## Romanelli C Bruno and G Regnoli

B.l INTRODUCTION

Exploring the Solar System and beyond requires the development of adequate propulsion techniques, and the need for reasonable mass consumption implies (as seen in Chapter 7) very great power. Here a simple estimate can help in understanding the terms of the problem. To accelerate a mass Mw up to a velocity vc in a time T requires an average thrust power P (kinetic energy of the mass accelerated divided by time) given by [Stuhlinger, 1964]

This condition defines a characteristic velocity vc given by vc = (2aT)1/2 (B.2)

where a = P/Mw, the so-called specific power (thrust power per unit mass), defined here in relation to the mass of the propulsion system. Note that mass consumption while power is "on" has been neglected, similarly to our procedure in Section 7.18. This assumption was made to obtain simple analytical solutions, but is rarely verified in actual missions and trajectory calculations.

The trajectory distance or length L is approximately given by L = k0vcT, k0 being a constant of order unity which depends on the details of the trajectory. On combining the previous conditions and taking, for instance, k0 = 1/3, it follows that

1 EFDA Associate Leader for JET, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK.

2 Graduate Student, EURATOM-ENEA Fusion Association, Via E. Fermi 45, 00044 Frascati, Italy.

the specific power is related to L and T by the following condition:

where L is in astronomical units (1 AU k 150 x 106 km) and T is in years.

Thus, once the mission target distance (L) is assigned, the request of a reasonable flight duration (T) sets a limit on the specific power a. As an example, a mission to Mars (Lk 1 AU) over one month requires a specific power in the range a k 1.7 kW/kg. A mission to the Oort Cloud (L k 104 AU) lasting 20 years requires a specific power in the range a k 12kW/kg. Thus, values of specific power in the range 1 kW/kg-10kW/kg are a rough estimate of the a needed to explore the Solar System. Also, note that a mission to Proxima Centauri (L k 2.5 x 105 AU), lasting less than 10 years, would require (neglecting relativistic corrections) a specific power in excess of 6 x 104 kW/kg, an extremely large value. However, for large L (large mass consumed) the simplifying assumption of constant Mw is no longer valid.

In assessing propulsion system performance, the other figure of merit, besides specific power, is the payload fraction ML/M0. Following [Stuhlinger, 1964], the payload fraction can be easily determined in terms of the characteristic velocity vc defined in Equation (B.2) from Tsiolkovski's equation. Upon defining M0 = Ml + Mw + Mp, with M0, Ml, Mw, and Mp being the initial, payload, propulsion system, and fuel mass, respectively, and expressing Mw in terms of the specific power (Mw = P/a), it is possible to show that

Ml/Mq = exp(-Vf/Vex) - (vex/vc)2[1 - exp(-vf/Vex)] (B.4)

where vf is the final velocity and vex the exhaust velocity of the propellant being ejected (related to the specific impulse Isp = vex/g in seconds). Equation (B.4) shows that a positive payload fraction can be obtained only for vf/vc = vf/(2aT)1/2 < 0.8 and within a finite domain of vex/vc (with the domain increasing as vf /vc decreases). The optimal payload fraction is approximately obtained for vc k 21/2vex (see Figure B.1)

Figure B.1 confirms that in order to have reasonable performance high values of specific impulse are mandatory. As an example, taking the optimal payload condition vc = 21/2vex, in order to fly in excess of 1 AU in one month with a specific power of 3.5 kW/kg and a payload fraction k 0.1 (vf/vc k 0.7), requires a specific impulse of the order of 104 s, well beyond the capabilities of chemical propulsion systems.

Note that the above conditions also determine thrust per unit mass (F/M) (i.e., average acceleration). Since P k Fvex, it follows that

Such a value is larger than the gravity acceleration in the Sun field at the Earth radius (k6 x 10 -4 g) for values of the specific power larger than 6 kW/kg and Isp = 105 s, so high-thrust missions are possible in such a parameter range.

It is for this reason (to achieve high specific impulse) that fusion propulsion was originally proposed. Indeed,

Vex /Ve

Figure B.1. Payload fraction vs. velocity ratio.

