The group of Solar and Heliospheric Physics has published a research paper on Ann. Geophys., focusing on how to identify slow magnetosonic waves in MHD turbulence. A new criteria is proposed in this paper. The advantage of this criteria lies in its insensitiveness to the propagation angle, which is not easy to estimate in the 3D simulation data. Therefore, the method of this work can be applied to the identification and statistical analysis of the compressive waves in 3D turbulence. The authors also qualitatively describe the physical feature and temporal evolution of four events of slow mode waves as identified.
For details please refer to dx.doi.org/10.5194/angeo-33-13-2015.
Gyro-averaged equations of particle motion for resonances with oblique whistler-mode waves were previously derived by multiple authors with inconsistent formulas. This study suggests a check on self-consistency: the energy variation resulting from momentum equations should not contain any wave magnetic components. We also show that the wave centripetal force, which was neglected in previous studies, can significantly enhance electron phase trapping. This force can also bounce low pitch angle particles out of the loss cone. 
Quasi-linear theory has been commonly used to study the Landau resonance between radiation belt electrons and magnetosonic waves. However, the parallel wavelengths of magnetosonic waves can exceed their spatial confinement and cause a transit-time effect. We introduce a particle-independent criterion to justify the validity of quasi-linear theory for magnetosonic waves: the wave spatial confinement should be longer than two parallel wavelengths.