Nonlinear pendulum equations and space plasma reveal potential radiation belt trick

Many space plasma wave phenomena are caused by nonlinear wave-particle interactions, physical processes which can be described in the form of nonlinear pendulum equations.

As they report in Physics of Plasmas, researchers constructed a pendulum equation model of energetic electrons interacting with Langmuir waves (plasma oscillations) and a nonoscillatory electric field. This allowed them to complete a comprehensive survey of the nonlinear dynamics of resonant particles interacting with coherent waves.

The nonlinear dynamics of charged particles in resonance with coherent waves results in acceleration or deceleration and thermalization — an increase in electron thermal velocity — of the particles. “Resonance enables the particles to form resonant currents that cause the growth or damping (decrease in amplitude) of the wave and variation of its frequency,” said co-author Miwa Tobita.

The work clarifies the basic properties of nonlinear trajectories of charged particles trapped by an electrostatic potential of Langmuir waves under different values of the inhomogeneity factor S, which is controlled by a nonoscillatory electric field in their model. “In the cases of more complex whistler-mode chorus waves and electromagnetic ion cyclotron waves, which play pivotal roles in the loss and formation processes of the radiation belts, S is controlled by the frequency sweep rate of the wave and the gradient of the background magnetic field,” said co-author Yoshiharu Omura.

Among their key findings is that resonant particles are most effectively thermalized with S=1. The researchers gained an understanding of not only the nonlinear wave growth mechanism of coherent waves in space plasmas, but also the acceleration and scattering mechanisms of the energetic particles that form the Earth’s Van Allen radiation belts. This may make it possible to use artificially generated coherent waves to control them and create safer operating conditions within the radiation belts.

Source: “Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves,” by Miwa Tobita and Yoshiharu Omura, Physics of Plasmas (2018). The article can be accessed at https://doi.org/10.1063/1.5018084 .