SBIR Phase I Final Progress Report PR-NA0001-03

A magnetically confined plasma which produces fusion reactions is to be used as a propulsion system for an upper stage of a launch vehicle which could be employed for interplanetary travel. Fusion reactions produce a significantly higher degree of energy per reactant mass than conventional chemical reactant propulsion systems and, thereby, offer the promise of more effective and productive specific impulses and thrust. The energy produced from the fusion reaction manifests itself initially as kinetic energy of the reaction products and then becomes available for generating thrust or other uses.

Our concept makes use of a confinement scheme known as the magnetic mirror in which a hot plasma is radially contained in a solenoidal geometry by a magnetic field with a configuration that allows a certain fraction of the plasma to escape axially producing thrust as desired. Unlike the ordinary mirror machine, the particle density in the proposed device is sufficiently high to allow the plasma to behave like a continuous medium - a fluid with properties that render it especially suitable for an advanced propulsion scheme. Such a system can be constructed with almost present day or near-term technology drawing on relevant research that has accumulated over the past three decades.

The objective of this project was to perform a detailed analytical and computational investigation of the confinement physics of the device as well as the propulsive capability of this Gasdynamic Mirror (GDM) Fusion Rocket in order to show that it is capable of producing desirable specific impulses and thrusts. The specific technical objectives were to:

• establish the equilibrium confinement properties of the Gasdynamic Mirror and
• examine the plasma instabilities that might arise in this propulsion system.

In order to meet the technical objectives, four tasks were defined and carried out:

1. Finalization of Propulsion System Nominal Requirements and Parameters
2. Confirmation of the Confinement Properties of the Gasdynamic Mirror
3. Analysis of the Magnetohydrodynamic (MHD) Stability Question
4. Analysis of the Microinstability (Flute Instability) Question

Details of the work performed are described further below:

The propulsion capability of the gasdynamic mirror (GDM) is critically coupled to the dynamics of the plasma in it. Under the appropriate operating conditions the confinement of such a plasma and its dynamics are governed by gasdynamic laws which we have deduced and utilized in assessing its propulsion performance. A very important quantity is the confinement time which we also derived and found to be directly proportional to the product of the mirror ratio and length, and inversely proportional to the thermal velocity of the particles, consistent with gasdynamic laws. The mass and energy conservation equations were subsequently derived and solved. Making use of the mass and energy equations and the confinement relationship, we solved for the important nominal requirements and parameters that would characterize the propulsive capability of the GDM.

Two sets of data were produced (as shown by the Table in Section 3). The first was generated ignoring the presence of an electrostatic potential, and the other with the potential included. Such a potential arises because the electrons in the system tend to escape more rapidly than the ions, leaving behind a positive potential that promotes faster ion escape and a slower electron escape until the two rates equalize. A mathematical expression for this potential was derived and incorporated in the governing dynamic equations for the system.

A critical question that was also addressed is one that pertains to plasma stability. It is well known that mirror magnetic geometries are susceptible to a magnetohydrodynamic (MHD) instability known as the flute instability. It arises when a hot plasma is located in a magnetic configuration that has concave curvature toward the plasma. Upon perturbation, charge separation can occur giving rise to electric fields which when coupled to the confining magnetic field can cause these perturbations to grow and result in a plasma loss from the system. These phenomena can occur an a time scale which is shorter than the confinement time, thereby, destroying the environment needed for energy production in the system.

Another instability that might also arise is microscopic in nature, and derives its energy from the deviation of the velocity distribution function of the plasma from Maxwellian as a result of particles escaping through the "loss cone". Because the plasma in GDM is collisional, and the operating conditions require the collision mean free path divided by the mirror ratio to be much shorter than the length , this feature, in essence, minimizes if not eliminates the escape through the loss cone and the conditions for triggering the instability in question. In the absence of turbulence, cross field diffusion of the plasma is negligible and, as a result, it is shown that the longitudinal confinement time alluded to earlier is the characteristic time that underlies the operation of GDM as a propulsion system.

The confinement time was derived and found to be directly proportional to the product of the mirror ratio and length, and inversely proportional to the thermal velocity of the particles, consistent with gasdynamic laws.

Making use of the confinement relationships and the mass and energy conservation equations, a set of nominal requirements and parameters which characterize the propulsive capability of GDM was generated. Two sets of data (without and with electrostatic potential) were produced as shown in the below table.

*Destination: MARS, (D = 7.80E+10 m)

From a study of the plasma's characteristics it was found that because of its large aspect ratio, the GDM will be stable against any potential MHD (flute) instability concerns. The microinstability is also not expected to occur in the GDM system because of its operationally required high density and short collisional free path.

The preceding Section's table shows the various plasma parameters as well as the propulsion characteristics of a gasdynamic mirror that burns a deuterium-tritium (DT) fuel mixture. Though not optimized, it is seen that such a device can be of reasonable size and mass, and could generate the propulsion parameters needed for quick interplanetary travel.

The Gasdynamic Mirror fusion propulsion is shown to perform in accordance with the physics principles deduced and addressed above. Specifically, the gasdynamic confinement time allows a hot (DT) plasma to produce sufficient fusion energy while allowing a fraction of the population to escape through the mirror to produce the thrust. These results reveal that a modest energy multiplication "Q" is required for the system to be self sustaining, and giving rise to acceptable sizes and mass.

The electrostatic potential is shown to result in longer confinement time to compensate for the faster ion escape, and that in turn results in a somewhat longer and a more massive device but with higher thrust and specific impulse to keep the travel time virtually unchanged. The presence of the plasma in the throat of the mirror (the magnetic nozzle) seems to assure plasma MHD stability in a GDM with high aspect ratio (large length to diameter ratio) since the magnetic curvature is on the average favorable i.e. neutral or convex towards the plasma. Furthermore, the high plasma collisionability as reflected in the operating conditions for GDM almost guarantees the absence of scattering of particles into the loss cone and the conditions required for kinetic instabilities. In short, this study shows that under the proper conditions GDM can function smoothly as a propulsion device with propulsive parameters that far exceed any available from chemical and/or nuclear thermal propulsion systems.

Though preliminary, this study has demonstrated the feasibility of the gasdynamic mirror fusion system as a propulsion device capable of meeting NASA's requirements for exploration of the solar system and beyond. It has also shown that such a system can be built with present day or near-term technology that has accrued from many years of research in the development of fusion terrestrial power reactors. It has demonstrated the potential of GDM as a reusable vehicle propulsion system that can positively impact the competitiveness of the United States space market. Because of the small amount of the fuel mass as a function of the total vehicle mass, considerable economic benefits can be expected from the use of such a propulsion device for interplanetary travel along with virtual elimination of interplanetary launch window constraints.

Although our study to date of the Gasdynamic Mirror as an upper stage propulsion system has provided remarkable results, we believe that some additional work of a nature more suitable to SBIR Phase I is needed and should be completed prior to proposing a Phase II Program. In the future, after this additional work is completed, we hope to propose and pursue a Phase II effort which will consist of final fine-tuning of the GDM model parameters and the development and implementation of a detailed test plan to validate our model's predictions.

Prepared By:
David A. Horvath, PE
Principal Investigator