SRIM Calculations Applied to Ionization Chambers

Tyler A. BaileyNE120 12/5/2016

Modes of Radiation Detectors

Current Mode: Radiation is converted into a current, and the current is manipulated and detected. This is how smoke detectors operate.

Pulse Mode: Radiation is converted into a voltage pulse, and the voltage is manipulated and detected. This is more useful for spectroscopy.

Ionization chambers can be operated with either modes.

Ionization Chamber Basics

A Common Application for Ionization Chambers (Current Mode Ionization Chamber)

Smoke Detectors: They utilize an air chamber and an Am-241 source. Am-241 undergoes alpha decay.

The half life of Am-241 is approximately 432 years and the alpha energy is 5.5 MeV.

This produces a constant current in the ionization chamber. When smoke particles enter the detector, they can interact with the

alpha particles, making them neutral, and disrupting the current which causes the alarm to go off.

Pulse Mode Ionization Chamber

Schematic

SRIM Features Utilized

Using gas targets. The projected range of an ion in the gas for different energies. Ionization or Stopping Power for the Ions and the recoiling target atoms. Since SRIM is a Monte Carlo code, the simulation is done until the

projected range converges. For gases, the gas is considered to be at standard temperature and

pressure. Also only a limited number of gases can be simulated accurately using SRIM. This is due to lack of experimental data and general theory. Gases that were used for this project that are simulated accurately in SRIM: Ar, He, H, N, air, O, and methane.

Assumptions used in Modeling the

Chamber The chamber is at standard temperature and pressure. Only alpha particles are simulated. The source is placed inside the chamber. This is to ensure that radiation

deposits its energy inside the gas of the chamber. Recombination inside the chamber is negligible. This is justifiable if a

sufficient voltage is applied.

Simulation Geometry

Decay of Interest for the Majority of the Presentation .1 micro Ci Po-210 source Only undergoes alpha decay with energy of 5.3 MeV Half Life of 138.4 days

Goals of the Simulations

Determine an ideal gas to use in the chamber. The projected range of ions in this gas is small allowing the chamber to

be more portable. This gas produces a large amount of ion pairs under incident radiation.

This allows for a larger signal pulse (in the form of a voltage). Energy loss by the recoiling gas particles is minimized.

Stopping Power and Bethe Formula

-Linear Stopping Power is defined as the differential energy loss for a charge particle moving through a material divided by a differential path length

S The value along the trajectory of the particle is referred to as its specific

energy loss This is described by the Bethe Formula

Stopping Power and Bethe Formula

Where B is: ) – ln(1 - ) - ] N is the density of the material while Z is the atomic number of the material. is the mass and charge of the electron while z and v are the charge and velocity

of the particle respectively. I is the Ionization Potential of the material. Since we are only concerned with gases (their low density at standard

temperature and pressure) and alpha particle at non-relativistic velocities (this causes the second and third term of B to become negligible), the most important term is the atomic number of the gas particles. The higher the atomic number of the gas particles, the larger the specific energy loss.

Stopping Power in SRIM

Stopping Power is referred to as Ionization in SRIM and is giving in units of (eV/angstrom).

Data can be extracted for the stopping power of the ion and recoiling gas particles.

From SRIM calculations, it is clear that the specific energy loss of recoiling gas particles is negligible compared to ions.

Bragg Curve for 5.3 MeV Alpha Particle in Air and Air Recoil Ionization

Main Characteristics of The Bragg

Curve For the majority of the ions trajectory, specific energy loss rises steadily

but slowly. Towards the end, the particles specific energy loss rises rapidly and

reaches a peak (this is due to the square of the velocity in the denominator and that the ion is effectively in the vicinity of the gas particles for a relatively longer period of time).

At the end of the trajectory, for the case of an alpha particle, the alpha particle picks up 2 electrons becoming neutral and its specific energy loss drops to 0.

