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Design Guide › Pedagogy

Cyclotron pedagogy design rules

16 of the guide’s 1545 rules carry the pedagogy tag. Rules for teaching with a machine: what a real cyclotron adds over textbook treatment, lesson and workshop structure around subsystems, and the demonstrations an internal-beam teaching machine can deliver without extraction. Each rule keeps its formula where the source gives one, a verbatim quote, a page-level citation, and a stable identifier (dg-NNNN) that resolves here and on the all-in-one guide. Where an editorial note says “the reference machine”, its parameters are on the guide’s front page.

By applicability level: level 1 (3) · level 2 (3) · level 3 (6) · level 4 (1) · 3 off the axis (no level) — levels rank breadth, never license to skip (method). Related domains, by shared rules: Beam measurement (6), Project management (4), Controls & instrumentation (2), Cyclotron general (2), Extraction (2). To combine tags or levels, open this domain in the filterable view.

Verify before use. Every rule here is a source extract in the vocabulary of the editorial methodology — faithful to its cited page, not an independently validated engineering requirement. Re-read any rule that drives a real design decision at the cited page before committing metal, money, or high voltage to it. The editorial note under each quote is this site’s extrapolation to a tabletop machine, not something the source said: an editor’s judgement, audited for overreach, never a citation.

  1. Dee voltage does not set the final energy (ideal on-crest model): the magnet and usable radius fix the ladder height, the voltage is the rung spacing - k = E_max/(q*U0) crossings, first-orbit radius r1 = sqrt(2*(q/m)*U0)/omega_cyc.

    k = E_max/(q*U0) ; v1 = sqrt(2*(q/m)*U0) ; r1 = v1/omega_cyc

    level 1 deecyclotron-generalpedagogy dg-1386

    Source quote & editorial note
    Die Endenergie der Ionen ist so etwas wie die Höhe einer Leiter und die Beschleunigungsspannung ist dann der Abstand der einzelnen Sprossen [tr.: final energy is the ladder height, voltage the rung spacing]

    Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 41-42

    Editorial note, tabletop extrapolation: Recomputed for 1000 V protons at 185 mT: r1 = 24.7 mm, matching the book. A 150 keV machine at 1 kV needs 150 ideal crossings; at 5 kV only 30 - relaxing vacuum and field-error tolerance roughly in proportion. The idealization to keep visible: real voltage also moves capture, turn separation and whether the top rung is reachable at all (dg-1376's ceiling-vs-attainability).

  2. Identify the accelerated species by specific charge without extraction: hold the RF fixed, ramp the magnet slowly (COLUMBUS: a 0.005 Hz triangle wave), plot Faraday-cup current against the Hall-probe field, and read candidate q/m values from the peak fields via q/m = 2*pi*f_RF/(h*B) with h the harmonic number (h=1 for fundamental operation).

    q/m = 2*pi*f_RF/(h*B_eff), B_eff the orbit-relevant (calibrated, orbit-averaged) field; peaks are q/m CANDIDATES pending harmonic assignment

    level 3 beam-measurementcontrolspedagogy dg-1422

    Source quote & editorial note
    Wir legen uns also mit einem geeigneten Detektor auf die Lauer und verändern das Magnetfeld solange, bis wir ein Signal erhalten [tr.: lie in wait with a detector and vary the field until a signal appears]

    Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 69-71

    Editorial note, tabletop extrapolation: Slow ramps help but don't grant immunity: characterize the electrometer/amplifier settling time and pick a sweep rate that resolves the narrowest expected peak - then confirm by comparing up- and down-sweeps (hysteresis and lag shift peaks in opposite directions). Correct the Hall reading to the median plane: a probe in the lid recess reads a different field than the orbit (the 1-7.5 percent class errors below), which moves every q/m assignment.

  3. Interpreting the smaller peaks 'is not always possible nor simple' (the book's own caution): the sinusoidal RF spreads effective accelerating voltage and arrival velocities, broadening the response - one contributor among several to the forest of small unassigned peaks.

    level 3 beam-measurementpedagogy dg-1426

    Source quote & editorial note
    Die Deutung der anderen, kleineren Peaks [...] ist nicht immer möglich und auch nicht ganz einfach [tr.: interpreting the other smaller peaks is not always possible nor simple]

    Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 71, 74

    Editorial note, tabletop extrapolation: Keep a running peak ledger (B, f, U0, gas flow, probe radius) across runs. Persistence at fixed B across U0 and flow changes is EVIDENCE toward species/harmonic assignments, and motion is evidence toward phase-spread or direct-ion artefacts - evidence, not a classification: confirm with frequency scaling and probe-radius scans (dg-1422, dg-1425).

