Pulsed expansion of plasma in a magnetic thruster

Citation

Iinoya, Fujio (1993) Pulsed expansion of plasma in a magnetic thruster. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/j09c-vb03. https://resolver.caltech.edu/CaltechTHESIS:10012010-143404379

Abstract

The inertial confinement fusion (ICF) pulse rocket is an advanced space propulsion system, which, through intermittent nuclear fusion energy production isolated from the vehicle structure, is capable of both extremely high specific impulses and high thrust-to-weight ratios. Such rockets, if realized, should revolutionize space travel by making possible very robust interplanetary missions as well as interstellar flight. The thruster of the rocket, which converts an initially isotropically expanding ICF debris plasma into a directed pulse jet exhaust, is to be fabricated out of magnetic fields created by current coils attached to the vehicle. The proper operation of such a thruster therefore rests upon the successful redirection of an initially spherical plasma of high conductivity by a suitably configured vacuum magnetic field against which the plasma expands. But to date, there have been no detailed analyses to guarantee that the concept in the present form will function satisfactorily as envisioned to yield reasonable propulsive efficiencies. Because of the highly dynamic behavior of the flow, which is bounded by an interface whose motion is unknown a priori, the first problem which must be investigated is that of the bulk flow under idealized conditions. In the work contained in this thesis, the plasma was assumed to be impermeable to the external fields, and the fields entered the debris dynamics only by way of applying a magnetic pressure force at the plasma-vacuum interface. The interface motion, bulk fluid profiles (when applicable), and resultant efficiencies were investigated for various parameter ratios and geometries. Such idealized bulk flow analyses are intended to serve as a basis for more detailed studies of how the flow will behave with a real plasma. Numerical simulations of the bulk flow process were conducted under both the thin-shell and the classical hydrodynamic approximations. The thin-shell calculation has been pioneered by other authors, but the present work is more complete, and as for the hydrodynamical calculations, application to the type of flows to be found in the magnetic thrusters of proposed ICF pulse rockets may be unique to this work, despite earlier claims. In the former approach, all of the plasma is assumed to be collected into an azimuthally symmetric perfectly conducting shell at the interface by virtue of the finite applied pressure at the interface. No fluid dynamics is considered under this approximation. These simulations showed that promising propulsive efficiencies could be obtained for a range of field-to-plasma energy ratios and thruster geometries, and the efficiencies reached a well-defined maximum for particular values of these parameters. However, because of the approximations used in this model, the efficiencies obtained do overestimate the real efficiencies. The thin-shell code is simpler to implement, and allows faster calculations and requires far less memory, than the more realistic hydrodynamic code, but the approximation made is not entirely accurate nor physical. In the second approach, the plasma is approximated by an unmagnetized perfectly conducting fluid obeying the laws of classical hydrodynamics. Here, we have a novel problem of a fluid expanding against a region of zero density, which nevertheless exerts a finite pressure on the fluid interface. In both the two-dimensional thin-shell and hydrodynamic calculations, the vacuum magnetic pressure applying at the plasma-vacuum interface was calculated from the quasi-static Maxwell Equations. By assuming the plasma and field coil structures to be perfectly conducting, the magnetic field in the vacuum region, from which the magnetic pressure at the interface was computed, was calculated by prescribing the initial flux through the field coils to remain trapped between the expanding plasma surface and the surfaces of the field coil structures. Such a prescription, which can be explained through the presence of surface currents, is valid as long as we have ideal perfect conductors. The hydrodynamic codes (both 1-D and 2-D) employed an advanced Classical Particle-In-Cell (PIC) scheme, and were successful at capturing the interface motion self-consistently (with pressure matching across the interface), and without iterations, via appropriate application of boundary conditions. The shock arising from the interface deceleration was also captured correctly. The formation of a shell-like structure originating close to the interface was observed in simulations of flows with large expansion ratios that were carried out in two dimensions employing realistic thruster fields. But depending upon the pressure history at the interface, these "shells" did not necessarily stay at the interfacial region. When tested on such processes as free expansion into a vacuum or shock-tube problems, for which well-known theoretical solutions exist, the one-dimensional planar-geometry simulations gave results that matched well with the analytical calculations. The qualitative features of the interface and its motion as found by the hydrodynamic simulations were similar to those obtained by the thin-shell simulations. Nevertheless, the physics of the internal flow was found to affect the performance of the thruster in ways not accountable by the thin-shell model. There were also implications that not all of the debris plasma may leave the thruster in one reflection. The substantial shock heating observed in the interfacial regions downstream of the inward-facing shock would help contribute towards maintaining high temperatures there for (possibly) achieving sufficient conductivities, provided the plasma stayed highly ionized. But because of the large expansion ratio experienced, the bulk temperature of an ICF debris plasma will fall below the ionization temperature from relatively early stages of expansion in the magnetic thrusters of currently proposed ICF pulse rockets, and the design parameters of these thrusters do not appear that promising. Because of memory limitations imposed by computers, the maximum expansion ratio treatable by the two-dimensional hydrodynamic codes was limited, and initial plasma states rather far removed from those typical of situations in proposed thrusters had to be employed. This also lowered the efficiency values quite notably. The ignorance of real plasma properties such as finite conductivities further rendered the results of this work very optimistic. However, the primary goal of this work, which was to acquire intuition for the bulk flow and performance under idealized conditions, was accomplished. Furthermore, techniques for handling this type of problem were developed. Future work should concentrate on treating more realistic parameters and on incorporating more precise plasma physics into the analysis, based on bulk flow results heretofore obtained.

Thesis Files