X-Ray Sources

Andreas Eckmüller, winter semester 2021/22

X-ray sources are technical systems that produce X-rays for subsequent use in areas such as medical technology, materials science, and biophysics. Computed tomography (CT) is one of the most important applications. The underlying physical principle of X-ray generation is the deceleration of charge carriers (such as electrons) or their deflection from their original path. For instance, in electron-impact X-ray sources, the radiation is generated by the deceleration of fast electrons entering a solid metal anode. This interaction then causes bremsstrahlung (continuous radiation spectrum), which makes up most of the usable X-rays ^[1].  

X-Ray Tubes

Electrons are mostly used for the generation of X-rays, because of the comparatively easy setup of X-ray tubes. 

Working Principle

As schematically depicted in Figure 1 an X-ray tube consists of an evacuated chamber or tube with a heated cathode on the one and an anode, serving as an X-ray target on the other side. Tungsten is a widely used material for both cathode and anode due to its high melting temperature, thermal conductivity and its X-ray generation efficiency ^[2]. When the cathode wire is heated to 2400 K, the thermionic effect causes free electrons, which are accelerated towards the target due to an applied high voltage . This process can be described via

$//<![CDATA[ \begin{array}{l}E_{electron}=e∆U=\frac{1}{2} m_e v²\end{array} //]]>$,

where $//<![CDATA[ \begin{array}{l}E_{electron}\end{array} //]]>$ [eV] is the energy of an electron reaching the target and $//<![CDATA[ \begin{array}{l}e\end{array} //]]>$ is the electric charge of an electron, equal to $//<![CDATA[ \begin{array}{l}1,6×10^{19}\end{array} //]]>$ C. The mass of an electron  is $//<![CDATA[ \begin{array}{l}9.1095×10^{-31}\end{array} //]]>$ kg and $//<![CDATA[ \begin{array}{l}v\end{array} //]]>$ is its velocity.  Typical acceleration voltage values for medical diagnostics lie between 25-150 kV and for non-destructive material testing between 10-500 kV ^{[2] [3]}. Using electron optics and filters, the electron beam is shaped and directed onto a small focal spot on the anode. X-rays emerge from the deceleration of the fast electrons following their entry into the target material of the anode.

The entire spectrum of X-rays contains continuous and characteristic components. The continuous components are caused by the deceleration of electrons in the positive electric field of the atomic nuclei of the target material, where the energy released is absorbed by the atomic nucleus and immediately re-emitted. In contrast, the characteristic components arise from collisions with shell electrons close to the nucleus. These interactions happen in a multi-process deceleration cascade ^{[1] [4]}.

The X-ray energy depends on the velocity or the impulse of the charge carrier ^[1]. The generated X-rays are characterized by their energy distribution (also called quality) and their intensity (flux).

It is possible, that the entire energy of an electron is transferred to a single photon. This limit defines the maximum energy of the X-ray radiation (Js, Planck's constant)

$//<![CDATA[ \begin{array}{l}e∆U=hv_{max}=E_{X,max}\end{array} //]]>$.

The highest X-ray energy present in the X-ray spectrum determines the penetrating power of the X-ray beam into matter. The limit  corresponds to the minimum wavelength ^[1]

$//<![CDATA[ \begin{array}{l}λ_{min}=\frac{hc}{e∆U}=\frac{1.24 nm}{∆U/kV}\end{array} //]]>$.

The intensity of an X-ray beam is a measure of the amount of radiation energy flowing per unit of time. ^[5].

Targets

The target can be made from different materials such as tungsten, molybdenum, copper or silver, resulting in different X-ray spectra at different photon energies ^[5]. For example, characteristic radiation happens just below 70 kV for tungsten, and just below 20 kV for molybdenum. Some manufacturers offer multi-metal targets that are fitted on one head, so that the most suitable X-ray spectrum can be chosen depending on the object under test ^[2].

The efficiency of the X-ray tube is only around 1 %, i.e. 99 % of the energy is converted into heat and 1 % into X-rays ^[4]. This limits the possible energy output and requires active cooling measures. In some cases, oil circulates inside the anode or a high mass copper block as carrier for the actual target material is used in order to conduct the heat towards a cooling medium. Heat generation makes it difficult to attain higher X-ray power. A too high energy density of the focused electron beam may lead to the destruction of the target due to localized melting at the focal spot ^[2].

There are various approaches to maximize the X-ray intensity while minimizing local melting. Line focus X-ray tubes for instance, as the name suggests, deploy a linear instead of a round focal spot, to spread the area of heat absorption, hence making higher X-ray intensities possible. Also, the focal spot size is a property of interest that needs to be as small as possible for highest resolution CT images. However, a small focal spot leads to high energy densities and, thus to high thermal stress^[6].

