X-ray Production: Bremsstrahlung & Characteristic

Q: What are the two types of x-rays produced in an x-ray tube?

Bremsstrahlung (braking radiation) and characteristic radiation. Bremsstrahlung is produced when high-speed electrons are deflected and decelerated by the tungsten nuclei, releasing photons across a continuous range of energies. Characteristic radiation is produced when an incident electron ejects an inner-shell electron and an outer-shell electron fills the vacancy, emitting a photon at a discrete energy specific to tungsten.

Q: What is the Duane-Hunt law?

The Duane-Hunt law sets the maximum photon energy in an x-ray beam. A photon cannot carry more energy than the kinetic energy of the electron that produced it, so the maximum photon energy in keV equals the tube potential in kV. Expressed as a minimum wavelength, it is approximately 1.24 divided by the tube potential in kV, in nanometers.

Q: Why does less than one percent of the electron energy become x-rays?

Most interactions between the incident electrons and the tungsten anode are small-angle collisions that transfer energy to the target as heat rather than producing a photon. For a tungsten anode at diagnostic tube potentials, only on the order of half a percent to one percent of the electron energy is converted to x-rays, which is why anode heat management is a central design constraint.

Q: At what tube potential does tungsten characteristic radiation appear?

Tungsten K-shell characteristic x-rays appear only when the tube potential exceeds the K-shell binding energy of about 69.5 kV. Below that, the incident electrons cannot eject a K-shell electron, so the beam is almost entirely bremsstrahlung plus low-energy L- and M-shell lines that are absorbed by filtration.

Q: What are the characteristic x-ray energies of tungsten?

The principal tungsten K characteristic lines are approximately 59.3 keV (K-alpha-1), 58.0 keV (K-alpha-2), and 67.2 keV (K-beta-1). These are discrete energies determined by the differences between tungsten's electron shell binding energies, and they sit below the 69.5 keV K-shell binding energy.

Q: Why is added filtration required on diagnostic x-ray tubes?

Filtration preferentially removes low-energy photons that would be absorbed in the patient and add dose without reaching the detector. Diagnostic tubes operated above 70 kVp generally require a total filtration of at least 2.5 mm aluminum equivalent per IEC and NCRP recommendations and most state codes, and U.S. federal rules enforce equivalent beam quality through minimum half-value-layer limits.

Q: How is beam quality measured in practice?

Beam quality is most often characterized by the half-value layer, the thickness of aluminum that reduces the beam's air kerma by half. Half-value layer increases with tube potential and filtration, and a minimum half-value layer at a given kVp is a regulatory requirement that a medical physicist verifies during equipment testing.

Introduction

Every diagnostic x-ray begins the same way: fast electrons strike a tungsten anode, and under one percent of their energy leaves as x-rays while the rest becomes heat. The photons that do emerge are a mixture of two physically distinct processes — bremsstrahlung and characteristic radiation — and understanding that mixture is the foundation of beam quality, patient dose, and image contrast.

X-ray production is the first thing taught in diagnostic physics and the last thing many people revisit, yet it quietly governs everything downstream. The shape of the emitted spectrum determines how much of the beam penetrates the patient, how much is absorbed as dose, and how much subject contrast reaches the image receptor. Beam quality, half-value layer, filtration rules, and even the reason x-ray tubes need rotating anodes all follow directly from how the photons are made. ¹

This article walks through what happens inside the tube: how bremsstrahlung and characteristic radiation arise, why the maximum photon energy is fixed by the tube potential, why tungsten's characteristic lines appear only above a threshold kilovoltage, and how the resulting spectrum is shaped by filtration before it reaches the patient. DRPS applies these fundamentals in routine equipment testing through its diagnostic radiography physics and medical physicist consulting services across Florida, Maryland, Virginia, Washington DC, California, and Nevada.

Topic Explanation

Inside the x-ray tube

An x-ray tube is, at its core, an energy converter. A heated filament (the cathode) releases electrons, which are accelerated across a vacuum by a potential difference — the tube potential, expressed in kilovolts (kV) — and slam into a tungsten target (the anode). The peak tube potential is the familiar kVp. When those electrons decelerate in the target, two things can happen, and both produce x-rays by entirely different mechanisms. ¹

Tungsten is the standard target material for several reasons: a high atomic number (Z = 74) that favors x-ray production, a very high melting point to survive the heat, and good thermal conductivity. The choice of tungsten is also why the characteristic lines sit where they do.