  4. The book states that physics and mathematics at class-11 (upper-secondary) level 'should be sufficient' to follow its presentation - each subsystem chapter opening with a student-teacher dialogue and closing with the quantitative dimensioning and a worked numbers table.

    pedagogy dg-1429

    Source quote & editorial note
    Physik- und Mathematik-Kenntnisse auf dem Level der 11. Klasse der Oberstufe sollten ausreichend sein [tr.: physics and maths at class-11 level should suffice]

    Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 13

    Editorial note, tabletop extrapolation: The chapter template (dialogue, then formula, then a per-subsystem results table) is a ready-made lesson structure for an educational accelerator - our reading of the book's organization, worth copying deliberately; the author's 'should suffice' keeps its hedge.

  5. The educational case for a real cyclotron: it appears in nearly every upper-secondary textbook, students can calculate it in detail, yet almost none has seen one - and the book's stated challenge was getting a cyclotron running in exactly this low-energy range so students can study it while it runs.

    level 2 pedagogysafety dg-1430

    Source quote & editorial note
    Die Herausforderung dieses Projekts bestand demnach darin, ein Zyklotron in diesem niedrigen Energiebereich zum Laufen zu bringen [tr.: the challenge was to get a cyclotron running in this low energy range]

    Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 7-8

    Editorial note, tabletop extrapolation: Define the teaching machine's safety envelope explicitly rather than declaring it hazard-free: maximum electrode potential (X-ray endpoint), ion species and energy (reaction thresholds - remembering exothermic channels like D-D have none, so deuterium is a different machine), beam current, target and contaminant composition, plus the ordinary electrical, RF, vacuum and stored-energy hazards that exist at ANY energy. Survey, don't assume; the low-energy regime shrinks the radiological terms, not the list.

  6. A teaching machine need not extract the beam - the book's point exactly: 'the particle beam does not even need to be extracted' - an internal probe, species identification by specific charge, and a visible running accelerator met the project's pedagogical objectives.

    level 1 pedagogyextraction dg-1431

    Source quote & editorial note
    Der Teilchenstrahl braucht dabei nicht einmal ausgelenkt zu werden [tr.: the particle beam does not even need to be extracted]

    Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 27

    Editorial note, tabletop extrapolation: A radial probe drive with a Faraday cup is the first detector to build on any small machine, and extraction is properly a separate later project - which, when undertaken, teaches its own lessons (septum design, transport, external diagnostics; the COLUMBUS Wien-filter plan, dg-1512, is that next chapter). Wait until internal beam is reproducible across days.

  7. Frame the first beam experiment as a replica of the classic specific-charge measurement - 'the specific charge is a particle's identity card' - measuring q/m = 2*pi*f_RF/(h*B) on the internal beam at known RF frequency (h the harmonic, 1 for fundamental).

    q/m = 2*pi*f/B

    pedagogybeam-measurement dg-1432

    Source quote & editorial note
    Die spezifische Ladung ist sozusagen der Personalausweis eines Teilchens. Wenn wir diese kennen, kennen wir auch das Teilchen [tr.: specific charge is a particle's identity card]

    Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 68-69

    Editorial note, tabletop extrapolation: Connecting to the e/m fine-beam tube students already know turns first beam into an assessable experiment with a literature value and a computable error - the PROTON value being 9.58e7 C/kg. Teach the degeneracy honestly: q/m alone does not name the particle (D+, H2+ and He2+ all sit near 4.8e7 C/kg), so the identity card needs the source-gas and charge-state context too (dg-1422's candidate discipline).

  8. Measure a pedagogical build by what follows first beam - the book poses its own test ('when would COLUMBUS not have been worth it?') and answers: 'certainly the project would not have been worth it had it ended after the successful conclusion in 2014' - the value lying in the years of workshops, teacher training, and continuous improvement since.

    level 2 pedagogyproject-management dg-1433

    Source quote & editorial note
    Sicher hätte sich das Projekt nicht gelohnt, wenn es nach dem erfolgreichen Abschluss im Jahre 2014 beendet worden wäre [tr.: the project would not have been worth it had it ended in 2014]

    Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 75-76

    Editorial note, tabletop extrapolation: The listed follow-on improvements (magnet stand, acceleration simulation, probe translator, mechanical model) are the kind of second-year items a small-machine program should schedule rather than improvise - as this case study's pattern, adapted to local aims, not a universal checklist.

