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32 ) • dk lo If an energy density is associated with the magnitude of the wave ( or
its absolute square ) , it is clear that in this approximation the transport of energy
occurs with the group velocity , since that is the rate at which the pulse travels ...
where we have introduced a vectorial Alfvén velocity : ( 10 . 70 ) 4072 The wave
equation ( 10 . 69 ) for v , is somewhat involved , but it allows simple solutions for
waves propagating parallel or perpendicular to the magnetic field direction .
107 ) v , ~ 34 % Up From the definition of ky we see that for such wave numbers
the phase velocity is much larger than , and the group velocity much smaller than
, the rms thermal velocity ( u2 ) % . As the wave number increases towards kp ...
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Introduction to Electrostatics
References and suggested reading
Multipoles Electrostatics of Macroscopic Media
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