Electromagnetic Physics

Ionization

In Geant4, ionization is the dominant electromagnetic process for charged particles passing through matter. It describes how particles such as electrons, positrons, protons, and heavy ions lose energy by knocking electrons out of atoms and molecules of the material.

In a physics list, ionization is added as a discrete and continuous process to charged particles. The continuous part represents the average energy loss per unit length, usually written as $dE/dx$, while the discrete part represents individual ionization collisions that can produce secondary electrons, often called delta rays. Geant4 handles both contributions internally once you include the appropriate electromagnetic physics constructors.

For a charged particle with charge $z e$ and speed $v$, the mean ionization energy loss is described by the Bethe formula and its variants. Geant4 implements an accurate parameterisation of this quantity across a wide energy range.

Ionization is especially important for:

1. Energy deposition and dose. The main contributor to deposited energy in many detectors and in tissue is the energy lost through ionization.
2. Track length and ranges. The stopping range of electrons and protons is determined by their ionization loss. Range cuts and production cuts in Geant4 rely on this modeling.
3. Delta electrons. When a charged particle produces high energy secondary electrons, Geant4 can track them explicitly, which affects spatial patterns of energy deposition.

In standard electromagnetic physics lists, such as those you will use later, ionization is automatically attached to all relevant charged particles, for example via classes like G4eIonisation for electrons or G4hIonisation for hadrons. As a user, you normally do not have to implement the physics yourself, but you must select a physics list that includes the appropriate electromagnetic package.

To understand the consequences for your simulation, consider a simple detector made of silicon. A minimum ionizing particle passing through will lose a nearly constant amount of energy per unit length in the material. Geant4 calculates the statistical fluctuations around this mean energy loss, often described by Landau or Vavilov distributions. These fluctuations are important if you simulate thin detectors such as silicon strip sensors, because they directly influence the signal distribution and, later, the detector resolution.

The step size of a particle track influences how Geant4 samples ionization losses. Very large steps can smear out the fine details of energy deposition, while very small steps increase CPU time. The electromagnetic physics models in Geant4 include step limitation mechanisms to balance accuracy and performance. From the user point of view, you mainly control this balance through the choice of physics list and production cuts, rather than directly changing ionization parameters.

In medical physics simulations, ionization is central to dose calculations. The absorbed dose $D$ in a small volume is defined as the energy deposited divided by the mass of that volume,
$$
D = \frac{\Delta E}{\Delta m}.
$$
That deposited energy $\Delta E$ comes primarily from ionization for most clinically relevant beams. By choosing appropriate electromagnetic physics models, you ensure that this dose is computed with the required accuracy.

When you enable detailed electromagnetic physics, Geant4 also models shell corrections, density effects, and low energy behavior of electrons and photons. These refinements affect ionization cross sections and therefore the depth dose curves, Bragg peaks, and other observables that are sensitive to subtle changes in $dE/dx$.

Bremsstrahlung

Bremsstrahlung is another key electromagnetic process for charged particles, in particular for electrons and positrons at high energies. The name means braking radiation. It describes the emission of photons when a charged particle is accelerated in the electric field of a nucleus or an atomic electron and loses energy in the form of radiation.

In Geant4, bremsstrahlung is treated as a discrete process that can produce secondary gamma photons. When an electron travels through high Z materials such as lead or tungsten, the probability of emitting bremsstrahlung photons becomes large at high energies, and the energy loss due to bremsstrahlung can exceed the energy lost by ionization.

The relative importance of bremsstrahlung and ionization depends on the particle energy and the material. For electrons, a useful concept is the critical energy, where the energy loss by bremsstrahlung equals the energy loss by ionization. Above this energy, radiative losses dominate. Geant4 uses detailed cross section models to decide when bremsstrahlung interactions occur and what energy and direction the emitted photons have.

Bremsstrahlung is crucial in several types of simulations:

1. Electromagnetic showers. In calorimeters, high energy electrons and positrons produce electromagnetic showers that result from repeated bremsstrahlung and pair production. Correct modeling of bremsstrahlung is essential to reproduce shower profiles and calorimeter responses.
2. Radiotherapy beams. In medical linacs, high energy electron beams striking a target produce therapeutic x ray beams primarily through bremsstrahlung. Simulating the target, collimators, and dose distributions in patients or phantoms requires accurate bremsstrahlung physics.
3. Shielding and radiation backgrounds. High energy electrons hitting beamline components or shielding can radiate photons that travel long distances. These photons can then interact via photoelectric effect, Compton scattering, and pair production, contributing to dose or detector backgrounds.

