

$3 [cm6 s-1] = 3 body recombination coefficient

!

X+

+ e"

+ B# X + B

X+ : Ion of interest or buffer gas ion

3 body recombination

!

X+

+ e"# X + h$

2 body dissociative recombination

B : Buffer gas atom

He3+ in He gas

80 K and < 65mbar

$ = (3.4±1.4) x 10-6 cm3 s-1

electron temperature dependence

(measured for 80 K < Te < 300 K)

Dominant ionic species at 77 K is He3+

$ of He3+ at 77 K is much larger than $ of He2

+ at 293 K

Recombination coefficient He3+

J. B. Gerardo and M. A. Gusinow Phys. Rev. A, 3(1):255, 1971.

$(Te) = (3.4±1.4) x 10-6 (Te/80)-a cm3 s-1 for 0.98 <a<1.6

Electron temperature

J. Dutton. J. Phys. Chem. Ref. Data, 4(3):577, 1975.

V. M. Atrazhev. J. Phys. D, 17(5):889, 1984.

Te [K

]

E/N [Td]

%#& [eV]

elec

tro

n t

emp

erat

ure electro

n en

ergy

!

" ="2

+ N"3

Theory : $3 ' Tg -2.5

$2 = -0.73 x 10-7 + 6 x 10-10 Tg

$3 = 3.6 x 10-21 Tg -2.5

Measured between 50 and 1200 mbar

between 200 - 295

Experimental error

$2 : ~10 %

$3 : ~10 - 20 %

20 % error on estimated $

R. J. van Sonsbeek, R. Cooper, and R. N. Bhave. J. Chem. Phys., 97(3):1800, 1992D. R. Bates.J. Phys. B, 13(13):2587, 1980.L. P. Pitaevskii. Sov. Phys. JETP, 15(5):919, 1962.Y. S. Cao and R. Johnsen. J. Chem. Phys., 94(8):5443, 1991.

$3 ' Tg-2.94

$3 ' Tg-2.54

$3 ' Tg -2.9 for O+ and N+ in helium at 77K, 125 K and 150 K

Neutral density: 2 x 1019 to 2.9 x 1020 cm-3

Recombination coefficient He3+

ln (T [K])

ln (

1027 $

3 [c

m6 s-1

])

With applied electric field

Steady state positive charge density!

µ" >> µ+

!

Vind =eQ

4"0µ#d2

µ+= positive ion mobility

µ-= electron mobility

Q = Ionization rate density

d = size of the ionization region

E = electric field

Induced voltage

electron and

positive ion mobility

M.Huyse et al., NIM B 187 (2002) 533

+

+

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

+

+

+--

-

-

--

--

-

-

-

-

-

-

--

-

Applied

electric field

Induced

electric field

+

+

+

+

+

+

+

+

+

+

+

+

+ +

+

+

+ +

+

Recombination losses

Q = Ionization rate density$ = e - ion recombination coefficientd = separation between platesµ+

= positive ion mobilityµ-

= electron mobility

E = electric field

Parallel plate ionization chamberformulation

+

+

+

+

+

+ +

+

++

+

+

+

+

+

+

+

+

+

+

+

+- -

-

-

-

-

-

-

-

-

-

--

--

--

-

--

--

-

-

-

Ion extraction efficiency

#extr=1 - f

given f is small

Recombination loss factor

d

E

J. Sharpe. Nuclear radiation detectors. John Wiley & Sons, New York, 1955.

!

f =Q"d2

6v+v#

=Q"d2

6µ+µ#E2

!

frel

=QP

µ"E2Tg

7 / 2

µ- = Electron mobility

E = Electric fieldTg= Gas temperature

Ion extraction efficiency = 1- f = 1 - Kfrel

!

µ+"Tg

P

!

" #Tg$5 / 2

Q = Ionization rate densityP = Gas pressureK = Constant

Relative recombination loss factor

!

f =Q"d2

6µ+µ#E2

Recombination loss factor

S. Purushothaman PhD Thesis, 2008, University of Groningen

Online setup at JYFL

Experimental cell

S. Purushothaman PhD Thesis, 2008, University of Groningen

13 Mev Proton beam

Proton beam

Ionization Region

Experimental cell

Experimental cell

13 Mev Proton beam

S. Purushothaman et al., NIM B 266 (2008) 4488

Efficiency vs. ionization rate density

Combined

efficiency of

ion survival

and

transport

[%]

Ionization rate density [cm-3 s-1]

Effect of electric field shielding


Combined

efficiency of

ion survival

and

transport

[%]

Induced voltage (Vind)/ Applied voltage (Vapp)

Relative recombination loss

Combined

efficiency of

ion survival

and transport

[%]

Relative recombination loss frel [arbitrary units]

efficiency = 30(1 - Kfrel)


Summary

• Realistic E/N range : 4 X 10-2 Td to 4 Td

• Electron mobility '(E/N)1/2

• Positive ion mobility falls within Low field mobility regime

• Dominant He ion is He3+

• Recombination coefficient of He3+ ' Tg

-5/2

• High external electric field is necessary to handle high ionization density

Within the context of Cryogenic Gas Ion Catcher

Thanks

P. Dendooven 1

I. Moore 2

K. Peräjärvi 2

H. Penttilä 2

A. Saastamoinen 2

N. Takahashi 3

1 KVI, University of Groningen, Netherlands

2 University of Jyväskylä, Finland

3 Osaka University and Osaka Science Museum, Japan

Physics process in Cryog enic Gas Ion Cat...

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