Paul Trap Mathieu Stability
Map a full RF cycle to distinguish dynamical confinement, exponential growth and deceptive unit-magnitude multipliers.
Free theory articleMap a full RF cycle to distinguish dynamical confinement, exponential growth and deceptive unit-magnitude multipliers.
Concept & interpretation
The Paul trap confines charged particles using a combination of static (DC) and oscillating (RF) electric fields. The idealized 1D motion of a single coordinate inside this trap is described by the Mathieu equation: x'' + (a - 2q cos(2τ))x = 0. By studying the monodromy matrix over one full RF cycle, we can map out the stability regimes of the trap.
experiment
In the Interactive Paul Trap module, you can investigate different parameters:
- Set DC parameter a to 0.
- Set RF parameter q to 0.2.
- Observe the Bounded elliptic classification and compare it to the worked example trace of ~1.80.
- Set RF parameter q to 0, and observe the Unbounded linear drift where the trace becomes exactly 2.