Modeling the Expansion Speed of Foreshock Bubbles

Foreshock transients, including hot flow anomalies (HFAs) and foreshock bubbles (FBs), are frequently observed in the ion foreshock. Their significant dynamic pressure perturbations can disturb the bow shock, resulting in disturbances in the magnetosphere and ionosphere. They can also contribute to particle acceleration at their parent bow shock. These disturbances and particle acceleration caused by the foreshock transients are not yet predictable, however. In this study, we take the first step in establishing a first-order predictive expansion speed model for FBs (which are simpler than HFAs). Starting with energy conversion from foreshock ions to solar wind ions, we derive the FB expansion speed in the FB's early formation stage and late expansion stage as a function of foreshock and solar wind parameters. We use local hybrid simulations with varying parameters to fit and improve the early stage model and 1D particle-in-cell simulations to test the late-stage model. By comparing model results with Magnetospheric Multiscale (MMS) and Time History of Events and Macroscale Interactions during Substorms (THEMIS) observations, we adjust the late-stage model and show that it can predict the FB expansion speed. Our study provides a foundation for predictive models of foreshock transient formation and expansion, so that we can eventually forecast their space weather effects and particle acceleration at shocks.