Cyclotron

Imagine pushing a child on a swing. A gentle push each time the swing returns gives it more and more height over time — you never need one giant shove. A cyclotron works on exactly this idea, but with charged particles instead of a swing: it uses a small, repeatable electric "push" to build up enormous kinetic energy, using a magnetic field to bring the particle back for the next push.

A cyclotron is a machine that accelerates positively charged particles — like protons and deuterons — to very high energies using repeated pushes from an electric field, guided into a circular path by a magnetic field. It was invented by Ernest Lawrence in 1932 to produce fast particles for nuclear disintegration experiments.

• Two D-shaped hollow metal boxes ("dees"), D1 and D2, placed with a small gap between them.
• Alternating voltage (~10⁵ volts) applied across the dees at a frequency of 10-15 megacycles/second.
• Strong magnetic field (~1.6 tesla) applied perpendicular to the plane of the dees, generated by a large electromagnet.
• Vacuum chamber maintained at ~10^-6 mm of mercury so particles don't collide with air molecules.
• Ion source at the centre, containing a heated filament and gas (hydrogen for protons, deuterium for deuterons).

1. A charged ion is released from the central ion source when dee D2 is negatively charged.
2. The electric field between the dees pulls the ion toward D2, accelerating it.
3. Inside D2, the ion is shielded from the electric field. The magnetic field alone acts on it, curving it into a semicircular path at constant speed.
4. The ion reaches the gap again just as the polarity has flipped — now D1 is negative — so it gets pushed again and speeds up further.
5. The larger the speed, the larger the circular radius, but the time to complete each semicircle stays exactly the same (this is the key trick that makes the whole process work).
6. Steps 2-5 repeat again and again, with the ion spiralling outward and gaining energy each time it crosses the gap.
7. Once the ion reaches the outer edge of the dee, a negatively charged deflector plate pulls it out of the machine as a high-energy beam.

Because the time to complete a semicircle depends only on the charge-to-mass ratio and the magnetic field — not on speed — a particle moving faster simply traces a bigger circle in the same amount of time. This means the alternating voltage can keep flipping at a fixed frequency, and the particle will always arrive at the gap exactly when it should for another push.

• Cannot accelerate electrons: electrons are so light that they quickly reach relativistic speeds, and their mass increase throws off the timing (resonance) needed to stay in sync with the alternating voltage
• Cannot accelerate uncharged particles: neutrons, for example, are unaffected by both electric and magnetic fields, so they cannot be pushed or steered
• Speed ceiling from relativity: as any particle's speed approaches the speed of light, its effective mass increases (m = \[\frac {m_0}{\sqrt{1−v^2/c^2}}​​\]), increasing the time per semicircle and breaking synchronisation with the fixed-frequency voltage
• Solution — synchro-cyclotrons: some machines solve this by gradually decreasing the applied frequency to match the increasing mass, keeping the particle in sync for longer

• Medical use: Cyclotrons produce short-lived radioactive isotopes used in PET scans and cancer treatment (proton therapy)
• Nuclear research: Used to bombard nuclei with high-energy particles to study nuclear structure
• Material science: Ion implantation in semiconductor manufacturing uses accelerated ions from cyclotron-like devices

• A cyclotron uses a small alternating electric field for repeated acceleration and a constant magnetic field to bring the particle back for the next push
• The time for one semicircular pass is independent of speed — this is the entire secret behind why the fixed-frequency voltage keeps working as the particle speeds up
• Resonance condition: applied frequency = qB / 2πm
• Maximum kinetic energy depends on the square of the dee radius and the square of the magnetic field: K = q²B²R² / 2m
• Cyclotrons cannot accelerate electrons or neutral particles
• Real machines correct for relativistic effects using synchro-cyclotrons (frequency decreases as mass increases)