What Is the Cyclotron Frequency & Larmor Gyroradius Calculator?
The Larmor radius (or gyroradius) is the radius of the circular motion of a charged particle moving perpendicular to a uniform magnetic field.
The cyclotron frequency is the angular frequency of this orbital gyration.
How Does the Cyclotron Frequency & Larmor Gyroradius Calculator Work?
The Lorentz force F = q(v × B) acts perpendicular to both velocity and magnetic field, supplying the centripetal acceleration for circular motion.
Because ions are thousands of times more massive than electrons, their gyroradii are much larger (millimeters vs. microns), while their gyrofrequencies are much lower (MHz vs. GHz).
Cyclotron Frequency & Larmor Gyroradius Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Computes gyromotion orbit radius and cyclotron frequency from Lorentz equation of motion.
How to Use the Cyclotron Frequency & Larmor Gyroradius Calculator
- Select the particle species (electron, proton, deuteron, or alpha).
- Input the magnetic field in Tesla and kinetic energy in eV.
- Compare gyroradius against device minor radius to verify magnetic confinement.
Step-by-Step Example Calculation
10 keV Deuteron in a 5.0 T Tokamak Field
Input Values:
Understanding Your Result
Larmor radius governs neoclassical transport and spatial resolution requirements for plasma simulations.
Cyclotron frequency dictates resonance frequencies for Ion Cyclotron Resonance Heating (ICRH) and Electron Cyclotron Heating (ECH).
Factors That Affect the Result
- Magnetic field: Doubling B halves the Larmor radius, dramatically improving plasma confinement.
- Particle energy: Faster, hotter particles orbit with wider gyroradii.
When Should You Use This Calculator?
- Sizing RF plasma heating antennas (ICRH, ECRH).
- Analyzing fast alpha particle confinement in fusion reactors.
Assumptions & Limitations
- Valid for uniform magnetic fields without magnetic gradient or curvature drifts.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Exact classical Lorentz motion formulation.