---
title: "Cyclotron and synchrotron compared"
subject: "Engineering Physics"
chapter: 8
key: "semester_1/engineering_physics:cyclotron-synchrotron-particles"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/cyclotron-synchrotron-particles
site: BCT Engineering
---

# Cyclotron and synchrotron compared

Engineering Physics · Chapter 8: Electromagnetism

- Asked in: 2074 Chaitra, 5 marks
- Video: [Cyclotron & Synchrotron (Particle Accelerator)](https://www.youtube.com/watch?v=rOXfm6EezeA) — For the Love of Physics
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/cyclotron-synchrotron-particles
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-8

## Question

What type of particles can be accelerated by a cyclotron? Explain the working of cyclotron and synchrotron with their differences.

## Short answer

Cyclotrons accelerate heavy charged particles such as protons and ions; electrons are unsuitable due to relativistic mass increase. A cyclotron uses a fixed-frequency RF voltage and uniform magnetic field to accelerate particles along a spiral path. In contrast, a synchrotron keeps particles on a fixed circular ring, synchronously increasing the magnetic field and RF frequency to reach much higher energies.

## Answer

#### Particles accelerated by a cyclotron
Only **charged particles** can be accelerated, and they should be heavy so that the mass stays nearly constant: protons, deuterons, α-particles and other ions. Electrons are unsuitable because their mass increases quickly with speed (relativistic), so they fall out of step. Neutrons, being neutral, are not accelerated.

#### Working of the cyclotron
```text
     B (uniform, into page)
      _____   _____
     / D1  \ / D2  \
    |  ion  |gap|   |   RF oscillator
     \_____/ \_____/    across the dees
```
1. Ions from a central source are accelerated across the gap between two hollow dees by an alternating voltage.
2. Inside a dee, the uniform magnetic field bends the ion in a semicircle: r = mv/(qB).
3. The time for a semicircle, πm/(qB), is independent of speed, so an oscillator of fixed frequency f = qB/(2πm) reverses the gap field exactly in time. The ion gains energy qV at every crossing and spirals outward.
4. At radius R, it leaves with K = q²B²R²/(2m).

#### Working of the synchrotron
A synchrotron holds particles in a **fixed-radius ring** inside a vacuum tube. Bending magnets around the ring have a field that is increased as the particles gain energy, and radio-frequency cavities at one or more points accelerate them. The RF frequency is also varied (synchronised) to match the particles' revolution frequency, which allows relativistic energies, GeV to TeV.

#### Differences
| Cyclotron | Synchrotron |
|---|---|
| Spiral path, increasing radius | Circular path, fixed radius |
| Constant B and constant frequency | B and frequency varied with energy |
| Large solid magnet with pole faces | Ring of many small magnets |
| Limited by relativistic mass, a few tens of MeV | Reaches GeV to TeV |
| Cannot accelerate electrons well | Can accelerate electrons and protons |
| Compact, cheap | Very large, expensive (e.g. LHC) |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which particles suit a cyclotron?
   A. Neutrons
   B. Heavy charged ones like protons and deuterons
   C. Electrons
   D. Photons
   Answer: B. They need charge, and heavy mass keeps relativistic change small. (Key point: Particles)

2. Why does a fixed-frequency oscillator work?
   A. Period πm/(qB) is independent of speed
   B. The ion's speed is constant
   C. The radius is fixed
   D. The dees move
   Answer: A. Half-turn time is independent of speed, so the gap field reverses on time. (Key point: Cyclotron working)

3. In a synchrotron
   A. Radius increases with energy
   B. Radius is fixed, with B and RF frequency varied
   C. B and frequency are constant
   D. It uses one solid magnet
   Answer: B. Particles stay on a fixed ring while B and frequency track energy. (Key point: Synchrotron)

4. Compared with a cyclotron, a synchrotron
   A. Reaches GeV to TeV
   B. Is limited to tens of MeV
   C. Cannot accelerate electrons
   D. Is compact
   Answer: A. Varying B and frequency permits relativistic energies. (Key point: Difference)

## Related in Engineering Physics

- [Cyclotron working; semicircle time constant](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Acyclotron-time-semicircle-independent) — Engineering Physics, chapter 8, asked 2×
- [Cyclotron frequency and maximum energy](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Acyclotron-proton-dees-field-numerical) — Engineering Physics, chapter 8

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