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Cyclotron and synchrotron compared

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.

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

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

     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

CyclotronSynchrotron
Spiral path, increasing radiusCircular path, fixed radius
Constant B and constant frequencyB and frequency varied with energy
Large solid magnet with pole facesRing of many small magnets
Limited by relativistic mass, a few tens of MeVReaches GeV to TeV
Cannot accelerate electrons wellCan accelerate electrons and protons
Compact, cheapVery large, expensive (e.g. LHC)

✓ Answer checked by Claude Opus 5.5 (high effort)

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