## Numerical simulation of coaxial magnetoplasmadynamic acceleration for space propulsion using the HiFi spectral element code with axisymmetric geometries.

Author: Peter C Norgaard

Requested Type: Poster Only

Submitted: 2010-01-07 01:35:44

Co-authors: E.Y.Choueiri, C.W.Rowley, U.Shumlak, W.Lowrie, V.S.Lukin, A.H.Glasser

Contact Info:

Princeton University

MAE EQuad, Olden St.

Princeton, NJ 08544

United States

Abstract Text:

The HiFi code is an implicit, adaptive, high-order finite (spectral) element code with a flexible user interface that allows for relative ease in specifying the model equations (e.g. physics, geometry, and boundary conditions). A major advantage of the HiFi interface is the ability to specify equations in 3D Cartesian form - the code accommodates geometry curvature by computing the Jacobian of the logical to physical coordinate transformation. A recent improvement to the code, referred to as “multi-block HiFi”, allows for a block-logical-Cartesian mesh that enables more complex geometries. In this work we demonstrate the use of HiFi to simulate a coaxial plasma accelerator, specifically a steady-state magnetoplasmdadynamic thruster (MPDT). The plasma regime under consideration is appropriate for 30-100kW space propulsion, but is conceptually similar to coaxial plasma accelerators for plasma injection on fusion devices.

We also consider the general problem of using HiFi, a 3D code, to solve axisymmetric or periodic mode solutions for an axisymmetric geometry. One method is to use a mesh that is dense in the radial, axial, and azimuthal dimensions. This fully resolves the physics, but the computational cost scales approximately as the mesh spacing cubed. A second method is to decrease the number of azimuthal cells - in the limiting case a single azimuthal cell is revolved around the axis of symmetry. The resolution of azimuthal modes is then constrained by the number and shape of the spectral basis functions. A third method is to create a “pie wedge” using a single azimuthal cell that spans a fraction of [0, 2pi] along with periodic boundary conditions. This reduces the amount of geometric curvature present in each element, but makes it impossible to resolve low-order azimuthal modes. Finally, a fourth method is to recast the axisymmetric cylindrical coordinate equations in 2D Cartesian form and solve on a one-cell-thick slab geometry. This introduces a geometric source term that accounts for the Cartesian representation of cylindrical coordinates. The downside of this method is that it requires an interface file specific to purely axisymmetric physics. Thus the third and forth method cannot be used to pursue solutions such as the m = 1 “kink” mode instability. The merits and penalties of each of the aforementioned methods are compared, using the MPDT as a model problem, to provide a clear picture of how HiFi can be used to obtain an axisymmetric or periodic mode solutions for an axisymmetric geometry.

Characterization: E10

Comments:

Please assign a poster location next to my collaboration group, the Plasma Science and Innovation (PSI) Center group, i.e. W. Lowrie, University of Washington.