Modeling & Simulations

Physics-based modeling & simulations (M&S) play an indispensable role in electric propulsion at JPL. Our modeling capabilities have been supporting a wide range of R&D activities and flight programs for NASA for over two decades. The mission of the M&S program at JPL has both near-term and long-term impacts for electric propulsion:

• To Understand Critical Physics that cannot be resolved or accessed by conventional diagnostics, leading to better-performing, longer-life engines
  • example: erosion in ion engine grid apertures
  • example: erosion of the hollow cathode orifice
• To Discover or Identify Unknown Physics that may lead to breakthrough capabilities, enabling new science missions for NASA
  • example: “magnetic shielding” in Hall-effect thrusters
• To Guide Designs of new engines (or refine past designs), reducing costly “trial-and-error” tests
  • example: NEXIS ion optics
• To Diminish Risk both real and perceived, by elucidating test and/or flight observations that are not well understood and publishing findings in peer-reviewed journals
• To Reduce Qualification Costs by verifying performance and/or life capability that is otherwise too costly to demonstrate by qualification tests
• To Shorten Time-to-Flight by reducing time to qualify

OrCa2D is used to simulate plasma and erosion processes in electric propulsion hollow cathodes and its development started in 2004. The code solves the conservation laws for the partially-ionized gas in these devices, in 2-D axisymmetric geometry. Specific features of OrCa2D’s solvers and capabilities are provided below.

• Electrons: Ohm’s law and time-dependent energy equation based on continuum approximation.
• Ions: time-dependent continuity and inviscid momentum equations based on continuum approximation.
• Neutrals: time-dependent full Navier-Stokes equations in the cathode interior transitioning to collision-less gas in the exterior. Time-dependent energy equation solved for the heavy species (ions & neutrals)
• Accounts for applied magnetic field. Uses magnetic field aligned mesh generator.
• Electrode boundary conditions including electron emission from insert. Large computational region encompassing cathode interior (emitter region), cathode plate and keeper orifice regions, near-plume and anode regions.
• Written in Fortran90 using the Intel Visual Fortran Composer XE 12.0 compilers (Intel Parallel Studio XE 2011 or higher) and the Intel Math Kernel Library (MKL) 10.3 (or higher).
• Makes use of Intel’s parallel sparse matrix solvers (PARDISO) to take advantage of multi-core multi-thread processors.
• References (for a more extensive list see the Publications section).
  • Mikellides, I. G., Katz, I., et al., "Hollow Cathode Theory and Experiment, II. A Two-Dimensional Theoretical Model of the Emitter Region," Journal of Applied Physics, Vol. 98, No. 11, 2005, pp. 113303 (1-14).
  • Mikellides, I. G., Katz, I., et al., "Wear Mechanisms in Electron Sources for Ion Propulsion, II: Discharge Hollow Cathode," Journal of Propulsion and Power, Vol. 24, No. 4, 2008, pp. 866-879.

Hall2De is used to simulate plasma and erosion processes in Hall thrusters and its development started around 2009. The code was the first to solve the conservation laws for the partially-ionized gas in these devices on a radial-axial (r-z) magnetic field aligned mesh (MFAM). The core code structure is the same as that of OrCa2D with several algorithms also taken from OrCa2D. Some more specific features associated with Hall2De’s solvers and overall capabilities are provided below.

• Magnetized electrons: anisotropic Ohm’s law and time-dependent energy equation. No assumptions made regarding isothermal properties of electrons along lines of force. Uses magnetic field aligned mesh to allow for highly-anisotropic solution to the equations for the electrons with minimal numerical diffusion.
• Un-magnetized ions: hybrid multi-fluid/PIC time-dependent numerical approach. Multi-fluid solution obtained on the MFAM; PIC ions tracked on a rectilinear mesh.
• Neutrals: Collision-less gas – solution obtained using view-factors.
• Insulator and conducting boundary conditions. Large computational region allowing for self-consistent incorporation of the cathode boundary. Fully 2-D Poisson solver on a refined mesh to allow resolution of thick sheaths along boundaries.
• Written in Fortran90 using the Intel Visual Fortran Composer XE 12.0 compilers (Intel Parallel Studio XE 2011 or higher) and the Intel Math Kernel Library (MKL) 10.3 (or higher).
• Makes use of Intel’s parallel sparse matrix solvers (PARDISO) to take advantage of multi-core multi-thread processors.
• References (for a more extensive list see the Publications section).
  • Mikellides, I. G. and Katz, I., "Simulation of Hall-effect Plasma Accelerators on a Magnetic-field-aligned Mesh," Phys. Rev. E, Vol. 86, No. 4, 2012, pp. 046703 (1-17).
  • Lopez Ortega, A. and Mikellides, I. G., “A New Cell-Centered Implicit Numerical Scheme for Ions in the 2-D Axisymmetric Code Hall2De,” AIAA-2014-3621, July 2014.

CEX-2D and CEX-3D are ion optics codes that compute ion trajectories and charge exchange reactions between beam ions and un-ionized propellant gas in two and three dimensions. They were developed in the early 2000’s. The 2-D version solves Poisson’s equation on a regular mesh in cylindrical geometry. The code models a single set of screen and accelerator grid apertures assuming cylindrical symmetry. The computational domain is divided into a grid of rectangular cells. With a few exceptions, the code uses a combination of algorithms used in earlier optics codes for ion thrusters. The CEX3D code was developed to solve for potentials and ion trajectories through a two-grid ion optics system. The computational domain is a triangular wedge extending from the axis of a hole-pair to the midpoint between two aperture pairs. The computational domain extends from the discharge chamber through the optics system into the beam downstream of the accelerator grid.

• References (for a more extensive list see the Publications section).
  • Brophy, J. R., Katz, I., et al., “Numerical Simulations of Ion Thruster Accelerator Grid Erosion,” AIAA-2002-4261, July 2002.
  • Anderson, J. R., Katz, I., et al., “Numerical Simulation of Two-Grid Ion Optics Using a 3D Code,” AIAA-2004-3782, July 2004.

HallPlume2D computes the expansion of the plasma from a Hall thruster on a radial-axial (r-z) domain that can extend several meters downstream of the discharge chamber. It was developed in the mid-2010’s and has incorporated many of the lessons learned in plume modeling over several decades. It uses the simulation results from Hall2De to define boundary conditions at the plume inlet. The ion solver in HallPlume2D follows the same strategy as that in Hall2De, allowing for both multi-fluid and discrete particle methods. In both strategies, ionization and charge-exchange collisions are accounted for. The neutrals gas also is solved in the same manner as that in Hall2De. For the electrons, the temperature is determined by solving an energy conservation equation that is subject to Dirichlet boundary conditions at the Hall2De-HallPlume2D interface. Because the thruster boundary in the plume simulation is deliberately chosen to be far from the thruster exit, the applied magnetic field is neglected and the electric field and plasma potential are computed using Boltzmann’s law for the electrons.

• References
  • Lopez Ortega, A., Katz, I., et al., "Self-Consistent Model of a High-Power Hall Thruster Plume," (in English), IEEE Transactions on Plasma Science, vol. 43, no. 9, pp. 2875-2886, Sep 2015.