Ion-Acoustic Wave Dynamics in a Two-Fluid Plasma

Abstract

Plasma is a medium containing free electrons and cations, where each particle group behaves as a conducting fluid with a single velocity and temperature in the presence of electromagnetic fields. The difference in roles electrons and ions play define the two-fluid description of plasma. This paper examines ion-acoustic waves generated by the particles in both hot and cold plasma using a collisionless "Euler-Poisson" (EP) system. Employing phase-space asymptotic analysis, we establish that for specific wave speeds, EP acquires homoclinic orbits at the steady-state equilibrium and consequently, traveling waves. Combining python and Wolfram Mathematica, we captured visualizations of such behavior in one spatial dimension.

Figures (16)

• Figure 1: A visual depiction of the $\mu$ values yielding $\mathcal{V}(\tilde{\phi}^*)>0$ (black) and $\mu > c \coloneqq \sqrt{\frac{1+\tau_i}{1+m_e}}$ (blue, dashed) in the two-fluid system.
• Figure 2: A Newton iterative approximation to $k_+(\tilde{\phi})$ with $\mu=1.5$ and $\tau_i=1$.
• Figure 3: A hot two-fluid plasma $(\tau_i = 1)$ with wave speed $\mu =1.5$, utilizing Newton's Method to approximate $k_\pm(\tilde{\phi}(\xi))$.
• Figure 4: A hot two-fluid plasma $(\tau_i = 1)$ with wave speed $\mu =1.6$, utilizing Newton's Method to approximate $k_\pm(\tilde{\phi}(\xi))$.
• Figure 5: A hot, single-fluid plasma $(\tau_i = 1, \; m_e=0)$ with wave speed $\mu =1.5$, utilizing Newton's Method to approximate $k_+(\tilde{\phi}(\xi))$.

Theorems & Definitions (4)

• Theorem 2.1
• proof
• Theorem 2.2
• proof