Page 11 - Transport studies in high-performance field reversed configuration plasmas

of waves with a high phase velocity: E=M ω vphi /q =n*2.4 x 105V/m = 7.2 x 105V/m, where M is the deuterium mass, ω~n*ωci and ωci is the deuterium cyclotron frequency, vphi is the phase velocity of this ion mode, and q is the deuteron charge. This theoretical value (E=7.2x105V/m) is on the same order of magnitude but is higher than the simulation value (E=4.0x105V/m). This may be due to the following reasons: (i) the simulation has several growing modes, whose phases tend to mix; (ii) the waves are not resonantly driven in the present case, a bit similar to the case of self-modulated (SM)LWFA [16; 49] in which the maximally available wave-breaking limit may not be reached; some partial particle-injection may have happened before the wave-breaking takes place. To delineate these further will take more future studies.
We may be able to interpret our simulation in light of our high phase velocity hypothesis, as follows. Robust ion-Bernstein cyclotron modes couple to the beam ring (sometimes the lower hybrid wave co-exists). These modes modulate and decelerate the beam, (Fig.7(a)). The wave phase velocity is less than the beam velocity but close to it and far above the plasma bulk thermal velocity. Thus this setup belongs to the category in which the hypothesis of robustness of waves with a high phase velocity. As the saturation of this kinetic instability of the beam-plasma interaction commences, the large body of the particles that belonged to the initial beam now plunges toward the bulk distribution, while the tails of the plasma distribution shows more prominent starfish-like arms (Fig. 7(b)). Because the phase velocity of the injected beam vb is far greater than the ion thermal velocity vti (<< vb ), the instability grows the mode amplitude high enough and robustly enough to scatter the perpendicular (to field) energy from the beam velocity down to the bulk ion thermal range. Note that the bulk of the thermal plasma remains intact even when the robust kinetic instability has set in and grown to high amplitude that is characterized and limited by the phase velocity trapping reaching down the bulk. This is an extended version of a magnetized non-relativistic ion branch from the nonmagnetized relativistic “wave breaking” limit phenomenon [10]. This behavior is in fact observed in the wakefield physics, where the large amplitude wake is excited by the beam or laser pulse, supported by the plasma, and approaches the Tajima-Dawson wave limit [10] (and when the relativistic effects are included, it even exceeds this value because of the relativistic coherence [18]). In the resonantly excited wakefield in which the beam bunch or laser pulse is chosen in such a way to directly resonate with the plasma eigenmode wavelength, the saturation amplitude reaches typically E=4.0 x 105 V/m and usually causes the phenomenon called the self-injection [39-41]. The self-injection in the wakefield dynamics is similar to the present anomalous heating and its subsequent fusion enhancement in this D-D reactivity considered in this Section. While such intense acceleration and self-injection happens, the plasma and integrity of the wake waves are intact just as shown in Fig. 1 (a) or the offshore portion of the tsunami wave in Fig. 1 (b). The tsunami wave loses its integrity and transfer its total energy to the shore only when its phase velocity reached near zero at the onshore. In other words, the plasma does not lose its integrity nor is led to a total destruction, though the robust kinetic effects caused significant perturbation. In the present ion beam- driven phenomenology of the deuteron plasma, this anomalous heating gives rise to the anomalous fusion enhancement, as observed in C-2U beam-plasma interaction. This observation thus may again join as another example exhibiting the phenomenon of the hypothesis of robustness of waves with a high phase velocity. The robust effects we see in this interaction such as enhanced heating and fusion reactivity in the present example of the D-D bulk plasma is manifest, while the bulk plasma may be maintained under the circumstance.
CONCLUSIONS
Veksler’s idea to avoid the metallic breakdown at higher accelerating fields was to adopt plasma as the medium and its collective field to increase the accelerating gradient inspired the research of Professor Norman Rostoker and others to investigate the processes involved. Since such strongly driven plasma exhibits highly nonlinear behaviors, the understanding of the phenomena involved took a long time and much effort. One such effort at the University of California at Irvine at the lab of Rostoker incubated many ideas and valuable lessons which his students learned. One of the experiments taught us the importance of accelerating ions in an adiabatic fashion, which led to the theory and understanding of how to ameliorate the sheath formation and its sudden cessation of the ion acceleration process. Such ideas led to revive research into more efficient acceleration in the new exploding efforts in laser driven ion acceleration that started in Year 2000 in the form of the Target Normal Sheath Acceleration. These efforts include Radiation Pressure Acceleration, Collective Acceleration of Ions by Laser (CAIL), and the more recent Single-Cycled Pulse Acceleration (SCPA) [50] methods. If any such methods produces the intended improvements over the abrupt acceleration characteristic of TNSA, the applications to various fields are immense, surpassing the conventional accelerators’ reach with a huge impact.
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