This award enables development and application of the Vlasov Multi-Dimensional (VMD) model to fundamental phenomena in non-equilibrium plasma dynamics. The VMD model takes advantage of directed plasma wave turbulence properties, encountered in laboratory and space environments, by rigorously joining particle and fluid aspects of plasma dynamics, something which has previously been unattainable. It had been thought that models which explicitly incorporate fluid dynamics must omit essential aspects of high temperature plasma dynamics. By showing that this is not necessarily the case, the VMD model advances our understanding, showing what is and what is not essential in standard plasma models.
VMD results in vastly more efficient simulation methods than afforded by traditional PIC ("particle in cell") methods. An early research goal is validation of the VMD model by comparison with results previously obtained by PIC simulations. Validation of the VMD model will allow its application to predicting the nonlinear evolution of plasma waves that naturally occur in high temperature plasma as found in the neighborhood of pulsars, in the earth's ionosphere, and, closer to earth, as they occur in the propagation of intense microwave and laser pulses in laboratory generated plasma. Of particular importance is the more accurate modeling of regime change. For example, how much power can be transmitted before plasma wave turbulence blocks laser propagation? Determination of laser intensity at regime change boundaries by PIC simulation may be obscured by unphysical noise. The VMD method is noise free, expanding the scope of plasma dynamics accessible by simulation.
Scientific challenges of high-temperature environments, such as those involving nuclear reactions (in stars and nuclear weapons), high intensity laser beams and the ionosphere, mainly arise from their ubiquitous plasma state: one whose dynamics cannot be emulated by the more familiar and better understood phenomena of fluid dynamics. While naturally occurring fluid motions are marvelously complex, one may often observe and take note of their key features with the naked eye, as Leonardo da Vinci accomplished some five centuries ago (Fig. 1). High-temperature plasma phenomena, however, are far removed from everyday experience and their mathematical models are far more difficult to analyze via theory and computer simulation than are fluid dynamical phenomena. Remote sensing of a laser beam propagating through plasma, with current technology, does not reveal spatial structures. Instead, typical experimental data is in the form of spectra that reveal how plasma wave energy is distributed in wavelength. Such data cannot distinguish between a totally chaotic collection of waves and a state that has both coherent structures and chaos, as in Fig. 1. We have developed a plasma dynamics model, the Vlasov Multi-Dimensional (VMD) model, and demonstrated that its properties are nearly identical to those of the standard (Vlasov) model when there is a dominant axis of power, such as when a laser beam propagates in plasma. A practical outcome is the relative ease of analysis and simulation of the VMD model compared with the Vlasov model. Plasma simulations that formerly required supercomputer resources may now be performed on a desktop computer, enabling participation by researchers without access to a supercomputer. By way of illustration, three-dimensional (3D) VMD simulation results are compared with a more familiar fluid dynamic phenomenon. Consider a fluid layer heated from below, e.g., a pan of water on a stovetop, and cooled on top by exposure to air. Even if heat is applied uniformly at the pan bottom, thermal transport through the layer is susceptible to the well-known Rayleigh-Bénard instability that couples temperature gradient to fluid flow and breaks the initially uniform state. A practical result is thermal energy (heat) transport far in excess of that found absent fluid motion. One manifestation is the complex spatial pattern seen in Fig. 2. The plasma example has electrons alternately pushed and pulled in the vertical direction by the electric field, uniformly so in the two horizontal directions. This is a simple model of laser propagation in plasma. The trapped electron filamentation instability results in non-uniform response of electron density, shown in Fig. 3, at the middle of the plasma layer, and in figures 4-5 in 3D perspective graphics. Blue corresponds to a relative density fluctuation of magnitude -5% while red to +5%. One consequence of this instability is better laser light transmission as its scatter from the initial spatially coherent electron density distribution, fig. 4, is greater than from the variegated distribution shown in figures 3 and 5. In summary, our VMD model of plasma dynamics has been verified by comparison with Vlasov equation solution properties. It enables participation by researchers in multidimensional simulations without needing access to a supercomputer, and has revealed consequences of electron filamentation not seen before.