Average Ionization for Different Gases for 5.3 MeV

Alpha

Ar He H2 N2 Air O2 CH40.00E+00

2.00E+04

4.00E+04

6.00E+04

8.00E+04

1.00E+05

1.20E+05

Average Ionization

Gas

ioni

zatio

n (e

V/m

m)

Peak Ionization for Different Gases for 5.3 MeV

Alpha

Ar He H2 N2 Air O2 CH40

50000

100000

150000

200000

250000

300000

Peak Ionization

Gas

Peak

Ioni

zatio

n (e

V/m

m)

Projected Range for Different Gases for 5.3 MeV Alpha

Ar He H2 N2 Air O2 CH40

50

100

150

200

250

Projected Range

Gas

Proj

ecte

d Ra

nge

(mm

)

Experimental Conclusion from Ionization

Simulations Smaller peak ionization (specific energy loss) or smaller average

ionization (specific energy loss), lead to larger projected ranges. This is self-explanatory since ionization (specific energy loss) is energy

loss per distance traveled.

W-Values

The energy that is loss by the alpha particle is used to ionize the gas particles.

For different types of incident radiation (beta and alpha particles) and different gases, different amounts of energy is needed to form an ion pair.

These values are called W-Value. Their units are in eV/ion-pair. These values were taken from Knoll.

W-Values for Different Gases from Alpha

Particles

Ar He H2 N2 Air O2 CH40

5

10

15

20

25

30

35

40

45

26.3

42.7

36.4 36.4 35.132.2

29.1

W-Values (From Knoll)

Gas

W-V

alue

s (eV

/ion

pair)

Calculations Done

For the Ionization curve showed above, a Reiman Sum was taken. This gives the total energy loss of the total particle.

A Reiman Sum was also done for the recoil ionization curve, in order to prove that the ionization of the recoil particles are negligible.

It is then assumed that all the energy that was loss by the ion, is used to ionize gas particles.

This energy is divided by the W-Value for the gas. This yields the total ion pairs formed.

Energy Loss by Ions and Recoil Particles

Ar He H2 N2 Air O2 CH45280000

5282000

5284000

5286000

5288000

5290000

5292000

5294000

5296000

Reiman Sum Energy Loss by Ions and Recoil Particles

Ions Recoil

Gas

Ener

gy Lo

ss (e

V)

Ion Pairs Formed

Ar He H2 N2 Air O2 CH40

50000

100000

150000

200000

250000

Reiman Sum Ion Pairs Formed

Gas

Ion

Pairs

For

med

Converting Ion Pairs into Voltage

In a given gas, the ionized atoms move much slower than electrons under the direction of an electric field. (due to the mass difference). For a typical chamber dimension, the time it takes for an ionized atom to reach its corresponding electrode is on the order of milliseconds while for electrons its on the order of microseconds.

Therefore we are only going to take into account the signal due to electrons. This can be done by making the RC time constant that is between the electron travel time and the ion travel time.

The electrons create a current when they come close to the electrodes. This current can be used to charge up a capacitor.

Converting Ion Pairs into Voltage

This leads to a peak voltage across the capacitor as a function of the capacitance and the number of electrons.

Arbitrarily, a capacitance of 100 pF is chosen. In reality though, the voltage pulse will have a slightly smaller peak

voltage due to geometrical characteristics of the chamber and entrance of the ion into the chamber.

Peak Voltages Calculated for a 5.3 MeV Alpha Particle in Different Gases

Ar He H2 N2 Air O2 CH40

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0.00035

Peak Voltage

Gas

Volta

ge (V

)

Voltage Pulse

Conclusions

Argon yields the largest peak voltage for a given alpha energy. This is because Argon has a relatively large atomic number (Z= 18)

compared to the other gas elements and has a small W-value. Argon also has the smallest amount of ionization due to the recoiling gas

particles. 5.3 MeV alpha particles also have approximately a 4 cm range in Argon

gas. This easily allows for smaller, portable ionization chambers.

Corresponding Different Alpha Energies to

Voltages If we pretend that we live in a fictitious universe where there is only

alpha decay, it is possible then to create a plot of peak voltage versus energy and range versus energy.

This would allow us to determine the alpha energy by observing the peak voltage of a pulse. From here we can use the energy to determine the source of the alpha particle.

We of course do not live in a fictitious universe, and much more complicated processing is necessary since other decays are possible and can ionize gas in the chamber.

Plots for Various Alpha Energies in Argon Gas

References

Knoll, Glenn. Radiation Detection and Measurement. John Wiley & Sons, Inc., 2000.