Ubiquitous throughout the universe, shocks form when a supersonic flow encounters an obstacle and are important particle accelerators through different acceleration mechanisms (e.g., Helder et al., 2012;Lee et al., 2012). On Earth, a bow shock forms when the supermagnetosonic solar wind encounters the magnetosphere. At the quasi-parallel bow shock (where the angle between the shock normal and the interplanetary magnetic field (IMF) is less than 45°), some solar wind particles are reflected by the bow shock and populate the region upstream known as the foreshock (e.g., Eastwood et al., 2005). Interactions between these foreshock particles and the incoming solar wind particles can generate ULF waves that permeate the foreshock (e.g., Eastwood et al., 2005;Wilson et al., 2016). In addition, transient kinetic phenomena are also observed in the foreshock (see review by Zhang et al., 2022), such as hot flow anomalies (HFAs) (

Midtail foreshock transients develop under mostly similar formation conditions as dayside ones • Almost all midtail foreshock transients have electron heating which is proportional to the solar wind speed • Foreshock transients may be stable for tens of minutes and continuously disturb the local bow shock and accelerate particles Supporting Information:

Hot flow anomalies (HFAs) and foreshock bubbles (FBs) are significant foreshock transients that can accelerate particles and disturb the magnetosphere‐ionosphere system. Yet, their early formation mechanisms are still not fully understood. To investigate the formation of tangential discontinuity (TD)‐driven FBs and HFAs, we use 2‐D local hybrid simulations where a reflected or an injected warm foreshock ion beam can interact with a TD whose half‐thickness is comparable to the ion inertial scale. We show that the foreshock ions perform a partial gyration within, or across, the TD. Bulk motion differences between partially‐gyrating foreshock ions and fluid‐electrons lead to the generation of currents. As the trigger, these foreshock‐driven currents change the magnetic field topology around the TD and force the frozen‐in solar wind plasma to redistribute along with the field lines, shaping the foreshock transient. This confirms a recently proposed kinetic formation model. The extent of the magnetic field direction change across the TD within the foreshock ion gyromotion determines the current profile and thus the type of foreshock transient that forms. For a thin TD, the foreshock ions generate a current that is much stronger on the upstream side than the downstream side, forming an FB with one upstream compressional boundary. For the same foreshock ion gyroradius and magnetic shear, a thick TD yields comparable foreshock‐driven currents on the upstream and downstream sides, forming an HFA with two compressional boundaries. Our study suggests that the TD thickness is one of the factors that determine the formation of FBs and HFAs.

Foreshock bubbles (FBs) are significant foreshock transients that can accelerate particles and disturb the magnetosphere‐ionosphere system. In the kinetic formation model, foreshock ions interact with the discontinuity by performing partial gyrations to generate currents that change the magnetic field topology around the discontinuity. However, how different foreshock ion properties affect the growth of the field variations is not well understood. Therefore, we use 2‐D local hybrid simulations to study the effects of different foreshock ion distributions and properties on the growth of tangential discontinuity (TD)‐driven FBs. We discover that for a gyrophase‐bunched distribution with an initial phase where the guiding center is on the other side of the TD, the foreshock ions gyrate together across the TD, causing more foreshock ions to cross the TD and leading to a faster expansion of the structure than for a Maxwellian distribution. A ring distribution also yields higher expansion speeds because of the higher projected velocity into the new perpendicular direction. For Maxwellian distributions, there are positive and linear correlations of the FB expansion speeds with the initial foreshock ion densities, thermal speeds, parallel speeds, and sine of the TD magnetic shear angles. These parameter dependencies grow in strength as the structures evolve with time. The foreshock ion distributions and properties that lead to stronger currents produce more significant magnetic field variations and higher expansion speeds. Our study helps quantify the formation and expansion of FBs to forecast their space weather effects and contribution to shock acceleration.

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.