About

There are a variety of factors that affect the spectrum of X-rays produced in a diagnostic imaging unit. This model shows the effect of varying the high voltage (kVp), added filtration and ripple in the high voltage supply to the X-ray tube.

The physical mechanisms by which X-rays are produced are Bremsstrahlung (in which collisions of the cathode electrons convert some of their energy into X-ray photons) and characteristic X-rays (in which the cathode electrons kick an inner shell electron out of an atom, and an X-ray photon is release when one of the atom's outer shell electron transitions to the inner shell). Changing the accelerating voltage of the cathode electrons (i.e. changing kVp) affects both mechanisms of X-ray production. Adding filtration to the X-ray beam reduces its intensity, but does not reduce all energy X-rays equally. Finally, voltage ripple actually causes the accelerating voltage of the cathode rays to vary below the peak voltage (kVp), so that X-ray tube is essentially averaging over a range of high voltages up to the set kVp.

Questions to explore:

The total X-ray energy is the area under the spectrum curve. What effect does changing kVp have on the total energy of the X-ray beam?

Characteristic X-rays cannot be created unless the kinetic energy of the cathode electrons can overcome the binding energy of the K shell electrons of the target atoms. Estimate this binding energy (in keV) by noting the accelerating potential at which the characteristic X-rays first appear. Does it make sense that this threshold energy is greater than the energies of the characteristic X-rays? (explain)

With kVp set at 120 kV, add filtration by setting the following characteristics of the filter material: atomic number (Z) =1, density (ρ in g/cm³) = 1 and thickness (d in cm) to 1.

• What happened to the overall intensity of the beam? (i.e. the area under the curve).
• Were all energy X-rays equally affected? Which part of the X-ray spectrum was affected the most?
• What happens to the total intensity of the filtered beam and the spectrum when Z is increased?
• What happens when the density is increased? Is this the same effect as increasing Z?
• What happens when the thickness is increased?

Remove the filters by setting all filter parameters to zero, and then increase ripple. The ripple in the high voltage waveform can be seen by selecting the "Ripple Plot" checkbox.

• What happens to the total intensity when ripple is increased?
• Which part(s) of the X-ray spectrum are affected the most?
• Does having ripple in the high voltage produce the same type of effect as filtration? (explain)

 

For Teachers

This applet uses a very simple model for the X-Ray spectrum.* The bulk of the spectrum is due to Bremsstrahlung while the reminder is from the characteristic X-Rays. The spectrum is further shaped by intrinsic filtering by the anode materials (since the X-rays are generally created beneath the surface of the anode).

Bremsstrahlung

• I(E)∝ Z(T−E)
• T = electron’s kinetic energy

Characteristic X-Rays (K-shell)

• I_K∝(T−E_K)^1.65
• E_K =K shell binding energy

Intrinsic Filtering: energy dependent attenuation of X-rays

• electrons penetrate anode
• attenuation by X-ray tube components
• modeled as: Z=29, ρt= .1 g/cm²

Additional Filtration

• filtration by design for diagnostic X-ray imaging
• beam “hardening” + attenuation

*Following simplified models from discussion in “Semiempirical model for generating tungsten target x-ray spectra” Douglas M. Tucker, Gary T. Barnes, and Dev P. Chakraborty, Med. Phys. 18, 211 (1991)

Translations

Code	Language		Translator	Run
es	es	es

Credits

Michael R. Gallis; lookang

http://iwant2study.org/lookangejss/06QuantumPhysics/ejss_model_XRaySpectrumwee/XRaySpectrumwee_Simulation.xhtml

Briefing Document: X-Ray Spectrum JavaScript HTML5 Applet Simulation Model

1. Overview

This document summarizes the key information about an interactive JavaScript HTML5 applet designed to simulate and explore the X-ray spectrum produced in a diagnostic imaging unit. The applet, developed by Michael R. Gallis and hosted on Open Educational Resources / Open Source Physics @ Singapore, allows users to manipulate several parameters and observe their effects on the generated X-ray spectrum. It is intended for educational purposes, particularly in the areas of quantum physics and junior college-level science.