Nano focus spots of less than or around 1 µm diameter are achievable with X-ray tubes using acceleration voltages higher than 250 kV. For voltages above 250 kV, the heat dissipated at the target gets that large that it may no longer be concentrated in a micrometre spot: such tubes are then called micro-focus sources with spot diameters ranging typically from 30 to 1000 µm. Today X-ray tube voltages are limited to 450 kV for commercial standard tubes, while 800 kV systems are under test ^[5].

Commercially available target designs include transmission targets, reflection targets, rotating targets, and liquid metal jet targets, which will be explained in the following.

Transmission Targets

X-ray tubes can be equipped with a transmission target that generates X-rays collinearly with the electron beam within the vacuum chamber [2]. X-rays are emitted in the same direction as the impacting electrons and the shape of the X-ray focal spot exactly matches the electron beam spot, while it becomes elliptic for reflecting targets ^[7].

Transmission targets are thin material components that allow the electrons to pass through their entire body. The thin layer of target material cannot resist high temperatures and are more challenging to cool, thus limiting the accessible X-ray intensities. Transmitting targets are only used for lower power X-ray sources ^{[5] [2]}.

Reflection Targets

Most X-ray sources are equipped with water cooled massive reflection targets ^[5]. The size and shape of the effective focal spot is determined by the inclination angle relative to the electron beam. Typical nominal powers of X-ray sources equipped with reflection targets are 60-450 W ^[2].

Rotating Targets

Rotating reflection targets allow to increase the electron flux without damaging the target, because the heat is dissipated over a larger, moving area. The anode target material is rotated around the central axis and therefore, new, and cooler anode material is constantly rotated into position at the focal spot and exposed to the high-energy electron beam. Rotating targets are commonly used in the medical field and have been introduced in the industrial CT field primarily for the higher power systems ^[1][5][2]. Figure 2 shows a typical rotating target X-ray tube.

The rotation frequency is very high, causing mechanical parts of the tube to be subjected to G-forces of up to 40 G. A significant part of the heat (about 30 %) is conducted via the bearing of the rotating anode. The rest of the heat is transferred via radiation to the housing of the X-ray tube ^[1].

The Straton® X-ray tube is a rotating envelope tube utilizing efficient convective target cooling exclusively rather than radiation. With rotating envelope tubes, the entire vacuum tube rotates with respect to the anode axis, versus rotating anode tubes, in which the target disk rotates inside a stationary vacuum tube. It is demonstrated that this cooling principle makes large heat storage capacities of the anode disk obsolete ^[8].

Liquid Metal Jet Targets

Another solution offered commercially to meet small focal spot diameter requirements is the use of liquid metal jet targets. Current generation liquid metal jet targets use gallium- or indium-based metal alloys that melt close to room temperature and have approximate X-ray emission characteristics of some regular solid material anodes. The heat is dissipated over a larger, moving area while continuously renewing the liquid material exposed to the high-energy electron beam. The potential for increasing power over focal spot size by approximately three orders of magnitude has been reported ^[2]. Liquid metal jet X-ray tubes provide very small focal spots but their photon flux and also the photon energy are limited by the tolerable heat load imposed at the small electron focal spots of the target, thus they are still more suited for lower power systems ^[6].

Particle Accelerators

Alternatively, Particle accelerators can be used to produce X-rays. A particle accelerator is a device or installation in which electrically charged particles such as electrons are accelerated to high speeds by electric fields. There are linear accelerators (LINAC) and circular accelerators like synchrotrons.

Linear Accelerators

Linear accelerators (LINAC) greatly increase the velocity of electrons or other charged particles by subjecting them to a series of oscillating electric potentials (radiofrequency waves) along a linear beamline and lead the electrons against a target to produce X-rays as depicted in Figure 3. Shorter linear accelerators (some meters long) are used for medical devices e.g., for radiotherapy. Thanks to their high energy, linear accelerators are also used for industrial nondestructive testing or dimensional CT measurements of larger and highly absorbing parts (e.g. meter thick blocks of concrete) ^{[5] [9]}.

Compared to the various types of ring accelerators, a linear accelerator is technically simpler and avoids energy losses of the particles through synchrotron radiation due to the straight particle path. On the other hand, it requires considerably more accelerating elements because the particles pass through each element only once and not repeatedly. This means that construction lengths of many kilometers are required for very high particle energies ^[10].

