1. What is Cyclotron Frequency?

The cyclotron frequency is the frequency at which a charged particle orbits in a uniform magnetic field. It's fundamental in cyclotrons and other particle accelerators, as well as in plasma physics and magnetic confinement fusion.

2. How Does the Calculator Work?

The calculator uses the cyclotron frequency equation:

Where:

• \( f \) — Cyclotron frequency (Hz)
• \( q \) — Charge of the particle (Coulombs)
• \( B \) — Magnetic field strength (Tesla)
• \( m \) — Mass of the particle (kg)

Explanation: The equation shows that the frequency is directly proportional to the charge and magnetic field, and inversely proportional to the mass of the particle.

3. Importance of Cyclotron Frequency

Details: Understanding cyclotron frequency is crucial for designing particle accelerators, mass spectrometers, and for research in plasma physics. It's also important in medical applications like proton therapy.

4. Using the Calculator

Tips: Enter the particle's charge in Coulombs, magnetic field strength in Tesla, and particle mass in kilograms. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does the cyclotron frequency depend on particle velocity?
A: No, remarkably the cyclotron frequency is independent of particle velocity in non-relativistic cases.

Q2: What's the difference between cyclotron frequency and Larmor frequency?
A: They're essentially the same for non-relativistic particles, but Larmor frequency is more general and can include relativistic effects.

Q3: How does relativity affect the cyclotron frequency?
A: At relativistic speeds, the frequency decreases due to mass increase, requiring synchrocyclotrons that vary frequency.

Q4: What particles is this calculator valid for?
A: It works for any charged particle (electrons, protons, ions) as long as relativistic effects are negligible.

Q5: Why is 2π in the denominator?
A: The 2π converts from angular frequency (radians/second) to regular frequency (cycles/second or Hz).