Vex /Ve

### Figure B.1. Payload fraction vs. velocity ratio.

Fusion reactions produce low-mass (atomic number A = 1-4), high-energy (up to 14MeV) fusion products with the associated specific impulse of the particles ejected in the range Isp = 4 x 106 s.

The reacting ("fusing") mixture is typically composed by H or He isotopes with average energy between 10 keV and 100 keV. If part of such a mixture is used for propulsion, rather than faster reaction products, specific impulse values in the range 5 x 104 s to 2 x 105 s can still be produced.

Even the low-temperature plasma flowing in the region surrounding the reacting core (in a fusion reactor the so-called scrape-off region) can have temperatures in the range of 100 eV corresponding to a specific impulse of x 103 s.

Chapter 8 discussed the two classes of devices using the fusion process for space propulsion:

— fusion-electric propulsion: similarly to NEP in Chapter 7, fusion power is converted to electric power either through a conventional thermodynamic cycle (in this case the waste power must be radiated in space) or through direct conversion; the main disadvantages of this scheme are the presence of a radiator, all the items needed for electricity conversion (e.g., turbines or other machinery), the large mass of the electric propulsion system, and especially overall conversion efficiency (thermal power into thrust power);

— direct propulsion: unreacted fuel and fusion products are expanded in a magnetic nozzle, possibly mixed with cold (inert) propellant to achieve a unidirectional jet, with an optimal combination of specific impulse and thrust that will depend on the specific mission. Note that some electricity production is needed for control and auxiliary heating. In addition, the ejection of unreacted propellant (e.g., fuel itself) requires lifting to space (to LEO) a substantial mass, and must be taken into account in evaluating overall performance.

Since fusion has the capability of producing high 7sp, the possibility of its application for space propulsion depends on the feasibility of building systems with specific power in the range 1 kW/kg-10kW/kg [Schulze, 1994]. For the reasons mentioned in Section 8.10, the most natural fusion rocket architecture must be of the mirror type (as sketched in Figure 8.9). Nevertheless, other potentially interesting architectures are of interest and should be investigated. The aim of this section is thus to assess the potential to achieve this target with open magnetic field configurations in a general sense (i.e., configurations capable of ejecting propellant while fusing). In Section B.5 an example of trajectories for a Mars mission is presented showing the potential of fusion propulsion to enable fast transit times.

Historically, the application of steady-state fusion reactors to space propulsion was investigated by NASA between 1958 and 1978 [Schulze and Roth, 1991]. That research addressed the application of fusion to generate electrical power in space as well as propulsion. These two applications are somewhat orthogonal, though the underlying plasma and fusion science are similar. The NASA-Lewis program focused on the simple mirrors and the electric field bumpy torus—both steady-state magnetic fusion energy approaches. The program was canceled in 1978 for budgetary reasons, as NASA was preparing to embark on the Shuttle Program. During the 1980s attention focused on the possibility of electric power generation in space over extended periods of time (> 1 day) and at the multi-megawatt level. These studies (see [Roth, 1989] for a review) predicted low values for specific power. Studies carried out since the late 1980s have therefore tried to optimize fusion performance in order to maximize specific power. Several concepts have been considered: the high-field tokamak [Bussard, 1990], the spherical torus [Borowski, 1995; Williams et al., 1998], mirror systems [Kulcinski et al., 1987; Santarius et al., 1988; Carpenter and Deveny, 1992, 1993; Kammash et al., 1995b], field-reversed configuration [Chapman et al., 1989; Cheung et al., 2004], and magnetic dipole [Teller et al., 1992]. These configurations will be reviewed in the context of discussion of the different confinement systems. They are summarized in Table B.1, which also shows the values of the specific power, the thrust power, and when available the mass of the various components.

This appendix is organized as follows. In Section B.2 general issues of magnetic confinement fusion for space propulsion are discussed. In Section B.3 the present status of research on open magnetic field configuration is reviewed. Section B.4 lists issues where R&D activities should focus for specific application of fusion to space propulsion. Section B.5 examines the performance possible with fusion propulsion, specifically for a manned Mars mission. Conclusions are reported in Section B.6.

B.2 SPACE FUSION POWER: GENERAL ISSUES

In this section we first review the kinetics of the most important fusion reactions and the conditions for achieving energy amplification; in Section B.2.6 a simple model for

 Reference Configuration