2. Main Themes and Concepts

• X-Ray Production Mechanisms: The primary focus of the applet is to visualize and understand the two main mechanisms by which X-rays are generated:
• Bremsstrahlung: "collisions of the cathode electrons convert some of their energy into X-ray photons." This process results in a continuous spectrum of X-ray energies.
• Characteristic X-rays: "cathode electrons kick an inner shell electron out of an atom, and an X-ray photon is release when one of the atom's outer shell electron transitions to the inner shell." This produces X-rays with specific, discrete energies.
• Factors Affecting X-Ray Spectrum: The simulation allows users to explore how various factors alter the X-ray spectrum:
• High Voltage (kVp): Changing the accelerating voltage of the cathode electrons affects both Bremsstrahlung and characteristic X-ray production. A higher kVp results in both higher energy X-rays, and more X-ray production
• Added Filtration: Adding filter materials to the X-ray beam reduces its intensity and alters its energy distribution, also known as beam hardening
• Voltage Ripple: Variations in the high-voltage supply, "causes the accelerating voltage of the cathode rays to vary below the peak voltage (kVp), so that X-ray tube is essentially averaging over a range of high voltages up to the set kVp."
• Educational Focus: The applet is designed to encourage inquiry-based learning by providing an interactive way to explore these concepts.

3. Key Facts and Ideas

• Simulation Model:
• The applet employs a simplified model of the X-ray spectrum.
• The model considers the "bulk of the spectrum" to be from Bremsstrahlung, with "the reminder" from characteristic X-rays.
• The spectrum is also affected by "intrinsic filtering by the anode materials."
• The applet is based on models discussed in "Semiempirical model for generating tungsten target x-ray spectra" by Tucker, Barnes, and Chakraborty (Med. Phys. 1991)
• Mathematical Model: The model for X-ray intensity (I) is given as:
• Bremsstrahlung: I(E) ∝ Z(T-E), where Z is the atomic number of the target, T is the kinetic energy of the electron, and E is the energy of the X-ray photon.
• Characteristic X-rays (K-shell): IK ∝ (T - EK)^1.65 where EK is the K-shell binding energy of the target atoms.
• Intrinsic Filtering: Modeled as attenuation based on material with Z=29 and ρt = .1 g/cm².
• Experimental Questions: The provided text explicitly lists questions for users to explore:
• How does changing kVp affect total X-ray energy?
• How can one estimate the K-shell binding energy by observing the appearance of characteristic X-rays?
• How does added filtration, i.e. variations in material Z, material density ρ, and thickness d, affect the X-ray spectrum?
• How does voltage ripple affect the X-ray spectrum?
• Does ripple produce similar effects as filtration?
• Impact of Filtration:
• Filtration reduces the overall intensity of the X-ray beam.
• Lower energy X-rays are disproportionately attenuated.
• Varying the filter's atomic number (Z), density (ρ), and thickness (d) each have a unique impact on the spectrum.
• Increasing the atomic number Z results in qualitatively different changes to the spectrum, compared to changes in density ρ or thickness d.
• Impact of Voltage Ripple:
• Increasing ripple also reduces the overall intensity.
• Lower energy parts of the spectrum are primarily affected.
• Ripple has a different effect on the spectrum compared to filtration because the voltage never exceeds kVp

4. Quotes from the Source

• "There are a variety of factors that affect the spectrum of X-rays produced in a diagnostic imaging unit. This model shows the effect of varying the high voltage (kVp), added filtration and ripple in the high voltage supply to the X-ray tube."
• "The physical mechanisms by which X-rays are produced are Bremsstrahlung (in which collisions of the cathode electrons convert some of their energy into X-ray photons) and characteristic X-rays (in which the cathode electrons kick an inner shell electron out of an atom, and an X-ray photon is release when one of the atom's outer shell electron transitions to the inner shell)."
• "Changing the accelerating voltage of the cathode electrons (i.e. changing kVp) affects both mechanisms of X-ray production."
• "Adding filtration to the X-ray beam reduces its intensity, but does not reduce all energy X-rays equally."
• "Finally, voltage ripple actually causes the accelerating voltage of the cathode rays to vary below the peak voltage (kVp), so that X-ray tube is essentially averaging over a range of high voltages up to the set kVp."
• "The bulk of the spectrum is due to Bremsstrahlung while the reminder is from the characteristic X-Rays. The spectrum is further shaped by intrinsic filtering by the anode materials"

