The simplest solutions of cold plasma equations: change in properties from a hydrodynamic to a kinetic model

Abstract

We consider the transition from the kinetic model of Landau cold plasma to the hydrodynamic one by constructing a "multi-speed" moment chain in the case of one spatial variable. Closing this chain at the first step leads to the standard hydrodynamic system of cold plasma. The change in the properties of the solution when closing the chain at the second step is discussed using the example of two classes of solutions - affine in space and traveling waves, and it is shown that their properties change significantly compared to the hydrodynamic model.

Figures (6)

• Figure 1: Behavior of phase trajectories of system \ref{['qe']}
• Figure 2: Continuation of the solution for $t>0$, non-uniqueness.
• Figure 3: Projections of phase curves of system \ref{['E']}-\ref{['U2']} on the plane $(U_1, U_2)$ depending on the region. Arrows indicate the motion with increasing $\xi$ at $E<0$, at the points marked in white the sign of $E$ changes and the direction of motion changes.
• Figure 4: Traveling wave for the second closure of parameter values from region 1 (red line), compared to the traveling wave for the first closure (black line), on the left $E$, on the right $U_1$. Everywhere $w=1$, $E(0)=0$, $U_1(0)=0.6$. For the first closure $U_2(0)=0.6$, for the second closure $U_2(0)=0.7$.
• Figure 5: Traveling wave for the second closure of parameter values from region 2, on the left $E$, on the right $U_1$. Everywhere $w=1$, $E(0)=0$, $U_1(0)=0.2$, $U_2(0)=0.7$. Traveling waves for the first closure do not exist in region 2

Theorems & Definitions (3)

• Theorem 2.1
• Proposition 1
• Proposition 2