Photons are uncharged. They cross tissue until they happen to interact, so a photon beam never stops; it only thins out exponentially (Module 03). Electrons are charged. They interact with every atom they pass, losing about 2 MeV for each centimetre of water, so a beam of a given energy runs out of energy at a predictable depth. That is the range.

Because electrons are light, every interaction also deflects them. They scatter in the air between the machine and the skin, they scatter sideways in tissue, and they scatter differently in bone, lung and air. Range explains the depth dose; scatter explains almost everything else: the shape of isodose lines, the loss of output in small fields, the sensitivity to air gaps and the hot and cold spots near heterogeneities.

In electron mode the linac (Module 02) removes the x-ray target and the flattening filter from the beam path. The narrow pencil of electrons leaving the bending magnet is spread into a broad, flat field by scattering foils: a thin high-Z primary foil that widens the beam, and a shaped secondary foil that flattens it. The foils, the monitor chambers and the air also produce bremsstrahlung x-rays, which is the origin of the photon tail at the end of every electron depth dose curve.

Electrons scatter so much in air that the jaws, about 60 cm above the patient, cannot define a sharp field edge. An applicator (cone) carries the collimation down to about 5 cm above the skin. The field is shaped by a cutout, a Cerrobend or lead insert in the end of the applicator. The jaws are set automatically to a larger opening matched to each applicator, which keeps scatter from the applicator walls consistent.

Three energies you will see named

A 12 MeV beam with R₅₀ = 5.15 cm has E₀ = 2.33 × 5.15 = 12.0 MeV. At 3 cm depth, with R_p = 6 cm, its mean energy is 12 × (1 − 3/6) = 6 MeV. The energy at depth matters whenever something sits inside the patient: an internal lead shield, a bone surface, a detector.

Read the curve in four parts, each with its own physics.

Surface. Electrons deposit dose from the moment they enter, so there is no real skin sparing. Surface dose is high, typically about 75 to 80 percent at 6 MeV and about 90 percent or more at 16 to 20 MeV. It rises with energy, the opposite of photons. Low-energy electrons scatter through larger angles near the surface, so the dose builds up more over the first centimetre (obliquely travelling electrons cross a thin layer with a longer path and deposit more); high-energy electrons travel straighter, so the surface already sits close to the maximum.

Build-up and plateau. The modest rise to d_max comes from electrons being scattered out of their straight paths, which increases fluence through each layer. d_max is broad and does not move deeper in proportion to energy; it plateaus at around 2.5 to 3 cm for higher energies and can even move shallower.

Fall-off. As electrons run out of energy, dose drops steeply. The gradient is sharpest at low energy and becomes more gradual at high energy, because range straggling and scatter spread the stopping points.

Bremsstrahlung tail. Beyond R_p, a few percent of dose remains from x-rays produced in the foils, collimation and the patient. It grows with energy because radiative losses scale with energy.

Each electron entering the patient spreads sideways as it goes deeper. A point on the central axis of a large field receives as many electrons scattered in from the sides as it loses to scatter out. That balance is lateral scatter equilibrium. When the field edge is closer to the axis than the electrons can travel sideways, more leave than return, and the central axis dose falls.

Equilibrium needs the field edge to be farther from the point than the lateral spread of the electrons. Khan quotes the radius needed as R_eq ≈ 0.88 √E_p,0 cm, about 3 cm at 12 MeV. A practical rule follows: once the smallest field dimension exceeds about the practical range R_p, depth dose no longer depends on field size.

Isodose shape: bulge and constriction

Lateral scatter pushes low-value isodose lines (10 to 20 percent) outward beyond the geometric field edge, especially at higher energies. The high-value lines (80 to 90 percent) are pulled inward with depth, because points near the edge lose electrons and are not compensated. The 90 percent line is therefore narrower at depth than the field at the surface.

Cutout output factors

Output for an electron field is measured for each applicator and for each cutout size, relative to the reference applicator and cutout. For a rectangular cutout that has not been measured, the square root rule estimates its output from two square fields.

A photon beam comes from a small spot on the target, so inverse square works from the nominal source position. An electron beam has no such spot. The scattering foils, the monitor chambers, the air and the applicator spread the electrons so that, seen from the patient, they appear to come from a point closer than the nominal source. Two different "sources" are used, for two different jobs.

The effective SSD is measured by placing a chamber at d_max in phantom and recording the reading I₀ with no gap and I_g with an air gap g between the applicator end and the surface. If inverse square holds from an effective source, the square root of the reading ratio is linear in the gap.

Because the effective source is closer, output falls faster with an air gap than the nominal inverse square predicts. Using 100 cm instead of an effective SSD near 85 cm underestimates the loss and under-doses the patient, by about 1.5 percent for a 5 cm gap at 12 MeV and more for larger gaps.

