Inputs
Formula used
A charged particle moving in a uniform magnetic field gyrates with cyclotron angular frequency: ωc = (qB)/m.
- fc = |ωc| / (2π) gives the cyclic frequency in hertz.
- Tc = 1 / fc gives the gyroperiod.
- If v⊥ is known, rL = v⊥ / |ωc| gives the gyroradius.
The sign of ωc indicates rotation direction and depends on charge sign.
How to use this calculator
- Enter the magnetic field strength and choose its unit.
- Select a particle preset, or choose Custom to enter q and m.
- Optionally provide v⊥ to compute the gyroradius.
- Alternatively, enable temperature mode to estimate v⊥ from T.
- Press Calculate to see results above the form.
Example data table
| Magnetic field B | Particle | fc (approx.) | Notes |
|---|---|---|---|
| 50 µT | Electron | ~1.40 MHz | Earth-scale field, rapid electron gyration. |
| 50 µT | Proton | ~0.76 kHz | Same field, much slower due to larger mass. |
| 1 T | Proton | ~15.2 MHz | Strong laboratory field increases frequency. |
Professional article
1) Meaning of gyrofrequency
Gyrofrequency is the rate a charged particle circles a magnetic field line. In a uniform field, the Lorentz force produces helical motion with angular rate ωc. Because ωc depends only on charge, mass, and B, it is a stable reference for plasma diagnostics and beam transport.
2) Inputs and unit discipline
Enter B carefully and pick the correct unit. Earth’s field is roughly 25–65 µT, while laboratory magnets often span 1–10 T. The converter also supports gauss, where 1 G = 10⁻4 T. Consistent units typically matter more than rounding in constants.
3) Electrons versus ions
Mass sets the scale. A standard benchmark is electron fc ≈ 28.0 GHz per tesla. Protons are much slower: fc ≈ 15.2 MHz per tesla. Alpha particles are about 7.6 MHz per tesla, reflecting a smaller charge-to-mass ratio than protons.
4) Frequency, period, and sign
The calculator reports ωc in rad/s and fc in hertz, related by fc = |ωc|/(2π). The gyroperiod is Tc = 1/fc, useful for resonance timing and sampling design. The sign of ωc indicates rotation direction: negative for electron-like charge and positive for ion-like charge under the right-hand rule.
5) Gyroradius and confinement
With a perpendicular speed v⊥, the Larmor radius is rL = v⊥/|ωc|. Smaller rL means tighter magnetic guiding. Example: at B = 1 T and v⊥ = 2×10⁶ m/s, an electron has rL ≈ 1.1×10⁻5 m, while a proton is near 2.1×10⁻2 m.
6) Temperature-based velocity option
If v⊥ is unknown, estimate it from perpendicular temperature using v⊥ ≈ √(2kT/m) in the non-relativistic regime. This is common in space-plasma work and low-energy labs. If the implied speed exceeds about 0.1c, the tool warns that relativistic effects may matter.
7) Practical ranges and applications
Gyrofrequency controls wave-particle interactions, magnetic heating, space-weather diffusion, and detector design. In fusion-scale fields of 2–7 T, electron cyclotron frequencies fall in tens to hundreds of gigahertz, while ion cyclotron frequencies sit in tens of megahertz. These scales guide antenna bands and digitizer rates.
8) Quality checks before exporting
Sanity-check scaling: fc rises linearly with B and |q|, and falls with m. Compare with the example table, then export CSV or PDF for reports. For custom particles, verify SI units for q and m and confirm the charge sign before saving, and keep a record of assumptions used.
FAQs
1) What is the difference between ωc and fc?
ωc is the angular gyrofrequency in rad/s. fc is the cyclic frequency in Hz and equals |ωc| divided by 2π. Both describe the same rotation rate, just in different units.
2) Why does the sign of ωc change?
The sign comes from the particle charge. Positive charges rotate in one sense and negative charges in the opposite sense for the same magnetic-field direction, following the right-hand rule for the Lorentz force.
3) Can I use gauss or microtesla?
Yes. Select the desired field unit and the calculator converts internally to tesla. Remember: 1 G = 10⁻4 T and 1 µT = 10⁻6 T.
4) How is the gyroradius computed?
If you provide v⊥, the tool uses rL = v⊥/|ωc|. This assumes uniform B and non-relativistic motion. For very high speeds, the true radius increases because effective mass is larger.
5) What does the temperature option assume?
It estimates v⊥ from v⊥ ≈ √(2kT/m). This is a non-relativistic approximation that treats T as an energy scale for perpendicular motion. Use it for quick estimates, not precision thermodynamics.
6) Which particle preset should I choose?
Use electron, proton, or alpha for common plasma cases. Choose the ion (+e, 1 amu) preset for quick singly charged estimates. Select Custom when you know the exact charge and mass of your species.
7) What should I export to include in reports?
Export CSV for spreadsheets and batch comparisons. Export PDF for a clean snapshot of inputs and outputs. If you later change inputs, recalculate first so downloads reflect the latest result table.
Accurate inputs produce clear results for better decisions.