Predicted Effects of Nonlinear Induced Scattering in the SMART Experiment

The upcoming SMART experiment [1] will inject neutral Barium gas at high speed (-10 km/s) perpendicular to the magnetic field into the upper ionosphere at an altitude of about 500 km from Wallops, VA. Neutral Barium photoionizes due to solar photons at a characteristic time of 30 seconds yielding a cloud on a scale of about 300 km. The charged Barium is accelerated by the Lorentz force and begins its gyration about the magnetic field forming anisotropic and nongyrotropic heavy ion beam distributions [2] that have a spiral shape in the velocity space perpendicular to the magnetic field. Waves that are doubly resonant with frequencies near the lower-hybrid frequency and phase velocities near the charged Barium velocities are unstable and grow exponentially. Because of the high Barium ion velocity these waves have wave-vectors that are predominantly perpendicular to the magnetic field with short perpendicular wavelengths of the order of 1 meter which is much smaller than the electron inertial length and hence these waves are predominantly electrostatic in nature. The distribution of wave¬vectors is broad due to the fact that wave-vectors in many directions perpendicular to the magnetic field may be excited by the gyrating beam and thus the weak turbulence approximation can be shown to be valid. In this paper, we focus on the saturation of the instability by the nonlinear induced scattering of the lower-hybrid waves into electromagnetic whistler/magnetosonic waves which occurs when γ L ∝ γ NL ( W ) where γ L is the linear growth rate of the instability and γ NL is the nonlinear scattering rate that depends on the energy density W of the electrostatic waves. This nonlinear scattering rate is a three-dimensional phenomenon [3] and thus any first- principles simulation must be three dimensional. We review particle-in-cell simulations of heavy ion ring instabilities and explain the low saturation amplitude in terms of the fast nonlinear scattering rate. We develop a simulation technique for the evolution of this instability called Wave-In-Cell (WIG) that solves the self-consistent weak turbulence equations and is capable of evolving the distribution function of the whole experiment as a function of time and space. We couple these equations with a ray-tracing method to track the propagation of these waves to the ground and out into the magnetosphere, thus giving a quantitative prediction of remote observations of the upcoming experiment.