Lesson Video: X-ray Tubes Physics

In this video, we will learn how to describe the production of X-rays using an X-ray tube and how the spectrum of X-rays produced can vary.

17:58

Video Transcript

The interaction of X-rays with matter can provide us with valuable information about an object’s internal structure and chemical makeup. To acquire this information though, we need a way to produce X-rays. In this lesson, we’re going to learn about the components of the Coolidge X-ray tube. We’ll learn about the functions of each of these components, as well as how the underlying physics allows this apparatus to produce X-rays.

Here’s a schematic diagram of the Coolidge X-ray tube. The parts of the tube that actually produce the X-rays are located in vacuum inside of a glass bulb. Inside the bulb are two electrodes, a hot cathode, and a target that serves as the anode. We’ll use the symbol 𝑉 𝑇 to denote the potential difference between the hot cathode and the target. This is set by some external source and is called the tube voltage.

Finally, there’s also an external source that provides power to the hot cathode. When the tube is switched on, the cathode emits a beam of electrons that is accelerated by the tube voltage until it hits the target. The reason the interior of the tube is kept at a vacuum is so that the electron beam is not interfered with by the presence of gases. When the electrons strike the target, X-rays are produced that can be used or measured.

Let’s now discuss these components and processes in detail. We’ll start with a hot cathode. The hot cathode consists of a wire coil connected by two terminals to a power source. We call this device a hot cathode because the purpose of the power source is to cause the wire coil to heat even as high as 2500 kelvin. At these temperatures, the thermal energy of the electrons in the coil is large enough that they can escape from the metal into the surrounding vacuum.

The process by which these electrons are actually emitted is called thermionic emission. Therm refers to heat, and ionic refers to charged particles. So we call it thermionic emission because high temperatures cause charged particles to be left behind when electrons are emitted from a surface.

A good analogy to understand this process is evaporating water from a heated pot. Here’s our pot full of water. The blue circles represent individual water molecules. The water is a liquid because there are attractive forces holding them together. And the individual water molecules don’t have enough energy to pull apart against that force. However, we can increase the energy of the molecules by heating them. If we place the pot on a fire, the temperature of the water will increase. And eventually some of the molecules will have enough energy to escape from the liquid into the surrounding air.

The result of this process is essentially similar to the process of boiling. If we replace the water molecules with electrons and the pot with a block of metal, we will see that the process of thermionic emission is very similar. In a piece of metal, there are many electrons that are free to move around as long as they stay within the confines of the metal, similar to the water molecules in the pot. However, just like the water molecules in liquid water don’t have enough energy to break free of the attractive forces holding them together, the negatively charged electrons don’t have enough energy to break away completely from the positively charged nuclei of the metal. And this is because the Coulomb attraction between opposite charges is holding them together.

However, if we again add heat either with a fire or by resistive heating, as is usually the case in a hot cathode, some of the electrons will acquire enough energy to overcome the Coulomb force and escape into the surrounding vacuum. This is the process of thermionic emission. Charged particles are emitted from a surface as a result of applied heat. Because we need to deliver a large amount of power to heat the coil sufficiently, the power source needs to be high current but not necessarily high voltage. Some power sources run on even fewer than 10 volts.

This is in contrast to the tube voltage, which must be quite large in order to sufficiently accelerate the electron beam, which brings us right into our next topic, the beam of electrons in the Coolidge tube. A beam of electrons is a group of electrons all traveling in a similar direction, clustered in space around the direction of travel.

Two important quantities that characterize an electron beam are the beam energy and beam current. One way to define the beam energy is as the average energy of the electrons in the beam. When the beam of electrons in the Coolidge tube strikes the target, it delivers energy to the target to produce X-rays.

The laws of conservation of energy tell us that the energy of the X-rays is at most the energy imparted onto the target by the beam. And the maximum energy that the beam can impart is just the energy of the beam itself. It is for this reason that the cathode and target are held at a potential difference of 𝑉 𝑇. This tube voltage creates an electric field that accelerates the electrons from the cathode to the target.

