Parameter Dependencies of Early‐Stage Tangential Discontinuity‐Driven Foreshock Bubbles in Local Hybrid Simulations

Abstract

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.

Modeling the Expansion Speed of Foreshock Bubbles

“…10.1029/2022JA030814 5 of 15 transfer from field to plasma; this should be calculated in the plasma rest frame.) Through a parameter scan (Vu et al, 2023), our simulations show that the expansion speed 𝐴𝐴 𝐴𝐴𝑒𝑒𝑒𝑒𝑒𝑒 is linearly correlated with foreshock ion parameters 𝐴𝐴 𝐴𝐴∕𝐴𝐴0 , 𝐴𝐴 𝐴𝐴𝐹𝐹𝐴𝐴𝐹𝐹 , and 𝐴𝐴 𝐴𝐴⟂ consistent with Equation 2. Our simulations also show that 𝐴𝐴 𝐴𝐴𝑒𝑒𝑒𝑒𝑒𝑒 is linearly correlated with 𝐴𝐴 sin 125 180 𝛼𝛼 (a possible reason of 125/180 could be that the magnetic field modification by the formed FB makes foreshock ions experience only a portion of the initial shear angle).…”

“…This may explain the transit speed criterion by Schwartz et al (2000). Moreover, a certain range of initial gyrophase of foreshock ions is needed; otherwise, they will barely gyrate across the discontinuity (e.g., Vu et al, 2023).…”

“…In the accompanying paper (Vu et al., 2023), we examined the early formation stage of FBs using varying parameters to test our model. We first compared the energy input from foreshock ions with the kinetic energy gain of solar wind ions in the solar wind rest frame.…”

“…In Section 4.1, we use our hybrid simulation database (Vu et al, 2023) to test and fit the equation and determine the time dependence.…”

“…These parameters especially relate to how foreshock ions cross the discontinuity. For example, when we use ring or gyrophase bunched distributions with the same or lower energy than the field‐aligned beam in our simulations, the expansion speed is faster because the strong perpendicular bulk motion makes foreshock ions cross the discontinuity more easily and have an increased velocity projection in the new perpendicular direction (Vu et al., 2023). Further work is needed to improve the model beyond the present first‐order calculations.…”