Cyclotron Simulation
Example 4.4: Proton Acceleration in Cyclotron
This simulation demonstrates proton acceleration in a cyclotron with 60 cm dees and 10 MHz oscillator frequency.
Oscillator frequency:
10 MHz
Magnetic field (B):
0.66 T
Proton velocity:
0 m/s
Kinetic energy:
0 MeV
Key Formulas
B = 2πmv/q (Cyclotron frequency condition)
v = r × 2πv (Final velocity)
E = ½mv² (Kinetic energy)
Calculations
B = 2π × 1.67×10⁻²⁷ kg × 10⁷ Hz / 1.6×10⁻¹⁹ C = 0.66 T
v = 0.6 m × 2π × 10⁷ Hz = 3.78×10⁷ m/s
E = ½ × 1.67×10⁻²⁷ kg × (3.78×10⁷ m/s)² = 7 MeV
