@Article{sen78b,
author = {Abhijit Sen and Charles F. F. Karney and
George L. Johnston and Abraham Bers},
title = {Three-Dimensional Effects in the Non-linear
Propagation of Lower-Hybrid Waves},
journal = {Nucl. Fusion},
volume = 18,
number = 2,
pages = {171-179},
month = feb,
year = 1978,
reprint = {nf78},
preprint = {M.I.T. Rept. \eref{PRR-77-16}{RLE PRR 77/16} (June
1977) 19 pp.},
abstract = {Self-modulation effects can become important for the
propagation of lower hybrid waves in plasma,
particularly for the high power levels envisioned in
r.f. heating schemes. Earlier studies in two
dimensions (in the plane defined by the electric field
of the pump wave and the background magnetic field)
have led to non-linear propagation equations, such as
the MKdV or the non-linear Schrödinger equations,
which admit multiple-soliton solutions. These could
physically manifest themselves by breaking up the
resonance cones into filaments with intense localized
electric fields and could further lead to localized
heating. This problem is studied in three dimensions
with the motivation of including two additional
physical factors. First, the non-linear effect
arising from the <b>E</b> × <b>B</b> motion of
electrons is included; this leads to an enhancement in
the threshold value for the formation of solitons.
Secondly, the stability of the two-dimensional
solitons to perturbations in the third dimension is
studied, and it is found that the third dimension
introduces additional dispersive effects which render
the solitons unstable to these perturbations.}
}