Field Technologies: Mass Spectrometers, Accelerators and MRI

Physics you can find in a hospital

In one large hospital you might find a mass spectrometer testing blood samples, a linear accelerator producing X-rays to treat cancer, an MRI scanner with a magnet tens of thousands of times stronger than Earth's field, and radioactive tracers made in a cyclotron. Every one of them runs on the equations from the last five lessons: qΔV = ½mv², F = qE, F = qvB and r = mv/(qB).

This lesson is about analysing technological systems (D1.1): following the path of a particle through a machine and naming the field and the physics at each stage. The next lesson in this unit, Comparing Fields and the Fundamental Forces, steps back to compare the fields themselves, and the final lesson, Fields, Technology and Society, weighs the benefits and costs of field technologies.

The mass spectrometer

A mass spectrometer sorts atoms and molecules by mass. Follow an ion through it:

1. Ionization: atoms in the sample lose an electron (become +1 ions), so fields can push them.
2. Acceleration: a potential difference speeds the ions up: qΔV = ½mv².
3. Velocity selector: crossed E and B₁ fields let through only ions with v = E/B₁ (previous lesson).
4. Deflection: in a second uniform field B₂, each ion moves in a semicircle of radius r = mv/(qB₂). With the same v and q, r is proportional to m: heavier ions make bigger semicircles.
5. Detection: ions land on a detector at a distance 2r from the entrance slit. The number arriving at each spot gives the amount of each mass.

Solving for mass: m = qB₂r/v.

Uses include identifying unknown substances in forensics, testing athletes for banned drugs, measuring isotope ratios for radiocarbon dating, checking food and water for contaminants, and analysing the gases of other worlds on space probes.

The cyclotron

To reach high energies with a modest voltage, give a particle many small kicks. In a cyclotron, invented by Ernest Lawrence in the early 1930s:

• Two hollow D-shaped electrodes ("dees") sit between the poles of a large magnet, with a gap between them.
• Inside the dees there is no electric field; the magnetic field bends the particle around a half circle.
• An alternating voltage across the gap flips direction every half turn, so the particle is pushed forward every time it crosses the gap.
• Each kick increases v, so r = mv/(qB) grows: the path is a spiral.
• Since T = 2πm/(qB) does not depend on speed (last lesson), the AC can run at one fixed frequency: f = qB/(2πm).

At the outer radius R, v = qBR/m, so the final kinetic energy is Ek = q²B²R²/(2m). Bigger magnets and stronger fields give higher energies.

Canada's TRIUMF laboratory in Vancouver operates a 520 MeV cyclotron, often described as the largest cyclotron in the world. Its beams are used for physics research and to produce medical isotopes, and from the mid-1990s until 2019 they were also used to treat more than 200 patients with eye tumours. Many hospitals have small cyclotrons that make short-lived isotopes for PET scans.

Beyond the cyclotron: synchrotrons and linacs

As particles approach the speed of light, the simple cyclotron stops working (their period starts to change; see Special Relativity). Synchrotrons keep particles in a ring of fixed size by raising B as they speed up, and give a kick with radio-frequency cavities each lap.

• The Canadian Light Source in Saskatoon is a synchrotron that circulates electrons to produce intense X-rays and other light for research on materials, medicines and crops.
• CERN's Large Hadron Collider (27 km around) accelerated protons to 6.8 TeV in its third run, which ended in June 2026. It is now in a long shutdown for its High-Luminosity upgrade, planned to restart around 2030.
• Linear accelerators (linacs) in cancer centres accelerate electrons in a straight line and fire them into a metal target to make high-energy X-rays aimed at tumours.

MRI: magnetism inside your body

An MRI scanner is a huge superconducting solenoid (B = μ₀NI/L from Magnetic Fields of Currents), usually 1.5 T or 3 T, cooled by liquid helium so its wires have no resistance.

1. Hydrogen nuclei (protons) behave like tiny magnets. In the strong field, slightly more of them line up with it.
2. Radio-wave pulses at just the right frequency (about 64 MHz at 1.5 T) tip them over.
3. As they relax back, they give off radio signals. Extra gradient coils make the field vary slightly across the body, so each position has its own frequency and the computer can map where the signals come from.
4. Different tissues relax at different rates, which gives contrast.

MRI uses no ionizing radiation. Its hazards come from the field itself: anything containing iron can be pulled violently into the magnet, so patients and staff are carefully screened for metal objects and some implants.

Magnetic stripes and hard drives

The stripe on the back of a card or hotel key holds data in tiny magnetized regions of iron oxide particles, arranged in a pattern. When you swipe the card, the reader's head (a small coil or sensor) feels the field change at each boundary between regions. The pattern of changes is decoded into the account number. A strong magnet can scramble the regions, which is why stripes get "wiped". Most Canadian payment cards now rely on chips and tap instead, but stripes remain on many cards and keys.

A computer's hard disk drive works the same way at a much smaller scale: a write head's electromagnet magnetizes tiny regions of a spinning disk, and a read head senses their fields. (Solid-state drives store charge instead, using electric fields.)