In order to accelerate the electrons in the correct direction, it is critical that the target be held at positive voltage relative to the cathode. Recall that electrons accelerated through a potential difference would have a kinetic energy gain of the charge on the electron times that potential difference. Symbolically, we can write that the energy of the beam when it hits the target is 𝑞, the charge on an electron, times 𝑉 𝑇, the tube voltage. This is also the maximum energy of the X-rays that are produced, since each X-ray is produced by an electron losing at most this much energy.

In order to produce high-energy X-rays, the tube voltage must be quite high, often tens of thousands of volts. For this reason, we can ignore the relatively modest energy of the electrons as they leave the hot cathode since these energies are negligible compared to the energies the electrons have after being accelerated through tens of kilovolts. The beam energy gives us information about the energy of the X-rays that are produced. The beam current will give us information about how many of these X-rays are produced per unit time.

Current, specifically electrical current, is the rate at which charge flows along a particular path. In a typical electrical circuit, the wire forms the path and the electrons make up the flow of charged particles. If we examine this picture carefully, we see that we have a group of electrons all traveling in a similar direction, located close together along the direction of travel. This is the same kind of situation we had when we defined an electron beam. So we should be able to define a current for electron beams since, as we can see in our picture, we have a flow of electrons, which is the same as a flow of charge on the path between the cathode and the target.

To define the current, let’s consider this plane that cuts across our electron beam. The current is just the total charge passing through this plane per unit time. To find that total charge, recall that each individual electron carries the same fundamental charge 𝑞. So then the total charge is just 𝑞 times the number of electrons. This means that to find the current, the rate at which charge flows past this plane per unit time, we would simply need to take 𝑞 times the number of electrons that pass through the plane per unit time.

Since all electrons in the beam follow roughly the same trajectory, the number of electrons passing through our particular plane in a given interval of time will be the same as the number of electrons passing through any other plane that cuts across the beam in the same interval of time. But this includes the plane that cuts across the beam right in front of the hot cathode. But we know the number of electrons passing through that plane per unit time. It’s just the rate of thermionic emission in the hot cathode.

So we can express the beam current as 𝑞, the charge on an electron, times the rate of thermionic emission at the cathode. This is a useful quantity because it also expresses the rate at which electrons strike the target. And the more electrons that strike the target per unit time, the more X-rays are produced per unit time.

If we recall that one definition of X-ray intensity is number of X-rays produced per unit time, we see that higher beam currents in the tube would result in the emission of more intense X-rays. And lower beam currents in the tube would result in the emission of less intense X-rays. So we can control the energy of the emitted X-rays by varying the tube voltage to control the beam energy. And we can control the intensity of the X-rays by varying the temperature of the hot cathode to adjust the rate of thermionic emission, which controls the beam current.

Let’s now talk about the target where these X-rays are actually produced. The target in a Coolidge X-ray tube is simply a piece of metal held at a positive voltage relative to the hot cathode. It turns out that the direction of the produced X-rays depends on the orientation of the target. So the target is usually tilted relative to the beam of electrons so that the X-rays will properly exit the tube. At any rate, electrons from the beam of electrons strike the target and produce X-rays.

There are two primary mechanisms that are responsible for X-ray production. The first mechanism is due to the free electrons in the beam slowing down inside the target. The second mechanism is due to the electron beam causing the electrons already in the target to change energy levels.

The X-rays produced by the electrons from the beam slowing down are known as Bremsstrahlung, from the German words for breaking and radiation. As an electron from the beam moves through the metal, its direction changes due to the attractive force between the negatively charged electrons and the positively charged metal nuclei. This process also causes the electrons to slow down, which reduces their kinetic energy.

Since electrons are charged particles, the energy they lose when slowing down is carried away by electromagnetic radiation, the Bremsstrahlung. Since each electron can slow down differently as it moves through the metal, the cumulative Bremsstrahlung for the entire electron beam will have a range of X-ray energies.

We can understand more about the distribution of X-ray energies in the Bremsstrahlung if we make a graph with X-ray energy on the horizontal axis and X-ray intensity, that is, the number of X-rays with a particular energy, on the vertical axis. The graph has a dome-like shape, which is characteristic of processes involving Bremsstrahlung. We call such a graph the Bremsstrahlung’s spectrum because it shows the distribution of X-rays in the Bremsstrahlung, among the various values for a particular quantity, in this case the energy.

