When a solar wind discontinuity interacts with foreshock ions, foreshock transients such as hot flow anomalies and foreshock bubbles can form. These create significant dynamic pressure perturbations disturbing the bow shock, magnetopause, and magnetosphere‐ionosphere system. However, presently these phenomena are not predictable. In the accompanying paper, we derived analytical equations of foreshock ion partial gyration around a discontinuity and the resultant current density. In this study, we utilize the derived current density strength to model the energy conversion from the foreshock ions, which drives the outward motion or expansion of the solar wind plasma away from the discontinuity. We show that the model expansion speeds match those from local hybrid simulations for varying foreshock ion parameters. Using MMS, we conduct a statistical study showing that the model expansion speeds are moderately correlated with the magnetic field strength variations and the dynamic pressure decreases around discontinuities with correlation coefficients larger than 0.5. We use conjunctions between ARTEMIS and MMS to show that the model expansion speeds are typically large for those already‐formed foreshock transients. Our results show that our model can be reasonably successful in predicting significant dynamic pressure disturbances caused by foreshock ion‐discontinuity interactions. We discuss ways to improve the model in the future.
Derivation of the ion equation
We consider the classical Euler-Poisson system for electrons and
ions, interacting through an electrostatic field. The mass ratio of an electron
and an ion is small and we establish an asymptotic expansion of
solutions, where the main term is obtained from a solution to a self-consistent
equation involving only the ion variables. Moreover, on R^3, the validity of such
an expansion is established even with \ill-prepared" Cauchy data, by including
an additional initial layer correction.
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- Award ID(s):
- 1810868
- NSF-PAR ID:
- 10157527
- Date Published:
- Journal Name:
- Quarterly of applied mathematics
- Volume:
- 78
- Issue:
- 2
- ISSN:
- 0033-569X
- Page Range / eLocation ID:
- 305-332
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract 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.
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