Combining Magnetic and Electric Sails for Interstellar Deceleration

Nikolaos Perakisa,∗, Andreas M. Heinb

aTechnical University of Munich, Boltzmannstr. 15, DE85748 Garching, Germany bInitiative for Interstellar Studies, 27-29 South Lambeth Road, London SW8 1SZ

Abstract The main benefit of an interstellar mission is to carry out in-situ measurements within a target star system. To allow for extended in-situ measurements, the spacecraft needs to be decelerated. One of the currently most promising technologies for deceleration is the magnetic sail which uses the deflection of interstellar matter via a magnetic field to decelerate the spacecraft. However, while the magnetic sail is very efficient at high velocities, its performance decreases with lower speeds. This leads to deceleration durations of several decades depending on the spacecraft mass. Within the context of Project Dragonfly, initiated by the Initiative of Interstellar Studies (i4is), this paper proposes a novel concept for decelerating a spacecraft on an interstellar mission by combining a magnetic sail with an electric sail. Combining the sails compensates for each technologys shortcomings: A magnetic sail is more effective at higher velocities than the electric sail and vice versa. It is demonstrated that using both sails sequentially outperforms using only the magnetic or electric sail for various mission scenarios and velocity ranges, at a constant total spacecraft mass. For example, for decelerating from 5% c, to interplanetary velocities, a spacecraft with both sails needs about 29 years, whereas the electric sail alone would take 35 years and the magnetic sail about 40 years with a total spacecraft mass of 8250 kg. Furthermore, it is assessed how the combined deceleration system affects the optimal overall mission architecture for different spacecraft masses and cruising speeds. Future work would investigate how operating both systems in parallel instead of sequentially would affect its performance. Moreover, uncertainties in the density of interstellar matter and sail properties need to be explored. Keywords: Magnetic Sail, Electric Sail, Interstellar Mission, Mission Design, Optimization

1. Introduction mankind. However, the scientific gain of an interstellar mission would be immensely increased with an exten- The concept of manned and unmanned interstellar sive scientific payload. In order to produce valuable sci- missions has been examined in different contexts by entific results, the deceleration of the probe is required many authors within the past decades [1]. The main ob- since it enables the study of star and planetary systems stacle connected to the design of such a mission, is the in detail [5]. For a more detailed analysis of exoplan- necessity for an advanced propulsion system which is ets, involving surface operations, a deceleration down able to accelerate the spacecraft towards the target sys- to orbital speeds is necessary. tem within a reasonable time span. To overcome the vast interstellar distances, propulsion systems with high Therefore, apart from the acceleration propulsion specific impulses, like the fusion based engines in the system, a further crucial mission component which is ICARUS and Daedalus projects have been proposed [2], often overlooked, is the deceleration system of an inter- [3]. Other methods rely on propellant-less systems like stellar mission. This has to demonstrate equally effec- laser-powered light sails, as described in [4]. tive ∆v capabilities as the propulsion system. For that Accelerating a probe to high speeds and reaching reason, methods utilizing propellant are not preferred, arXiv:1603.03015v1 [physics.space-ph] 22 Jan 2016 the target system within short duration using advanced since they would induce large amounts of mass, which propulsion systems would be a big achievement for are inert during the acceleration and cruising phases of the mission. Two attractive concepts rely on utilizing magnetic ∗Corresponding author Email addresses: [email protected] (Nikolaos and electric fields in order to deflect incoming ions of Perakis ), [email protected] (Andreas M. Hein) the interstellar space and thereby decelerate effectively.

Preprint submitted to Acta Atsronautica March 10, 2016 These systems called Magnetic Sail (Msail) and Elec- that can be achieved with the superconducting mate- tric Sail (Esail) were first proposed by Zubrin [6] and rial, since this dictates the minimal cross sectional area Janhunen [7] respectively. Since each one of those sys- for a specific current. According to Zubrin [6], the tems has a different design point and velocity applica- current densities of superconductors can reach up to 10 2 tion regime in which it performs optimally, the combi- jmax = 2 · 10 A/m and this is the value used in the nation of the two can induce great flexibility in the mis- analysis. For the material of the sail, the density of sion design as well as better performance. To demon- common superconductors like copper oxide (CuO) and 3 strate these points, the example of a mission to Alpha YBCO was used, with ρMsail = 6000 kg/m . Centauri is analyzed. This star system was chosen be- The shielding mass required to protect the sail was cause it is the closest one to the earth at a distance of modeled according to [3]. This mass vaporizes due to 4.35 light years and because the deceleration concept collisions with interstellar atoms and ions and the total described in this paper, was inspired by the Dragonfly mass vaporized after time T is given by Equations 2 and Competition of the i4is, which involved a light-powered 3: light sail mission to Alpha Centauri [8].

