@Article{karney79e,
  author =       {Charles F. F. Karney},
  title =        {Stochastic Ion Heating by a Lower Hybrid Wave: {II}},
  journal =      {Phys. Fluids},
  volume =       22,
  number =       11,
  pages =        {2188-2209},
  month =        nov,
  year =         1979,
  reprint =      {pf79d},
  doi =          {10.1063/1.862512},
  preprint =     {Princeton Univ. Rept. PPPL--1528 (Apr. 1979) 68 pp.},
  eprint =       {physics/0501034},
  abstract =     {The motion of an ion in a coherent lower hybrid wave
                  (characterized by |<i>k</i><sub>||</sub>| &lt&lt;
                  |<i>k</i><sub>&perp;</sub>| and &omega; &gt;&gt;
                  &Omega;<sub><i>i</i></sub>&nbsp;) in a tokamak plasma
                  is studied.  For ions satisfying
                  <i>v</i><sub>&perp;</sub> &gt;
                  &omega;/<i>k</i><sub>&perp;</sub>, the Lorentz force
                  law for the ions is reduced to a set of difference
                  equations which give the Larmor radius and phase of an
                  ion on one cyclotron orbit in terms of these
                  quantities a cyclotron period earlier.  From these
                  difference equations an earlier result [<a
                  href="karney78c.html">Phys. Fluids <b>21</b>,
                  1584&ndash;1599 (1978)</a>] that above a certain wave
                  amplitude the ion motion is stochastic, is readily
                  obtained.  The stochasticity threshold is given a
                  simple physical interpretation.  In addition, the
                  difference equations are used to derive a diffusion
                  equation governing the heating of the ions above the
                  stochasticity threshold.  By including the effects of
                  collisions, the heating rate for the bulk ions is
                  obtained.}
}