5. Intended Use The applet is designed to be used:

• as an interactive resource for students learning about X-ray physics
• to help students visualize key concepts such as bremsstrahlung and characteristic x-ray production
• to support inquiry based learning through exploration and experimentation with the applet

6. Technical Details

• The simulation is an HTML5 applet, making it accessible on various platforms (Windows, MacOS, Linux, Android, iOS, etc.).
• It is embedded within the provided webpage using an iframe.
• The applet is part of the Open Educational Resources / Open Source Physics @ Singapore project.

7. Conclusion

This X-Ray Spectrum simulation applet provides a valuable, interactive tool for visualizing and understanding the complex processes involved in X-ray generation and modification. By allowing users to manipulate parameters such as high voltage, filtration, and voltage ripple, it provides an engaging way to learn about Bremsstrahlung, characteristic X-rays, and other factors impacting the X-ray spectrum. The applet's explicit inquiry-based questions make it particularly well-suited for educational settings.

 

X-Ray Spectrum Study Guide

Quiz

1. What are the two primary mechanisms by which X-rays are produced in an X-ray tube, and how do they differ?
2. How does changing the accelerating voltage (kVp) of the cathode electrons affect the production of X-rays?
3. Explain how adding filtration to the X-ray beam impacts its overall intensity and energy distribution.
4. What is voltage ripple, and how does it affect the accelerating voltage of the cathode rays in an X-ray tube?
5. Describe the relationship between the kinetic energy of cathode electrons and the creation of characteristic X-rays.
6. According to the provided formulas, what does the intensity of Bremsstrahlung radiation depend on?
7. How does the model account for intrinsic filtering by the anode material in an X-ray tube?
8. What are some of the key properties of a filter that affect its interaction with the X-ray beam, according to the description?
9. In the simulation, how does increasing the atomic number of the filtration material affect the total intensity and the X-ray spectrum?
10. What is the difference in the way that the model represents the effects of increasing the thickness and density of the filter, compared to increasing the atomic number?

Answer Key

1. The two primary mechanisms are Bremsstrahlung and characteristic X-rays. Bremsstrahlung occurs when cathode electrons collide with the target atoms, converting some kinetic energy into X-ray photons, while characteristic X-rays are produced when cathode electrons eject inner-shell electrons from atoms, and outer-shell electrons transition to fill the vacancy, releasing X-ray photons.
2. Changing kVp affects both Bremsstrahlung and characteristic X-ray production. Higher kVp increases the kinetic energy of cathode electrons, leading to higher energy X-rays and more total X-ray production.
3. Adding filtration reduces the overall intensity of the X-ray beam. However, it does not reduce all energy X-rays equally; it attenuates lower-energy photons more than higher-energy photons, shifting the spectrum toward higher energies.
4. Voltage ripple causes the accelerating voltage of the cathode rays to vary below the peak voltage (kVp). This results in the X-ray tube averaging over a range of high voltages up to the set kVp, and affects the intensity and distribution of the spectrum.
5. Characteristic X-rays are created when the kinetic energy of the cathode electrons is greater than the binding energy of the inner-shell electrons of the target atoms. The threshold is that the kinetic energy of the cathode electrons must be sufficient to eject the inner shell electron.
6. According to the provided formula, the intensity of Bremsstrahlung radiation, I(E), is proportional to the atomic number Z of the target material, multiplied by the difference between the electron's kinetic energy (T) and the energy of the photon produced (E)
7. The model accounts for intrinsic filtering by the anode material by representing it as an energy-dependent attenuation. It accounts for the penetration of electrons in the anode and subsequent attenuation. It has a modeled atomic number of 29 and a ρt = .1 g/cm².
8. The key properties of a filter are its effective atomic number (Z), density (ρ), and thickness (d). Changing Z has a different qualitative effect on the spectrum compared to changes in ρ or d.
9. Increasing the atomic number (Z) of the filter material decreases the total intensity of the beam. Also, a higher Z affects the lower energy end of the spectrum more, shifting it toward higher energies.
10. Increasing the thickness (d) and density (ρ) of the filter material primarily affects the intensity of the beam but has a more uniform affect on the spectrum. While higher Z causes qualitative changes in the spectrum.

