the field, is close to 90 degrees. Thus the instability will be most likely when the wave vector is close to perpendicularity. However, it is important to remember that our derivation does not hold if the wave vector is exactly perpendicular to the field, although we can go as close as 1 / 3 of a degree from perpendicularity. Following Perkins and Valeo, the rf field vector can be written as: where we assume that , the plasma frequency. Note that reference 1 used where we use since our is the component of the wave vector perpendicular to the magnetic field while their k was the entire wave vector in the Y-direction (so that it is perpendicular to the rf propagation direction and not perpendicular to the magnetic field). Substituting Equation (B-l) into Maxwell's equations, we find that satisfies the parabolic equation:
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