WAVES IN M AGNETISED COLD PLASM A

2.4.4.1 PROPAGATION PA RALLEL TO B

T R A N S V E R S E R IG H T -H A N D C IR C U L A R L Y P O L A R IS E D W A V E S (R C P )

These are electromagnetic waves with a transverse electric field that rotates in the same direction as the electrons about the B field. They propagate in two different frequency ranges;

CÙ < Ogc and w > cor,cutoff (RCP cut-off frequency), depicted in Figure 2.4-3, and have a

resonance at the electron gyrofrequeney, At lower frequencies than the electron

gyrofrequeney these waves are commonly known as electron cyclotron or whistler mode waves. The dispersion relation for right-hand polarised waves is given by:

14- a = 1

V /

C h a p te r 2 - P h ysics o f th e E a r th ’s In n er M a gn etosph ere / W /k = C T- 'cel A (Electron Cyclotron W ave) Whistler

F ig u re 2.4-3 D is p e rs io n d ia g ra m s fo r th e R -m ode a n d L -m ode p a ra lle l p r o p a g a tin g e le c tro m a g n e tic w a v e s in a cold, m a g n e tis e d p la sm a . T he tw o d if f e r e n t c a se s a r e (a) fo r CÛL > O g c a n d (h) fo r c o l < Q g i- [Kivelson a n d Russell, 1995].

W H IS T L E R M O D E W A V E S

Whistler mode waves are low frequency (ion gyrofrequeney, Qi « o) < Qge) RCP waves. These waves experience dam ping due to thermal effects that rapidly increase near the electron gyrofrequeney. However, far away from the electron gyrofrequeney whistler mode waves are

only weakly damped. At high frequencies whistler mode waves are absorbed by the plasma

electrons, resulting in perpendicular heating o f the resonant electron population and damping of

the waves. The whistler mode waves therefore provide a potential source o f energy for the

acceleration o f electrons in the outer radiation belt and have been invoked in such a mechanism by Summers et a i, [1998] (see Chapter 2.5.2).

F A S T M O D E W A V E S

At very low frequencies, comparable to the ion gyrofrequeney, Qj, it is necessary to treat the

plasma as a two-fluid plasma as it is no longer acceptable to neglect ion dynamics. At these

very low frequencies in a two-fluid plasma the RCP wave is known as a fast mode wave. The name results from the higher phase velocity of the fast mode wave for propagation angles, 0#O , compared with the Alfvén phase velocity. These waves can generally propagate at all angles with respect to the magnetic field (see MHD waves).

T R A N S V E R S E L E F T -H A N D C IR C U L A R L Y P O L A R IZ E D W A V E S (L C P )

The LCP wave is an electromagnetic wave. At high frequencies, (O > cOpc > Qi, where we can neglect ion motions, the solutions for the LCP wave correspond to light waves or radio waves.

C h a p te r 2 - P h ysics o f the E a r th ’s Inner M agn eto sp h ere_____________________________________________________________________

The cutoff for this wave lies just below cOpc, with no wave propagation at frequencies between the cutoff and Qj. The dispersion relation for LCP waves is given by:

V Q)

E q u a tio n 2.4-4

E M IC W A V E S

If ion motions are taken into account then a new branch is created with frequencies co < These waves are sometimes referred to as electromagnetic ion cyclotron (EMIC) waves. They are found in two regions, for (o < f2nc+ and for to > Qn<ri with a stop band just above Qnc+ and a

resonance at the ion gyrofrequeney. These waves are responsible for the heating of

magnetospheric ions and of electrons in stable auroral red arcs (SAR arcs). The EMIC waves also cause pitch angle scattering of ions and are an important loss mechanism of ring current

ions during the recovery phase o f magnetic storms. These waves have been found to be

ineffective at heating energetic electrons (100 keV - 1 MeV), but have been proposed as a likely source o f rapid pitch angle scattering of > 1 MeV electrons near the dusk-side plasmapause

[Summers et a i, 1998] (see Chapter 2.5.2).

Note that at very low frequencies in the cold plasma approximation involving ion motions the phase velocities of the RCP and LCP waves go to zero. It is found that in order to find Alfvén waves (see MHD waves) it is necessary to use warm plasma theory, where the low frequency phase velocity is approximately the Alfvén velocity.

2.4.4.2 PROPAGATION PERPENDICULAR TO B

O R D IN A R Y W A V E S (O -M O D E)

The dispersion relation for 0-m ode waves is given by:

2 2 , , 2 2

Û? = + k C

E q u a tio n 2.4-5

The propagation of O-mode waves is not affected by the magnetic field. It is an

C h a p ter 2 - P h ysics o f the E a r th ’s In n er M a gn etosph ere_____________________________________________________________________

propagation, k. It has a cutoff at the electron plasma frequency (Figure 2.4-4) but at higher

frequencies the wave is a light wave or radio wave.

0 - M o d e X -M o d e W /k = c 'UH X-Mode F ig u re 2.4-4 T he d is p e rs io n d ia g ra m fo r O -m ode a n d X -m ode

p e rp e n d ic u la r p r o p a g a tin g e le c tro m a g n e tic w av es [Kivelson a n d

Russell, 1995].