Guided Exercises for the Virtual Cyclotron Laboratory

Six short exercises, each built around one thing you make happen with your own hands in the Virtual Cyclotron Laboratory (hosted; illustrative, not a calibrated replica). They follow How a Cyclotron Works and assume its vocabulary: dee, gap, RF, resonance.

Predict, act, compare

Every exercise has one learning goal and one phenomenon. The mechanic is the same on each page: predict what the machine will do, in writing, before opening the laboratory; act, with one control and the plot named on the page; compare what happened with what you wrote down. The comparison is the lesson, and a prediction that turns out wrong is the best outcome an exercise can have, because the page then has something to explain. Several of the questions are phrased around what most people expect, which is often the answer the machine refutes.

Nothing is scored, timed or stored. Each page ends with a question to answer in one sentence, for the reader alone. Where a formula exists, the page works the expected number from the laboratory's displayed settings so that "compare" has a number to compare against.

Who they are for

Someone learning to run a cyclotron rather than design one: a curious visitor, a school physics student, an operator in training. The mathematics stops at a square root and a logarithm. Two pages, the second and the last, carry a little more arithmetic than the rest. The order below is a path, and each page also stands alone.

The six exercises

1. 1. Find the resonance

   Acceleration happens only when the RF frequency matches the field, and that frequency does not depend on how fast the ions already are.

2. 2. Watch an ion fall out of step

   A slightly wrong frequency does not take a slice off the beam; the error accumulates, turn by turn, until the pushes stop helping.

3. 3. More voltage, same energy

   The final energy is set by the magnet and the radius; the dee voltage buys fewer turns, not more energy.

4. 4. Where the ions are born

   How much beam a machine makes is decided in the first millimetres: capture depends on where ions start, not on how many are made.

5. 5. What the leftover gas costs

   Vacuum is a beam-transport requirement with an exponential price, and the price depends on the length of the spiral.

6. 6. Weigh the ion

   The machine is a measuring instrument: the resonance frequency and the field together weigh the particle.

What the laboratory is, and is not

The laboratory runs an illustrative machine shaped like the reference machine, not a calibrated replica of any real machine. The exercises teach methods and mechanisms. The laboratory's readings are the settings and outputs of a simulated machine, and no page in this series quotes them as facts about a real cyclotron. Every reading comes from an ensemble of simulated ions, so repeated runs differ by a few percent, as repeated measurements do; the physics behind each exercise is cited to the Design Guide, rule by rule.

Open the Virtual Cyclotron Laboratory (hosted; illustrative, not a calibrated replica), or start with the first exercise, Find the resonance.