# Some basic definitions

*spaceweb@oulu.fi - last update: 1 July 1998, 1200 UT (RR)*

## Cone angle

The IMF cone angle acos(Bx/|B|)
is the angle between the IMF direction and the sun-Earth line.
Statistically typical IMF orientation is 45 degrees in ecliptic
(tailward and duskward).
It has been shown that the cone angle controls the formation of
some Pc 3 pulsations types.

## Dispersion relation

Relates the wave number **k** to the wave frequency. Contains all the information about the
propagation of a given plasma wave mode.

## Fukushima-Bostrom theorem

Of any ionospheric current system **I**, only the source-free part **I**sf can be detected
below the ionosphere.

## Gyration

From the **equation of motion**, m d**v**/dt = q(**v** x **B**) one can calculate
that, in a presence of magnetic field **B**, a charged particle is accelerated in direction
perpendicular to both **v**(perp) and **B**. This forms a circular motion about a imaginative
**guiding center** of the particle. The sense of rotation is opposite for positive and negative
charges, being clockwise for negative particles when viewed in the direction of **B**. The electrons
producing auroras are thus rotating counterclockwise when viewed from the ground in the norther
hemisphere. They are also in **helicoidal** trajectories because of a additional velocity component
parallel to **B**.

## Gyrofrequency

Angular frequency of gyration, cyclotron frequency, or Larmor frequency. The magnitude of the angular
velocity of a charged particle gyrating around its guiding center, w = |q|B/m (in radians/s). The smaller
the particle mass, the larger its gyrofrequency will be, and the higher the magnetic field, the higher the
gyrofrequency, also. See also gyroradius.

## Gyroradius

Radius of gyration, or cyclotron radius. The radius of the circular orbit of a charged particle gyrating
around its guiding center, r = v(perp)/w = mv(perp) /(|q|B). The smaller the particle mass, the smaller its
gyroradius will be, and the higher the magnetic field, the smaller the gyroradius, also. See also
gyrofrequency (w).

## Heliopause

Boundary where the outgoing solar wind meets the incoming plasma of
the local interstellar medium (LISM). Believed to be at least 120
astromnomical units away.
## Langevin equation

Equation of motion for a weakly ionized cold plasma.

## Linear perturbation theory

Assumption that the variations in the plasma parameters, due to the presence of waves,
are small (to the first order) as compared to the undisturbed parameters. This makes it
possible to linearize equations by dropping out second order (and higher) nonlinear
terms.

## Lorenz gas

The type of plasma in which only the electron motion is important. A valid approximation with high
frequency phenomena, when the much heavier ions don't have time to respond. Used succesfully
when studying the propagation of electromagnetic waves in cold magnetoplasmas.

## Magnetic moment

To the circular motion of a charged particle in a magnetic **B** field there is associated a circular
electric current I which, in turn, has an associated magnetic field. This field is parallel to the external
field outside the gyroradius of the particle, and opposite inside. The magnetic moment of the particle
points thus in opposite direction to **B**, and has magnitude |**m**| = IA, if the particle orbit
covers an area A. It can be shown that |**m**| = W(perp)/B, where W(perp) is the part of the
particle kinetic energy associated with the transverse velocity V(perp).

## Magnetic rigidity

The magnitude of B times the gyroradius of a charged particle equals to its momentum per unit charge,
called also magnetic rigidity; Br = mv(perp)/|q|.

## Magnetoionic theory

Theory of wave propagation in a cold homogenous, magnetized electron gas.

## Pitch angle

The angle *a* between magnetic field **B** and velocity vector of a charged particle,
**v**., i.e., sin*a* = v(perp) / v(total), where v(perp) refers to the velocity component
perpendicular to **B**.

## Pitch Angle Distribution (PAD)

A form of presenting particle fluxes at a given energy as a function of pitch angle.

## Plasma frequency

Space charge oscillations at the natural frequency of the plasma. For the electrons also known as
Langmuir oscillations. In cold plasma approximation, and when ion motion is neglected, these
oscillations are stationary (no wave propagation), longitudinal (electron velocity is in the same
direction as the electric field), and electrostatic (there is no magnetic field associated with the
oscillations). In the warm plasma model, these oscillations become propagating disturbances known
as space charge waves or Langmuir waves. Since plasma frequencies are proportional to the
square root of the density of the particles, one can estimate densities by measuring them.

## Plasma instability

Waves in some mode growing exponentially or faster.

## Wave packet

Superposition of waves with different values of k and f.
See also: