@TechReport{karney76,
  author =       {Charles F. F. Karney and Abraham Bers},
  title =        {Nonlinear Orbit Perturbation and Ion Heating},
  institution =  {M.I.T.},
  year =         1976,
  number =       {RLE PRR 76/7},
  month =        jan,
  reprint =      {PRR-76-7},
  note =         {Reprint of M.I.T. RLE Progress Rept. No. 117,
                  pp. 193--197 (Jan. 1976)},
  abstract =     {In proposed Tokamak RF heating schemes using waves
                  near the lower hybrid frequency, fields with large
                  <i>k</i><sub>&perp;</sub><i>a</i><sub><i>i</i></sub>
                  can be generated, either directly by linear conversion
                  into lower hybrid waves or by the parametric decay
                  into lower hybrid waves and ion Bernstein waves.  The
                  fields can significantly perturb the motion of an ion,
                  and hence can nonlinearly heat the ions.  In this
                  report we present the results of a numerical solution
                  of the orbit equation and give an approximate formula
                  for the ion energy gain.}
}