Particle-in-Cell Simulations of the Fast Magnetosonic Mode in a Dipole Magnetic Field: 1-D Along the Radial Direction
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An electromagnetic particle-in-cell code is used to investigate self-consistent evolution of the fast magnetosonic mode in a one-dimensional configuration along the radial direction in a dipole background magnetic field. A previous observation of this wave mode is used to select the simulation parameters. A partial shell velocity distribution of energetic protons with a moderate pitch angle anisotropy is used to excite the waves self-consistently. Consistent with local linear theory analysis, wave growth occurs only at exact harmonics of the local proton cyclotron frequency, Omega(p). However, radial propagation quickly removes the waves from the region where they can grow, leading to a time scale of wave amplification much longer than that predicted by linear theory. In addition, radial propagation from multiple wave sources makes the frequency spectrum measured at a single point much broader. The warm background plasma plays an important role in two ways. First, it increases the phase speed of the fast magnetosonic mode; and second, it causes the breakup of the extraordinary mode dispersion relation in the vicinity of the harmonics, where the broken dispersion curves are connected with multiple ion Bernstein modes. In this case, the waves propagating radially are absorbed at locations where their frequency reaches integer multiples of Omega(p) and background protons experience perpendicular heating at those locations.