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To investigate how magnetic reconnection (MR) accelerates electrons to a power-law energy spectrum in solar flares, we explore the scaling of a kinetic model proposed by Che & Zank (CZ) and compare it to observations. Focusing on thin current sheet MR particle-in-cell (PIC) simulations, we analyze the impact of domain size on the evolution of the electron Kelvin–Helmholtz instability (EKHI). We find that the duration of the growth stage of the EKHI ($t_G\sim {\mathrm{\Omega }}_e^{-1}$) is short and remains nearly unchanged because the electron gyrofrequency Ω_eis independent of domain size. The quasi-steady stage of the EKHI (t_MR) dominates the electron acceleration process and scales linearly with the size of the simulations asL/v_A0, wherev_A0is the Alfvén speed. We use the analytical results obtained by CZ to calculate the continuous temporal evolution of the electron energy spectra from PIC simulations and linearly scale them to solar flare observational scales. For the first time, an electron acceleration model predicts the sharp two-stage transition observed in typical soft–hard–harder electron energy spectra, implying that the electron acceleration model must be efficient with an acceleration timescale that is a small fraction of the duration of solar flares. Our results suggest that we can use PIC MR simulations to investigate the observational electron energy spectral evolution of solar flares if the ratiot_MR/t_Gis sufficiently small, i.e., ≲10%.

 

Research Experience for Teachers (RET) programs are National Science Foundation (NSF) funded programs designed to provide K- 12 Science, Technology, Engineering, and Mathematics (STEM) teachers with immersive, hands-on research experiences at Universities around the country. The NSF RET in nanotechnology encourages teachers to translate cutting-edge research into culturally relevant Project-Based Learning (PjBL) and engineering curriculum. Traditionally, the evaluation of RET programs focuses on the growth and development of teacher self-efficacy, engineering content knowledge gains, or classroom implementation of developed curriculum materials. However, reported methods for evaluating the impact of RETs on their female, minority student populations' high school graduation and undergraduate STEM major rates are limited. This study's objective was to compare RET high school student graduation rates and undergraduate STEM major rates across gender, race, and ethnicity to a comparison sample to determine the RET program's long-term impact on students' likelihood of pursuing STEM careers. The approach of collecting and analyzing the Texas Education Research Center Database (EdRC) data is a novel methodology for assessing RET programs' effectiveness on students. The EdRC is a repository of K-12 student data from the Texas Education Agency (TEA) and Higher Education data from the Texas Higher Education Coordinating Board (THECB). This joint database contains demographic, course registration, graduation, standardized testing, and college major, among others, for all students that attended a K-12 public school in Texas and any college in Texas, public or private. The RET program participants at Rice University (2010 – 2018) taught numerous students, a sample size of 11,240 students. A propensity score matching generated the student comparison group within the database. Students' school campus, gender, race/ethnic status, and English proficiency status were applied to produce a graduation comparison sample size of 11,240 students of Non-RET participants. Linking the TEA database to the THECB database resulted in college STEM participants and comparison sample sizes of 4,029 students. The project team conducted a logistic regression using RET status to predict high school graduation rates as a whole and by individual variables: gender, Asian American, Black, Caucasian, and Latinx students. All models were significant at p less than 0.05, with models in favor of students RET teachers. The project team conducted a logistic regression using RET status to predict student STEM undergraduate major rates as a whole and by individual variables: Gender, Asian American, Black, Caucasian, and Latinx students. African American and Caucasian models were significant at p less than 0.05; Gender, Asian American, and Latinx models were marginally significant (0.05 less than p greater than 0.1), where RET students had higher STEM major rates than matched controls. The findings demonstrate that RET programs have a long-term positive impact on the students' high school graduation rates and undergraduate STEM major rates. As teachers who participate in the RET programs are more likely to conduct courses using PjBL strategies and incorporate real-world engineering practices, female and minority students are more likely to benefit from these practices and seek careers utilizing these skills.