Electrostatic ion cyclotron wave

# Electrostatic ion cyclotron wave

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An electrostatic ion cyclotron wave is a longitudinal
Longitudinal wave
Longitudinal waves, as known as "l-waves", are waves that have the same direction of vibration as their direction of travel, which means that the movement of the medium is in the same direction as or the opposite direction to the motion of the wave. Mechanical longitudinal waves have been also...

oscillation of the ions (and electrons) in a magnetized plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

, propagating nearly (but not exactly) perpendicular to the magnetic field. The angle (in radian
Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit...

s) between the direction of propagation and the direction perpendicular to the magnetic field must be greater than about the square root of the mass ratio,
,

in order that the electrons can move along the field lines from crest to trough to satisfy the Boltzmann relation
Boltzmann relation
In a plasma, the Boltzmann relation describes the number density of an isothermal charged particle fluid when the thermal and the electrostatic forces acting on the fluid have reached equilibrium...

. The dispersion relation
Dispersion relation
In physics and electrical engineering, dispersion most often refers to frequency-dependent effects in wave propagation. Note, however, that there are several other uses of the word "dispersion" in the physical sciences....

is,

where Ωc is the ion cyclotron frequency and vs is the ion sound speed
Ion acoustic wave
An ion acoustic wave is one type of longitudinal oscillation of the ions and electrons in a plasma, much like acoustic waves traveling in neutral gas. However, because the waves propagate through positively charged ions, ion acoustic waves can interact with their electromagnetic fields, as well as...

. This relation is the result of restoring forces due to the Lorentz force
Lorentz force
In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:...

(see Upper hybrid oscillation
Upper hybrid oscillation
An upper hybrid oscillation is a mode of oscillation of a magnetized plasma. It consists of a longitudinal motion of the electrons perpendicular to the magnetic field with the dispersion relation...

for more details), the electrostatic force (the Te term in vs), and the ion pressure (the Ti term in vs).

• Waves in plasmas
Waves in plasmas
Waves in plasmas are an interconnected set of particles and fields which propagates in a periodically repeating fashion. A plasma is a quasineutral, electrically conductive fluid. In the simplest case, it is composed of electrons and a single species of positive ions, but it may also contain...

• Ion acoustic wave
Ion acoustic wave
An ion acoustic wave is one type of longitudinal oscillation of the ions and electrons in a plasma, much like acoustic waves traveling in neutral gas. However, because the waves propagate through positively charged ions, ion acoustic waves can interact with their electromagnetic fields, as well as...

• Upper hybrid oscillation
Upper hybrid oscillation
An upper hybrid oscillation is a mode of oscillation of a magnetized plasma. It consists of a longitudinal motion of the electrons perpendicular to the magnetic field with the dispersion relation...

• Lower hybrid oscillation
Lower hybrid oscillation
A lower hybrid oscillation is a longitudinal oscillation of ions and electrons in a magnetized plasma. The direction of propagation must be very nearly perpendicular to the stationary magnetic field, within about √ radians...