Project of integral ion counter Project of integral ion counter

Project of integral ion counter Project of integral ion counter

Hannes Tammet 25. veebruar 2009. a.

Why we need this?

• Device for calibration of ion spectrometers

• Device for experiments in CLOUD chamber

Both devices are needed for episodic measurements and, therefore, to built one universal instead of two means

substantial economy of resources.

We have our old Gerdien-type universal ion counters.

Deficiency of these devices:

 Sample air flow rate is not well checked and under the control,

 Connection with the CLOUD chamber is complicated,

 Uncertainty of calibration of electrometers is inappropriate,

 Pressure drop between inlet and outlet should not exceed 10-20 Pa.

What should be measured?

• Concentration of cluster ions n

• Mean mobility of cluster ions Z

• Electrical conductivity of air

λ

λ = enZ

Elementary charge

Practical and SI units:

n – 1 cm^–3 = 10^–6 m^–3

Z – 1 cm²V^–1s^–1 = 10^–4 m²V^–1s^–1 λ – 1 fS m^–1 = 10¹⁵ Ω^–1m^–1

e = 1.602×10^–19 C

Reminder:

λCV

/ ε

= neF → enZ

CV

/ ε

= enF

F

I V

Monomobile ions, Z = Z_o I

V

I = λCV / ε_a

ε_a = 8.86 pF/m

I = enF V_o

0

0

CV

Z  

F

Minimal project

F

I_C V

ε_a = 8.86 pF/m e = 1.602×10^–19 C I_L

Z₀ Z₁ Z₂

Simplifying assumptions:

• All the cluster ions have

mobility in the range Z1…Z2 ,

• Electric current caused by larger ions is insignificant,

• Z₀ >> Z₁ .

C_L C_C

V C

I

L L





 eF

I n  I



Z  en 

Example for positive ions: Z₀ = 250, Z₁ = 2.5, Z₂ = 0.5

Recommended project

F

I_C V

ε_a = 8.86 pF/m e = 1.602×10^–19 C I_L

Z₀ Z₁ Z₂

Assumptions:

• Cluster ion mobility is in the range Z₁…Z₂ ,

• Current of intermediate ions Z₂…Z₃ is insignificant,

• Z3 recommended ≈ Z2 / 2 . C_L C_C

V C

I

L L

a

"

 

 eF

I

n I "

 '

 Z en 



Correction due to Z₀ : I’_L= I_L (1+Z₁/Z₀)

Z₃ C_D

I_D

Current of ions Z<Z₃ to collecting sections: (C_L/C_D) I_D, (C_C/C_D) I_D, I_D Total correction: I”_L= I_L (1+Z₁/Z₀) – (C_L/C_D) I_D , I’_C = I_C – (C_C/C_D) I_D

V C

I

D D p a

 



Parameters to be known for the absolute calibration of ion counter

• Sampling air flow rate

• Signal to current ratio for each electrometer

• Active capacitances of four sections of the measuring condenser (including the capacitance due to the edge effect

determining Z

)

Technique of absolute calibration 1 Air flow rate

For ordinary measurements:

• Calibrated ventilator (pump)

• orifice with air pressure meter For high accuracy measurements :

• External ventilator and gas-meter

For CLOUD chamber (Δp up to 5000 Pa):

• pump and gas-meter

Ion counter Buffer Gas-

meter Pump

Technique of absolute calibration 2 Electric current

F

I_C

V I_L

Z₀ Z₁ Z₂ C_L C_C

Z₃ C_D

I_D

V₂

const V 

)

2

f ( t V 

dt C dV

I



NB! This method assumes that the active capacitances

of condenser sections are known with high accuracy

Technique of absolute calibration 3a

Capacitances of condenser sections

NB! Empirical methods for designing of ion counter are too complicated

 

 





 

1

ln

2 r r

C

l

C_L C_C C_D

R₁

~

Directly applied for C_D only

• Equation for cylindrical condenser

• External capacitance bridge

• Internal capacitance bridge

Technique of absolute calibration 3b Capacitances

NB! Cannot be applied for C

!

 

 





 

1

ln

2

r r

C

l

C_L C_C C_D

This 50 year old figure is

based on measurements and its accuracy is insufficient

Technique of absolute calibration 3c

Capacitances

1 0

2 2 2

2





 



 





x u r

u r

r u

  



i j

i j

i j

i j

i j

i

u u

r u h

u u

u

u

8

4 1













    



Accelerated Jacobi-Seidel iteration method for quadratic grid:

* , ,

, _j

: ( 1 )

i

p u pu

u   

This is a robust method

• Simple and trustworthy,

• Compared to the best methods, it is about ten time more time consuming and, therefore, in certain cases about 10 s is needed instead of 1 s.

Example follows

Inlet grid is also taken into account

Live example is replaced by screenshots: