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Cavity Theory

 Cavity theory is the basis of operation for ionization chambers used in reference dosimetry. Cavity theory relates measured dose in a cavity, such as an ion chamber, to dose at the same point in the medium in absence of the cavity.

Bragg-Gray Cavity Theory

Bragg-Gray (BG) theory relates dose to the medium, Dmed, to dose to the cavity fill gas, Dgas, via the ratio of mass collision stopping powers between the medium and gas, .

Bragg-Gray Assumptions

1. Charged particle equilibrium (CPE) or transient charged particle equilibrium (TCPE) exist
2. All electrons causing ionization in the cavity arise from phantom material
3. Secondary electron spectrum is unchanged by presence of the cavity
4. Energy of secondary electrons created inside the cavity are deposited locally
• Neglects secondary electrons (delta rays) generated within the cavity as a result of interactions with scattered electrons

Spencer-Attix Cavity Theory

The Spencer-Attix formulation of cavity theory resolves the issues of the Bragg-Gray so that it applies for small cavities.

•  is the ratio of restricted mass collision stopping power from the medium to the cavity fill gas.
• Restricted mass collision stopping power uses a cutoff energy, Δ, which removes the requirement that secondary electrons deposit their energy locally.

Spencer-Attix Requirements

1. Requires charged particle equilibrium (CPE) or transient charged particle equilibrium (TCPE)
2. All electrons causing ionization in the cavity arise from phantom material
3. Secondary electron spectrum is unchanged by presence of the cavity

Burlin Cavity Theory

The Burlin formulation generalizes cavity theory for large and small cavities.

•  is the ratio of restricted mass collision stopping power from the medium to the cavity fill gas.
• d is a parameter related to cavity size
  • d = 1 for small cavities
  • d approaches 0 for large cavities
•  is the ratio of mass energy absorption coefficients from the medium to gas.

Burlin Requirements

1. Charged particle equilibrium (CPE) exists in medium and cavity

Bragg-Gray Limitations

Because of contradictory and non-physical assumptions, Bragg-Gray theory is only an approximate solution for physical systems.

Assumptions 2 and 3 imply a need for a small cavity volume while requirement 4 requires a large volume to collect all electrons. These conditions cannot be met simultaneously.

Requirement 3, that the spectrum be unchanged, would mean that no energy could be collected to rigorously meet this theory. This is generally disregarded as the effect is minimal with a small cavity.

Ionization chamber

 he ionization chamber is the simplest type of gas-filled radiation detector, and is widely used for the detection and measurement of certain types of ionizing radiation, including X-rays, gamma rays, and beta particles. Conventionally, the term "ionization chamber" refers exclusively to those detectors which collect all the charges created by direct ionization within the gas through the application of an electric field.^[1] It only uses the discrete charges created by each interaction between the incident radiation and the gas. Gaseous ionization detectors include ionization chambers and devices that use gas multiplication, namely the proportional counter and the Geiger counter.

Ion chambers have a good uniform response to radiation over a wide range of energies and are the preferred means of measuring high levels of gamma radiation. They are widely used in the nuclear power industry, research labs, radiography, radiobiology, and environmental monitoring.

Principle of operation

A gas ionization chamber measures the charge from the number of ion pairs created within a gas caused by incident radiation. It consists of a gas-filled chamber with two electrodes; known as anode and cathode. The electrodes may be in the form of parallel plates (Parallel Plate Ionization Chambers: PPIC), or a cylinder arrangement with a coaxially located internal anode wire.

A voltage potential is applied between the electrodes to create an electric field in the fill gas. When gas atoms or molecules between the electrodes are ionized by incident ionizing radiation, ion-pairs are created and the resultant positive ions and dissociated electrons move to the electrodes of the opposite polarity under the influence of the electric field. This generates an ionization current which is measured by an electrometer circuit. The electrometer must be capable of measuring the very small output current which is in the region of femtoamperes to picoamperes, depending on the chamber design, radiation dose and applied voltage. Each ion pair created deposits or removes a small electric charge to or from an electrode, such that the accumulated charge is proportional to the number of ion pairs created, and hence the radiation dose. This continual generation of charge produces an ionization current, which is a measure of the total ionizing dose entering the chamber.^[1]

The electric field is sufficiently strong to enable the device to work continuously by mopping up all the ion pairs, preventing the recombination of ion pairs which would diminish the ion current. This mode of operation is referred to as "current" mode, meaning that the output signal is a continuous current, and not a pulse output as in the cases of the Geiger–Müller tube or the proportional counter.^[1] Because the number of ion pairs produced is proportional to the energy of the incident radiation, this continuously measured current is proportional to the dose rate (energy deposited per unit time) in the ionization chamber. Referring to the accompanying ion-pair collection graph, it can be seen that in the ion chamber operating region the charge of a collected ion pair is effectively constant over a range of applied voltage, as due to its relatively low electric field strength the ion chamber does not have any multiplication effect. This is in distinction to the Geiger–Müller tube or the proportional counter whereby secondary electrons, and ultimately multiple avalanches, greatly amplify the original ion-current charge.

Applications[edit]

Nuclear industry[edit]

Ionization chambers are widely used in the nuclear industry as they provide an output that is proportional to radiation dose They find wide use in situations where a constant high dose rate is being measured as they have a greater operating lifetime than standard Geiger–Müller tubes, which suffer from gas break down and are generally limited to a life of about 10¹¹ count events.^[1] Additionally, the Geiger–Müller tube cannot operate above about 10⁴ counts per second, due to dead-time effects, whereas there is no similar limitation on the ion chamber.

Smoke detectors[edit]

The ionization chamber has found wide and beneficial use in smoke detectors. In an ionisation type smoke detector, ambient air is allowed to freely enter the ionization chamber. The chamber contains a small amount of americium-241, which is an emitter of alpha particles which produce a constant ion current. If smoke enters the detector, it disrupts this current because ions strike smoke particles and are neutralized. This drop in current triggers the alarm. The detector also has a reference chamber which is sealed but is ionized in the same way. Comparison of the ion currents in the two chambers allows compensation for changes due to air pressure, temperature, or the ageing of the source. ^[7]

Medical radiation measurement[edit]

Diagram of a nuclear medicine dose calibrator or radionuclide calibrator that uses a "well-type" ionization chamber. The dipper is used to give a reproducible source position. The radioactive substance in this example is liquid.

In medical physics and radiotherapy, ionization chambers are used to ensure that the dose delivered from a therapy unit^[8] or radiopharmaceutical is what is intended. The devices used for radiotherapy are called "reference dosimeters", while those used for radiopharmaceuticals are called radioisotope dose calibrators - an inexact name for radionuclide radioactivity calibrators, which are used for measurement of radioactivity but not absorbed dose.^[9] A chamber will have a calibration factor established by a national standards laboratory such as ARPANSA in Australia or the NPL in the UK, or will have a factor determined by comparison against a transfer standard chamber traceable to national standards at the user's site.^[4][10]

Guidance on application use[edit]

In the United Kingdom the HSE has issued a user guide on selecting the correct radiation measurement instrument for the particular application concerned.^[11] This covers all radiation instrument technologies, and is a useful comparative guide to the use of ion chamber instruments.

GEIGER MULAR COUNTER

 Geiger counter is a device which is used to detect and measure particles in the ionized gases. It is widely used in applications like radiological protection, radiation dosimetry,  and experimental physics. It is made up of the metallic tube, filled with gas and a high voltage range of multiples of 100V is applied to this gas. It detects alpha, beta, and gamma particles.

When radioactive isotopes are used in medical research work on humans, it is important to make sure that the amount of radioactive material administered to human subjects is as little as possible. In order to achieve this, a very sensitive instrument is necessary to measure the radioactivity of materials. A ‘particle detector’ to measure the ionizing radiation was developed by Geiger and Muller in the year 1928 and they called it a ‘Geiger Muller Counter’ which in short is known as the ‘GM counter.’

In the large and dominant use as a hand-held radiation survey instrument, it would be one of the planet’s renowned radiation detection instruments.

Principle of Geiger Counter

The Geiger counter would contain Geiger-Müller tube, the element of sense that detects the radiation and the electronics that processes that would provide the result.

The Geiger-Müller tube is filled with a gas such as helium, neon, or argon at the pressure being the lowest, where there is an application of high voltage. There would be the conduction of the electrical charge on the tube when a particle or photon of incident radiation would turn the gas conductive by the means of ionization.

Types of Geiger Counter

The Geiger counter is dictated entirely by the design of the tube, can be generally categorised into two types:

• End Window
• Windowless

End Window

This style of the tube would have a small window at one of its ends. This window would be helpful in ionizing particles that could travel easily.

Windowless

As the name suggests, this type of tube would not have any windows and the thickness would be in the range of one to two mm. This type of tube is used for detecting high penetrating radiations.

Geiger Counter Units

The measurement of particles would be in different units, the widely used one of them is the Counts Per Minute (CPM). The measurement of radioactivity would be in micro-(µSv/hr) – Sieverts per hour and (mR/hr)milli-Roentgens per hour.

Stay tuned with BYJU’S to learn more about geiger counter, radiation detector and much more.

 What is the basic physical principle responsible for the presence of energy bands rather than specific energy levels in a solid?

In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energies that an electron within the solid may have (called energy bands, allowed bands, or simply bands) and ranges of energy that it may not have (called band gaps or forbidden bands).Band theory derives these bands and band gaps by examining the allowed quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules. Band theory has been successfully used to explain many physical properties of solids, such as electrical resistivity and optical absorption, and forms the foundation of the understanding of all solid-state devices (transistors, solar cells, etc.).

 How does Laue’s approach differ from Bragg’s approach?

According to Bragg's law,the crystal is considered as a set of equal spaced parallel planes of ions on atoms.X-ray are reflected by the ions on atoms on one plane.Reflected rays from two successive planes interfere constructively.

But in Laue’s approach ,there is no concept of parallel planes.X-rays are scattered from the lattice points(atoms or ions) in all directions and maximum will occur when scattered rays interfere constructively.