# Paul trap

Paul trap from 1955 in the Deutsches Museum Bonn

In a Paul trap (also known as a Paul ion cage ), electrically charged particles are stored by means of an alternating electrical field . Occasionally she is also called quadrupole - ion trap called, which refers to the geometry of the field used. The German physicist Wolfgang Paul received the 1989 Nobel Prize in Physics for the development .

## theory

Cross-sectional diagram of a Paul trap with positively charged particles (red) surrounded by a cloud of similarly charged particles. The electric field (blue) is generated by a quadrupole consisting of end caps (a) and ring electrode (b). 1. AC voltage phase with positive charge on the end caps, 2. with negative charge. The particle cloud is periodically distorted.

In its classic design, the Paul trap consists of three electrodes : a ring-shaped electrode and two electrically connected end cap electrodes that are attached to both sides of the ring. The electrodes have hyperbolic inner surfaces. An alternating voltage with a high frequency (HF) of usually 1  MHz is applied between the ring electrode and the end cap electrodes , which generates an electric quadrupole field inside the trap that exerts a force that changes periodically over time on the ions. The further the ions move away from the center of the trap, the greater the storage force.

A cloud of ions inside the trap experiences alternating forces in the frequency of the alternating field: focusing in the ring plane (through the ring electrode) with simultaneous defocusing force perpendicular to it (through the end cap electrodes). During the phase change, there is then a focusing perpendicular to the ring plane with simultaneous defocusing in the ring plane. Both effects alternate at a high frequency and create an effective focus in all three dimensions, i.e. storage.

The precise paths of the ions are described by Mathieu's differential equations - named after the mathematician Émile Léonard Mathieu . A presentation of the Paul trap that is understandable even for non-experts and its theoretical treatment with the Mathieu equation was written by RE March.

## Linear design

Photo of a linear Paul trap during maintenance at the University of Calgary

In practice, a linear Paul trap design is often preferred. For this purpose, four metal rods of equal length are used, which are arranged parallel to one another in a rectangle so that they form a cuboid. The rods each consist of three sections that are electrically separated from one another by insulator rings. They are now operated with an alternating electric field in the same way as the classic structure; the center pieces of the rods form the ring electrode and the end pieces form the end cap electrodes. This allows ions to be stored inside the resulting cuboid.

This design is simpler and has the decisive advantage that it contains an opening on both long sides through which, for example, a laser can be used to measure or cool the particles more easily, without disturbing the field geometry. It can also be used as a mass spectrometer (so-called quadrupole mass spectrometer ).

## use

The Paul trap is a simple way of storing charged particles. Since the stability of the orbits depends on the mass-charge ratio of the ions, the Paul trap can be used, for example, for mass analysis in ion trap mass spectrometers. The Paul trap also played a major role in the first attempts to implement a quantum computer .

## Mechanical analogue

A vivid model after Wolfgang Paul on the occasion of his Nobel Lecture makes it easier to imagine the principle: A ball would roll down from a stationary saddle surface . If the surface rotates, however, the ball can be stabilized. The further the ball moves away from the center, the steeper the surface and the stronger the repulsive force. A video from the University of Freiburg shows a demonstration of the mechanical analog.

## Patents

• Patent DE944900 : Method for the separation or for the separate detection of ions with different specific charges. Registered on December 24, 1953 , inventor: W. Paul, H. Steinwedel (German priority December 23, 1953).
• Patent GB773689 : Improved arrangements for separating or separately detecting charged particles of different specific charges. Inventor: W. Paul (German priority December 23, 1953).
• Patent US2939952 : Apparatus for separating charged particles of different specific charges. Inventor: W. Paul, H. Steinwedel (German priority December 23, 1953).