Bremsstrahlung: the continuous spectrum

Most x-rays in a diagnostic beam are bremsstrahlung, German for "braking radiation." When an incident electron passes near a tungsten nucleus, the nucleus's positive charge deflects and decelerates it. The electron loses kinetic energy, and that energy is emitted as a photon. ^{1, 4}

Because an electron can lose any fraction of its energy — a glancing deflection yields a low-energy photon, a near-direct hit can convert nearly all of it — bremsstrahlung forms a continuous spectrum from near zero up to a maximum. The maximum occurs when a single electron gives up all of its kinetic energy in one photon, which is the basis of the Duane-Hunt law discussed below. ¹

Characteristic radiation: the discrete lines

The second mechanism is characteristic radiation. If an incident electron carries enough energy, it can eject an inner-shell (for example, K-shell) electron from a tungsten atom, leaving a vacancy. An electron from a higher shell immediately drops down to fill it, and the energy difference between the two shells is emitted as a photon. ¹

Because shell binding energies are fixed properties of the element, these photons appear only at discrete energies characteristic of tungsten — hence the name. They show up as sharp spikes superimposed on the continuous bremsstrahlung background, but only once the tube potential is high enough to eject the inner-shell electron in the first place.

Key Technical Principles

Bremsstrahlung versus characteristic radiation

Property	Bremsstrahlung	Characteristic
Mechanism	Electron decelerated by the nucleus	Inner-shell vacancy filled by an outer electron
Spectrum	Continuous, from ~0 up to E_max	Discrete lines fixed by tungsten shell energies
Energy set by	Electron kinetic energy and deflection	Differences between tungsten shell binding energies
Threshold	None (produced at all kVp)	Only above the shell binding energy (K-shell ≈ 69.5 kV) ²
Share of diagnostic output	Majority of photons	A few discrete peaks, significant mainly above ~80 kVp
Depends on	Tube potential, tube current, target Z, filtration	Target element only (tungsten)

The Duane-Hunt law: the maximum photon energy

A photon can carry no more energy than the electron that created it. Since each electron is accelerated through the tube potential $V$ , its kinetic energy is $e V$ , and the maximum photon energy is:

E_{m a x} = e V_{tube} \Rightarrow E_{m a x} (keV) = V_{tube} (kV)

Expressed as the shortest wavelength in the beam (the Duane-Hunt limit), using $h c = 1239.84 eV\cdotnm$ from the fundamental constants: ⁵

λ_{m i n} = \frac{h c}{e V _{tube}} = \frac{1239.84 eV\cdotnm}{e V _{tube}} \approx \frac{1.24}{V _{tube} ( kV )} nm

At 100 kVp, the maximum photon energy is exactly 100 keV and the minimum wavelength is about 0.0124 nm (12.4 pm). No photon in a 100 kVp beam can exceed 100 keV — a hard ceiling set purely by the tube potential.

Kramers' law: the shape of the unfiltered spectrum

The idealized, unfiltered bremsstrahlung intensity per unit photon energy is described by Kramers' law, which is linear in energy and falls to zero at the maximum:

I (E) \propto Z (E_{m a x} - E)

where $Z$ is the target atomic number. The true emitted spectrum is close to this linear form but not exact — rigorous treatments use the Bethe-Heitler and NIST bremsstrahlung cross sections rather than Kramers' approximation. ⁴ Critically, a real clinical spectrum never looks linear at the low-energy end, because filtration (next section) strips away the low-energy photons before the beam leaves the tube. The useful insight from Kramers is qualitative: more bremsstrahlung is produced at low photon energies, higher target Z yields more x-rays, and the spectrum terminates sharply at $E_{m a x}$ . ^{1, 4}

Tungsten's characteristic energies

The principal tungsten K characteristic lines are fixed by the element: ²

Line	Transition	Energy
K-alpha-2	K ← L2	≈ 58.0 keV
K-alpha-1	K ← L3	≈ 59.3 keV
K-beta-1	K ← M3	≈ 67.2 keV
K-shell binding	(ionization)	≈ 69.5 keV

Note the subtlety that trips people up: the K characteristic photons (58–67 keV) are lower in energy than the 69.5 keV K-shell binding energy. ^{2, 3} That is because each line is the difference between two shell binding energies, whereas 69.5 keV is the energy needed to eject the K-shell electron entirely. This is exactly why K-characteristic radiation requires a tube potential above about 69.5 kVp: the incident electron must first supply enough energy to create the K-shell vacancy. Below that threshold the beam is essentially pure bremsstrahlung (plus low-energy L/M lines around 8–12 keV that filtration removes).

