Particle Accelerators in Hospitals: PET Scans Explained

The Lorentz force is the total force experienced by a charged particle moving through both electric and magnetic fields, calculated as the vector sum of the electric force (F = qE) and the magnetic force (F = qvB sinθ). When a positive charge moves perpendicular to an electric field, it experiences a force parallel to the field lines; when moving perpendicular to a magnetic field, it experiences a force perpendicular to both velocity and field, causing circular motion. The magnetic force is maximum when velocity is perpendicular to the magnetic field (90°) and zero when parallel (0°). This principle is applied in cathode ray tubes to control electron beam paths.

The Tesla (T) is the SI unit for magnetic field strength, equivalent to 1 Weber per square meter (Wb/m²) or 1 Newton per Ampere-meter (N/A·m). One Gauss equals 10⁻⁴ Tesla. The Lorentz force combines electric and magnetic forces on charged particles: F = q(E + v × B). For a current-carrying conductor in a magnetic field, the force is F = ILB sinθ. When a charged particle moves through a magnetic field, it experiences a force F = qvB sinθ. When moving perpendicular to the field (θ = 90°), the force is maximum (F = qvB) and causes circular motion with radius r = mv/(qB). When moving parallel (θ = 0°), the force is zero. The frequency of circular motion is f = qB/(2πm), independent of velocity. The Biot-Savart law gives the magnetic field produced by a current element: dB = (μ₀/4π) × (I dl × r̂)/r². The magnetic field at the center of a circular coil is B = (μ₀NI)/(2r). The magnetic field at a distance r from a long straight wire is B = (μ₀I)/(2πr). The speed of light in vacuum is c = 1/√(μ₀ε₀), showing light is an electromagnetic wave.

Magnetic field is defined as the force experienced by a moving charge: F = q(v × B). Unlike electric fields that act on both stationary and moving charges, magnetic fields only act on moving charges. The Lorentz force combines electric and magnetic effects: F = q(E + v × B). This force is invariant across all inertial reference frames. The SI unit is Tesla (T), where 1 T = 1 N/(C·m/s). Magnetic fields are produced by moving charges (currents) and bar magnets containing microscopic atomic currents. Magnetic field lines emerge from north poles and enter south poles. When a charged particle enters a magnetic field with velocity having both parallel and perpendicular components to the field, it undergoes helical motion. The perpendicular component causes circular motion with radius r = mv⊥/(qB), while the parallel component causes uniform motion along the field direction. The pitch of the helix is p = v∥ × T, where T = 2πm/(qB) is the time period independent of velocity.

The total force on a charged particle in the presence of both electric and magnetic fields is given by the Lorentz force: F = q(E + v × B), where q is the charge, E is the electric field, v is the velocity, and B is the magnetic field. This equation combines the electric force (qE) and the magnetic force (qv × B).

The Lorentz force combines electric and magnetic forces: F = q(E + v × B). When a charged particle enters a magnetic field perpendicularly, it moves in a circular path with radius r = mv/(qB). When entering at an angle, it follows a helical path with radius r = (mv sinθ)/(qB) and pitch p = (mv cosθ)/(qB) × T. The time period of revolution is T = (2πm)/(qB), independent of velocity.

Beta plus decay (also called positron emission) occurs when a proton within an atomic nucleus transforms into a neutron, emitting a positron (antielectron) and a neutrino. This process decreases the atomic number by one, transforming the original element into a new element located one position to the left in the periodic table. The emitted positron carries a positive charge of +1, balancing the decrease in nuclear charge caused by the proton-to-neutron conversion. Positrons are antimatter counterparts of electrons and will annihilate upon encountering ordinary matter, releasing energy in the form of gamma rays.

The positrons (anti-electrons) produced during beta plus decay quickly collide with the leftover normal electrons from hydrogen atoms. When matter and antimatter particles meet, they annihilate each other, producing a flash of gamma radiation. This annihilation process eliminates both particles and adds additional heat to the sun's core.

Matter-antimatter annihilation is the most energetic process in the universe, achieving 100% conversion of mass to energy. Antimatter is not exotic but a mirror-image of matter with opposite charges (e.g., positrons are anti-electrons). When matter and antimatter contact, they completely annihilate and release enormous energy. One kilogram of matter-antimatter produces 42.95 megatons of TNT equivalent—enough to power a house for 4 million years or the entire US for 4 months. A 90 kg human would release 4,000 megatons, exceeding most atomic bombs and powering a country for 30 years. This process is governed by Einstein's E=mc², which explains mass-energy equivalence.

