@MastersThesis{karney74,
  author =       {Charles F. F. Karney},
  title =        {Parametric Coupling to Low Frequency Plasma Waves},
  type =         {{SM} Thesis},
  department =   {Department of Electrical Engineering},
  school =       {Massachusetts Institute of Technology},
  reprint =      {thesis74},
  month =        jan,
  year =         1974,
  abstract =     {Nonlinear excitation of ion waves by a pump near the
                  lower hybrid frequency is examined.  The ion waves
                  considered are ion acoustic, electrostatic ion
                  cyclotron and magnetosonic waves.  The approach
                  adopted is coupling of modes carried out to second
                  order.  We examine the effects of varying the angles
                  of the excited waves, and apply the results to
                  excitation of such waves in a bounded inhomogeneous
                  plasma.  The plasma is assumed uniform and is
                  described by the two fluid equations.  Considerable
                  complexity is introduced by taking the angles of
                  propagation to be arbitrary (subject to frequency and
                  wave number matching conditions), and by taking the
                  magnetic field to be finite.  In order to treat this
                  problem analytically, we have made extensive use of
                  MACSYMA, a large symbolic computation system, that has
                  been developed by the Mathlab group at M.I.T.  Using
                  this facility we have been able to obtain approximate
                  analytic results for the growth rates of the excited
                  waves.  Using damping rates from kinetic theory,
                  thresholds for these interactions have been
                  calculated, for typical tokamak plasmas.  With the
                  interaction in a uniform plasma well understood, we
                  have tried to examine some of the effects of exciting
                  the pump from a waveguide at the wall of an
                  inhomogeneous plasma.  We find that in tokamak plasmas
                  it is possible to excite electrostatic ion cyclotron
                  waves, but since the pump ray is very narrow unstable
                  pulses are unable to grow significantly before
                  convecting out of the pump region.  However if it is
                  possible to set up an array of waveguides at the
                  boundary of the plasma, a larger region of pump fields
                  is attainable, and strong excitation of the
                  electrostatic ion cyclotron wave should take place
                  with reasonable external rf powers.}
}