Page 6 - Transport studies in high-performance field reversed configuration plasmas

wave breaking onshore (see Fig. 1 (b)). On the surface of the electron entry point we form a sheath that cannot adiabatically pick up ions and is unable to gradually accelerate them. Only the sheath acceleration ensues and no acceleration beyond. Thus we learned that we have to make the driver gradually accelerates from the starting point of interaction. This is the need for adiabaticity for such application as ion acceleration, as we have already discussed in an introductory fashion in Secc.II. We show this transition from the sheath formation TNSA and the early experiment at Rostoker’s lab to more adiabatic ion acceleration by a cartoon of Fig. 4.
The second lesson is to accelerate electrons instead of heavier ions. Because electrons are light, strong enough waves can immediately trap electrons (at least some of the injected electrons) and accelerate them. In so doing we wish to use a wave with a high phase velocity that can have large amplitude and still remain intact and robust without perturbing the plasma. Again this serenity of robust waves may be seen in Fig. 1(a) for the wake wave of the boat-driven lake surface wave and the offshore portion of the tsunami wave before it hits the shore (Fig.1 (b)).
In this section we focus on the topic of the second lesson: how to make more coherent and more adiabatic acceleration of ions. See Fig. 4. According to the analysis in [33,34] in 1D Particle-In-Cell (PIC) simulation it was observed that momenta of electrons show in fact coherent patterns directing either to the ponderomotive potential direction, the backward electrostatic pull direction, or the wave trapping motion direction, in a stark contrast to broad momenta of thermal electrons of TNSA. In another word, through a very thin target the partially penetrated laser fields enable the electrons to execute dynamic motions still directly tied with the laser rather than thermal motions. The ponderomotive force due to this trapped radiation contributes to the acceleration of electrons in this sheet and thus retards these electrons from being decelerated by the electrostatic force emanated from the diamond foil. This topic is a current research topic in the laser-driven ion acceleration (See example of [33]).
After Tajima witnessed the meager energy amplification as compared to the speculated large enhancement by an ion-to-electron mass ratio over the energy of the electron beam and exponentially decaying spectral shape in the laboratory of Professor Rostoker, as mentioned above, the lesson learned by him was to accelerate, instead of ions that need adiabatic acceleration, electrons which are light and can be trapped even with a sudden (or non-adiabatic) acceleration. As he went on to UCLA working with Dawson after graduation from UCI, he and Dawson employed a short laser pulse to cause a large ponderomotive force in plasma, whose collective accelerating field is the resonantly excited plasma wake. This wakefield traps electrons at rest from the bulk (They could be injected otherwise). In this scheme (now called Laser Wakefield Acceleration (LWFA)[10]) the wake propagates with the group velocity of the laser pulse, which is near the speed of light. Tajima and Dawson observed that because of the large phase velocity of the wake wave of ~ c, the wake wave grows robustly large without directly disturbing the plasma bulk particles that support the wake. This situation is similar to the serene surface water wake wave driven as a wake of the motorboat, as shown in Fig, 1(a). Because the wakefield propagates at ~ c, the wake does not trap (or otherwise disturb) the bulk electrons or ions, unlike the onshore tsunami wave whose phase velocity is near zero onshore and which delivers all the wave energy into the shore destruction. The laser wakefield can grow serenely till the trapping width of the wake becomes so large that the arms of the wakefield (e.g. in Fig. 2(a)) now reach from the thermal velocity of bulk cold plasma particles to the speed of the phase velocity which sits at (or near) the speed of light of the laser pulse. When this happens, the wake growth begins to stop and / or to trap a class of injected electrons. This is the first manifestation and example of the principle (or hypothesis) of robustness of waves with a high phase velocity in the example of LWFA. Such was experimentally demonstrated by many experiments including [13-15].
Thus employing this LWFA principle (or the robustness hypothesis), Esirkepov et al. [35] proposed a very intense laser pulse to excite so huge a ponderomotive force that even ions may be immediately trapped (i.e. non- adiabatically) in this ultrarelativistic laser intensity regime of the Radiation Pressure Acceleration scheme. In this scheme, not only are ions accelerated with a quasi-monoenergetic spectrum, but can also reach relativistic energies. The only inconvenience of [35] is the requirement of ultrarelativistic laser pulse amplitudes, where the normalized vector potential of the laser pulse a0 = eEl / mcωl is exceedingly greater than unity (such as ~103, where El and ωl are the laser electric field and frequency.) Such laser requires an intensity on the order of 1023W/cm2, whose technology has yet to be realized. One more comment as to RPA in the ultrarelativistic regime is that in the when a0 >> 1, the wakefield tends not to be resonantly excited any more (see [39]).
One way to improve this situation without the required laser intensity is to employ a circularly polarized laser on a thin target. For example, in [32] an experiment with a reduced target mass (by choosing nanometrically thin carbon (diamond)), even linearly polarized (LP) laser irradiation produced a much improved acceleration (higher energies and less spread energy spectrum) than that observed in the TNSA experiments in which the energy spectra is typically found to be exponentially decaying. With circularly polarized (CP) laser irradiation of the target, the experiment [32] found that in addition to the energy improvement, the energy spectrum had a quasi-monoenergetic
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