The Early‐Phase Growth of ULF Waves in the Ion Foreshock Observed in a Hybrid‐Vlasov Simulation

Abstract Large‐amplitude ultra‐low frequency (ULF) waves in Earth's ion foreshock play a crucial role in the dayside dynamics and solar wind‐magnetosphere coupling. This study uses global hybrid‐Vlasov simulation results from Vlasiator to investigate the detailed physical processes in the early growth phase of the foreshock ULF waves. Using both spatial and temporal information, the wave phase speed is determined and used to track a specific phase front as the wave evolves. The space‐time evolution of the foreshock waves and the backstreaming ions responsible for the wave growth is analyzed and presented in the wave frame for the first time. We employ a state‐of‐the‐art linear dispersion solver, LEOPARD, to solve the wave dispersion relations using the ion distributions and compare the theoretical predictions with the measured wave phase speed and growth rate. The measured phase speed in the spacecraft (or stationary) frame is unexpectedly high at the initial growth stage but later decreases to the predicted level and exhibits an increasing trend over time that aligns with theoretical expectations. The measured and predicted growth rates share the same decreasing trend over time, but the predicted values are consistently lower than the measured growth rate by 25%. The comparison suggests that the foreshock waves in the Vlasiator simulation are likely generated through the ion‐ion right‐hand resonant instability, but there are discrepancies with linear theory that are not explained yet and require further investigation.