Plasma oscillation

In physics, a plasma oscillation is a periodic oscillation of the charge density in a medium, for example in a plasma or a metal. The quasi-particles, which results from the quantization of these oscillations is the plasmon.

• 3.1 reflection of light on metals
• 3.2 Reflection of radio waves in the atmosphere

Plasma frequency

If the free electrons in an electron gas is compressed locally, acts on it, the Coulomb force, is attempting to establish the homogeneous charge distribution again. Due to their inertia, the electrons shoot past the neutral position and build a new charge excess, resulting in a periodic oscillation. Is the angular frequency, oscillates with the electron density to the average density is the plasma frequency:

Wherein

• The electron density is
• The elementary charge,
• The electric field constant and
• The electron mass.

Looking at the charge carriers in a dielectric with a permittivity, the reduction in the plasma frequency:

The plasma resonance is a dispersionless, ie independent of the expansion, excitation. A penetrating into the material electromagnetic wave can excite the vibration, undergoing both absorption and refraction.

Derivation

The three necessary equations to derive the plasma frequency are:

1 ) the Poisson equation of electrostatics which describes the potential as a function of the charge density:

In which

• Particle density
• Electrical charge of the particles
• Electrostatic potential
• Permittivity

2 ), the equation of continuity, which describes the conservation of particles:

With

• Current density with particle velocity ( The equation can be used both for the conservation of charge - or be formulated for the Teilchenerhaltung - as here. )

3 ) The Newton's second law, which describes the kinetic response of the particles with respect to the force of the electric field:

With

For small variations in density can, using the relationship shown in 2 ) for the current density, the time derivative of the particle velocity can be expressed only by the time derivative of the current density:

This implies the assumption that the relative density variations are small compared to the relative changes in the particle velocities. This is obtained by inserting back into the third ) equation

That by use of the divergence operation on the entire equation

Insertion of the Poisson equation of electrostatics at the left and the equation of continuity on the right side allows:

This results in the equation for a harmonic oscillation with the plasma resonance frequency

Dispersion relation

Because the plasma frequency is independent of the wavelength (? ) Plasma oscillations having a phase velocity which is proportional to the wavelength, and a vanishing group velocity. In the above example, the incident electromagnetic wave excites the charge carriers of the plasma to oscillate to ( perpendicular to the propagation direction because the wave is polarized transversely ), but causes no charge transfer in the direction of incidence of the wave.

If the electrons have a finite thermal velocity with

• : Boltzmann constant
• : Rest mass of the electron
• : Based on normalized electron temperature,

Effect of the electrons in addition to the electric field pressure as a restoring force. Then the oscillations propagate with the Bohm -Gross dispersion relation

If the spatial scale is large compared to the Debye length, the pressure plays a minor role:

On small scales, however, dominates the pressure:

I.e., the waves are dispersionless the phase velocity, so that the individual electron plasma wave can accelerate. This process is called a kind of collision -less damping, Landau damping. For the reason, the dispersion relation is difficult to observe at large and rarely important.

Application

Electrons with a given plasma frequency can thus perform almost instantaneous movements that run "slower" than the plasma frequency. This means in particular that plasmas electromagnetic waves with frequencies below the plasma frequency almost completely reflect, for waves with frequencies above the plasma frequency, however, are transparent.

Reflection of light by metals

The plasma frequency is in the metallic solids in typical electron densities in the range of what can be converted on the phase velocity of electromagnetic wave in a wavelength of which lies in the UV range. Therefore metals reflect light in the optical range and even radio and radar waves. Electromagnetic wave with a higher frequency, such as UV or X-rays are transmitted on the other hand, as long as no other resonances above the plasma frequency (e.g., low energy electronic transitions from Shell ) absorb.

Reflection of radio waves in the atmosphere

Plasma oscillations in the Earth's ionosphere are the reason that short wave broadcast radio programs have a very wide reach. Meet The radio waves on the ionosphere and excite the electrons to vibrate. The relatively low electron density of the F- layer 1012 of only M-3, a plasma frequency of about 9 MHz may be calculated. This results in a reflection of all normally incident waves with lower frequency in the ionosphere. At shallower angles of incidence the usable frequency limit may rise to values ​​above 50 MHz. About shortwave transmitted programs can therefore receive even in places that actually are in the sender's point of view shadows. Communication with higher -altitude satellites or GPS is only possible through even higher frequencies in the VHF band.