5:15 PM - 6:45 PM
[PEM17-P12] Linear theory of oblique whistler wave generation at collisionless shocks
Keywords:wave generation, linear theory, shock acceleration
Diffusive shock acceleration (DSA) stands as the primary mechanism to generate high-energy particles in supernova remnant shock. However, it faces a challenge known as injection problem since DSA cannot accelerate the low-energy particles efficiently. Overcoming this challenge necessitates higher-frequency waves capable of scattering these low-energy electrons to confine them around the shock.
In simulations, Matsukiyo et al. (2011) observed oblique whistler wave generation and electrons confinement in the upstream of a quasi-perpendicular shock. Similar oblique wave generation ahead of the shock has been observed in various simulations of non-relativistic shocks (Guo et al. 2014, Kobzar et al. 2021, Bohdan in 2022). Understanding shock parameters conducive to wave generation may help to solve the injection problem. This process entails two aspects: understanding how shock parameters determine the upstream particle distribution and identifying the particle distribution that leads to wave generation and effective confinement.
First, in the shock drift acceleration (SDA) model (Wu 1984), the electrons can be reflected by the magnetic mirror force towards upstream of the shock. The reflected electron beam may give rise to the wave generation as has been discussed by Matsukiyo et al. (2011) and others. The upstream plasma can be assumed to comprise three particle populations: background ions and electrons, and a hot electron beam. We can estimate the velocity distribution of particles in the upstream and hot it depends on shock parameters based on the theory of SDA.
Next, we analyze the wave generation via linear theory and two-dimensional (2D) Particle-In-Cell (PIC) simulations with a simplified periodic model. We have previously confirmed that the results from both approaches are consistent, and the wave growth rate is positively related to beam velocity as predicted theoretically (Verscharen et al. 2019). However, the standard linearized Vlasov-Maxwell solver is limited to simple particle distributions, such as Maxwellian and kappa distribution. To derive the growth/damping rate with a more realistic upstream distribution as predicted by SDA, we adopt the semi-analytical method proposed by Kennel & Wong (1967). This approach allows us to calculate the growth/damping rates of waves analytically under the condition that the growth/damping rate is significantly smaller than the real frequency. We have confirmed that the semi-analytical method gives a reasonable approximation to the fully numerical solution at long wavelength, which is our primary focus, as small wavelengths are subject to cyclotron damping effects. We will discuss how the wave generation depends on shock parameters, such as Mach number, obliquity, and electron plasma beta.
In simulations, Matsukiyo et al. (2011) observed oblique whistler wave generation and electrons confinement in the upstream of a quasi-perpendicular shock. Similar oblique wave generation ahead of the shock has been observed in various simulations of non-relativistic shocks (Guo et al. 2014, Kobzar et al. 2021, Bohdan in 2022). Understanding shock parameters conducive to wave generation may help to solve the injection problem. This process entails two aspects: understanding how shock parameters determine the upstream particle distribution and identifying the particle distribution that leads to wave generation and effective confinement.
First, in the shock drift acceleration (SDA) model (Wu 1984), the electrons can be reflected by the magnetic mirror force towards upstream of the shock. The reflected electron beam may give rise to the wave generation as has been discussed by Matsukiyo et al. (2011) and others. The upstream plasma can be assumed to comprise three particle populations: background ions and electrons, and a hot electron beam. We can estimate the velocity distribution of particles in the upstream and hot it depends on shock parameters based on the theory of SDA.
Next, we analyze the wave generation via linear theory and two-dimensional (2D) Particle-In-Cell (PIC) simulations with a simplified periodic model. We have previously confirmed that the results from both approaches are consistent, and the wave growth rate is positively related to beam velocity as predicted theoretically (Verscharen et al. 2019). However, the standard linearized Vlasov-Maxwell solver is limited to simple particle distributions, such as Maxwellian and kappa distribution. To derive the growth/damping rate with a more realistic upstream distribution as predicted by SDA, we adopt the semi-analytical method proposed by Kennel & Wong (1967). This approach allows us to calculate the growth/damping rates of waves analytically under the condition that the growth/damping rate is significantly smaller than the real frequency. We have confirmed that the semi-analytical method gives a reasonable approximation to the fully numerical solution at long wavelength, which is our primary focus, as small wavelengths are subject to cyclotron damping effects. We will discuss how the wave generation depends on shock parameters, such as Mach number, obliquity, and electron plasma beta.