Ponderomotive forces

The ponderomotive force (English: ponderomotive force , therefore sometimes also called ponderomotive force ) is the low-frequency component of the force of a spatially inhomogeneous, high-frequency electromagnetic field on a system of (moving in this field) electrical charges .

Explanation

When a homogeneous (i.e. not location-dependent) alternating field acts on a charged particle, the particle oscillates around its rest position due to the changing force. Since the field acts alternately with the same strength in two opposite directions, the particle trajectory is strictly periodic, that is, no force acts on the particle on average over time.

In the case of an inhomogeneous (location-dependent) field, the particle experiences a different field strength when deflected to one side than when deflected to the other side. As a result, the force is no longer zero over time; the mean force is called the ponderotor force. Since the force varies very quickly with high-frequency alternating fields and the oscillation amplitudes of the particles are therefore very low, only the averaged, i.e. the ponderomotive force, is decisive for a macroscopic observation of the particle trajectories.

For a charged particle, the ponderomotive force is proportional to the gradient of the intensity of the electromagnetic field and, for a free particle, acts in the direction of a lower field strength. The intensity of the electromagnetic field is essentially the square of the field strength. The force is inversely proportional to the mass of the particle. This is explained by the fact that light particles have greater oscillation amplitudes and are therefore more sensitive to spatially different field strengths than massive particles.

On a bound particle, the ponderomotive force above the binding resonance frequency also acts against the spatial intensity gradient. Below the resonance frequency, the ponderomotive force acts in the direction of the spatial intensity gradient of the field.

Basically, the effect only depends on the particle dynamics - not on what kind of interaction is the cause of the force. For example, the acoustic radiation force that acts on particles (or gas bubbles in liquids) in ultrasound is based on the same phenomenon, but in the sound field.

In a many-particle system, it is not only the detector inertia that ensures low-pass filtering, but also the thermodynamic ensemble averaging during the transition from the microscopic to the macroscopic perspective.

calculation

The ponderomotive force results from

${\displaystyle \mathbf {F} _{p}=-{\frac {e^{2}}{2\,m\,\omega ^{2}}}\nabla {\overline {\mathbf {E} \cdot \mathbf {E} }}}$,

where is the electrical charge and mass of the particle; and are the angular frequency and field strength of the electric field. The line above the square of the field strength represents the mean value over time. If the location-dependent amplitude of the field strength used, the pre-factor is instead to use. ${\displaystyle e}$ ${\displaystyle m}$ ${\displaystyle \omega }$ ${\displaystyle \mathbf {E} }$ ${\displaystyle -e^{2}/4m\omega ^{2}}$ ${\displaystyle -e^{2}/2m\omega ^{2}}$

Applications

Ponderomotive forces are used in ion traps , for example in the Paul trap , to store ions without contact with the walls of the vacuum vessel. A similar arrangement to the Paul trap is the quadrupole mass analyzer, which is used for mass spectrometry . This exploits the fact that ions that are too massively have only a low oscillation amplitude and therefore the ponderomotive force is not sufficient to overcome a constant field that counteracts them.

Ponderomotive forces also act on electrons in laser beams with an extremely high energy density (femtosecond laser).

In addition, ponderomotive forces play a decisive role in the free electron laser (FEL), because they are the cause of the effect known as microbunching , which leads to the generation of photons.

Individual evidence

1. ↑ UCLA PBPL: Free-Electron Laser - FEL Amplification