  9. A school-scale teaching cyclotron's documented timeline: the COLUMBUS project started in 2012 (FZ Juelich provided the magnet, VACOM sponsored the chamber), registered first beam in April 2014, held its first student workshop that autumn, and - in the authors' 2022 retrospective - 'has developed very positively in the last 10 years' of continuous incremental improvement.

    level 2 project-managementpedagogy dg-1506

    Source quote & editorial note
    After the FZ Juelich provided a magnet, VACOM, a company for vacuum components, sponsored a suitable vacuum chamber ... the cyclotron COLUMBUS began in 2012. ... The first beam was registered in April 2014 (see Fig. 2), which was followed by the first workshop with students in autumn of the same year. ... The COLUMBUS project, started in 2012, has developed very positively in the last 10 years.

    Wolf & Prechtl, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — THPO001, Proceedings of Cyclotrons2022 (2022) — p. 1

    Editorial note, tabletop extrapolation: A realistic schedule anchor for the plan's teaching-machine ambitions: two years start-to-beam WITH a donated magnet and sponsored chamber - the in-kind support is part of the datum. And the methodological point stands: a conference paper's year dates the claim; prefer the builders' own retrospective dates when reconstructing a machine's history.

  10. Beam-species spectroscopy by field sweep, as COLUMBUS practices it: fix the detector position and RF frequency, continuously increase the magnetic field, and log beam current - peaks appear at very specific fields, from which q/m follows via q/m = 2*pi*f/(h*B).

    q/m = 2*pi*f / B (peak assignment from known f and measured B)

    level 3 beam-measurementcontrolspedagogy dg-1510

    Source quote & editorial note
    the detector is set to a specific position and the magnetic field is continuously increased. With very specific magnetic fields, there are peaks in the beam current

    Wolf & Prechtl, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — THPO001, Proceedings of Cyclotrons2022 (2022) — p. 2

    Editorial note, tabletop extrapolation: A B-sweep at fixed frequency is a q/m RESONANCE SURVEY - the cheapest species diagnostic a small machine has, not a full mass spectrometer: state the harmonic number, calibrate the field reading (dg-1428), and resolve the q/m degeneracies and harmonic ambiguities by field-ratio checks or frequency scaling (dg-1422/dg-1423) before naming species.

  11. An extraction upgrade for a keV-class machine can pair a deflection system with a Wien filter, as the COLUMBUS project aims to, guiding the extracted beam through the filter 'to measure the speed and energy of the ions' - the filter selecting velocity (v = E/B), from which energy follows for a known species.

    level 3 extractionbeam-measurementpedagogy dg-1512

    Source quote & editorial note
    The aim of this project is to deflect the ion beam and guide it through a Wien Filter to measure the speed and energy of the ions.

    Wolf & Prechtl, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — THPO001, Proceedings of Cyclotrons2022 (2022) — p. 3

    Editorial note, tabletop extrapolation: A Wien filter is a realistic first external beamline element for a low-energy machine: it measures VELOCITY directly and yields energy only once the species is known (or paired with a separate analyzer) - which is exactly why it also cross-checks species assignments. It needs crossed electric AND magnetic fields; at keV energies both are modest, but 'electrostatic-only' it is not.

  12. The cyclotron was continuously improved and expanded with the involvement of pupils and students - the paper's own history listing the magnet cooling system, detector linear translator, mechanical model and simulation, and the first 3D-printed vacuum chamber among the student-era improvements.

    level 3 pedagogyproject-management dg-1514

    Source quote & editorial note
    The cyclotron was continuously improved and expanded with the involvement of pupils and students.

    Wolf & Prechtl, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — THPO001, Proceedings of Cyclotrons2022 (2022) — p. 1

    Editorial note, tabletop extrapolation: An educational machine CAN make learner projects its upgrade workforce when they are scoped as real subsystem work - a Faraday-cup translator or a field map is simultaneously curriculum and infrastructure; whether that is the fastest improvement route is a program-design judgment, not this paper's measurement.

