Page 10 - Transport studies in high-performance field reversed configuration plasmas

The incurred kinetic beam-plasma instability begins to draw a tail portion of the bulk plasma distribution [Figs. 7(a) and 7b]. On the other hand, at the time t=0.53 μs, a large portion of beam particles merge with the plasma bulk distribution, which shows a protruded structure Fig. 7(a) and is manifested in Fig. 7(b) as stretching the thermal distribution to higher velocities. Figure 6(b) shows the dispersion relation as obtained by 1D fully electromagnetic PIC simulation of the same physics as in Fig. 6(a). The two methods agree on the location of the mode in the ω-k plane as well as the growth rate of the most unstable mode to be 0.8 ωci. In Fig. 8 the computationally measured time history of the deuteron-deuteron reactivity normalized to the standard thermonuclear fusion reactivity at the given plasma parameters (the vertical number unity means that the observed reactivity is equal to that of thermonuclear reactivity) can only occur among the plasma particles in the simulated beam-plasma system, as the hydrogen beam and deuteron plasma do not react to yield fusion.
FIGURE 8. Enhancement of the D-D fusion reactivity over the thermonuclear value. Reactivity enhancement tracks the growth of the unstable mode as seen in Fig. 8. The normalization is to the thermonuclear value as unity.
In this example (which is not atypical of our simulations) the maximal enhancement factor is as large as 3000 over the well-known thermonuclear reactivity [48]. This enhancement arises in our simulation due to the creation of the energetic particles in the plasma bulk particles, as we see in Fig. 7(a,b). Shown also is a typical time history of the most unstable mode in Fig. 9.
FIGURE 9: The fastest growing mode with location at kρi=0.97. Plot of Fourier transform of Ex to k-space vs. time is shown. Linearly growing mode saturates at 0.7 μs, afterwards nonlinear phase commences and energy sloshing between particles and fields is observed.
Here the maximum amplitude of the most unstable mode occurs about the same time of the total wave energy saturation. (We note that the beam instability allows the wave amplitude to increase exponentially first (till t=0.75 μsec), followed by the saturation around t=1.0 μsec). The saturated amplitude of the electric field E=4.0 x 105 V/m. This value is high and robust, and the plasma shows relatively benign behavior overall, except that we observe some tongue-like structures of Fig. 7a. The amplitude of the mode is consistent with the estimated value by the hypothesis
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