Laser Propulsion using a Molecular Absorber V.P. Chiravalle,∗ R.B. Miles,† and E.Y. Choueiri‡ MAE Dept. Princeton University Princeton, New Jersey 08544 AIAA-98-3932§ Abstract energy into the kinetic energy of propellant gas is a critical figure of merit. In addressing laser thruster This paper explores the concept of laser propulsion performance it is useful to consider both the absorp- using a molecular absorber. Unlike the conventional tion efficiency as well as the the propulsion efficiency. approach of using a laser sustained plasma to heat In the context of laser thrusters, the propulsion ef- a propellant, molecular absorption of laser energy ficiency is a measure of how much absorbed energy makes it possible to avoid the frozen flow losses appears as kinetic energy of the propellant at the noz- associated with the high temperature and complex zle exit. chemistry of a plasma. The molecular absorption concept is developed by exploring several thermody- namic pathways for energy addition in the supersonic The established approach for achieving energy regime, which are visualized as curves in H-K coordi- conversion is to create a laser sustained plasma nates. The case of an isothermal expansion is stud- (LSP) in the flowing propellant. The plasma is lo- ied in depth. The absorption physics of a promis- calized near the focal point of a laser beam, and ing molecular absorber, SF , is described at arbitrary 6 laser energy is absorbed through the electron inverse laser beam intensities using a two-temperature non- bremsstralung process. As the propellant gas flows equilibrium model, which is then applied to calculate through and around the stationary plasma high bulk the required length of the supersonic energy addition temperatures are sustained which can be in excess of region in a laser rocket nozzle. 10,000 K in gases such as argon. Stable LSPs were created and observed by Keefer et. al.[4], who re- port absorption efficiencies as high as 86 %. Several 1 Introduction attempts have been made to visualize the physical in- teractions occurring in laboratory LSPs using two di- As high-power laser technology continues to mature mensional numerical simulations[5, 6]. Although the the possibility of using a laser to generate rocket coupling of laser energy to a plasma has been found thrust for propulsion applications grows more feasi- to be quite high, the overall propulsion efficiency is ble. The laser propulsion concept was first introduced not as good. There are several processes that de- by Kantrowitz[1] , more than twenty five years ago, grade the efficiency. In general, plasma radiation is a and was experimentally demonstrated by Krier et. significant contributor, and in the case of molecular al.[2] and by Myrabo[3] . As with any thermal propul- propellants such as hydrogen, dissociative frozen flow sion system, the efficiency of conversion of laser beam losses are also important. The equilibrium fraction ∗Graduate Student, Mechanical & Aerospace Engineering, of dissociated hydrogen is known to vary exponen- AIAA tially with temperature, and the reduction of frozen †Professor, Mechanical & Aerospace Engineering, Associate flow losses in hydrogen thermal thrusters necessitates Fellow AIAA ‡ finding a way to add significant amounts of energy Assistant Professor, Mechanical & Aerospace Engineering, Se- without completely dissociating the propellant. The nior Member AIAA §This work was supported by an AASERT award from the Air dissociation fraction of hydrogen for various temper- Force Office of Scientific Research (AFOSR). atures and densities is shown in Fig. 1. 1 2 CHIRAVALLE, MILES, CHOUEIRI: LASER PROPULSION USING A MOLECULAR ABSORBER 1.0 ρ = 0.001 0.01 laser thruster with molecular absorption. 0.8 0.1 0.6 α 1 0.4 10 0.2 100 0.0 0 2000 4000 6000 8000 T (K) Figure 1: The calculated equilibrium dissociation fraction of H2 is presented above, as a function of temperature and density. A different approach for energy addition, one that does not utilize a plasma, is the molecular absorption of radiation in the supersonic regime. Adding energy using a molecular absorber involves the excitation of an internal mode such as rotation or Figure 2: Illustrated above are the laser rocket vibration of a seed molecule, the seed molecule sub- propulsion concepts discussed in this paper: a: En- sequently transfers its energy to the propellant gas ergy addition using a laser sustained plasma in the by relaxation collisions. The molecular absorption plenum region. b: Energy addition in the supersonic approach for laser propulsion was previously identi- region using a molecular absorber. fied by Caledonia et. al.[7] in 1975. More recently, molecular absorption has been considered as an en- ergy addition mechanism in the supersonic region for a proposed atmospheric, hypersonic wind tunnel and 2 Fluid Model for Energy Ad- has been the focus of an ongoing research effort[8, 9]. dition The central issues with this approach involve the choice of the thermodynamic path over which energy Within the constraints of one dimensional theory, the is added and the choice of the seed molecule, with its physics of an absorbing fluid in steady state is ex- associated set of physical parameters. Fig. 2 shows pressed by the fluid conservation equations, that with a molecular absorber it is possible to ex- 1 dA 1 dρ 1 du tend the energy addition region throughout the noz- + + = 0 (1) zle rather than concentrating all the energy in the A dx ρ dx u dx plenum, the way it is done in conventional propul- dP du + ρu = 0 (2) sion systems. The goal of this paper is to explore dx dx relatively simple energy pathways, such as constant dT du dT c + u = 0 . (3) temperature expansion to gain insight into the more p dx dx dx complicated cases that may be of use to laser propul- dT0 sion. The interaction between the seeded propellant T0 is the total temperature of the fluid and dx = dPw mixture and the laser beam is described in general κ dx . Pw is the laser power which is assumed to be terms, using a familiar quasi-one dimensional model. uniform across the beam cross section. It is assumed It is understood that this approach is useful in a re- also that the gas is ideal and perfect i.e. with P = stricted sense, and is intended as a starting point for ρRT and constant cp. more robust numerical simulations. This formalism The absorption coefficient, κ, is in general a func- is then applied using absorption data for SF6 to cal- tion of the gas thermodynamic variables T and ρ and culate the length of the energy addition region in a the laser intensity, I. There are more variables in CHIRAVALLE, MILES, CHOUEIRI: LASER PROPULSION USING A MOLECULAR ABSORBER 3 this system than equations relating them. When the fer with constant area, adiabatic, isentropic expan- nozzle area, A, is specified everywhere and when the sion and constant Mach number heating of the gas. laser power incident to the energy addition region, The appropriate χ functions for these three cases are Pw0, is known, the above equations uniquely deter- given below mine the thermodynamic and mechanical state of a 2 2 gas with a given set of initial conditions. χ =(1− γM )/M (γ − 1), (6) It is well known that if a transformation is per- χ = −1, (7) formed, expressing all quantities in terms of the op- χ =2/(γ − 1)M 2, (8) tical length, τ = κdx, the conservation equations can be solved without reference to the properties of where Eq. 6 refers to the constant area heat trans- the absorbing species[7, 10]. The solution in physical fer case, Eq. 7 refers to the adiabatic, isentropic ex- space is recovered, for a chosen absorber, by revers- pansion case and Eq. 8 refers to the constant Mach ing the transformation. There are limitations to the number case. The example cases just discussed are effectiveness of this approach since the radius of the illustrated in Fig. 3, and do not exhaust the set of nozzle is now a function of τ. Choosing A(τ) to give a specific shape in physical space is not intuitively obvious. 6 This difficulty can be removed, if instead of con- A straining the nozzle to have a given profile in space, 5 an additional relation among the fluid variables is specified. The enlarged system of equations is solved 4 with A as a variable. In this way nozzle profiles B 3 are determined to satisfy thermodynamic constraints. H (MJ/kg) The additional relation can be chosen as 2 C P dH D = χ, (4) 1 dK 2 0 with K = u and H = c T . Going a step further, all 2 p 1.5 2.0 2.5 3.0 3.5 the variables that describe the fluid, A, T0, ρ, T , and K (MJ/kg) u, can be written in terms of M 2, γ and χ, 1 dA ((γ − 1)χ + γ)M 2 − 1 dM 2 = , Figure 3: This figure shows the H-K coordinates of − − 2 A dτ 2 χ(γ 1)M dτ four trajectories in the supersonic regime that inter- 2 1 dT0 (γ − 1)(χ +1) dM sect at point P. The conditions at P represent a mix- = γ−1 , T dτ 2 − − 2 dτ ture of H2 with 2 % SF6 at T=300 K with M=3.0. 0 (1 + 2 M )(1 χ(γ 1)M ) (A) refers to a cooling process with constant area, (B) 1 dρ (γ − 1)χ + γ dM 2 = − , refers to an adiabatic, isentropic expansion process, − − 2 ρ dτ 2 χ(γ 1)M dτ (C) refers to an isothermal expansion process and (D) 1 dT χ(γ − 1) dM 2 = , refers to a heating process at constant Mach number.