2. Sail Properties Z T dm m = shield dt (2) shield dt Before the comparison of the different deceleration 0 methods takes place, the properties of each sail will be shortly analyzed and the assumptions used in the simu-   A m n 3 lation of their performance will be explained. dmshield ion p o βc  1  = p  p − 1 (3) dt ∆H 1 − β2  1 − β2  2.1. Magnetic Sail (Msail) In Equation 3, A represents the cross sectional area The Msail consists of a superconducting coil and sup- ion of the coil, as seen from the direction of the incoming port tethers which connect it to the spacecraft and trans- ions, ∆H is the vaporization enthalpy of the shielding fer the forces onto the main structure. The current material and β = v/c. Graphite was chosen as a shield- through the coil produces a magnetic field. When the ing material since it combines a low density with high spacecraft has a non-zero velocity, the stationary ions vaporization enthalpy. The shielding mass is calculated of the interstellar medium are moving towards the sail separately for each configuration, since its calculation in its own reference frame. The interaction of ions with requires knowledge of the time-dependent profile for β. the magnetosphere of the coil leads to a momentum ex- For that reason, its calculation is carried out with an it- change and a force on the sail, along the direction of the erative procedure. incoming charged particles. For the tether and support structures, a mass equal to The force on the sail is calculated according to Equa- 15 % of the sail mass was used. tion 1 [9]. It is evident from the formula in Equation 1, that the magnetic sail is efficient for higher current values and larger dimensions. In the analyses presented in this 3 0.5 2 2 2 FMsail = 0.345π mpnoµ IR v (1) work, the radius of the Msail was limited to 50 km. Al- though even larger dimensions can demonstrate better where mp is the mass of the proton, no the number performance, it was thought that the deployment of big- density of interstellar ions, µ the free space permeabil- ger radii is far from the current or near-future techno- ity, I the current through the sail, R its radius and v logical capabilities and was therefore excluded from the its speed. Values for no are proposed in [10] in the analyses. case of a space probe traveling to Alpha Centauri. In The main disadvantage of the magnetic sail is also this work, a rather conservative value was implemented, evident when taking the force formula into account. At −3 with no = 0.03 cm corresponding to the expected val- lower speeds, the force keeps getting reduced asymp- ues in the Local Bubble [10]. totically, and hence the effect of the Msail at these ve- The main structural component introducing extra locities becomes negligible. This has as consequence mass into the system is the sail itself, as well as its that reaching orbital speeds (10-100 km/s) requires long shielding and its deployment mechanism. The mass deceleration duration. A magnetic sail would there- of the sail is defined by the maximal current density fore be optimal for missions where no orbital insertion 2 or surface operations in planetary systems are required 0.5 Voltage = 250 kV 0.45 but where a deceleration for prolonged measurements in Voltage = 750 kV the target system is sufficient. Its inefficiency in lower 0.4 Voltage = 1500 kV speeds indicates the need for a secondary system able to Voltage = 2500 kV bring the velocity down to orbital values. 0.35 0.3 2.2. Electric Sail (Esail) 0.25 Force [N] Similar to the Msail, where a magnetic field deflects 0.2 incoming ions, the Esail uses an electric field to change 0.15 the trajectories of the interstellar protons. The sail con- 0.1 sists of extended tethers which are charged with a high 0.05 positive voltage. 0 The force on the Esail demonstrates a more complex 0 2 4 6 8 10 dependency on the velocity compared to the Msail. The Velocity [x0.01 c] force can be described by Equation 4 [11]. Figure 1: Force on an electric sail as a function of velocity

However an increase in tether length and voltage does · 2 3.09 mpnov ro not only imply a higher mass of the wires, but also a big- FEsail = NL r (4) m v2 ger power supply system. The positively charged teth- exp p ln ro − 1 eVo rw ers collide with the interstellar plasma electrons, which leads to a decrease of the voltage. In order to maintain with N standing for the number of tethers, L their the positive voltage of the wires, an electron gun has to length, Vo the voltage of the sail, e the charge of the be placed on board, leading to an additional mass for electron, rw the wire radius and ro the double Debye the power supply subsystem. The required power is de- length λD, given by Equation 5: scribed by Equation 6 [11]:

