Electrostatic Wave Models of Reflection in a Dipole Magnetic Field

It is known that plasma experiments can measure reflected waves. Therefore, we utilize one-dimensional numerical models as a means of calculating the reflection coefficient of electrostatic plasma waves in a dipole magnetic field. We use two models for both cold and hot plasma effects (Ä1Ñ). As a first approach, we analyze about the midplane of the dipole field and equate the parallel wavelength to be inversely proportional to the field line length. Our model equations result from the taking the dispersion relation for both cold and hot plasma effects, and, under the premise of energy conservation, invert with the equation with k_x -> -i d/dx. These equations are numerically solved and analyzed for to solve for a reflection coefficient. The cold-plasma equation yields 100 percent reflection with an incident Ion Acoustic Wave that mode transforms into an electrostatic Ion Cyclotron Wave. This occurs due to a cutoff at $omega = omega_{ci}$, and the phase shift of reflection depends on the frequency of the incident wave. The hot-plasma equation yields more complex results, because of mode conversion into the Ion Bernstein Wave. We then discuss the limits of the model, and improvements to the models as a next step.

Ä1Ñ: Swanson, D. G. (2008). Plasma Kinetic Theory. Taylor and Francis, Boca Raton, FL.