Source: https://guthlabs.ai/docs/instruments/cyclotron-motion-calculator/mechanism/

instrument mechanism / verified-clean

# Cyclotron Motion Calculator mechanism

The inspectable method record for Cyclotron Motion Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The core non-relativistic magnitude formulas are standard after replacing q with |q| and defining velocity as v_perp. The specification needs review because it does not define charge-sign handling, perpendicular-velocity handling, kinetic-energy units/conversion, zero-input validation, or the numerical criterion for the relativistic warning.

- For scalar radius and cyclotron frequency, use |q| rather than signed q: r=m|v_perp|/(|q|B) and f=|q|B/(2πm). The signed charge determines rotation direction, not a negative radius or negative frequency.

- The stated r=mv/(qB) is valid only when v means the component perpendicular to the magnetic field, v_perp. A particle with a velocity component parallel to B follows a helix rather than a purely circular orbit.

- The period output is not explicitly provided; under the non-relativistic convention it should be T=1/f=2πm/(|q|B).

- If kinetic energy is accepted, the required non-relativistic conversion is v=sqrt(2K/m), and this constraint should be explicit. The kinetic-energy input unit is not specified.

## Units and conventions

- Mass m is in kilograms.

- Charge q is in coulombs; B is in tesla; velocity is in metres per second; radius is in metres; frequency is in hertz; period is in seconds.

- B denotes the positive magnitude |B| of a uniform magnetic field.

- Velocity is the magnitude of the component perpendicular to B unless the instrument explicitly rejects non-perpendicular input.

- Kinetic energy K must be converted to joules before using v=sqrt(2K/m); 1 eV=1.602e-19 J.

- The test calculations use π=3.1415926536 and the supplied numerical particle constants rather than hidden preset rounding.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "mass_kg": 1.673e-27,
    "charge_C": 1.602e-19,
    "velocity_perpendicular_m_per_s": 1000000,
    "B_T": 1
  },
  "expected_outputs": {
    "radius_m": 0.0104432,
    "cyclotron_frequency_Hz": 15239800,
    "period_s": 6.56165e-8
  },
  "working": "r=m v/(|q|B)=(1.673e-27×1.000e6)/(1.602e-19×1.00)=1.673e-21/1.602e-19=1.04432e-2 m. f=|q|B/(2πm)=1.602e-19/(2×3.1415926536×1.673e-27)=1.602e-19/1.0511769e-26=1.52398e7 Hz. T=1/f=1/(1.52398e7)=6.56165e-8 s."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

A zero-charge input creates an undefined radius and period and should be rejected. The non-relativistic-only formulas also produce materially inaccurate results at 0.6c unless the calculator flags or handles the relativistic regime. Signed charge and field conventions can additionally yield negative radius/frequency values that require explicit interpretation.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/cyclotron-motion-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/cyclotron-motion-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/cyclotron-motion-calculator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`