s r okbTe 2eV r λ o o = 2 D = 2 2 (5) P = Vo · I = 2rwVoNLeno (6) noe me

In the Debye length definition, o is the electric per- with me being the mass of the electron. The total mass mittivity of vacuum, kb the Boltzmann constant and Te of the Esail is put together from the mass of the tethers the electron temperature of the interstellar plasma. Te and the power system required for the operation of the was estimated according to [10], so for the present anal- electron gun. In the present work, the power system ysis the value Te = 8000 K was used. The wires were for the Esail was modeled with a specific power supply designed according to [11], with radius rw = 5 µm and of 50 W/kg. Although the details of the power system density 1500 kg/m3 were not part of this analysis, photovoltaic cells could It is evident from Equation 4, that the force increases be used, utilizing the laser beam power in combination proportionally to the number and length of the tethers with radioisotope thermoelectric generators and batter- as well as for a higher voltage. The dependency of the ies. Another option is the use of electromagnetic tethers Esail force on the velocity of the probe however, dis- as an energy source, by means of electromagnetic in- plays a more complex character than the one for the duction as described in [12]. Msail. Figure 1 demonstrates this effect qualitatively for It becomes clear that the Esail has a disadvantage a constant total length of the tethers. It follows that the when dealing with high speeds, because of the very high Esail is effective only within a region close to its maxi- voltage and consequently system mass needed. For that mal force. In order to decelerate a probe efficiently from reason, an additional system would be necessary for the high cruising speeds (≥ 0.04 c) down to orbital values, initial deceleration from the high cruising speeds until a very high voltage is required according to Figure 1, or the point where an optimally designed Esail can take an increased total length of the tethers. over. 3 3. Combination of Msail and Esail the Esail tethers can be used for energy production according to [12] for the velocities that are far from their After establishing the properties and the disadvan- optimal design point. This way, instead of spending tages of the individual sails in Section 2, the benefits electric power for the operation of the Esail, which only of combining the two subsystems for an effective decel- has a small effect on the overall deceleration, the Esail eration in interstellar missions become clear. can serve as a significant power supply source. Missions to neighboring star systems require high Additionally, allowing the Msail to operate even at cruising speeds in order to reduce the total trip duration. the velocity regime where it has lost its efficiency in There have been proposals based on fusion propulsion parallel to the Esail instead of detaching it, would in- that aim to keep the total mission duration underneath crease the decelerating force. However, the mass being 100 years [3], [13], which means that an average speed decelerated would also increase and hence the magni- bigger than 0.0435 c is necessary in the case of Alpha tude of acceleration would not necessarily improve. A Centauri [14]. The present analysis focuses on mis- complete optimization model could include the start of sions with the objective of performing scientific mea- operation of the Esail and the detachment of the Msail as surements in the target system, hence requiring orbital two separate events. This brings some additional com- insertion around a star or a planet. In this context, the plexity to the model since it requires the optimization combination of Msail and Esail seems to be an elegant of a further parameter. However, it was examined for a solution. single test case which is not in the scope of this paper Starting the deceleration phase of the mission with and the obtained results showed a < 5% performance the use of a magnetic sail is beneficial as mentioned improvement, so it was ignored in this analysis. in Section 2.1, due to the high forces produced in the An extra benefit of ceasing the use of the Msail when large velocity range. As the velocity decreases, the force the Esail starts operating, lies in utilizing the magneti- drops also and the Msail starts being ineffective. At this cally stored energy of the superconductor for the opera- moment (which has to be optimally chosen as described tion of the Esai. The current through the Msail could be later), the Msail can be switched off and detached from discharged into batteries used for the power system of the spacecraft and the Esail can start operating. The the electron gun before detachment, thereby turning the electric sail must be designed to perform optimally in Msail to a Superconducting Magnetic Energy Storage this velocity region and can decrease the velocity of the [15]. spacecraft further, until the required value for orbital in- These considerations explain why a tandem switch- sertion is achieved. The high flexibility of the tandem ing method was preferred to a method where both sys- system comes in the expense of additional optimization tems run in parallel. It is easy to understand that the effort. The two subsystems are dependent on each other switching point should occur at a speed value where the and have to be designed simultaneously and an extra acceleration with the Msail is equal to the acceleration optimization parameter influences their design, namely with the Esail. Switching at a lower speed would imply the velocity value at which the start of operation for the that there is a time span where the probe is decelerat- Esail takes place. ing with a force smaller than what it could achieve by This idea resembles the concept of staging in conven- switching to the Esail and would become less effective. tional launchers with chemical engines. As soon as the The same issue occurs for switching at higher speeds, first stage is done burning, it is detached, and the second since it means that the magnetic sail did not reduce the stage, which has been optimally designed to operate in kinetic energy by the amount it was optimally designed the higher altitude, is ignited. Similarly, as soon as the to. Msail reaches its weak performance point, it is dropped The consideration of the optimal switching point be- off and the Esail, which has been optimally designed to tween Esail and Msail can be qualitatively seen in Fig- decelerate the remnant mass, starts operation. ure 2. In this image, a fixed design point for the Esail is The switching method presented in this paper is only chosen and an optimal design for the Msail is searched one of the alternatives that can be realized with a com- for. It is obvious, that the choice of an overly dimen- bination of Msail and Esail. A further option would be sioned Msail, like in the case of the design point A, that the Esail starts operation simultaneously with the is not very efficient. The intersection point of the ac- Msail even at higher speeds, where it is not so effec- celeration profiles for Esail and Msail lies at velocities tive. One would expect that this extra bit of braking smaller than the point of the maximum Esail decelera- force could improve the overall performance. This idea tion. Therefore, after the switch, the magnitude of ac- was not implemented in the present analysis, because celeration would keep dropping and the highest Esail 4 1 necessary. The parameters N,L,Vo,R and I allow for the 0.9 determination of mEsail and mMsail. The combination of

