Simulation Topics
Opportunities in Computational Plasma and Beam Physics
There are many opportunities for graduate student research in computational physics of plasmas and beams, including the study of nanoscale vacuum channel transistors, the study of the formation of plasma targets for laser-wakefield acceleration, and the development of new algorithms for simulating plasmas.
Nanoscale Vacuum Channel Transistors
Figure 1: Simulated electric field strength for different NVCT geometries. [J-W Han et al., Nano Lett. 17, 2146 (2017)]
Vacuum tubes were long ago replaced by solid-state transistors because they are smaller, faster, and more energy efficient. However, new fabrication techniques have recently enabled production of nanometer-sized vacuum tubes, or nonoscale vacuum transistors (NVCTs), which promise several advantages over solid state transistors. First, NVCTs are effectively "in vacuum" even at atmospheric pressure because they are much smaller than the mean free path of air molecules; i.e., electrons rarely collide with air molecules while traveling through the NVCT. The short travel distance and fast speed of electrons in vacuum (faster than conduction in solid state devices) allow NVCTs to respond faster than their solid-state counterparts. Second, because NVCTs are nanometer-sized, a potential difference of just a few volts can induce an electric field well in excess of 1 GV/m, strong enough to extract electrons efficiently from the electrodes via field emission (where electrons tunnel quantum mechanically through the work function barrier). Thus, NVCTs consume much less power than their vacuum tube ancestors. In addition, NVCTs should be very robust, able to operate in extreme temperatures and harsh radiation environments. The properties of an NVCT depend sensitively on the geometry, i.e., on the local electric field necessary for field emission, as well as on the behavior of space charge once emitted. We model proposed NVCTs, characterizing electron emission, travel, the subsequent circuit characteristics, robustness to fabrication errors, etc., to achieve optimal performance.
Formation of Plasma Targets for Plasma Acceleration
Figure 2: Electrons (yellow) accelerated by the wake (blue) generated by a laser pulse (red).
Electrons can be accelerated to high energies from the interaction of a laser pulse (frequency 蠅) with a plasma (plasma frequency). The laser pulse travels with a group velocity v_g < c and creates a wake of the same velocity. The wake has an electric field along its direction of motion and so can accelerate particles behind the wake. The maximum acceleration obtainable by such interaction is to relativistic factor, where 纬_g is the relativistic factor corresponding to v_g, and is given approximately by 纬_g=蠅/蠅_p. Therefore, one can accelerate to higher energies with lower density plasmas.
Creating lower-density plasmas with the right characteristics is difficult, because at low density one has low collisionality. Collisions are critical to plasma heating and formation of shocks, which are needed to get a focusing profile -- a hollow plasma guides a laser pulse much like an optical fibre -- that allows the laser pulse to propogate far enough for the acceleration to take place.
This project is investigating the use of optical field ionization (OFI) to generate the plasma. In this process, electrons are stripped from the molecules directly, after which the plasma dynamics occurs. The goal of this project is to learn whether one can generate plasmas of the right density and profile for subsequent use as a target for laser plasma acceleration.
Speed Limited Particle in Cell Simulation
Figure 3: The phase space distribution of electrons, simulated by SLPIC in a prescribed 1D wave with phase velocity v_蠒 , for various speed limits v_0 . As long as the speed limit is sufficiently above the phase velocity, SLPIC accurately captures wave-particle interaction, but as the speed limit nears the phase velocity, SLPIC loses fidelity. [from G. R. Werner et al., Phys. Plasmas 25, 123512 (2018)]
The particle-in-cell (PIC) method provides first-principles kinetic simulation, i.e., capturing full particle velocity distributions. Although very powerful, the separation between electron and ion scales can be challenging for PIC simulation, leading to high corruptional cost. Because electrons, being less massive, typically move much faster than ions, faithfully following electron motion requires very small timesteps (compared with the time it takes ions to travel a significant distance). For many simulation applications, this timestep may be much smaller than the time it takes fields and particle distributions to change significantly. In such cases, speed-limited particle-in-cell (SLPIC) simulation reduces electron travel speeds (while keeping track of the real velocity that they would have), and thus allows much larger timesteps. To be physically justifiable, the "weights" of the electrons must vary with their speed. This novel approach decouples the simulated macroparticles from real particles, but continues to appear very much like a standard PIC algorithm with some small modifications. In initial tests modeling an argon plasma sheath, SLPIC yielded the correct sheath profiles (of potential, density, etc.) more than 100 times faster than the comparable PIC simulation. The SLPIC method is in its early stages; much work is still needed to characterize the accuracy of SLPIC (as a function of the speed limit) and especially its ability to simulate wave-particle interactions, such as Landau damping.