### Taming Ions: the Paul Trap

Tags: Paul trap / Mathieu differential equation

We will study the movement of charged particles in a so-called Paul trap by solving the equations of motion using approximative methods.

In the following problems we will be concerned with the movement of charged particles under the influence of an electrostatic field. Depending on the question we will have to solve **Euler-Lagrange equations** of motion or use similar approaches. A lot of the problems are historically motivated to which we shall refer in the respective background sections.

Published
in
Electrodynamics /
Electrostatics /
Charges and Movement

Tags: Paul trap / Mathieu differential equation

Tags: Paul trap / Mathieu differential equation

We will study the movement of charged particles in a so-called Paul trap by solving the equations of motion using approximative methods.

Published
in
Electrodynamics /
Electrostatics /
Charges and Movement

Tags: Equations of Motion / Metric / Christoffel Symbols

Tags: Equations of Motion / Metric / Christoffel Symbols

The movement of a charged particle along a surface subject to an external electric field is considered. We find the same equations of motion as for geodesic movement in general relativity.

Published
in
Electrodynamics /
Electrostatics /
Charges and Movement

Tags: Dipole / Equations of Motion

Tags: Dipole / Equations of Motion

The movement of a dipole-like molecule in a constant electric field is derived using the Euler-Lagrange equations.