0.8 Msail and Esail requires the additional parameter of the switching velocity vswitch which results to the force pro- 0.7 ﬁle. Combining the mass and the force leads to the ac- 0.6 celeration capabilities of the system. This way, the op- 0.5 timization parameters of the mathematical problem are Esail design profile summarized in Table 1 for the three deceleration meth- 0.4 Msail design profile A ods. 0.3 Msail design profile B Msail design profile C For a given acceleration dependency on the velocity, Acceleration [arbitrary units] 0.2 a(v), the total duration of the deceleration period (the cost function) is given by the expression in Equation 7: 0.1

0 0 2 4 6 8 10 Velocity [x0.01 c] Z v dv dv target dv a(v) = ⇒ dt = ⇒ Tdecel = (7) Figure 2: Qualitative description of Msail and Esail acceleration pro- dt a(v) vcruise a(v) files In the case of tandem deceleration, this takes the form of Equation 8: force would never be utilized. Although the acceleration magnitude would be bigger than what the Msail could have produced, the full potential of the Esail would still Z v Z v remain unused. switch dv target dv Tdecel = + In the case of profile B, the Msail is under dimen- vcruise aMsail(v) vswitch aEsail(v) Z vswitch sioned, hence leading to a high velocity for the switch- (mMsail + mEsail + ms/c)dv ing point. At this regime, the Esail demonstrates a very = + (8) v FMsail(v) low force and therefore does not reduce the speed of the cruise Z vtarget (m + m )dv probe efficiently. A significant time period has to elapse Esail s/c F (v) until the velocity reaches the optimal design point of the vswitch Esail Esail, where the acceleration value is big enough to pro- and the objective of the minimization problem is sum- duce an effective braking of the spacecraft. marized in: Finally, case C seems to produce a better deceleration profile. The switching point lies in speeds higher than the optimal design point of the Esail. The Esail acceleration starts increasing immediately after the de- Tdecel = min! (9) tachment of the Msail and is close to the optimal value, therefore utilizing the full potential of the electric sail, before starting to drop again. Pure Msail I, R The combination of the two sails requires the op- Pure Esail N · L, Vo timization of the individual parameters for Msail and Tandem Msail and Esail I, R, N · L, Vo, vswitch Esail (radius and current of superconductive loop, volt- Table 1: Optimization parameters for each deceleration method age, number and length of tethers) as well as of the velocity at which the operation of the Msail ceases. Since the acceleration part of the mission is not cap- 4. Optimization process tured in this analysis, the absence of any further constraints would shift the optimal solution to very high The optimization problem that was solved to come up deceleration system masses. Since the performance of with the optimal design of the deceleration system can the system increases with increasing mass, an overly be expressed as the minimization of the total decelera- dimensioned Msail and Esail with infinite mass would tion duration Tdecel. minimize the cost function Tdecel. When combined with To determine Tdecel for a given sail configuration, the the acceleration system however, such a large system mass of the system and the force profile over time are would be inefficient since it would pose a large inert 5 mass during the acceleration phase. For that reason, an At the same time, there has to be some finite distance additional constraint was introduced, namely an upper available for the acceleration and cruising phases, which bound for the maximal deceleration mass. Hence this are not part of the optimization and this was estimated extra constraint was introduced as in Equation 10: equal to 1.5 light years. For that reason, the constraint was defined as in Equation 14:

mdecel ≤ C (10) Z v target v dv with C being a predeﬁned upper mass limit and rdecel = ≤ 2.85 light years (14) vcruise a(v)

