1. 1 Introduction
The minimum mission requirement for “Project Icarus” is to receive first data
from Alpha Centauri in 100 years. For maximum data-return the probe needs
to decelerate into orbit around the target star from interstellar transit speeds –
at a minimum the vehicle needs to undergo a total velocity change of 0.09c
(27,000 km/s.) The most conservative approach to achieve this is to use fusion
thrust for the whole velocity change, but this increases the required fuel
considerably, even using a two-stage rocket, as assumed in this paper.
Magnetic-Sails, or Mag-Sails, are a non-propellant means of reducing the
vehicle’s speed from its cruise speed to something closer to orbital velocity, via
creating drag against the thin gas between the stars known as the Interstellar
Medium (ISM) [Ref 1-5].
For the purposes of this paper two vehicle configurations will be studied – the
Pure Fusion and the Hybrid. The 1st Stage will be assumed to accelerate both
kinds of vehicles to cruise speed, while the 2nd Stage will perform either full
deceleration under fusion thrust, in the Pure Fusion case, or deploy a
magnetic-sail, in the Hybrid case, to decelerate to a lower speed, then use
fusion-thrust for deceleration to orbital speeds in the star-system from 1500
km/s (0.005c), at which speed the magnetic-sail becomes increasingly
inefficient as a brake. Matloff  has explored the possibility of braking in the
destination star’s astrosphere – the region dominated by its stellar wind – but
this may require determining the size and density of the astrosphere via as yet
undeveloped remote means before a starship can successfully brake within it,
thus it’s an option left for future studies.
2. 2 Magnetic Sails: A Primer
Figure 1: Magnetosphere (from Janhunen )
A Magnetic-Sail, or Mag-Sail, for interplanetary or interstellar travel is an
example of drag (or lift) creation via generating an artificial magnetosphere
and interacting with the in-space medium. A Magnetosphere is created by the
interaction between a near dipolar magnetic-field, such as exist around several
planets in our solar system, and a large plasma flow, such as the Solar Wind
(Figure 1). The interaction between the two creates a structure defined by the
behavior of plasma in that region. The border between free-flowing plasma
and the magnetic field is defined by equilibrium between the plasma flow’s
ram pressure and magnetic pressure of the magnetic field encountered.
Ram-pressure is defined as
…where is product of the number density and average particle mass of
the plasma flow and is the relative speed of the plasma flow to the magnetic
field. Ram-pressure of the plasma in the Interstellar Medium (ISM) at the
speeds in question will be much higher than the intrinsic magnetic pressure of
the ISM in the Galactic magnetic field.
3. 2.2 Magnetic Pressure
Magnetic pressure is defined (from Cole )...
The magnetic-field strength, B, can be be found by where is the
Dipole Moment of the magnetic loop generating the field and R is the distance
from the centre. Substituting into (2) we get [Eqn.W.7, Ref. 7]…
2.3 Radius of Magnetosphere
Equating the ram-pressure, and the magnetic-pressure, lets us find the
radius of the magnetosphere formed…
This forms the basis for determining performance of magnetic sails, but is an
approximation and only applicable when the assumptions of the
magnetohydrodynamic (MHD) plasma flow are valid . Experiments with
laboratory scale plasma sources and mini-magnetospheres have confirmed
that the approximation is applicable to magnetic-sails .
2.4 Mag-Sail Dynamics
At its simplest a Mag-Sail uses a single-loop of current to produce the
magnetic-field to form an artificial magnetosphere as seen in Figure 2.
