Arxiv – Breakthrough Starshot is an initiative to prove ultra-fast light-driven nanocrafts, and lay the foundations for a first

launch to Alpha Centauri within the next generation. Along the way, the project could generate important supplementary benefits to solar system exploration. A number of hard engineering challenges remain to be solved before these missions can become a reality.

In this paper, a system model is formulated to describe a beam-driven sailcraft. It minimizes beamer capital cost by trading off the relative expenses of lasers, optics, and storage. The system model employs nested numerical optimizers and trajectory integration, whereas earlier models were based on closed-form approximations. The outcome is that the solution is cheaper and generates more accurate requirements, but it also exhibits more complex behaviors.

The system model is used to compute point designs for a 0.2 c Alpha Centauri mission and a 0.01 c solar system precursor mission. Also, a family of solutions is computed for a ground-based vacuum tunnel in which beam-riding and other aspects of the sail can be tested.

It describes how it computes cost-optimal point designs.

Using the model, three scenarios are examined:

1. A 0.2 c mission to Alpha Centauri,

2. a 0.01 c solar system precursor mission, and

3. a ground-based test facility based on a vacuum tunnel.

All assume that the photon pressure from a 1.06 µm wavelength beam accelerates a circular dielectric sail. The 0.2 c (20% of light speed) point design assumes $0.01/W lasers, $500 per square meter optics, and $50 per kilowatt hour energy storage to achieve $8.3 billion capital cost for the ground-based beam director. In contrast, the energy needed to accelerate each sail costs $7 million. Beam director capital cost is minimized by a 4.2 meter diameter sail that is accelerated for 10 min.

The 0.01 c (1% of lightspeed) point design assumes $1 per watt lasers, $10k/m2 optics, and $100/kWh energy storage to achieve $517M capital cost for the beam director and $8,000 energy cost to accelerate each 19 cm diameter sail.

The ground-based test facility assumes $100 per Watt lasers, $1 million per square meters optics, $500 per kilowatt hour energy storage, and $10,000 per meter vacuum tunnel. To reach 20 km per second, fast enough to escape the solar system from Earth, takes 0.3 km of vacuum tunnel, 16 kW of lasers, and a 0.9 m diameter telescope, all of which costs $6 million.

The system model predicts that, ultimately, Starshot scales to cruise velocities of greater than 0.9 c (90% of lightspeed).

**Objectives**

Breakthrough Starshot. Send 1 gram of scientific instrumentation to the Centauri System to study it. Image its planets, look for life and transmit the results to Earth. Do so by using a beam emitted from the Earth to accelerate a sail carrying the instrumentation to 0.2 c. The capital cost of the equipment shall be less than $10Billion.

Systems Engineering Work. Ensure that Starshot engineering activities amount to a mission that fulfills the Breakthrough Starshot objectives.

System Model. Replace physical experiments with simulations in cases where it saves time and money to do so. Verify Breakthrough Starshot feasibility and estimate performance. Design, optimize, trade-off, and analyze alternatives. Generate and quantify requirements. Model the impact of changes.

**Table 1: System model inputs for 0.2 c mission**

0.2 c target speed

1.06 µm wavelength

60 000 km initial sail displacement from laser source

1 g payload

0.2 g m−2 areal density

10^{−8} spectral normal absorptance at 1.06 µm

70% spectral normal reflectance at 1.06 µm

625 K maximum temperature

0.01 total hemispherical emittance (2-sided, 625 K)

$0.01/W laser cost

$500/m2 optics cost

$50/kWh storage cost

50% wallplug to laser efficiency

70% of beam power emerging from top of atmosphere

**System model outputs for 0.2 c mission**

$8.3B capex comprised of:

$2.0B lasers (200 GW max. transmitted power)

$2.9B optics (2.7 km primary effective diameter)

$3.4B storage (67 GWh stored energy)

$7M energy cost per Starshot (67 GWh @$0.1/kWh)

2.9% system energy efficiency

4.2 m sail diameter

3.8 g sailcraft mass (includes payload mass)

9 min (520 s) beam transmit duration

10 min (590 s) sailcraft acceleration duration

40 Pa temperature-limited photon pressure

560 N temperature-limited force

15 200 g’s temperature-limited acceleration

2300 g’s final acceleration (0.15 au), 73 ls from source

34 kW m^{−2} beamer maximum beam radiant exitance

14.5 GW m^{−2}−2 sailcraft temperature-limited irradiance

The 8.7 GW m^{−2} sail irradiance produces only 40 Pa photon pressure, equivalent to a moderate breeze. But the sail is very thin and the breeze moves at the speed of light, resulting in 15 200 g’s initial acceleration. Such acceleration is experienced by bullets and artillery shells, but for fractions of a second and not 10 min duration. The sailcraft reaches 0.2 c even as it is still accelerating at 2300 g’s. Such is the cost-optimum truncation point for the trajectory.

If the costs increase by 10X for various key systems, the total project CAPEX (capital expense) is calculated.

**System model inputs for 0.01 c precursor mission**

0.01 c target speed

1.06 µm wavelength

300 km initial sail displacement from laser source

1 mg payload

0.2 g m−2 areal density

10^{−8} spectral normal absorptance at 1.06 µm

40% spectral normal reflectance at 1.06 µm

625 K maximum temperature

0.01 total hemispherical emittance (2-sided, 625 K)

$1/W laser cost

$10k/m2 optics cost

$100/kWh storage cost

50% wallplug to laser efficiency

70% of beam power emerging from top of atmosphere

**System model outputs for 0.01 c mission**

$517M capex comprised of:

$285M lasers (285 MW max. transmitted power)

$224M optics (169 m primary effective diameter)

$8M storage (81 MWh stored energy)

$8k energy cost per mission (81 MWh @$0.1/kWh)

0.01% system energy efficiency

19 cm sail diameter

6.6 mg sailcraft mass (includes payload mass)

6 min (359 s) beam transmit duration

6 min (362 s) sail acceleration duration

23 Pa temperature-limited photon pressure

0.65 N temperature-limited force

10 000 g’s temperature-limited acceleration

6 g’s final acceleration (0.007 au), 3.4 ls from source

13 kW m^{−2} beamer maximum beam radiant exitance

10.2 GW m^{−2} sailcraft theoretical maximum irradiance

8.7 GW m^{−2} sailcraft temperature-limited irradiance

**System model inputs for the vacuum tunnel**

1.06 µm wavelength

1 m initial sail displacement from laser source

10 ng payload

0.25 g m−2 areal density

10−9

spectral normal absorptance at 1.06 µm

35% spectral normal reflectance at 1.06 µm

625 K maximum temperature

0.01 total hemispherical emittance (2-sided, 625 K)

$100/W laser cost

$1M/m2 optics cost

$500/kWh storage cost

$10k/m vacuum tunnel cost

50% wallplug to laser efficiency

For a 200 km per second sail speed at cutoff, which equals or exceeds the fastest human-made craft, the model infers:

A $400 million tunnel, 730 kW of lasers, and a 9.1 meter diameter telescope, costing a total of $400 million

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