Page 2 - Transport studies in high-performance field reversed configuration plasmas

which states that large orbits of energetic particles (that might be formed by injection of a beam of accelerated particles) have a tendency to stabilize instabilities whose wavelengths may be averaged out by the largeness of the orbit size and that perhaps as a consequence plasma confinement may be improved [4]. Such a conjecture was based on the paper of finite Larmor radius (FLR) stabilization [5] that Dr. Rostoker co-authored with flash of mathematical brilliance. Dawson and collaborators [6] found a computer simulation of drift waves which may be stabilized with large FLR effects. Such effects are fully adopted as a central guiding principle of the beam-driven Field Reversed Configuration (FRC) and its recent research is underscoring Norman’s Conjecture [7, 8]. Further confirmation of Norman’s conjecture is found in [9] of this Proceedings.
In the plasma-based accelerators Tajima and Dawson suggested the laser-driven wakefield accelerator method (LWFA) to drive electrons (and other particles) that are trapped in the wake [10]. In later renditions, the laser may be replaced by an electron beam [11] or by an ion beam [12]. In the wake of the laser pulse (or charged particle bunch), a large amplitude plasma wave is excited, whose amplitude may be relativistically large. The relativistic amplitude means that the amplitude of the wave is so large that particles may be driven to relativistic energies in just one oscillation, i.e. E = mcωp / e, where ωp is the plasma frequency [10] (In the case of the laser being also relativistic (we will discuss on this later) the field expression takes a slight modification). When such a theoretical (and computational) proposal was made, there were some opinions that plasma would become unstable and unable to support such waves. Over the years (particularly after 2004 [13-15] since the first LWFA experiment [16],) large and robust plasma waves excited with a phase velocity nearly equal to the speed of light c have been observed (Downer’s group could even “see” the wakefield by holographic method [17]). These experiments supported the idea that the plasma waves are robust, stable, intense, and almost rigid, the last of which is referred to as the relativistic coherence [18]. Why is this? The ponderomotive force of the laser (corresponding to the motorboat in Fig.1 (a)) is moving with the group velocity of the laser (~c) and has the resonant length lb with the plasma wavelength λp (lb =1⁄2 λp). It excites and feeds the plasma eigenmode with the high phase velocity of ~c. Such a wave cannot trap thermal electrons of plasma, since the wave phase velocity sits far from the thermal velocities of particles that are around zero. This remains the case until the wave amplitude reaches the relativistic amplitude eE/mωp ~ c, when the wave growth saturates. This is similar to the fast wake wave of the motorboat that only bobs the floating swimmer behind the boat (Fig.1(a)). The tsunami wave offshore does not carry stationary ships and the ships escape wreckage. However, the tsunami wave that slows down to near zero velocity on shore can deliver devastating wave energy to the onshore ships, surfers, or the coastline (see Fig.1(b)).
In addition to the above reasons for the wave with a high phase velocity staying robust and intact, there is an additional mechanism why LWFA remains sturdy; the relativistic coherence [18]. When the wave amplitude grows, the wave form steepens and further steepening goes over to break the wave (see Fig.2(b)) [19]. However, relativistic wave steepening dynamics is quite different from the nonrelativistic wave steepening (Fig.2(a)) when the wake wave is propagating with the relativistic speed (Fig.2(a)). Since the wave moves near at the speed of light, electrons cannot pass over the steepened wave and thus are hard to tip over and to break the wave and by doing so, electrons cohere to form a steep sheet (a cusp singularity). This is the manifestation of relativistic coherence.
In this paper we will focus on the robustness of the wave dynamics with a high phase velocity, including the original LWFA but also extending its reach to other applications. We also touch on the issue that if we do not fulfill this high phase velocity condition, what kind of inconvenience we encounter. An example for this was encountered in the early research of collective accelerators. This issue now has a new added importance in the recent laser-driven ion acceleration research. This will be reviewed in Sec.II. The lesson learned in Sec.II has led us to introduce the high phase velocity concept of LWFA. An additional learned lesson is applied to increase the adiabaticity in laser- driven ion acceleration. This is discussed in Sec.III. In Sec. IV we will expand the utility of the high phase velocity hypothesis on the wave robustness to a plasma fusion reactor research. In this we step out of nonmagnetized plasma with the waves of the electron branch modes at the phase velocity ~ c and to extend the concept to magnetized plasma with the waves of the ion branch modes driven by an ion beam at the phase velocity near the beam velocity.
COLLECTIVE ACCELERATORS
Veksler introduced the concept of collective acceleration in 1956 [20]. His vision consisted of two elements. The first element is the introduction of plasma as the accelerating medium. In the conventional acceleration method when we increase the accelerating electric field in a vacuum surrounded by a metallic tube, the electric field on the surface of the metallic wall increases and eventually the surface begins to spark, yielding electron breakdown of the metal. As is necessary in most accelerator structures, waveguides are formed with a slow wave structure. Such a
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