Essay Questions

1. Discuss the interplay between Bremsstrahlung and characteristic X-ray production. How does changing the kVp affect each process? How are these processes affected by the characteristics of the target material?
2. Analyze the role of filtration in shaping the X-ray spectrum. How does changing the atomic number, density, and thickness of a filter affect beam hardening, and what are the implications for diagnostic imaging?
3. Explain the concept of voltage ripple and its impact on the X-ray spectrum. How does ripple differ from filtration in altering the intensity and energy distribution of the X-ray beam? Consider the causes of ripple.
4. Evaluate the simplified models used in the simulation for Bremsstrahlung, characteristic X-rays, intrinsic filtering, and additional filtration. What are the advantages and limitations of these simplified models?
5. Compare and contrast the effects of changing the kVp, adding filtration, and increasing ripple on the X-ray spectrum, taking into account both the overall intensity and the energy distribution of the photons.

Glossary of Key Terms

• Bremsstrahlung: X-ray radiation produced when charged particles (electrons in this context) are decelerated or deflected by other charged particles, resulting in the emission of photons of various energies.
• Characteristic X-rays: X-ray photons emitted when an inner-shell electron is ejected from an atom and an electron from an outer shell transitions to fill the vacancy, releasing energy equal to the difference in energy levels.
• kVp: Kilovoltage peak, referring to the maximum accelerating voltage applied to the cathode electrons in an X-ray tube; higher kVp results in higher energy X-rays.
• Filtration: The process of attenuating or absorbing X-ray photons, typically using materials with specific atomic numbers, densities, and thicknesses, to modify the X-ray beam's intensity and energy spectrum.
• Voltage Ripple: Fluctuations in the high voltage applied to an X-ray tube, resulting in variations in the energy of the cathode electrons and the resulting X-ray photons.
• Atomic Number (Z): The number of protons in the nucleus of an atom, which affects its interaction with X-rays. Higher atomic numbers increase the attenuation of lower energy X-rays.
• Density (ρ): A measure of mass per unit volume, which affects the attenuation of X-rays in a material.
• K-shell Binding Energy: The minimum energy required to remove an electron from the innermost electron shell (K-shell) of an atom.
• Intensity: The amount of radiation (in this case, X-rays) emitted per unit area; often used to describe the overall strength or quantity of the radiation.
• Attenuation: The reduction in intensity of an X-ray beam as it passes through a material, which is due to absorption and scattering of photons.
• Beam Hardening: The process of increasing the average energy of an X-ray beam by preferentially removing lower-energy photons through filtration.
• Intrinsic Filtering: The attenuation of X-rays due to the materials that make up the X-ray tube components.

Physics Explained

There are a variety of factors that affect the spectrum of X-rays produced in a diagnostic imaging unit. This model shows the effect of varying the high voltage (kVp), added filtration and ripple in the high voltage supply to the X-ray tube.

The physical mechanisms by which X-rays are produced are Bremsstrahlung (in which collisions of the cathode electrons convert some of their energy into X-ray photons) and characteristic X-rays (in which the cathode electrons kick an inner shell electron out of an atom, and an X-ray photon is release when one of the atom's outer shell electron transitions to the inner shell). Changing the accelerating voltage of the cathode electrons (i.e. changing kVp) affects both mechanisms of X-ray production. Adding filtration to the X-ray beam reduces its intensity, but does not reduce all energy X-rays equally. Finally, voltage ripple actually causes the accelerating voltage of the cathode rays to vary below the peak voltage (kVp), so that X-ray tube is essentially averaging over a range of high voltages up to the set kVp.