Production efficiency: why most of it is heat

X-ray production is strikingly inefficient. A useful rule of thumb estimates the efficiency $η$ as proportional to the target atomic number and the tube potential:

η \approx k Z V, k \approx 1 \times 1 0^{- 9} V^{- 1}

For tungsten ( $Z = 74$ ) at 100 kVp ( $V = 1.0 \times 1 0^{5} V$ ):

η \approx (1 \times 1 0^{- 9}) (74) (1.0 \times 1 0^{5}) \approx 7.4 \times 1 0^{- 3} \approx 0.7%

Heat fraction = 1 - η \approx 99%

So under one percent of the electron-beam energy leaves as x-rays, and more than 99% is dissipated as heat. ¹ (The coefficient $k$ is an approximate textbook value, 0.9–1.1 × 10⁻⁹, and the linear form is a diagnostic-range approximation only; for a rigorous figure the NIST ESTAR "radiation yield" gives the exact fraction of electron energy radiated as bremsstrahlung in tungsten. ⁴) This single fact drives anode design: rotating anodes, heat-unit limits, and cooling schedules all exist to manage the ~99% that becomes heat. See x-ray tube heat loading and thermal management for the downstream engineering.

Clinical Impact

The emitted spectrum is not an academic curiosity — it is what the patient and the image receptor actually see.

Low-energy photons are pure dose. Photons at the very low end of the bremsstrahlung spectrum are almost entirely absorbed within the patient; they never reach the detector, so they contribute dose without contributing to the image. Removing them with filtration is one of the most basic dose-reduction tools in radiography. ⁷

Beam quality controls penetration and contrast. The "hardness" of the beam — its penetrating ability — is summarized by the half-value layer (HVL), the thickness of aluminum that halves the beam's air kerma. A higher kVp and heavier filtration both raise the HVL and the mean photon energy. As a practical rule of thumb, the mean energy of a filtered diagnostic beam is roughly one-third to one-half of the kVp, though the exact value depends on kVp, filtration, and generator ripple and is best obtained from a computed spectrum. ¹ Raising kVp increases penetration and lowers patient dose for a given receptor exposure, but it also reduces subject contrast — the fundamental trade-off behind technique selection.

Characteristic lines shift the spectrum. Above roughly 80 kVp, tungsten's K-characteristic lines add a cluster of photons around 58–69 keV, which is well-matched to imaging thicker body parts and contributes usefully to the beam. Below the K-shell threshold, those lines are simply absent.

Generator waveform matters. A constant-potential generator keeps electrons near the peak energy throughout the exposure, producing a harder, more efficient beam than a heavily rippled supply at the same nominal kVp. See x-ray generator waveform, ripple, and power QC.

Practical Optimization Tips

The physics of production turns into a handful of concrete QC and optimization practices.

1. Verify filtration and beam quality

Confirm that total filtration meets the applicable requirement and that the measured HVL at each tested kVp meets or exceeds the regulatory minimum. A beam that is too soft (low HVL) delivers unnecessary skin dose. See half-value layer and kVp radiography QC.

2. Check kVp accuracy and reproducibility

Because the maximum photon energy and the position of the characteristic lines depend on tube potential, kVp accuracy directly affects beam quality and the appearance of the characteristic peaks. A tube reading 5–10 kV off will produce the wrong spectrum. See kVp accuracy and reproducibility QC.

3. Use filtration deliberately, not just to pass inspection

Added aluminum (and, for some applications, copper) shapes the spectrum. Spectral shaping is a dose-optimization tool, not merely a compliance box. See x-ray beam filtration and spectral shaping.

4. Respect the heat

Because ~99% of the input is heat, honor anode heat-unit limits and cooling intervals, especially for high-output work. Thermal stress is a leading cause of tube failure.

5. Remember the anode heel effect

The angled anode that makes x-ray production practical also causes the heel effect — a reduction in intensity toward the anode side of the field — which follows from the geometry of where the photons are produced in the target. See the anode heel effect in radiography.

Regulatory Considerations

Diagnostic x-ray equipment is regulated under a federal performance standard plus state rules — not by the NRC, which governs radioactive material. Several frameworks bear on x-ray production and beam quality.

21 CFR 1020.30 — the U.S. federal performance standard for diagnostic x-ray systems. Rather than mandating a filter thickness directly, it enforces beam quality through minimum half-value-layer requirements tabulated by tube potential; a tube must produce an HVL at or above the specified value for its operating kVp. ⁶
IEC 60601-1-3 and NCRP recommendations (e.g., NCRP Report No. 102) — these establish the familiar total-filtration guidance: generally at least 2.5 mm aluminum equivalent for tubes operated above 70 kVp, and at least 1.5 mm Al for the 50–70 kVp range. Most U.S. state radiation-control codes adopt this filtration requirement. ^{7, 8} It is a common error to attribute the literal "2.5 mm Al" figure to 21 CFR 1020.30; the federal rule reaches the same goal indirectly via the HVL limits.
State radiation-control programs — because diagnostic x-ray machines are regulated by states (with the FDA setting the equipment performance standard), facilities must register their units and meet state testing and filtration requirements. Of the states DRPS serves, X-ray machine registration and inspection are handled at the state level across the board.

