electron fluid, however, the Coulomb collision can be neglected, and fluid elements
can catch up and overtake with each other.
When the catch up and overtaking of the wave components occur, the phenomenon is called wave-breaking. In order to see the physics image before and after the
wave-breaking, the result of numerical solution is shown in Fig. 3.32, where x 0 is the
initial coordinate, x is the fluid element position at time t, and V is the oscillation
velocity [20]. On the left of Fig. 3.32, the displacement of cold fluid elements is
Fig. 3.32 A numerical solution of the exact equation of plasma oscillation (3.6.5). The left figures
are the real position x as function of the initial points of electron elements x 0 . The right figures are
the oscillation velocity as function of the real position of each particle. This easily demonstrates the
behavior of wave-breaking
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3 Ultra-Short Pulse and Collisionless Absorption
can catch up and overtake with each other.
When the catch up and overtaking of the wave components occur, the phenomenon is called wave-breaking. In order to see the physics image before and after the
wave-breaking, the result of numerical solution is shown in Fig. 3.32, where x 0 is the
initial coordinate, x is the fluid element position at time t, and V is the oscillation
velocity [20]. On the left of Fig. 3.32, the displacement of cold fluid elements is
Fig. 3.32 A numerical solution of the exact equation of plasma oscillation (3.6.5). The left figures
are the real position x as function of the initial points of electron elements x 0 . The right figures are
the oscillation velocity as function of the real position of each particle. This easily demonstrates the
behavior of wave-breaking
122
3 Ultra-Short Pulse and Collisionless Absorption