KAHIBARO
Table of Contents
What bremsstrahlung is
Bremsstrahlung is electromagnetic radiation produced when a charged particle, usually an electron, is accelerated or decelerated by the electric field of another particle, usually an atomic nucleus. The word comes from German and means "braking radiation". In matter, this happens when a fast electron passes near a nucleus and its path bends. Because the electron changes velocity, it emits a photon.
This is one of the main ways energetic electrons lose energy in matter. It becomes especially important for high electron energies and for materials with high atomic number, such as lead.
A charged particle that changes its velocity emits radiation. In matter, fast electrons radiate bremsstrahlung mainly when deflected by the Coulomb field of nuclei.
Why electrons produce it so easily
Electrons are very light compared with heavy charged particles such as alpha particles or protons. Because they have small mass, the electric field of a nucleus can change their motion strongly. A strong acceleration means stronger radiation emission.
Heavy charged particles can also emit bremsstrahlung, but the effect is much smaller. The radiative loss is roughly much less important for heavier particles because they are harder to deflect.
Physical picture inside matter
Imagine an electron entering a solid. It passes close to many atoms. Sometimes it interacts with atomic electrons and loses energy through collisions. Sometimes it passes near a nucleus and its path curves. During this curved motion, part of its energy is emitted as an X ray or gamma ray photon.
The electron does not need to hit the nucleus. A close pass is enough. The closer the pass, the stronger the deflection, and the more energetic the emitted photon can be.
Energy of the emitted photon
The photon carries away part of the electron's kinetic energy. If the electron initially has energy $E_i$ and ends with energy $E_f$, then the emitted photon energy is
$$
h\nu = E_i - E_f
$$
where $h$ is Planck's constant and $\nu$ is the photon frequency.
A single interaction can produce a low energy photon or a high energy photon, depending on how much energy the electron loses in that encounter. Because many different energy losses are possible, bremsstrahlung produces a continuous spectrum of photon energies.
Bremsstrahlung gives a continuous photon spectrum because the electron can lose any fraction of its kinetic energy in a given interaction.
Continuous spectrum
Unlike atomic line radiation, which appears at specific photon energies, bremsstrahlung forms a broad continuous distribution. In an X ray tube, electrons strike a metal target and generate both characteristic X rays and bremsstrahlung. The bremsstrahlung part fills a continuous range of energies up to a maximum value set by the electron's initial energy.
If an electron has kinetic energy $K$, then the largest possible photon energy is
$$
E_{\gamma,\max} = K
$$
This maximum would occur if the electron gave essentially all its kinetic energy to one photon in a single event.
Dependence on atomic number and electron energy
Bremsstrahlung becomes stronger in materials with large atomic number $Z$. A nucleus with larger charge produces a stronger electric field, which causes stronger electron acceleration and more radiation.
It also becomes more important as electron energy increases. At low energies, collisional losses usually dominate. At higher energies, radiative losses become increasingly important.
A simple qualitative summary is shown below.
| Factor | Effect on bremsstrahlung |
|---|---|
| Higher electron energy | Increases importance |
| Higher atomic number $Z$ | Increases production |
| Heavier charged particle mass | Decreases production strongly |
In many practical cases, the radiative stopping power increases approximately in proportion to electron energy and roughly with $Z^2$ for the target nucleus in simplified descriptions. Exact behavior is more complicated and depends on material and energy.
Competition with collisional losses
When electrons move through matter, they lose energy mainly by two mechanisms. One is collisional loss, due to ionization and excitation of atoms. The other is radiative loss, mainly bremsstrahlung.
At low electron energies, collisional loss is usually the main process. At high energies, bremsstrahlung can dominate, especially in dense high $Z$ materials.
This is why shielding for high energy electrons must also consider the X rays they produce. Stopping the electron is not the whole problem, because bremsstrahlung photons can travel farther.
For energetic electrons in high $Z$ materials, stopping the electron can generate penetrating bremsstrahlung photons. Shielding must account for both electrons and the photons they produce.
Bremsstrahlung in X ray production
A common example is the X ray tube. Electrons are accelerated through a voltage and then strike a metal target. As they slow down in the target, they emit bremsstrahlung X rays. If the accelerating voltage is $V$, then the maximum photon energy is
$$
E_{\gamma,\max} = eV
$$
where $e$ is the elementary charge.
This gives the short wavelength limit
$$
\lambda_{\min} = \frac{hc}{eV}
$$
These formulas explain why higher tube voltage produces more energetic X rays.
Radiation yield
Not all the electron's energy becomes bremsstrahlung. Often only a fraction is radiated, while the rest goes into collisional processes and heating. The fraction converted into bremsstrahlung is called the radiation yield, and it increases with both electron energy and target atomic number.
In low $Z$ materials, such as plastic, bremsstrahlung production is relatively small. In high $Z$ materials, such as tungsten or lead, it is much more significant.
Angular emission
The emitted photon can leave in different directions. For low energy electrons, the emission is spread over a wide range of angles. For very high energy electrons, the radiation becomes strongly forward directed, meaning the photons are emitted mainly along the original electron direction.
This forward peaking is important in accelerator physics and radiation shielding.
Practical importance
Bremsstrahlung matters in medical physics, radiation protection, detector design, and accelerator science. In X ray machines, it is the desired source of X rays. In beta radiation shielding, it is often an unwanted byproduct. For this reason, low $Z$ materials are often used first to stop beta particles, which reduces bremsstrahlung production compared with using lead directly.
A common shielding strategy is to use a low $Z$ layer to slow the electrons, followed by a high density material to absorb the photons that are produced.
Key relations
| Quantity | Relation |
|---|---|
| Photon energy from one event | $h\nu = E_i - E_f$ |
| Maximum bremsstrahlung photon energy in an X ray tube | $E_{\gamma,\max} = eV$ |
| Minimum wavelength in an X ray tube | $\lambda_{\min} = \dfrac{hc}{eV}$ |
Important ideas for bremsstrahlung.
The radiation is produced when electrons are accelerated in the electric field of nuclei.
It produces a continuous spectrum.
It becomes more important for high electron energy and high $Z$ materials.
For energetic electrons, radiative losses can compete with or dominate collisional losses.