A medical physicist verifies these requirements during acceptance and routine testing: measuring HVL to confirm beam quality, checking kVp accuracy, and confirming total filtration. A beam that fails the minimum HVL is a direct patient-dose concern, not a paperwork detail.

Frequently Asked Questions (FAQs)

What are the two types of x-rays produced in an x-ray tube?

Bremsstrahlung and characteristic radiation. Bremsstrahlung is produced when electrons are decelerated by tungsten nuclei, giving a continuous range of photon energies. Characteristic radiation is produced when an inner-shell electron is ejected and an outer electron fills the vacancy, emitting a photon at a discrete energy specific to tungsten.

What is the Duane-Hunt law?

It sets the maximum photon energy in the beam. Because a photon cannot carry more energy than the electron that made it, the maximum photon energy in keV equals the tube potential in kV, and the minimum wavelength is approximately 1.24 divided by the kV, in nanometers.

Why does less than one percent of the electron energy become x-rays?

Most electron interactions in the target transfer energy as heat rather than producing a photon. For tungsten at diagnostic potentials, only about half a percent to one percent of the energy becomes x-rays, which is why anode heat management is a central design constraint.

At what tube potential does tungsten characteristic radiation appear?

Tungsten K-characteristic x-rays appear only above the K-shell binding energy of about 69.5 kV. Below that, the incident electrons cannot create a K-shell vacancy, so the beam is essentially bremsstrahlung plus absorbed low-energy lines.

What are the characteristic x-ray energies of tungsten?

The principal K lines are approximately 59.3 keV (K-alpha-1), 58.0 keV (K-alpha-2), and 67.2 keV (K-beta-1). These discrete energies are set by differences between tungsten's shell binding energies and sit below the 69.5 keV K-shell binding energy.

Why is added filtration required on diagnostic x-ray tubes?

Filtration removes low-energy photons that would be absorbed in the patient and add dose without reaching the detector. Tubes above 70 kVp generally require at least 2.5 mm aluminum equivalent total filtration per IEC and NCRP recommendations and state codes, with federal rules enforcing equivalent beam quality through HVL limits.

How is beam quality measured in practice?

Most often by the half-value layer — the aluminum thickness that halves the beam's air kerma. HVL rises with kVp and filtration, and a minimum HVL at each kVp is a regulatory requirement that a physicist verifies during testing.

Key Takeaways

Two mechanisms make every x-ray beam: continuous bremsstrahlung from decelerated electrons, and discrete characteristic lines from inner-shell transitions in tungsten.
The Duane-Hunt law caps the spectrum: maximum photon energy in keV equals the tube potential in kV; nothing in the beam exceeds it.
Tungsten K-lines (≈58–67 keV) appear only above ≈69.5 kVp, because the incident electron must first eject a K-shell electron.
Production is ~1% efficient; more than 99% of the electron energy becomes heat, which is why anode and cooling design dominate tube engineering.
Filtration shapes the clinical spectrum by removing low-energy, dose-only photons — generally ≥2.5 mm Al above 70 kVp per IEC/NCRP and state codes, with 21 CFR 1020.30 enforcing beam quality via HVL.
Beam quality (HVL) ties it together: it is the measurable summary of the spectrum that a physicist verifies to protect both image quality and patient dose.

Conclusion

The diagnostic x-ray spectrum is not an arbitrary shape — it is the direct, predictable result of how electrons interact with a tungsten anode. Bremsstrahlung sets the continuous backbone and its maximum energy; the characteristic lines add discrete peaks once the tube potential clears tungsten's K-shell binding energy; and filtration carves away the low-energy photons that would only add dose. Every number a physicist measures at the console — kVp, HVL, filtration, output — is a window onto that production physics.

Understanding where the beam comes from is what lets a facility optimize technique intelligently: trading kVp against contrast, using filtration to cut dose, and keeping beam quality within the limits that protect patients. The console settings are the easy part; the spectrum they produce is the physics that actually reaches the patient.

How DRPS Can Help

Diagnostic Radiation Physics Services performs the equipment testing that turns x-ray production physics into documented compliance and dose optimization. This includes HVL and beam-quality measurement, kVp accuracy and reproducibility testing, filtration verification, output and linearity checks, and technique-optimization support — all performed by board-certified medical physicists through diagnostic radiography physics and medical physicist consulting.

DRPS supports facilities across our service locations, including Florida, Maryland, Virginia, Washington DC, California, Nevada, New York, Pennsylvania, New Jersey, and Delaware.

Good imaging starts with a well-characterized beam — and a well-characterized beam starts with understanding how it is made.

Related Resources

References

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National Institute of Standards and Technology. X-Ray Transition Energies Database (SRD 128): Tungsten (Z = 74). physics.nist.gov
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