Enabling direct kinetic simulation of dense plasma plume expansion for laser ablation plasma thrusters

Abstract

Laser ablation plasma thrusters are an emerging space propulsion concept that provides promise for lightweight payload delivery. Predicting the lifetime and performance of these thrusters hinges on a comprehensive characterization of the expansion dynamics of the ablated plasma plume. While state-of-the-art techniques for simulating plasmas are often particle-based, a grid-based direct kinetic solver confers advantages in such a transient and inhomogeneous problem by eliminating statistical noise. A direct kinetic solver including interparticle collisions is employed on a plume expansion model problem spanning one dimension each in configuration and velocity space. The high degree of thermodynamic nonequilibrium inherent in plume expansion is characterized, justifying the need for a kinetic rather than a hybrid or fluid solver. Thruster-relevant metrics such as the momentum flux are also computed. The plume dynamics are observed to be highly inhomogeneous in space with insufficient time for thermalization in the region preceding the expansion front, and the theoretical possibility of reducing the local grid resolution by up to two orders of magnitude at the far end of the domain is established. These grid-point requirements are verified via the employment of nonuniform grids of various expansion ratios, several of which also employ coarsening in velocity space. Longer domain lengths are explored to characterize thruster-scale phenomena and larger ambient pressures are simulated as a testbed to probe facility effects due to collisions with background particles.

Effects of multi-dimensionality and energy exchange on electrostatic current-driven plasma instabilities and turbulence

“…This is consistent with the conservation of charge in phase space. The computational domain is discretised in space with a parallelised second-order finite-volume method, which is described by Chan & Boyd (2022 a , b ). Assuming small induced magnetic fields and their rates of change, we adopt the electrostatic approximation, where Gauss's law is expressed using as a Poisson equation for the electric potential of the form where and respectively denote the vacuum permittivity and elementary charge, and and respectively denote the (singly charged) ion and electron number densities Periodic and no-flux boundary conditions are employed for and , respectively.…”

“…We will analyse the transfer of energy between the modes defined in § 2.2 and reiterated here: the electrostatic potential energy 1 2 ε 0 | Ẽ| 2 d Ṽ, the bulk kinetic energy Figure 10 plots the time evolution of the exchange between different modes of energy for the larger initial electron Mach number considered in § 3.2, in a manner analogous to the energy decomposition considered by Chan & Boyd (2022a). For both dimensionalities, energy is initially transferred from electron bulk kinetic energy (due to the initial non-zero M e ) to the plasma waves, leading to an exponential growth of the electrostatic potential energy.…”

Modeling of Ionized Gas Flows with a Velocity-space Hybrid Boltzmann Solver

“…The family of discrete velocity methods (DVM), which is the main focus of the present work, operates by discretizing the velocity distribution function on a grid in velocity space, and obtains a system of partial differential equations for the values of the distribution function at each grid node. A significant advantage offered by discrete velocity methods is the noticeable reduction in noise compared to particle-based methods, which is needed to better understand the small time-scale dynamics of complex rarefied flows, especially in unsteady scenarios [5,6,7].…”

“…These include stochastic approaches, such as the Direct Simulation Monte Carlo (DSMC) method [1], and deterministic approaches, such as discrete velocity methods [2] and spectral methods [3,4].The family of discrete velocity methods (DVM), which is the main focus of the present work, operates by discretizing the velocity distribution function on a grid in velocity space, and obtains a system of partial differential equations for the values of the distribution function at each grid node. A significant advantage offered by discrete velocity methods is the noticeable reduction in noise compared to particle-based methods, which is needed to better understand the small time-scale dynamics of complex rarefied flows, especially in unsteady scenarios [5,6,7].Within the discrete velocity framework, the complex collision operator is often replaced with a simple relaxation term [8,9]. Such relaxation terms include the Bhatnagar-Gross-Krook (BGK) model [10] and its extensions, the ellipsoidal-statistical BGK model (ES-BGK) [11] and the Shakhov model (S-model) [12].…”