An air gap also widens the penumbra, because electrons keep scattering sideways in the extra air. Depth dose shape changes little.

When the beam strikes the skin obliquely, electrons travel along slanted paths. The slant packs more electron track into each shallow layer and also lets electrons scattered from neighbouring regions add dose near the surface. Dose near the surface and at d_max rises, d_max moves shallower, and the dose at depth falls because the path to a given perpendicular depth is longer. The penetration measured perpendicular to the skin shrinks.

Surface shape matters on a smaller scale. Electrons scatter preferentially from the thicker side of a step toward the thinner side. Below a sharp ridge or the edge of a depression (the nasal ala, the ear, a surgical defect), this produces adjacent hot and cold spots that a pencil beam calculation may not show.

Electrons lose energy in proportion to the electron density they cross. A centimetre of lung removes far less energy than a centimetre of water, so the beam travels farther; a centimetre of compact bone removes more, so the beam stops sooner. The simplest correction is the coefficient of equivalent thickness (CET): the thickness of water that has the same effect on the beam as 1 cm of the material.

CET corrects depth on the central axis of a broad inhomogeneity. At the edges of a small inhomogeneity, scatter creates its own pattern: more electrons scatter out of the denser medium than into it, so a hot spot forms on the low-density side of the interface and a cold spot on the high-density side. Behind the edge of a bone or an air cavity, these hot and cold streaks can be large. Monte Carlo calculation (TG-105) handles them; a pencil beam algorithm handles them poorly.

Internal shields and backscatter

When lead sits inside the patient (an eye shield under the lid, a lip or buccal mucosa shield), electrons striking it backscatter into the tissue in front of it. The dose upstream of the lead rises substantially, by tens of percent at the energies used for these sites, and more at lower electron energy at the interface. The usual fix is a coating of low-Z material, such as wax, dental acrylic or aluminium, on the beam side of the lead, a few millimetres thick, to absorb the backscattered electrons.

Bolus is tissue-equivalent material on the skin. For electrons it does two jobs. It raises surface dose, by moving the skin into the high part of the curve. And it pulls the whole distribution toward the surface by its thickness, which is how you treat a superficial lesion with an energy whose range would otherwise reach a critical structure. A variable-thickness bolus shaped to the distal target surface (bolus electron conformal therapy) uses the second job to sculpt the 90 percent line.

How much lead stops an electron beam

Electrons have a finite range in lead as in water, but lead also converts some of their energy into bremsstrahlung, so a shield can never reach zero. The rule for the minimum lead thickness that brings transmission to about 5 percent is simple.

Photon junctions are a matter of divergence (Module 08). Electron junctions add scatter. Because low-value isodose lines bulge beyond the field edge, two electron fields abutted at the skin overlap at depth and produce a hot spot below the junction; separating them on the skin produces a cold strip at the surface. There is no perfect gap, so electron junctions are usually abutted with a planned shift (feathering) every few fractions, or aligned so the beam edges are parallel at the junction.

When an electron field abuts a photon field at the skin, the asymmetry is the board point. Electrons scatter out of the electron field into the photon field, where the photon dose is already full at depth. The result is a hot spot on the photon side and a cold spot on the electron side of the junction.

Pick an energy, then add bolus, a slab of lung or bone, or an air gap, one at a time. Watch which part of the curve moves and say why before you read the numbers. The dashed curve is the same energy in plain water at 100 cm SSD.

Work each one on paper first. Factors are given as they are on the exam.

Ballpark numbers to carry in your head

Sources

1. American Board of Radiology. Radiation Oncology Qualifying Exam: Study Guide for Medical Physics for Radiation Oncology (2023 domain ranges).
2. Khan FM, Gibbons JP. The Physics of Radiation Therapy, 5th ed. Chapter on electron beam therapy.
3. Khan FM et al. Clinical electron-beam dosimetry: report of AAPM Radiation Therapy Committee Task Group 25. Med Phys 1991;18:73-109.
4. Gerbi BJ et al. Recommendations for clinical electron beam dosimetry: supplement to the recommendations of Task Group 25 (TG-70). Med Phys 2009;36:3239-3279.
5. Almond PR et al. AAPM TG-51 protocol for clinical reference dosimetry of high-energy photon and electron beams. Med Phys 1999;26:1847; Muir B et al. WGTG51 Report 385, electron addendum. Med Phys 2024;51:5840.
6. Hogstrom KR, Almond PR. Review of electron beam therapy physics. Phys Med Biol 2006;51:R455-R489.
7. Ford E. Primer on Radiation Oncology Physics. CRC Press, 2020.

The bench uses a simplified depth dose model fitted to typical published 6 to 20 MeV behaviour and assumed effective SSDs. It teaches direction and magnitude. Clinical numbers come from your machine's commissioning data.