Questions to explore:

The total X-ray energy is the area under the spectrum curve. What effect does changing kVp have on the total energy of the X-ray beam?

Characteristic X-rays cannot be created unless the kinetic energy of the cathode electrons can overcome the binding energy of the K shell electrons of the target atoms. Estimate this binding energy (in keV) by noting the accelerating potential at which the characteristic X-rays first appear. Does it make sense that this threshold energy is greater than the energies of the characteristic X-rays? (explain)

With kVp set at 120 kV, add filtration by setting the following characteristics of the filter material: atomic number (Z) =1, density (ρ in g/cm³) = 1 and thickness (d in cm) to 1.

• What happened to the overall intensity of the beam? (i.e. the area under the curve).
• Were all energy X-rays equally affected? Which part of the X-ray spectrum was affected the most?
• What happens to the total intensity of the filtered beam and the spectrum when Z is increased?
• What happens when the density is increased? Is this the same effect as increasing Z?
• What happens when the thickness is increased?

Remove the filters by setting all filter parameters to zero, and then increase ripple. The ripple in the high voltage waveform can be seen by selecting the "Ripple Plot" checkbox.

• What happens to the total intensity when ripple is increased?
• Which part(s) of the X-ray spectrum are affected the most?
• Does having ripple in the high voltage produce the same type of effect as filtration? (explain) 

Model Theory

This applet uses a very simple model for the X-Ray spectrum.* The bulk of the spectrum is due to Bremsstrahlung while the reminder is from the characteristic X-Rays. The spectrum is further shaped by intrinsic filtering by the anode materials (since the X-rays are generally created beneath the surface of the anode).

Bremsstrahlung

• I(E)∝ Z(T−E)
• T = electron’s kinetic energy

Characteristic X-Rays (K-shell)

• IK∝(T−EK)^1.65
• EK =K shell binding energy

Intrinsic Filtering: energy dependent attenuation of X-rays

• electrons penetrate anode
• attenuation by X-ray tube components
• modeled as: Z=29, ρt= .1 g/cm2

Additional Filtration

• filtration by design for diagnostic X-ray imaging
• beam “hardening” + attenuation

*Following simplified models from discussion in “Semiempirical model for generating tungsten target x-ray spectra” Douglas M. Tucker, Gary T. Barnes, and Dev P. Chakraborty, Med. Phys. 18, 211 (1991) 

Description

There are a variety of factors that affect the spectrum of X-rays produced in a diagnostic imaging unit.
This applet shows the effect of varying the high voltage (kVp), added filtration and ripple in the high voltage supply to the X-ray tube.

The physical mechanisms by which X-rays are produced are Bremsstrahlung (in which collisions of the cathode electrons convert some of their energy into X-ray photons) and characteristic X-rays (in which the cathode electrons kick an inner shell electron out of an atom, and an X-ray photon is release when one of the atom's outer shell electron transitions to the inner shell).
Changing the accelerating voltage of the cathode electrons (i.e. changing kVp) affects both mechanisms of X-ray production.
Adding filtration to the X-ray beam reduces its intensity, but does not reduce all energy X-rays equally. The details of how the filter interacts with the X-Ray beam depends upon several properties of the filter: the effective atomic number Z, the density ρ and the thickness d.
Changing Z will produce a qualitatively different change in the spectrum compared to ρ and d.

Finally, voltage ripple actually causes the accelerating voltage of the cathode rays to vary below the peak voltage (kVp), so that X-ray tube is essentially averaging over a range of high voltages up to the set kVp.