In standard electromagnetic physics constructors, electron and positron bremsstrahlung is handled by classes such as G4eBremsstrahlung and G4eplusBremsstrahlung. These processes generate secondary G4Gamma particles. The details of the angular distribution and energy spectrum of these photons are controlled by the chosen model within the physics list, such as standard, Livermore, or Penelope models. Each model targets a particular energy range and accuracy.

Bremsstrahlung also affects the spectrum of electrons as they propagate through matter. For instance, in a thick target, an initially monoenergetic electron beam will broaden in energy due to both ionization and bremsstrahlung. Geant4 keeps track of these continuous and discrete energy losses separately, and the total energy conservation is enforced event by event.

When you analyze your simulation data, you may often be interested in the number and energy of bremsstrahlung photons produced in a given region. Although this belongs to later chapters, it is useful to be aware that in Geant4 you can define sensitive detectors and analysis objects that count or histogram emitted gamma energies, which then allow you to study the bremsstrahlung spectrum generated by a beam in a specific material and geometry.

By choosing a standard reference physics list that includes complete electromagnetic physics, you automatically obtain a consistent treatment of bremsstrahlung along with other related photon processes, such as pair production and Compton scattering. For most applications, this selection is sufficient and you do not need to adjust model parameters manually.

Multiple scattering

Multiple scattering describes the cumulative effect of many small angle deflections that a charged particle experiences when it traverses matter. Each deflection is caused by Coulomb interactions with nuclei and atomic electrons. Instead of simulating every individual scattering, which would be too slow, Geant4 uses condensed history models that represent the combined angular and spatial deflections over a step.

In a physics list, multiple scattering is added as a process that acts on charged particles and modifies their directions and possibly their step lengths. It is responsible for the lateral spread and angular divergence of tracks, especially for electrons, positrons, and low energy protons or heavier ions.

Multiple scattering affects several important aspects of your simulation:

1. Track shape and spatial resolution. In thin tracking detectors, the distribution of hit positions depends strongly on multiple scattering. This is especially relevant for low momentum charged particles.
2. Beam spreading. In medical physics, charged particle beams traversing tissue or beamline elements are broadened by multiple scattering. This affects dose distributions and penumbra.
3. Shower development. The lateral spread of electromagnetic showers is influenced by the scattering of electrons and positrons inside the material.

Geant4 provides multiple scattering processes such as G4eMultipleScattering for electrons and positrons, and G4hMultipleScattering or more specific ion scattering models for hadrons. Internally, these use theoretical models and parameterisations that are tuned to experimental data, such as Urban or Wentzel models.

The effect of multiple scattering becomes more pronounced as the material thickness increases compared to the radiation length, and as the particle momentum decreases. Qualitatively, the root mean square scattering angle $\theta_0$ after traveling a thickness $x$ is often estimated by a Highland like formula,
$$
\theta_0 \approx \frac{13.6\ \text{MeV}}{\beta p} z \sqrt{\frac{x}{X_0}},
$$
where $p$ is the particle momentum, $\beta$ is $v/c$, $z$ is the charge number, and $X_0$ is the radiation length of the material. Geant4 does not use this formula directly for tracking, but the same physics ideas guide the modeling.

From a practical point of view, multiple scattering interacts with step limitation. If steps are too long, the approximation of multiple scattering over the step can become less accurate and you may lose fine structure in track shapes. The standard electromagnetic physics constructors set reasonable default step limits, but in very precise tracking studies, users sometimes introduce region specific step limits to improve angular and spatial accuracy in sensitive areas of the geometry.

In proton therapy simulations, multiple scattering contributes to the lateral penumbra of the beam in the patient or water phantom. If multiple scattering is not modeled correctly, the simulated lateral dose profiles will disagree with measurements, even if the longitudinal depth dose curve is acceptable. Selecting a physics list that provides an appropriate hadron multiple scattering model for your energy range is therefore essential.

In high precision tracking detectors, such as those in particle physics experiments, multiple scattering is a dominant limitation on track momentum resolution. Geant4 is widely used to design and optimize such detectors. In those studies, you rely on the fact that the multiple scattering physics is implemented consistently with the chosen materials, radiation lengths, and geometry.

By choosing an appropriate reference physics list that includes standard electromagnetic physics, you automatically obtain a consistent treatment of ionization, bremsstrahlung, and multiple scattering. Later, when you tune your application, you may adjust production cuts and region specific settings, but the core behavior of these electromagnetic processes is entirely controlled by the physics list you select at the beginning of the simulation.

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