Laser-propelled Interstellar Probe (schematic)
Fixed laser, at left, illuminates a light-weight solar array, shown here as a centrifugally-tensioned thin-film membrane supported by tension wires. Power from the array is fed to an ion engine.
Energy efficiency is defined as delta-V achieved per kilogram per kilowatt of input power.
Maximum energy efficiency does not occur at maximum specific impulse.
Maximum energy efficiency is achieved when exhaust velocity equals the mission velocity
(Ve = V)
For exhaust velocity = mission velocity, mass ratio is infinite for a mission that starts out at zero velocity!
Obviously this is not practical unless the mission starts out at some non-zero velocity.
By conservation of momentum, mfvf = mimi
Assume that the mission starts out with a initial velocity Vi equal to the Earth's orbital velocity, 30 km/sec = 10^(-4)c
(produced, for example, by a powered perihelion maneuver around the sun)
In this case the mass ratio mi/mf = vf/vi = 0.11c/(10^(-4)c) = 1100
Fuel mass required is 1100 x empty vehicle mass
(For comparison, the payload of the Saturn V rocket on a lunar mission is roughly 1% of launch mass)
For maximum energy efficiency Ve = 2/3 final mission velocity.
At this exhaust velocity, the mass ratio for the vehicle = 4.92:
e.g., the fuel mass is 3.92 times the empty vehicle mass.
The final kinetic energy in the vehicle is thus (9/4) / 3.92 = 57% of the total energy consumed.
Efficiency has a price: decreasing the mass ratio 200x (from 1000 to 5), results in energy efficiency decreased by less than a factor of two!
At maximum efficiency, the probe kinetic energy = 57% of energy delivered to exhaust
Assume the electric propulsion is powered by a power system which uses a future 1.85 eV solar cell with efficiency of 60% at wavelength of 670 nm.
24% of the laser power is converted to kinetic energy of probe
Thus, the laser must deliver 4.15 times the probe energy
For mission velocity of 0.11c (Forward fly-by mission):
Probe energy is 5.10(^15) joules per kilogram
Required laser energy is 70 MW-years per kilogram
Limiting maximum intensity to 16.5 kW/m^2 to keep temperature low for efficient solar cell operation, the solar array must have a minimum area of 2.2 square km (1.7 km diameter)
This could either be a 1.7 km diameter thin-film array, or a larger mirror focussing light onto a 1.7 km diameter array.
Assume a GaInP2 array of thickness t=1000 nm. At a density of 4.44 grams/cubic cm (444 kg/cubic km), 2.2 square kilometers will have a mass of 1000 kg.
Assuming the same 270 kg payload assumed by Forward , and the same structural parameter, structural mass = 70% of sail (or solar array) mass, the total probe mass is 1970 kg (compares to 1000 kg for probe assumed by Forward ).
If the lens diameter is the same as that for the laser-pushed lightsail mission, D=1000 km, then for the wavelength lambda=670 nm, the probe enters the diffraction-limited regime
d = 2.4 s(lambda)/D
at d=0.11 LY from launch, compared to d=0.17 for the (larger) laser-pushed lightsail. However, since the acceleration for the laser-electric probe is low at the launch and increases by a factor of 4.5 during flight, this is not a problem.
The electric-propulsion option reduces the power required to from 65 to 46 GW, an improvement of a factor of roughly 1.5 over the reference laser-pushed lightsail.
This reduces the required power reduced to 38 GW
This reduces the required power reduces to 18 GW
note that in this case, the 9% increment in specific impulse due to the light pressure must be subtracted from the specific impulse, rather than added, for the first half of the boost.
Solar cells illuminated under monochromatic (laser) illumination achieve far higher efficiency than under solar illumination. Laser conversion efficiency of 55% has been demonstrated in lab, and 60% efficiency is not a difficult challenge for high bandgap cells.
The operating intensity of 16.5 kW/m^2 (about 12 times solar intensity) should not present a problem for solar cells of this bandgap. The assumed efficiency of 60% means that far less of the incident light is converted into heat, and the wider bandgap and higher voltage mean that the temperature coefficient of the solar cell will be comparatively low. Nevertheless, the operating temperature will be high, and this could produce problems.
The mass of the power conditioning system and the actual engine has been neglected. This is not inconsiderable, and will likely make the system considerably less attractive:
Question: Is there a physical lower bound on the mass of an ion engine? Can ultra-light ion engines be manufactured?
The paralens could be made smaller by the expedient of using many smaller lenses: e.g., instead of one 1000-km lens, ten 100-km lenses
(see Landis 1989 for discussion)
The laser-powered electric propulsion concept and the laser-pushed lightsail concept need not be considered an exclusive alternatives. From the energy considerations discussed earlier, a multi-stage concept, using the lower specific impulse laser-powered electric propulsion for the initial part of the boost, and the higher specific impulse laser-pushed lightsail for the second part of the boost, could probably be more efficient than either of the individual concepts alone. The two sails could perhaps be designed to work in synergy, for example, using a large reflective lightsail to focus laser light onto a smaller high-efficiency solar panel.
It remains to be seen whether the increased engineering complexity of a multi-stage system would be worth the increase in efficiency.
Using the (somewhat optimistic) parameters discussed, the laser-powered electric propulsion system can be seen to be comparable in performance, and potentially slightly better in performance, than the laser-pushed lightsail for an interstellar probe mission.
Practical Robotic Interstellar Flight: Are We Ready?
The laser-powered probe is an attractive concept,
not yet a near-term possibility, due to the mass of the engine and the diameter of the lens required.
Thrust of the vehicle is 178 nt
Lightsail force on the photovoltaic array: 3.3 nt/GW
(equals half the force on a sail, since light is absorbed instead of reflected)
Lightsail force contributes 9% additional thrust
Actual vehicle mass ratio, including lightsail effect, is 4.5
The laser-powered probe has an additional advantage over the laser-pushed lightsail in that it is possible to use this technique to brake, as well as to accelerate. In this case, though, the specific impulse is decreased by 9% due to the light pressure, rather than increased.