Other Resources

1. http://web.stanford.edu/group/glam/xlab/MatSci162_172/LectureNotes/01_Properties%20&%20Safety.pdf 

 

Version: 

1. http://weelookang.blogspot.sg/2016/04/x-ray-spectrum-by-michael-gallis-remixed.html Blogpost by Loo Kang Wee
2. http://www.compadre.org/osp/items/detail.cfm?ID=13391 by Michael R. Gallis

 

X-Ray Spectrum FAQ

1. What are the two primary mechanisms by which X-rays are produced in an X-ray tube? X-rays are primarily produced through two mechanisms: Bremsstrahlung and characteristic X-rays. Bremsstrahlung occurs when cathode electrons collide with the target material, converting some of their kinetic energy into X-ray photons. Characteristic X-rays are generated when a cathode electron ejects an inner-shell electron from a target atom, and an outer-shell electron transitions to fill the vacancy, releasing an X-ray photon with a characteristic energy.
2. How does changing the accelerating voltage (kVp) affect the X-ray spectrum and total X-ray energy? Increasing the accelerating voltage (kVp) of the cathode electrons affects both the Bremsstrahlung and characteristic X-ray production. A higher kVp increases the kinetic energy of the electrons, leading to the production of higher energy X-ray photons. This also increases the intensity and total energy of the X-ray beam, as more photons are produced at higher energies, resulting in a larger area under the spectrum curve.
3. What role does filtration play in modifying an X-ray beam? Adding filtration to the X-ray beam reduces its overall intensity. However, the reduction is not uniform across all energy levels. Lower energy X-rays are attenuated (reduced) more than higher energy X-rays. This process is called "beam hardening", because it shifts the average energy of the X-ray beam towards higher energies. The effectiveness of filtration depends on the filter material's atomic number (Z), density (ρ), and thickness (d).
4. How do changes in the filter's atomic number (Z), density (ρ), and thickness (d) affect the X-ray spectrum? Increasing the atomic number (Z) of the filter material causes a qualitatively different change in the X-ray spectrum compared to changes in density or thickness. Increasing Z leads to a more pronounced reduction in the intensity of the lower energy X-rays, as the absorption cross-section for those X-rays is higher for higher Z materials. Increases in the filter's density (ρ) and thickness (d) result in a greater overall attenuation of the beam, reducing intensity more equally across the energies, with a greater impact at lower energies. Increasing density and thickness generally produce a similar effect on the total beam intensity.
5. What is voltage ripple, and how does it affect the X-ray spectrum? Voltage ripple refers to fluctuations in the accelerating voltage of the cathode rays below the peak voltage (kVp). In effect, the X-ray tube is averaging over a range of voltages up to the set kVp. Increased ripple effectively broadens the spectrum of generated X-rays, as it creates a range of electron energies hitting the anode, leading to a corresponding range of X-ray energies. Ripple also decreases the overall intensity of the beam, as the majority of the voltage is below the peak kVp, and thus generating lower energy photons. The effect of ripple is therefore similar to filtration: a reduction of lower energy photons and overall intensity.
6. What is the threshold energy for the production of characteristic X-rays, and what is the significance of the relationship between the threshold energy and the energies of the characteristic X-rays? Characteristic X-rays are only produced if the kinetic energy of the cathode electrons is greater than the binding energy of the inner-shell electrons of the target atoms. The threshold energy, approximately the accelerating potential at which characteristic X-rays first appear in the spectrum, must be greater than the energies of the resulting characteristic X-rays because an amount of energy is required to eject the electron before the outer-shell electron transitions and generates an X-ray.
7. What is Bremsstrahlung and how does it relate to the X-ray spectrum? Bremsstrahlung is a type of radiation produced when charged particles (such as electrons) are decelerated or deflected by the electric field of a nucleus. In an X-ray tube, the cathode electrons undergo this process. The energy of Bremsstrahlung photons is dependent on the deceleration amount and the initial electron's energy. The Bremsstrahlung radiation accounts for the bulk of an X-ray spectrum and its intensity depends on the atomic number Z of the target atom and the kinetic energy T of the incoming electrons according to the formula: I(E) ∝ Z(T-E)
8. Besides Bremsstrahlung and characteristic x-rays, what else affects the X-ray Spectrum? The X-ray spectrum is also shaped by intrinsic filtering by the anode materials. Because the X-rays are generally created beneath the surface of the anode and must therefore traverse it to exit the tube, this absorption is energy dependent. Also, components of the X-ray tube itself may cause further attenuation, which are factored into the simulation through the model parameters for effective atomic number and density of the internal filtration.