 The cost function to be minimized (Tdecel) is highly mMsail, for Msail deceleration  non-linearly dependent on the optimization parameters, mdecel = mEsail, for Esail deceleration and therefore linear programming methods were not  mMsail + mEsail, for tandem deceleration useful. Moreover, due the lack of knowledge of the function gradient, the optimization took place with a Further constraints involve the initial and end velocity pattern search method similar to the ”direct search” pro- of the probe. This reads as in Equation 11: posed by Hooke [16]. This is the method utilized for all analyses in the present paper. After obtaining the optimal deceleration duration, the

v(t = 0) = vcruise and v(t = Tdecel) = vtarget (11) velocity and acceleration profiles as a function of time were calculated by means of numerical integration. A This constraint is directly applied in the definition of time propagation was implemented using a 4th order the cost function Tdecel, since it sets the limits of the Runge-Kutta scheme, which served as a validation of integral calculation. the optimization results and provided a complete time In the case of the Msail and Esail combination, the profile of the spacecraft trajectory. switching velocity is to be modeled as well. One constraint for vswitch is already present in Equation 8, since it is set as the limit of the integral to be evaluated. More- 5. Results: Comparison of deceleration profiles over, it has to be made sure, that the acceleration at the switching point between Msail and Esail remains con- Using the optimization method in Section 4, the per- tinuous, as described in Section 3. Mathematically this formance of three separate deceleration methods was yields: compared and the resuls are shown in this section. The three deceleration architectures are the following:

1. Pure Msail deceleration aMsail(v = vswitch) = aEsail(v = vswitch) ⇒ 2. Pure Esail deceleration F (v = v ) F (v = v ) (12) Msail switch = Esail switch 3. Combination of Msail and Esail in tandem mMsail + mEsail + ms/c mEsail + ms/c In this test case, the mass of the spacecraft ms/c was where ms/c stands for the spacecraft mass. chosen to be approximately equal to the launch mass of Moreover, as explained in Section 3, the switching Voyager 1, so equal to 750 kg. Voyager is a space probe point has to take place for velocities larger than the op- which was launched to perform ﬂybys of Jupiter, Sat- timal operation point of the Esail and therefore: urn and Titan and continued to explore the boundaries of the outer heliosphere [17]. Since it is the only man- made probe so close to entering the interstellar space [18], it was considered relevant to calculate how its de- vswitch > v(aEsail = max) (13) celeration would look like in the case of a mission to Finally, the total deceleration distance rdecel poses a another star system, requiring a deceleration phase. further constraint. It has to be ensured, that there is suf- Only the deceleration phase of the mission was ex- ﬁcient distance available for the spacecraft to decelerate amined, so a cruising speed vcruise = 0.05 c was cho- completely before it reaches Alpha Centauri. For that sen. The target speed was set to be equal to vtarget = reason this should remain shorter than 4.35 light years. 35 km/s. This would correspond approximately to the 6 0 orbital speed at a distance of 1 AU around Alpha Cen- 10 Combination Msail and Esail tauri A, which has a mass of 1.1 M [19]. Msail −1 For each one of the three deceleration methods, an 10 Esail optimal design point was calculated in order to mini- ] mize the total deceleration duration Tdecel. The mass of 2 −2 the deceleration system was restricted to be underneath 10 7500 kg, which corresponds to the tenfold spacecraft −3 mass. A direct comparison is thereby possible, since all 10

systems have the same eﬀect on the acceleration phase Acceleration [m/s and hence the overall mission design. −4 At this point it has to be noted, that the restriction 10 of the Msail radius described in Section 2.1 produces −5 very week forces in the low speed limit (close to v ), 10 target 0 5 10 15 20 25 30 35 40 thereby resulting in duration close to 300 years. It was Time [years] therefore dismissed from the calculations of pure Msail deceleration. The results shown here required a sail ra- Figure 3: Comparison of deceleration methods: Acceleration proﬁle over time dius of 1000 km, which was considered to be unrealistic

1 but was still included for completion. This demonstrates 10 once again that the Msail as a standalone component is Combination Msail and Esail not suﬃcient for missions requiring orbital insertion in Msail Esail the target system.