  13. The COLUMBUS workshop format as adopted: groups of up to 6 participants; up to 12 accepted and split into two groups; offered as two-day, one-day, and online (three remote sessions plus one lab session) variants.

    pedagogy dg-1515

    Source quote & editorial note
    A workshop takes place in groups with up to 6 participants. If more people register, up to 12 persons can be accepted, who will then be divided into two groups.

    Wolf & Prechtl, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — THPO001, Proceedings of Cyclotrons2022 (2022) — p. 2

    Editorial note, tabletop extrapolation: Six-per-group is the format the team settled on for one machine - a reasonable planning anchor for hands-on accelerator teaching, not a demonstrated pedagogical ceiling; whether hybrid delivery preserves learning quality is an outcomes question the paper doesn't measure. Copy the structure, evaluate your own.

  14. State a teaching cyclotron's requirements as two conditions before any dimensioning, per the 2013 design account: every operating parameter (vacuum, magnetic field, frequency) kept low enough that standard commercial components suffice, and the final energy kept small enough that no harmful radiation can arise, so that students can experiment at the running machine; the whole parameter table is then presented as the consequence of these two conditions.

    level 1 cyclotron-generalproject-managementpedagogy dg-1516

    Source quote & editorial note
    In order to build such a small cyclotron one has to meet two conditions: Vacuum, magnetic field, frequency etc. must be so low that one can use standard components as far as possible, otherwise the costs will go to infinity; The final energy of the cyclotron must be small enough so that no harmful radiation can arise, so that the students can do experiments with the cyclotron. Table 1 shows the technical data of COLUMBUS. One can easily recognize that COLUMBUS meets all the conditions mentioned above.

    Wolf, Frank & Held, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — WE1PB03, Proceedings of Cyclotrons2013 (2013) — p. 1

    Editorial note, tabletop extrapolation: A hobby-scale build benefits from the same requirements discipline; writing the cost condition and the radiation condition down first turns every later component choice into a check against them. The radiation condition itself needs its own verification, not just an energy number: whether 'no harmful radiation can arise' at a given operating point is the paper's claim for its machine, and X-rays begin when high voltage or RF is energized, before any beam.

  15. Structure a teaching-scale orbit simulation in three layers — an input layer holding three parameter groups (ion properties, experiment settings, machine geometry), a simulation engine, and a presentation layer whose plot modules (XY orbit plot, intensity plot, spectrometer plot) each also export data to file for external processing.

    level 4 modelingpedagogy dg-1528

    Source quote & editorial note
    As shown in Fig. 1 the simulation consists of three sections, the input-layer, the simulation-layer and the presentation-layer. … The input-layer incorporates three groups of parameters which define the ions, the experiment and the geometry of the cyclotron. So the simulation can be easily adapted to different situations. … The simulation engine described above has three modules for the evaluation: XY-Plot, Intensity-Plot and Spectrometer-Plot. Every module - apart from the graphical output - allows also a data export to a file so that the measured values can be processed by external programs.

    Wolf, Rueß & Prechtl, Simulation and Detection of the Helical Ion-Paths in a Small Cyclotron — MOB02, Proceedings of Cyclotrons2016 (2016) — p. 1, 2

    Editorial note, tabletop extrapolation: Separating ion, experiment, and geometry parameter groups lets one code serve several machine configurations and several experiments; the data-export hook is what allows direct overlay of simulated and measured detector scans.

  16. Operate the machine as a mass spectrometer for beam diagnosis by fixing the detector position and sweeping the magnetic field: peaks in current versus field identify the species present (the paper's Fig. 7 shows the measured spectrum), and the same experiment can be pre-computed with the orbit simulation's spectrometer module.

    level 3 beam-measurementpedagogy dg-1532

    Source quote & editorial note
    In this experiment the beam is measured in dependence of the magnetic field at a fixed position of the detector. Here one can identify the ions in the beam … The Spectrometer-Plot (Fig. 8) shows the caluculated probability as a measure for the beam-current vs. the magnetic field and allows to simulate this experiment.

    Wolf, Rueß & Prechtl, Simulation and Detection of the Helical Ion-Paths in a Small Cyclotron — MOB02, Proceedings of Cyclotrons2016 (2016) — p. 3

    Editorial note, tabletop extrapolation: A fixed-cup B-sweep is a species diagnostic using hardware a small hydrogen machine already carries, separating proton from molecular-ion contributions; simulating the sweep first tells the operator which peak to expect where. The assignment rests on rigidity plus the assumed charge and energy, so overlapping peaks can stay ambiguous.