Let’s observe some of the features of this spectrum. First, we can see that all of the X-rays in the Bremsstrahlung have energies less than some maximum energy. If the electron slowing down in the metal emits only a single X-ray, that X-ray will have exactly the energy the electron lost. The electron will lose the maximum possible energy by coming to a complete stop when its kinetic energy will be zero. In this case, the energy of a single emitted X-ray will be the energy of the electron before it came to a complete stop. But that energy is at most the energy the electron has when it enters the target, which is just the charge on the electron times the tube voltage, in other words the beam energy.

This is really just a statement of the conservation of energy. The energy of the electrons when they enter the target is 𝑞 times 𝑉 𝑇. And so the most energy they can lose to produce X-rays is 𝑞 times 𝑉 𝑇. The electrons don’t need to slow down all at once. Instead, they can slow down multiple times a little bit at a time and so release multiple lower-energy X-rays instead of a single higher-energy X-ray. This possibility gives rise to the characteristic shape of the Bremsstrahlung spectrum.

It is far more likely that the electrons will slow down in a small number of steps, emitting several medium-energy X-rays, than that they will slow down all in one go, emitting a single high-energy X-ray, or slow down in a great many small steps, emitting low-energy X-rays each time. So since the most likely X-ray to be produced will be of medium energy, the intensity will be maximum there.

Let’s now see what happens to the spectrum as we change the beam energy and the beam current. If we increase the tube voltage, the maximum energy of the X-rays will increase as will the energy of the most intense X-rays. The result will be that the entire spectrum stretches out, although there will still be a characteristic dome and there will be a maximum cutoff energy. If we decreased 𝑉 𝑇, then the spectrum would shrink instead of stretch. If we increase the beam current, there will be more electrons to produce X-rays. But those electrons would have the same energies as before. This would result in more X-rays being produced per unit time, so the intensity of the entire spectrum would increase.

However, the intensity maximum and intensity cutoff would still be at the same energies they were at before. Conversely, if we decreased the beam current, the overall intensity would decrease. But again, the maximum intensity and the intensity cutoff wouldn’t shift in energy.

The other process that produces X-rays is energy-level transitions from electrons already in the target. To understand this process, we’ve drawn a schematic diagram of an atom. In the center of the atom is the positively charged nucleus made of protons and neutrons. Each circle represents a possible energy for electrons in the atoms. And each blue dot on a particular circle represents one electron in the atom with that energy. Circles with smaller radii correspond to lower energies, while circles with larger radii correspond to higher energies.

Just as a matter of terminology, the energy levels represented by these circles are often called shells. The two innermost shells are often known as the K- and L-shells, respectively. In our diagram, the third shell that we’ve drawn is not necessarily the third shell out from the nucleus. Rather, there may be several shells between the L-shell and this higher shell. What’s important is that this shell is high enough energy relative to the K- and L-shells to produce X-rays.

It’s worth noting briefly that while this diagram is a reasonably accurate picture of the energy-level structure of an atom, it is not an accurate picture of the physical structure of an atom. This is an important point because, in a moment, we’ll talk about electrons moving between these shells. This is not a statement about electrons physically moving from one circle to another circle. Rather, it is strictly a statement about the electrons changing energy.

Okay, so let’s see how these transitions produce X-rays. An electron from the beam can enter an atom in the target and collide with one of the electrons in the K- or L-shells. If the electron from the beam gives the electron in the atom enough kinetic energy, it can break free of the attractive pull of the nucleus and be ejected from the atom. The electron from the beam will also leave the atom, leaving a space in the inner shell to be filled with another electron. When this occurs, an electron from the higher-energy shell can relax and fill the void in the lower-energy shell. The electron from the higher-energy shell now occupies a lower-energy shell, which means its energy has decreased.

Like with Bremsstrahlung, the energy lost by the electron is carried away as electromagnetic radiation. The energy of this radiation is exactly the difference in energy between the higher-energy shell where the electron started and the lower-energy shell at which the electron fell. If this difference in energy is sufficiently large, the electromagnetic radiation will be X-rays.

Although both of these processes involve electrons losing energy to produce X-rays, the electrons that produce Bremsstrahlung are free electrons, while the electrons involved in the energy-level transitions are bound electrons. This means that, unlike Bremsstrahlung, the possible energies for these emitted X-rays are discrete. This is because the possible energies for the bound electrons are discrete. And so the differences between them, that is, the possible energies for the emitted X-rays, are also discrete.

The spectrum of X-rays emitted by this process will show a series of bright monochromatic peaks corresponding to the different possible energy-level transitions. We see that the peaks are bright because their maximum intensity is much greater than the intensity of the surrounding spectrum. And we say that the peaks are monochromatic because they’re much narrower than they are tall, so they’re effectively located at a single energy. This reflects the discrete nature of the possible X-ray energies.

There is some broadness to the measured peaks just because of the quantum mechanical limitations on assigning and measuring the energy of processes that involve changes with time. Furthermore, each pair of energy levels involved in a transition would result in a different peak appearing in the spectrum. And since the energy levels of each type of atom are unique, the peaks appearing in the spectrum are a unique signature of the type of material used in the target.

Anyway, just like with Bremsstrahlung, if we reduce the electron beam current, the intensity of the spectrum will decrease, but the peaks will stay in the same positions. However, unlike the Bremsstrahlung, if we change the beam energy, the peaks do not move. This is because the energy of the peaks in this spectrum depends only on the energy of the higher-energy shell and the lower-energy shell involved in the transition. The only function of the incoming electron from the beam is to knock out the electron from the lower-energy shell to allow the transition to take place. So as long as there’s enough energy to dislodge the inner-shell electron, the actual beam energy doesn’t matter.

Okay, so X-rays are produced in the target either by Bremsstrahlung or by energy-level transitions. And the total spectrum of X-rays produced will just be the sum of the spectra from these two processes. We have the characteristic Bremsstrahlung dome, with its maximum energy at the beam energy. And interrupting this smooth spectrum are the characteristic peaks from the energy-level transitions. It’s worth noting that in order to compare the relative intensity of the characteristic peaks, given the total spectrum, we have to take into account that the Bremsstrahlung background is not constant.

All right, now that we’ve seen all the components and processes involved in a Coolidge X-ray tube, let’s review what we’ve learned in this lesson. In this video, we learned about the Coolidge X-ray tube, which produces X-rays from components located in vacuum inside of a glass bulb. We saw that X-ray production starts at the cathode. The cathode is connected to a high-current, low-voltage source that provides it with enough power to heat up to temperatures of several hundred to a few thousand kelvin. This elevated temperature gives some of the negatively charged electrons in the metal enough energy to break free of the attraction to the positively charged nuclei and escape into the vacuum. This process is called thermionic emission and in many ways is similar to water evaporating from a heated pot.

A large voltage is applied across the tube to accelerate the electrons from the cathode to the target. This acceleration causes the electrons to form a beam that strikes the target with an energy given by the charge on an electron times the tube voltage and a current given by the charge of an electron times the rate at which electrons are produced at the cathode.

The beam hitting the target produces X-rays through two distinct mechanisms. In the Bremsstrahlung mechanism, electrons from the beam emit X-rays as they slow down in the target and lose kinetic energy. The maximum energy of the X-rays produced this way is just the maximum kinetic energy loss of the electrons, which is the same as the energy of the beam. The second mechanism of X-ray production is energy-level transitions in the target atoms. In this mechanism, electrons from the beam collide with electrons in the inner K- or L-shells of the target atoms. This ejects those inner-shell electrons from the atom, leaving space for the outer-shell electrons to relax to the inner shells and emit X-rays.

The total spectrum of X-rays produced by the Coolidge X-ray tube is a combination of the spectra from these two processes. We have the characteristic Bremsstrahlung dome with its cutoff at the beam energy, as well as the discrete monochromatic peaks from the energy-level transitions that provide a unique signature of the type of material used in the target. Because the location of these peaks depends on the energy levels of the target atoms and not on the energy of the electron beam, if we vary the tube voltage, the location of these peaks will remain fixed, while the Bremsstrahlung spectrum narrows or widens. On the other hand, if we vary the beam current, we’ll change the total number of electrons available to produce any X-rays at all. And the intensity of the entire spectrum will either be enhanced or diminished.

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