0 The acceleration and velocity profiles over time are 10 shown in Figure 3 and 4 respectively. Note that the curves in Figure 3 represent the magnitude of the acceleration, since the numeric values of acceleration are negative during the braking phase. The combination of −1 Velocity [x0.01 c] 10 the two sails requires 28.8 years as opposed to the 39.7 years of the Msail and the 34.9 years of the Esail. In the acceleration profile of the dual system, the discontinuity in the gradient represents the point where the switch −2 10 0 5 10 15 20 25 30 35 40 between Msail and Esail takes place. This occurs after Time [years] 13.67 years and at a speed equal to approximately 0.03 c according to Figure 4. This change is not detectable Figure 4: Comparison of deceleration methods: Velocity profile over in the velocity profile, since the acceleration shows no time discontinuity during the switch from the one system to the other, leading to a smooth velocity curve. This test case demonstrates the potential that a com- Initially, the acceleration of the Msail method is the bination of Msail and Esail has in the design of an in- highest. This makes sense because the magnetic sail terstellar mission, since it outperforms each individual used in the tandem method is smaller than in the pure system in particular mission configurations. However, Msail method, in order to satisfy the equal mass require- during a complete mission design, the minimal deceler- ment. After some time however, the magnitude of the ation duration is not the only parameter to be optimized acceleration in the tandem method becomes larger and and the interaction of the deceleration system with the eventually leads to a smaller duration. other components (influence on acceleration, effect of At this point, it is also important to mention that the deceleration distance) has to be taken into account. pure Msail method is the optimal solution when a higher target speed is needed. Figure 4 demonstrates this effect since the velocity curve of the Msail is lower than the 6. Interaction with mission design other two for the whole duration apart from the lower velocity range, where it flattens. The absence of orbital After having established that the method of tandem insertion (leading to vtarget being an order of magnitude deceleration with Msail and Esail can bring benefits to larger), would therefore make the Msail the most effec- the total duration of the deceleration phase before or- tive solution. bital capture, it is interesting to determine how this sys- 7 tem interacts with the acceleration and cruising phases. 3 m =750 kg s/c m =4000 kg 6.1. Influence of cruising velocity 2.5 s/c

In Section 3, a single value for the cruising speed was 2 examined. In this section, the effect of a variable cruising speed on the design characteristics of the tandem 1.5 deceleration system is presented. For this analysis, two different spacecraft masses are 1 compared. Apart from the Voyager-like spacecraft in- Deceleration distance [ly] troduced in Section 3, the profile of a heavier vehicle 0.5 with ms/c = 4000 kg is calculated. This value was chosen since it is approximately equal to the launch mass 0 of the Mars Science Laboratory (MSL). This robotic 4 5 6 7 8 9 10 Cruising speed [x0.01 c] space probe was sent to Mars and included a rover with a landing system and instruments for biological, geo- Figure 6: Deceleration distance of optimal configuration as a function chemical and geological measurements on the surface of the cruising velocity of the planet [20]. Since a similar mission to an exo- planet would be of high scientific value [13], an MSL- like spacecraft was used. The restriction for the total cruising speed leads to a deceleration distance close to mass of the deceleration system being maximally ten 2.5 light years. When taking into account that the dis- times the spacecraft mass was maintained. tance to Alpha Centauri is 4.35 light years, one deduces that there are only 1.85 light years available for the ac- 65 celeration and cruising phases. However, the buildup m =750 kg 60 s/c of such a high speed could require a larger acceleration m =4000 kg s/c distance depending on the propulsion system. There- 55 fore, reaching such a high speed in a mission to Alpha 50 Centauri may not be necessary or useful, due to the ex-

45 treme deceleration distance connected to it. The mass and velocity change distribution between 40 Msail and Esail are also interesting to examine as a 35 function of the cruising speed. Figure 8 shows the ra-

Deceleration duration [years] 30 tio of the Msail mass mMsail to the Esail mass mEsail and Figure 7 the ratio of the velocity changes ∆vMsail 25 and ∆vEsail at the optimal configuration for each crusing 20 speed. 4 5 6 7 8 9 10 Cruising speed [x0.01 c] The velocity change ratio demonstrates a nearly linear profile in Figure 7, which increases with the cruis- Figure 5: Deceleration duration of optimal configuration as a function of the cruising velocity ing speed. This can be explained with the good performance of the Msail in higher speeds. Since the Msail Figures 5 and 6 show the dependency of the decel- is efficient in the high speed regime, it is logical that it eration duration and distance on the cruising speed. It will also take over most of the deceleration. Moreover, is intuitive that a larger initial speed requires a larger the results show that a higher spacecraft mass leads to a deceleration duration, since the total ∆v that has to be lower ∆v-ratio. provided by the deceleration system increases. Since the velocity changes are proportional to the The same occurs for the deceleration distance, as Fig- mass of each subsystem, it is expected that the mass ure 6 demonstrates. A higher spacecraft mass also in- ratio also increases with the cruising speed, as shown in creases the inertia of the system during deceleration and Figure 8. In this case however, the increase in mass ratio hence the time and distance required. An important in- tends to be slower and resembles a logarithmic growth. direct result stemming from Figure 6 is that high cruis- The results show a general preference towards the ing speeds are not always optimal for a minimal mission Msail deceleration for higher cruising velocities which duration. In the case of the 4000 kg spacecraft, a 0.1 c is reflected in the ∆v and mass distribution of the decel- 8 3 being smaller than ten times the spacecraft mass was uti- m =750 kg s/c lized. This boundary condition was introduced so that m =4000 kg 2.5 s/c an easier comparison between different configurations could take place. In the present analysis however, the 2 ratio between deceleration system mass and spacecraft [−]