Synchrotrons

X-rays can also be generated by the acceleration of electrons in synchrotrons. Synchrotrons are large particle accelerator facilities (like SOLEIL in France), in which electrons can be accelerated to relativistic velocities by circularly arranged undulator magnets. Synchrotron radiation is produced when a moving electron changes its direction, resulting in the emission of a photon like schematically shown in Figure 4. When the electron is moving fast enough, the emitted photon is at X-ray wavelengths ^[2].

This radiation is  monochromatic, of high brilliance, coherence, and intensity, low emittance, and wide tunability in its wavelength ^{[7] [9]}. Synchrotrons are applied in industrial CT and material testing. Monochromatized synchrotron X-rays provide excellent measurement accuracy and avoid beam hardening ^[5]. The brilliance of radiation produced with synchrotrons is around 10 orders of magnitude higher than with x-ray tubes, but the use of one of the few existing synchrotron facilities is very expensive ^[6].

Over the past decades, compact synchrotron X-ray sources, based on inverse Compton scattering, have been developed to fill the gap between conventional X-ray tubes and synchrotron facilities. These so-called Inverse Compton Sources (ICSs) provide a tuneable, quasi-monochromatic X-ray beam in a laboratory setting with reduced spatial and financial requirements ^[11].

X-Ray Lasers

An X-ray laser is a device that converts the working principle of a LASER (light amplification by stimulated emission of radiation) onto electromagnetic radiation in the near X-ray or extreme ultraviolet region. It uses amplified stimulated emission (ASE) and self-amplified spontaneous emission (SASE) to generate or amplify X-rays ^[12].

X-ray lasers usually operate without mirrors, because of the high gain in the lasing medium and problems associated with construction of mirrors that could reflect X-rays. The beam of X-rays is generated by a single pass through the gain medium ^[13].

On the one hand, a hot, highly ionised gas or plasma can be used as gain medium in a plasma laser. This medium contains large densities of multiply charged ions. It can be obtained by intense electrical discharges in a gas or by focusing an intense laser on a solid or gaseous target ^[14]. The PALS (Prague Asterix Laser System) in the Czech Republic and the COMET (Compact Multipulse Terrawatt) laser at LLNL (Lawrence Livermore National Laboratory) in the United States are examples of plasma laser X-ray sources.

An X-Ray Free-Electron Laser (XFEL) on the other hand uses a beam of relativistic electrons generated by a particle accelerator. This beam is fed into an undulator (e.g. 30 m long), in which the electrons emit X-rays similar to synchrotron radiation, while changing direction frequently ^[14]. The radiation moves faster than the electron bunch and interacts with electrons farther up and exponential amplification occurs through self-amplified spontaneous emission (SASE) so that the X-rays reach very high energies ^[12]. The electron beam is guided into an electron trap at the end of the undulator. Figure 5 shows a schematic drawing of this working principle.

Figure 5: Principle Sketch of a X-ray free electron laser (XFEL) Source: Andreas Eckmüller

Examples of XFELs include FLASH (Freie-Elektronen-Laser in Hamburg) and European-XFEL at DESY (Deutsches Elektronen-Synchrotron) in Germany and SLAC (Stanford Linear Accelerator Center) in USA.

The XFEL sources generate spatially coherent X-rays with characteristics similar to the light from conventional optical lasers comprising ultrashort time duration, and an additional increase of 6–8 orders of magnitude on the peak brilliance compared to synchrotrons ^[12].

Other Sources

X-ray bremsstrahlung arises principally and mostly undesirably in various technical devices such as electron microscopes, electron beam welders and in the area of the power stages of large radar systems, where electron tubes such as the magnetron or amplitron are used to generate large amounts of non-ionising radiation. X-rays were also produced in the first colour television receivers using cathode ray tubes (1960s) because the colour picture tubes required higher anode voltages than single-colour cathode ray tubes ^[15].

On earth, X-rays are produced at low intensity during absorption of other types of radiation originating from radioactive decay and cosmic radiation. X-rays produced on other celestial bodies do not reach the earth's surface because they are shielded by the atmosphere. They are studied with X-ray satellites such as Chandra and XMM-Newton.

X-rays are also produced in lightning and occur together with terrestrial gamma-ray bursts. The underlying mechanism is the acceleration of electrons in the electric field of a flash and the subsequent production of photons by bremsstrahlung. This produces photons with energies from a few keV to a few MeV ^[16].

Moreover, characteristic X-rays are produced during the deceleration of fast, positively charged particles in matter. This is used in particle-induced X-ray emission or proton-induced X-ray emission (PIXE) for chemical analysis ^[17].

