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Cramer N.F. The physics of Alfven waves (Wiley-VCH, 2001)(400dpi)(K)(T)(304s)_P_.djvu |
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к > 0, are also left-hand polarized for v+, but correspond to the fast wave, and are right-hand
polarized for г>_, but correspond to the slow ion cyclotron wave...
In the low-frequency, long-wavelength limit, u>0 <C п{ and v\k2 <C Qf, both excited
waves have the same frequency, u>sj = u>o/2, and the growth rate is
7 = ewo/8...
E.98)
dt oz
A physical interpretation of the nonlinear interactions may be gained by noting that the right-
hand side of Eq...
The decay instability is not expected to be of importance in the solar wind
(/? ~ 1/2), or the vicinity of the Sun down to about twice the solar radius (/? ~ 0.1)...
Such standing waves have been observed by the Viking
satellite in the 0.1-1 Hz frequency range trapped within a density cavity of high va between
a half and a few Earth radii...
In these cases the dispersive term results from the finite width of
the cylinder or the slab...
It is therefore possible that nonlinear surface Alfven
waves at frequencies approaching the ion cyclotron frequency may contribute to the spectrum
of the fluctuations...
The interplay of localized waves with eigenmodes of the bounded
plasma is also considered here...
These modes correspond to shear Alfven waves that
are localized about the Alfven resonance points defined by Real(u) = uA (see Section 3.2.4)...
Such a wave mode is a surface wave, which has
been analysed for a planar surface in Chapter 4...
The elec-
63 Cylindrical Geometry 175
trie field component Ez is zero in the plasma, and Eqs...
As a approaches zero, the ICW
spectrum becomes infinitely dense, and is equivalent to the Alfven wave with indeterminate
value of kc...
The transition is illustrated in Figure 6.5(a), where
the m = +1 lowest compressional eigenmode magnetic field profiles are shown for three
wavenumbers k...
A similar technique can be used to calculate the perturbation of the frequency for
a resistive plasma, for which the short-wavelength resistive mode must be taken into account
(Collins, Cramer & Donnelly 1984)...
However, if the width of the transition region in the stratified plasma where a resonance is
encountered is not small, that is, when s is not small, a numerical solution is usually necessary...
F.55), r0 moves from
the centre to the edge of the plasma as / increases from /th to a value /m = 1...
In addition to the CAW eigenmodes, a separate family of
spatial eigenmodes of the KAW or IAW in the bounded plasma may occur...
An iterative expansion, in the finite ion Larmor radius (FLR) parameter A; = k\V^/Ц2
(assumed much less than unity), is made on the wave equation F.14) with the kinetic the-
theory expressions for the components of the dielectric tensor (see Appendix)...
The
results are also relevant to the modes of cylindrical current-carrying flux tubes in the solar
atmosphere (see Chapter 7)...
The Alfven resonance a; = uja is indicated, (a) krp = 0.1 (k >
-mJ/2rp), (b) krp = 0.02 (к < -mJ/2rp)...
This can result in a global mode, the DAW mode, which propagates with
a phase speed that is independent of position in the nonuniform plasma, but which has wave
fields characteristic of the shear Alfven wave rather than the CAW mode...
Slab Plasma
It is instructive first to consider a planar slab plasma, that is, a plasma bounded by a vacuum
at the two planes x = ±R...
F.97) are considerably simpler in the planar case than in the cylindri-
cylindrical case given by Eq...
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