Esail mass was varied. The two spacecraft masses described v

∆ 1.5

/ in Section 6.1 as well as two diﬀerent cases for the cruis-

Msail ing speed were compared to each other. Figure 9 shows v

∆ 1 the results.

140 0.5 m =750 kg, v =0.05 c s/c cruise m =750 kg, v =0.08 c 120 s/c cruise 0 m =4000 kg, v =0.05 c 4 5 6 7 8 9 10 s/c cruise Cruising speed [x0.01 c] m =4000 kg, v =0.08 c 100 s/c cruise Figure 7: Optimal mass ratio of Msail to Esail as a function of the cruising velocity 80

4 60 m =750 kg s/c

3.5 Deceleration duration [years] m =4000 kg s/c 40 3

20 2.5 0 2 4 6 8 10 [−] m /m [−] decel s/c Esail 2 /m Figure 9: Optimal deceleration duration as a function of the decelera- Msail 1.5

m tion system mass

1 An increased mass of the deceleration system leads, 0.5 as expected, to a shorter deceleration duration. It is however notable, that the curves tend to saturate for 0 4 5 6 7 8 9 10 Cruising speed [x0.01 c] larger masses. This implies that a larger deceleration mass, although having a great impact on the design Figure 8: Optimal ∆v ratio of Msail to Esail as a function of the cruis- of the acceleration phase because of additional inertia, ing velocity only provides a small benefit to the overall deceleration performance. Quantitatively, taking the example of the 4000 kg spacecraft with 0.08 c cruising speed in Figure eration system. 9, one observes that a mass ratio of 10 leads to a minimal duration equal to 53.83 years whereas a mass ratio 6.2. Effect of deceleration system mass equal to 4 results in 55.90 years. Hence an increase of 150 % in the mass of the deceleration system, produces The deceleration system is an integral part of the mis- only a 3.7 % increase in the performance of the system. sion design and cannot be analyzed independently of the This trend is maintained for all configurations and it is acceleration phase when an interstellar mission is being evident, that when the complete mission is designed and developed. The main effect that the deceleration system all mission phases are optimized simultaneously, decel- has on the acceleration phase is its mass, which needs to eration system masses are preferred, which are further be accelerated as well. Therefore, a deceleration system from the saturation limit and still produce sufficient per- which is as light as possible but still produces the nec- formance. essary ∆v change in short amount of time and in short distance is required. 7. Conclusion The effect of the tandem deceleration system mass on its performance was examined. In the previous sec- Magnetic and electric sails have been proposed as tions, the requirement of the deceleration system mass propulsion systems for interstellar and interplanetary 9 missions. In the case of interstellar missions with short References trip duration and need for orbital insertion around a target system, each one of these sails demonstrates some References disadvantages: Msails fail to produce sufficient forces in the low speed limit and Esails require very large masses [1] A. R. Martin, A. Bond, Nuclear pulse propulsion: a historical in order to decelerate from the high cruising speeds of review of an advanced propulsion concept, Journal of the British interstellar missions. Interplanetary Society 32 (1979) 283. The present paper demonstrated that a combination [2] K. F. Long, M. Fogg, R. Obousy, A. Tziolas, A. Mann, R. Os- borne, A. Presby, Project Icarus - Son of Daedalus - Flying of the two systems in tandem (initial deceleration with Closer to Another Star, JBIS 62 (2009) 403–414. arXiv: Msail and following braking with Esail) can have a bet- 1005.3833. ter performance in certain configurations. Small un- [3] A. Bond, A. R. Martin, Project Daedalus The Final Report on manned missions were examined in this context and a the BIS Starship Study, JBIS Interstellar Studies. [4] R. L. Forward, Roundtrip Interstellar Travel Using Laser- generalization of this method for manned missions with Pushed Lightsails, Journal of Spacecraft and Rockets 21 (2) larger spacecraft masses would be interesting since it (1984) 187–195. doi:10.2514/3.8632. would show the applicability limits of the system. The [5] I. A. Crawford, The Astronomical, Astrobiological and Plan- etary Science Case for Interstellar