4. Figure 2: The Magnetic-Sail (from )
Dipole Moment for a single loop of conductor is computed as:
Janhunen et.al.  derived the following equation for drag created by an
artificial magnetosphere in a plasma flow:
where D is the drag, the ram-pressure of the vehicle’s motion against the
interstellar medium, I the current in the loop, and magnetic-sail loop
The vehicle mass is Mv, thus deceleration of the vehicle is: D/Mv
A useful quantity is the mass of the magnetic-sail, Ms. The minimum cross-
sectional area required of superconductor, As, is computed by the ratio of the
current, I, to the maximum super-current density, Jc. However in actual
application bare superconducting wire will be surrounded by protective
layering, a cooling system and normal conductor to allow “quenching” of the
super-current in case of failure of superconductivity. Thus the engineering
super-current density, Je ,is more appropriate, a fraction of the ideal. The
minimum Mag-Sail mass, Ms is therefore:
5. Ms = 2.π.Rm.(I/ Je)
For a given set of magnetic-sail characteristics, I & Rm , and vehicle mass, the
variables reduce to a Deceleration constant, κ
Substituting in Equation (1) & (6) into Equation (7), and some algebra, allows
the Deceleration constant to be computed as follows:
This allows analysis of the magnetic-sail’s equations of motion. According to
Zubrin  the following relationship for an interstellar vehicle braking against
the ISM applies, with vehicle speed, V, a function of time:
is the initial velocity and is the time since the start of braking.
Taking the first derivative with respect to time gives acceleration as a function
κ κ (10)
At t=0, this equates to:
…which allows the Deceleration constant to be expressed as a function of the
initial acceleration, and initial velocity, :
6. Integrating Equation (9) with respect to time allows us to derive the
This can be simplified by substituting equation (11) for κ for
κ to give the displacement in terms of the initial and final
The ratio has the dimensions of time and provides the useful variable of
the characteristic time, , of the magnetic-sail’s deceleration. Substituting in,
Equation (13) becomes:
Total deceleration time, to reach a final velocity, can be computed as:
3 Two Stage Fusion Rockets
“Project Daedalus” remains the most well-defined interstellar fusion rocket,
and has been chosen as the base-line for comparison. The following
characteristics (from  & ) are germane to this discussion:
7. Table 1: Daedalus Two-Stage Fusion Rocket
1 7.54E+6 1.4E+6 1.06E+7 0.72 0.047
2 6.63E+5 9.31E+5 9.21E+6 0.0711 0.053
*computed from data in Ref 11 & 12
A significant fraction of the vehicle dry mass is tied up in the propellant and
propulsion system tankage. Helium-3 at 3 K has a vapor pressure of 81.3 kPa,
so the tanks require their void space (26%) to be filled to maintain constant
pressure else the pellets of frozen deuterium and liquid helium-3 would out-
gas. As the tank is emptied some kind of contracting walls would be required
to maintain constant pressure. The tank walls are titanium, with a safety factor
of 1.33. These, with 117 layers of insulation, add a considerable mass also –
212 tonnes for the 1st
Stage, 28.4 tonnes for the 2nd
. Over 1,700 tonnes of mass
for the first stage, and 156 for the second, are required for the helium-3
This limits the maximum mass-ratio that can be achieved by a single-stage
“Daedalus” class vehicle. For a given fuel-tank mass-fraction, b, then the
required propellant mass, P, to achieve a given mass-ratio, R, can be computed
for a given vehicle mass, Ms, via:
The numerator implies an upper limit to the mass-ratio of:
As is approached the propellant mass goes to infinity.
Rocket motion, at constant thrust, is described by the following equations for
the acceleration and deceleration phases (derived from Appendix A, in Orth
…where is the exhaust velocity, is the time required to expel in exhaust
mass the equivalent of the vehicle’s dry-mass at the mass-flow rate for that
8. stage, R is the mass-ratio. The deceleration stage variables are primed as they
are different for the 2nd
Stage of “Daedalus”.
Using the parameters from Table (1) and Equations (16), (18) & (19) the flight
time can be computed via:
Where the acceleration and deceleration times, are computed via the
With taking their relevant stage values.
For various cruise velocities the results for travel-time were plotted against the
resulting vehicle total mass in Figure 3:
Figure 3 Time (years) vs Mass (tonnes)
The minimum flight time, 71.58 years, is achieved at a cruise velocity of 0.07c
and an initial mass of 281,181 tonnes. Increasing the trip-time by just 5 years
decreases the initial mass by 66%. For the same mass budget as the original
“Daedalus” star-probe (just over 54,000 tonnes) the flight to Alpha Centauri
takes 81.6 years at a cruise speed of 0.05516c, while the “Project Icarus”
minimum mission requirement of a 95.6 year flight-time, to achieve first data
reception on Earth in 100 years, requires an initial mass of 28,600 tonnes and a
0.04635c cruise speed.
0 500000 1000000 1500000
Time vs Mass
Time vs Mass
9. 4 The Interstellar Medium
The Interstellar Medium (ISM) is a thin mix of mostly hydrogen and helium, in
plasma, atomic and molecular form. About 1% of the ISM is in the form of
heavier elements, called “metals” by astrophysicists, either as gas or very small
dust grains. Some fraction of the ISM is in the form of larger objects, perhaps
comet-size or larger, but so spread-out that it can be ignored for the purposes
of this discussion.
Relevant to the operation of magnetic-sails is the hydrogen/helium plasma/gas
mix. Only the charged component, the plasma (a mix of ions and electrons),
interacts directly with the artificial magnetosphere created by the Mag-Sail.
However, relative to the ISM, the magnetic-field is moving very rapidly, and
this rapid change is potentially sufficient to cause ionization of the electrically
neutral atoms and molecules in the ISM.
According to Crawford’s  review of the Local ISM (LISM), the nearby G
cloud might extend all the way to Alpha Centauri, with a gas density of
between 0.1-0.2 atoms/cm3
. Interestingly an astrosphere has been detected
around Alpha Centauri, though its properties are yet to be determined. For the
purposes of this study, a density of 0.1 atoms/ cm3
will be assumed.
On average the particles comprising the ISM mass 2.2 x 10-27
hydrogen, 25% helium, by mass) which, combined with the number density
above, allows the Deceleration constant to be computed for Mag-Sails of a
given super-current and radius.
The astrospheres of the stars, and the Sun’s own heliosphere, also suggest a
possible means of protecting magnetic-sail structures against the hail of hyper-
velocity dust particles. Dust particles become charged by UV photons and
cosmic-rays removing electrons from their surfaces. Sufficiently charged dust is
thus deflected by an astrosphere and prevented from entering the inner Solar
System in the case of the Sun . Possibly the artificial magnetosphere of an
operating magnetic-sail will allow dust to be deflected away.
10. 5 Performance of the Magnetic-Sail Fusion-Rocket
The Mag-Sail equipped “Daedalus” 2nd Stage deploys a magnetic-sail to
decelerate from the cruise speed to 1500 km/s, then use fusion-thrust for
deceleration to orbital speeds in the star-system. A “Daedalus” 2nd
450 tonnes Payload, will need an initial mass of 1097 tonnes to decelerate
from 1500 km/s. The Mag-Sail is assumed to mass 1,000 tonnes, with a size
optimized for a lower maximum magnetic-field strength for the
superconductor (assumed to be of the same density as magnesium diboride,
MgB2 ) and an engineered Deceleration constant, κ , of 2x10-11
assumed ISM density of 0.1 atoms/cm3
The mass of the “Daedalus” 2nd
Stage has been modelled, with the same
assumed tankage fraction and exhaust velocity used for the two-stage Pure
Figure 4 summarises the results:
Figure 4: Initial Mass (tonnes) vs Total Trip Time (years)
The minimum is achieved at a cruise speed of 0.08015c, with a total trip-time
of 68.033 years and a mass of 73,700 tonnes. The total trip time drops under
11. 70 years for masses between 43,000 and 126,000 tonnes. The minimum
“Project Icarus” requirement (95.6 years total travel time) is met for an initial
mass of 12,300 tonnes. This is a significant improvement over the 28,600
tonnes of the two-stage pure-fusion case.
Also due to the runaway hyperbolic rise of the propellant mass, as discussed
above, the minimum mission can’t be achieved by a single-stage vehicle based
on “Project Daedalus” vehicle characteristics.
6 Conclusions & Recommendations
Magnetic-Sails/Mag-Sails provide a means for significantly improving the
performance of fusion rockets on missions to nearby stars, possibly eliminating
the need for deceleration fuel to be carried to the destination. Future research
will be required to determine the best means of protecting such large, thin
structures against the dust component of the ISM. In particular the suggested
magnetic deflection of charged ISM dust needs to be modeled in detail.
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