Phased-Array Laser Power Beaming from Cislunar Space to the Lunar Surface

TL;DR

The paper develops a rigorous, end-to-end framework for delivering lunar surface power via cislunar laser beaming, linking on-orbit solar generation, terrain-aware visibility, diffraction-limited beam propagation, and surface electro-optical conversion. It introduces a time-domain model with Gaussian encircled-energy capture and a PSD-based jitter budget, enabling concrete design maps that compare laser beaming to surface PV with storage and to compact fission. Through NRHO Shackleton-rim case studies and constellation-level modeling, the work quantifies how delivered daily energy scales with transmit aperture, power, and visibility, and identifies regimes where phased-array transmitters offer mass- and energy-efficient advantages, especially in shadowed polar regions. The framework also addresses practicalities including dust lofting, acquisition/tracking, thermal management, safety, and regulatory aspects, framing a path to scalable cislunar power infrastructure using modular optical transmitters. Overall, the results demonstrate that laser beaming is a competitive, scalable complement to traditional lunar power sources for polar operations and deep-storage challenges, with explicit design maps informing mission and system-level trade decisions.

Abstract

We present a time-dependent, end-to-end framework for laser power beaming from cislunar orbits to the lunar surface. The model links on-orbit generation (solar arrays and wall-plug to optical), terrain-masked visibility and range, beam propagation with realistic divergence and jitter, and surface conversion with thermal and dust limits, returning delivered daily energy. Baseline loads for early polar activities (habitat survival, mobility, comm/nav, pilot ISRU) set target Wh\,day$^{-1}$ and are used consistently in scaling laws and design maps. A near-rectilinear halo orbit (NRHO) to a Shackleton-rim site provides a worked example: for a 2\,m-class phased array at 1064\,nm the reference geometry yields $\sim$0.6--0.8\,kWh\,day$^{-1}$ to a 1\,m$^2$ receiver (about 28\,W averaged over the day). We place this result in context by comparing on the same daily-energy metric to surface photovoltaics (PV) with storage and to compact fission, and by showing how delivered energy scales nearly linearly with transmit power and as $D_{\rm eff}^{2}$ via encircled-energy capture, with a multiplicative gain from visibility (constellations). The same framework indicates practical regimes already within reach: e.g., a 10\,m effective-aperture optical phased array at $P_{\rm tx}=100$\,kW delivers $\sim$30--50\,kWh\,day$^{-1}$ at polar sites with typical single-orbiter visibility, as quantified by the delivered-energy and sizing maps. Thus, laser beaming is mass-competitive where darkness or permanent shadow forces deep storage for PV, or where distributed and duty-cycled users can amortize a shared transmitter; compact fission retains advantage for continuous multi-kW baseload at fixed sites.

Figures (5)

• Figure 1: Closed-loop one-sided LoS jitter PSD for a 2 m-class phased-array optical transmitter in NRHO (0.1--1000 Hz). The nominal case includes low-frequency rigid-body residuals, reaction-wheel-line features at 50/75/100 Hz, a structural/thermoelastic floor (20--300 Hz), and fine-sensor/FSM noise. Perturbations applied individually: +50% wheel-line amplitudes, +10 ms outer-loop latency, and $-3$ dB loop gain. Numerical integration of each PSD yields the total RMS LoS jitter in $\mu$rad (see the legend).
• Figure 2: Left: $\eta_{\rm main}(F)$ from \ref{['eq:eta_main_bounded']} using $(\eta_0,\eta_\infty,F_c,p)=(0.25,0.98,0.10,1.4)$; markers show reported fills ($F\!\approx\!0.80,0.20,0.10$). Right: the corresponding fill-factor penalty $\beta(\eta^{-1}_{\rm main}(F)-1)$ (i.e., the last term in (\ref{['eq:m2_bounded']})) for $\beta=1.5,2.5,3.5$.
• Figure 3: Iso--daily energy contours (kWh/day) as a function of transmitter aperture $D$ and transmitted power $P_{\rm tx}$ for range $d=1000$ km and $N_{\rm orb}=1$. The model uses $\theta = M_{\rm eff}^2(F)\,2\lambda/(\pi D)$, $w_{\rm eff}=\sqrt{(\theta d)^2 + (d\,\sigma_{\rm point})^2}$, Gaussian encircled-energy capture $\eta_{\rm cap}=1-\exp[-2 r_{\rm rx}^2/w_{\rm eff}^2]$ for a $1~\mathrm{m}^2$ receiver ($r_{\rm rx}=\sqrt{1/\pi}$). Daily energy is $E_{\rm day} = P_{\rm tx}\,\eta_{\rm chain}\,\eta_{\rm cap}\, \min(1, N_{\rm orb} D_{\rm single}) \times 24$ h. Parameters here: $\lambda=1064$ nm, $\eta_{\rm chain}=0.35$, $M_{\rm eff}^2(F)=1+k(1-F)$ with $F=0.8, k=1, \sigma_{\rm point}=0.2~\mu\mathrm{rad}$, $D_{\rm single}=0.10$ m.
• Figure 4: Parametric sizing maps: (a) daily kWh delivered, (b) transmitter PV area, (c) receiver radiator area, (d) transmitter radiator area. Defaults: $\lambda=1064$ nm, $M^2=1.2$, $\sigma_\theta=0.10\,\mu$rad, $d=3000$ km, $T_{\mathrm{vis},24\mathrm{h}}=2$ h in $24$ h (i.e., $f_{\mathrm{vis},1}^{24\mathrm{h}}=2/24\approx 0.083$), $A_{\mathrm{rx}}=1~\mathrm{m}^2$. The contours are intended to be read directly against Eqs. (\ref{['eq:mpv']})–(\ref{['eq:mfis']}): select $(D_{\rm eff},P_{\rm tx},A_{\rm rx},N)$ to meet a site’s $E_{\rm day}$ target, then compare $M_{\mathrm{LPB}}$ to $M_{\mathrm{PV+bat}}$ and $M_{\mathrm{fis}}$ on the same $P_{\mathrm{eq}}$ basis.
• Figure 5: Daily energy delivery $E_{\mathrm{day}}(N_{\mathrm{orb}})$ for integer $N_{\mathrm{orb}}$ and representative single--orbiter visibility fractions $f_{\mathrm{vis},1} = 0.05,\ 0.10,\ 0.15$, each scaled to its corresponding $E_{\mathrm{day},1}$ assuming identical link performance. Curves use \ref{['eq:fvisN']} with $\kappa=0.95$; correlation ($\kappa<1$) shifts them downward. Vertical separation between curves reflects the proportional increase in total energy for higher single--orbiter visibility.