Cyclotron Sim
2D charged particle in uniform B and E fields. Equations of motion from Hamiltonian mechanics.
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B (T)
1.0
E (V/m)
0.0
Particle
e/m (C/kg)
1.0
Initial Conditions
x₀
0.0
y₀
0.0
vx₀
1.0
vy₀
0.0
Display
Show analytic solution
Show guiding center
Show velocity vector
Show E field arrows
Speed
1×
Live Readouts
Position
(0, 0)
Velocity
(0, 0)
ωc (cyc. freq)
1.00
E×B drift
0.00
Larmor radius
1.00
Energy
0.50
Equations of Motion
m ẍ = eB ẏ + eE
m ÿ = −eB ẋ
Drift velocity: v_drift = E/B (ŷ direction)
Cyclotron freq: ωc = eB/m
Larmor radius: rL = v⊥ / ωc
Numerical (RK4)
Analytic
Guiding center