Literature

1. Buzug, Thorsten. Computed Tomography. Springer Berlin Heidelberg, Berlin, Heidelberg (2008), p. 15-31.

2. Carmignato, Simone, Dewulf, Wim, and Leach, Richard. Industrial X-Ray Computed Tomography. Springer International Publishing, Cham (2018), p. 26-94.

3. Große, C. U.: Durchstrahlungsprüfung (Radiographie). In: Grundlagen der Zerstörungsfreien Prüfung. Arbeitsblätter im Rahmen der Vorlesung. “Durchstrahlungsprüfung (Radiographie).” Grundlagen der Zerstörungsfreien Prüfung. Arbeitsblätter im Rahmen der Vorlesung Vol. 2020 (2020), p. 120–131.

4. Schiebold, Karlheinz. Zerstörungsfreie Werkstoffprüfung - Durchstrahlungsprüfung. Springer Berlin Heidelberg, Berlin, Heidelberg (2015), p. 6-196.

5. Kruth, J. P., Bartscher, M., Carmignato, S., Schmitt, R., Chiffre, L. de, and Weckenmann, A. “Computed tomography for dimensional metrology.” CIRP Annals Vol. 60 No. 2 (2011), p. 821–842. DOI 10.1016/j.cirp.2011.05.006.

6. Bartzsch, Stefan and Oelfke, Uwe. “Line focus x-ray tubes-a new concept to produce high brilliance x-rays.” Physics in medicine and biology Vol. 62 No. 22 (2017), p. 8600–8615. DOI 10.1088/1361-6560/aa910b.

7. Hanke, Randolf, Fuchs, Theobald, and Uhlmann, Norman. “X-ray based methods for non-destructive testing and material characterization.” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment Vol. 591 No. 1 (2008), p. 14–18. DOI 10.1016/j.nima.2008.03.016.

8. Schardt, Peter, Deuringer, Josef, Freudenberger, Jörg, Hell, Erich, Knüpfer, Wolfgang, Mattern, Detlef, and Schild, Markus. “New x-ray tube performance in computed tomography by introducing the rotating envelope tube technology.” Medical physics Vol. 31 No. 9 (2004), p. 2699–2706. DOI 10.1118/1.1783552.

9. Chiffre, L. de, Carmignato, S., Kruth, J.-P., Schmitt, R., and Weckenmann, A. “Industrial applications of computed tomography.” CIRP Annals Vol. 63 No. 2 (2014), p. 655–677. DOI 10.1016/j.cirp.2014.05.011.

10. Samy Hanna. RF Linear Accelerators for Medical and Industrial Applications. Artech House (2012).

11. Kulpe, Stephanie, Dierolf, Martin, Günther, Benedikt, Brantl, Johannes, Busse, Madleen, Achterhold, Klaus, Pfeiffer, Franz, and Pfeiffer, Daniela. “Spectroscopic imaging at compact inverse Compton X-ray sources.” Physica medica PM an international journal devoted to the applications of physics to medicine and biology official journal of the Italian Association of Biomedical Physics (AIFB) Vol. 79 (2020), p. 137–144. DOI 10.1016/j.ejmp.2020.11.015.

12. Canova, Federico and Poletto, Luca. Optical Technologies for Extreme-Ultraviolet and Soft X-ray Coherent Sources. Springer Berlin Heidelberg, Berlin, Heidelberg (2015), p. 1-15.

13. Schmüser, Peter, Dohlus, Martin, Rossbach, Jörg, and Behrens, Christopher. Free-Electron Lasers in the Ultraviolet and X-Ray Regime. Springer International Publishing, Cham (2014), p. 1-163.

14. Sebban, Stéphane, Gautier, Julien, Ros, David, and Zeitoun, Philippe. X-Ray Lasers 2012. Springer International Publishing, Cham (2014), p. 175-179.

15. Braestrup, Carl B. and Richard T. Mooney. “X-Ray Emission from Television Sets.” Science, vol. 130, No. 3382 (1959), p. 1071–1074.

16. Köhn, Christoph and Ebert, Ute. “Angular distribution of Bremsstrahlung photons and of positrons for calculations of terrestrial gamma-ray flashes and positron beams.” Atmospheric Research 135-136 (2014), p. 432–465. DOI 10.1016/j.atmosres.2013.03.012.

17. Paul, Helmut and Muhr, Johannes. “Review of experimental cross sections for K-shell ionization by light ions.” Physics Reports Vol. 135 No. 2 (1986), p. 47–97. DOI 10.1016/0370-1573(86)90149-3