Spaceflight, Journal of the combination of the two systems in series is not the only British Interplanetary Society 62 (2010) 415–421. arXiv: method that could improve the deceleration characteris- 1008.4893. tics. Although this was the main architecture analyzed [6] R. M. Zubrin, D. G. Andrews, Magnetic Sails and Interplanetary in the paper, operation of the two sails in parallel should Travel, Journal of Spacecraft and Rockets 28 (2) (1991) 197– 203. doi:10.2514/3.26230. also be further examined and controlled for additional [7] P. Janhunen, Electric Sail for Spacecraft Propulsion, Journal of increase in performance. Propulsion and Power 20 (4). The overall design of an interstellar mission requires [8] A. M. Hein, K. F. Long, R. Swinney, R. Osborne, A. Mann, the optimization of the deceleration system not as a M. Ciupa, Project Dragonfly: Small, sail-based spacecraft for interstellar missions, Manuscript submitted for publication to standalone component, but simultaneously with the the Journal of the British Interplanetary Society (2016). main propulsion system of the acceleration phase and [9] R. M. Freeland, M5: Secondary Propulsion: Mathematics of with the design of the cruising phase. The flexibility of Magsails, in: Project Icarus, 2012. the combination of the two sails includes further opti- [10] I. A. Crawford, Project Icarus: A review of local interstellar medium properties of relevance for space missions to the nearest mization parameters in the mission architecture, since stars, Acta Astronautica 68 (7–8) (2011) 691–699. the switching point between Msail and Esail decelera- [11] P. Janhunen, A. Sandroos, Simulation study of solar wind push tion has to be also optimized for maximal performance. on a charged wire: basis of solar wind electric sail propulsion, Annales Geophysicae 25 (3) (2007) 755–767. doi:10.5194/ Finally, the technical design of each sail, includ- angeo-25-755-2007. ing the chosen density of the materials, power system, [12] G. L. Matloff, L. Johnson, Applications of the Electrodynamic shield masses etc. as well as parameters with uncer- Tether to Interstellar Travel, JBIS 58. tainty, like the properties of the interstellar plasma, in- [13] A. M. Hein, A. Tziolas, R. Osborne, Project Icarus: Stakeholder Scenarios for an Interstellar Exploration Program, Journal of the fluence the optimal solution and should be carefully British Interplanetary Society 64 (2011) 224–233. treated when an interstellar mission is being designed, [14] K. Long, R. Obousy, A. M. Hein, Project icarus: Optimisation because they directly affect the deceleration perfor- of nuclear fusion propulsion for interstellar missions, Acta As- mance and consequently the overall mission architec- tronautica 68 (11) (2011) 1820–1829. [15] P. Tixador, Superconducting magnetic energy storage; status and ture. perspective, in: IEEE/CSC&ESAS European Superconductivity news forum, no. 3, 2008. [16] R. Hooke, T. A. Jeeves, “Direct search”: Solution of numeri- 8. Acknowledgments cal and statistical problems, Journal of the ACM (JACM) 8 (2) (1961) 212–229. [17] C. E. Kohlhase, P. A. Penzo, Voyager mission description, The authors would like to thank the Initiative for Space Science Reviews 21 (2) (1977) 77–101. doi:10.1007/ Interstellar Studies for organizing the Project Drag- BF00200846. onfly Competition, which gave the inspiration for the URL http://dx.doi.org/10.1007/BF00200846 [18] G. Gloeckler, L. A. Fisk, Has Voyager 1 really crossed the he- present study. Moreover, the authors would like to liopause?, Journal of Physics: Conference Series 577 (1) (2015) thank the members of the WARR Interstellar Space- 012011. flight Team at the Technical University of Munich, Jo- [19] P. Demarque, D. Guenther, W. F. van Altena, The case of Al- hannes Gutsmield, Artur Koop, Martin J. Losekamm pha Centauri- Mass, age and p-mode oscillation spectrum, The Astrophysical Journal 300 (1986) 773–778. and Lukas Schrenk for their ideas during the design of [20] J. P. Grotzinger, J. Crisp, A. R. Vasavada, R. C. Anderson, C. J. the Dragonfly mission. Baker, R. Barry, D. F. Blake, P. Conrad, K. S. Edgett, B. Fer- 10 dowski, et al., Mars Science Laboratory mission and science in- vestigation, Space science reviews 170 (1-4) (2012) 5–56.