This segment covers nuclear physics, specifically beta plus decay and positron emission. In beta plus decay, a proton in the nucleus converts into a neutron, emitting a positron (positive electron) and a neutrino. The instructor explains that the positron is the antiparticle of the electron, having the same mass but opposite charge. The decay process follows the equation: p → n + e⁺ + ν. The positron is emitted from the nucleus and quickly annihilates with an electron, producing gamma rays. This type of decay occurs in proton-rich nuclei and is important in nuclear physics and medical applications.

In beta plus decay (β+), a neutron in the nucleus transforms into a proton, emitting a positron (β+) and a neutrino. The atomic number increases by 1 while the mass number remains unchanged. For example, when a nucleus with Z=26 and A=56 decays to Z=27 and A=56, it emits a positron. The positron is the antiparticle of the electron with positive charge.

All medical imaging systems operate through a general mechanism: they require an energy source that emits energy (such as ionizing radiation for X-rays), this energy passes through or is absorbed by different body tissues, and then a detection component captures the remaining energy that passes through. Computer programs and algorithms process this detected energy to create visualizations of internal body structures.

Radiation is essential in medical imaging, with both non-ionizing and ionizing types capable of producing images. Non-ionizing radiation includes ultrasonic waves (used in ultrasound) and radiofrequency waves (used in MRI), which differ from ionizing radiation in properties and intensity. The key distinction between ionizing and non-ionizing radiation lies in frequency and energy: higher frequency means higher energy and ionizing capability. X-rays, discovered in 1895, are the most commonly used ionizing radiation in medical imaging, applied in mammography, tomography, dental radiology, and bone densitometry. When combined with contrast agents, X-rays produce higher quality images.

Ionizing radiation, which includes X-rays and computed tomography (CT), is a fundamental method for obtaining medical images; X-rays were discovered by Wilhelm Röntgen in 1895 and work by accelerating electrons toward a photosensitive surface to create latent images, while CT scanners use rotating X-ray emitters and detectors to generate cross-sectional images through computer reconstruction; the radiation damage depends on absorbed dose measured in Gray and biological effect measured in Sievert, with risks ranging from low (chest X-ray at millisieverts) to high (5000+ millisieverts causing mortality), and protection follows the ALARA principle (As Low As Reasonably Achievable) through limiting exposure time, increasing distance from the source, and using shielding.

Ionizing radiation leaves detectable traces when interacting with matter, enabling measurement of both presence and energy. Medical diagnosis utilizes these detectors to identify disease origins by detecting radiation absorbed by organs and generating images. Detectors function through four core components: a sensor where radiation interacts, an amplification system for signal formation, signal processing systems, and a display showing flux, energy spectra, absorbed dose, or dose rate. Two localization methods exist: sound wave emission increasing in intensity near radiation sources, and tracing back radiation paths to identify affected organs. This foundational understanding enables precise medical imaging and diagnostic applications.

Ionizing radiation is radiation capable of producing ions in the human body by stripping electrons from atoms. There are three main types: alpha particles (helium nuclei, stopped by paper), beta particles (electrons or positrons, stopped by aluminum), and gamma rays (high-energy photons, requiring lead or concrete). X-rays are similar to gamma rays but less energetic. Radiation measurement involves multiple units: activity (Becquerel) measures disintegrations per second, absorbed dose (Gray) measures energy deposited per kilogram, equivalent dose (Sievert) accounts for radiation type using weighting factors (alpha=20, beta/gamma=1), and effective dose considers organ sensitivity. Natural background radiation includes cosmic rays, radon gas, and internal radioactive elements. A flight at 10 km altitude exposes a person to about 0.03 mSv; a chest X-ray delivers about 0.1 mSv; a CT scan delivers about 10 mSv. At doses above 100 mSv, there is a visible increase in cancer risk. Ultrasound uses high-frequency sound waves (1-50 MHz) to create images of internal organs. Gel improves sound transmission between transducer and skin. Higher frequencies provide better resolution but less penetration. Doppler ultrasound measures blood flow velocity by detecting frequency shifts in reflected waves. Thermography uses infrared cameras to detect heat patterns, identifying tumors (higher metabolic activity) and circulatory problems. X-rays are produced when high-energy electrons strike metal targets, creating Bremsstrahlung (continuous spectrum) and characteristic radiation (specific energies). Filtration removes low-energy X-rays that would be absorbed without contributing to images. Dense tissues (bone) absorb more X-rays and appear white; less dense tissues appear darker. Modern digital detectors replace photographic film, providing immediate images that can be enhanced by computers.