9:45 AM - 10:00 AM
[PEM17-04] Investigation of high-frequency whistler wave generation mechanism at Earth’s bow shock
Keywords:linear theory, whistler wave generation
The origin of cosmic rays (CRs) remains a fundamental question, with supernova remnants (SNRs) widely considered their primary accelerators. The standard model, diffusive shock acceleration (DSA), explains the observed energy spectrum of CRs but struggles to accelerate particles below the required threshold (~100 keV), far above the thermal energy (~0.1 keV) in SNR shock downstream. This gap, known as the injection problem, remains an open challenge. One way to address the injection problem is employing high-frequency wave generation near the shock to scatter and energize electrons, enabling their transition into the DSA cycle.
Understanding high-frequency wave generation mechanisms is crucial for resolving the electron injection problem. Our research investigates wave generation mechanisms in shock regions through a linear instability analysis using advanced models of electron distributions. First, we modeled the particle velocity distribution in the shock region using Liouville mapping, assuming a steady, monotonic magnetic field profile for the shock structure. The electron distribution was constructed based on assumed upstream and downstream distributions given by shock parameters, allowing us to capture the local features. Then we perform a linear analysis of the derived distribution. Due to its complexity, the standard Vlasov-Maxwell solver is not applicable. Gendrin (1981) suggests that wave generation or damping is determined by the slope of distribution along the diffusion curve. We employed the semi-analytical method proposed by Kennel & Wong (1967) to calculate the wave growth/ damping rate based on the distribution slope, applicable to arbitrary distributions.
With this framework, we establish a model linking shock parameters to wave generation and apply it to Earth’s bow shock. We modeled electron distribution with Earth’s bow shock parameter from Oka et al. (2017) and calculated the resulting wave growth rate. Our modeled distribution shows better consistency with observation compared with previous classic models like bi-Maxwellian distribution, capturing local features such as reflected electron population, and temperature anisotropies induced by magnetic field compression. These features serve as key sources of free energy to drive instabilities. With the modeled distribution, we predicted multiple instabilities in both the upstream region and the shock transition region. Notably, the transition region exhibited significantly stronger instabilities due to its more complex electron distribution, which provides greater free energy for wave generation. The instabilities drive whistler wave generation in quasi-parallel propagation, with predicted dominant frequencies ranging from tens to hundreds of Hz. These predictions are consistent with spacecraft observations of Earth’s bow shock, where the dominant wave frequency is approximately 300 Hz. This agreement validates our model.
With the developed model, we can apply it to various shock parameters, trying to explain the wave generation dependence on shock parameters observed in Earth’s bow shock (Amano et al. 2024).
Understanding high-frequency wave generation mechanisms is crucial for resolving the electron injection problem. Our research investigates wave generation mechanisms in shock regions through a linear instability analysis using advanced models of electron distributions. First, we modeled the particle velocity distribution in the shock region using Liouville mapping, assuming a steady, monotonic magnetic field profile for the shock structure. The electron distribution was constructed based on assumed upstream and downstream distributions given by shock parameters, allowing us to capture the local features. Then we perform a linear analysis of the derived distribution. Due to its complexity, the standard Vlasov-Maxwell solver is not applicable. Gendrin (1981) suggests that wave generation or damping is determined by the slope of distribution along the diffusion curve. We employed the semi-analytical method proposed by Kennel & Wong (1967) to calculate the wave growth/ damping rate based on the distribution slope, applicable to arbitrary distributions.
With this framework, we establish a model linking shock parameters to wave generation and apply it to Earth’s bow shock. We modeled electron distribution with Earth’s bow shock parameter from Oka et al. (2017) and calculated the resulting wave growth rate. Our modeled distribution shows better consistency with observation compared with previous classic models like bi-Maxwellian distribution, capturing local features such as reflected electron population, and temperature anisotropies induced by magnetic field compression. These features serve as key sources of free energy to drive instabilities. With the modeled distribution, we predicted multiple instabilities in both the upstream region and the shock transition region. Notably, the transition region exhibited significantly stronger instabilities due to its more complex electron distribution, which provides greater free energy for wave generation. The instabilities drive whistler wave generation in quasi-parallel propagation, with predicted dominant frequencies ranging from tens to hundreds of Hz. These predictions are consistent with spacecraft observations of Earth’s bow shock, where the dominant wave frequency is approximately 300 Hz. This agreement validates our model.
With the developed model, we can apply it to various shock parameters, trying to explain the wave generation dependence on shock parameters observed in Earth’s bow shock (Amano et al. 2024).