SCALPSS Plume-Surface Diagnostics

• SCALPSS Plume-Surface Diagnostics is a multi-instrument system that quantifies plume–regolith interactions during rocket landings on the Moon, Mars, and icy satellites.
• It employs stereo-photogrammetry, optical backscatter arrays, and piezoelectric sensors to capture ejecta kinetics, particle size distributions, and electric field properties.
• The diagnostics enable predictive modeling of surface erosion and deposition, guiding lander design and operational safety in extreme planetary environments.

SCALPSS Plume-Surface Diagnostics concerns the multi-instrument, physics-based quantification of plume–regolith and plume–surface interactions in rarefied and planetary environments, emphasizing direct in-situ and remote diagnostics during rocket landings, as well as comparative analysis of plumes and surface phenomena across the Moon, Mars, and icy satellites. The SCALPSS (Surface & Cratered Atmosphere and ejection Landed Particle Stereo System) architecture is engineered to provide time-resolved, height-dependent, and compositionally sensitive constraints on ejection kinematics, number densities, PSDs, electrical environments, and resultant erosion or deposition processes at the micro- and macro-scales.

1. Instrumentation, Observables, and Data Acquisition

SCALPSS comprises a stereo-photogrammetry subsystem (dual 1024×1024 px, 30° FOV, up to 500 fps; 25 cm baseline, boresight 45° down), optical backscatter arrays (660 nm; 10° geometry; 10 µs sampling), and piezoelectric impact disks (0.1–10 kHz bandwidth). These channels provide surface-near, high-frequency measurements of ejecta grain position, speed, number flux, and angular distribution. Time-tagged metadata (engine thrust, nozzle/gimbal angle, lander attitude) allow contextual phase-space reconstruction across the entire “ignition-through-settle” window (−10 to +20 s about engine cutoff). Calibration involves pre-flight grid methods (±0.1 mm reprojection error), vacuum-chamber cross-references, and in-flight fiducial checks.

Extracted parameters include:

Parameter	Technique	Observed Range / Notes
$n_d(z,t)$	Stereo photogram.	$10^4$–$10^6$ particles/m³ at 0.5 m
PSD($a$)	Stereo/backscatter	$dN/da \propto a^{-3.5}$, $a=1$–$50\,\mu$m, mode $\sim6\,\mu$m
$w(a)$	Displacement/FR	$20$–$200$ m/s, smaller $a$ faster
$F(\theta)$	Video statistics	Peaked near $30^\circ$ from cosine function
$n_e(z)$	Floating-probe	$10^7$–$10^8$/m³, scale $\lambda\sim0.08$ m
$E(z)$	Probe/multimeter	$200$–$800$ V/m, $\lambda\sim0.05-0.15$ m

Empirically, dust density peaks $\sim 2$ s post-touchdown, decaying with $z$; PSD slope is typical of mechanical comminution during plume acceleration. The measured sheath field and electron density inform the launching electrostatic environment.

2. Theoretical Framework and Diagnostic Equations

SCALPSS data reduction builds on closed-form expressions that couple microphysical lift-off, sheath structure, and near-surface dust transport. The adhesion-aware threshold for detachment of a grain of radius $a$ is:

$$F_{\rm lift}(a) = \frac{4}{3}\pi a^3\rho_p g_{\rm Moon} + \frac{3}{2}\pi W R$$

$$E_{\rm req}(a) = \frac{F_{\rm lift}}{q} = C_{\rm no} a^2 + C_{\rm adh} a^{-1}$$

where $$C_{\rm no} = \rho_p g_{\rm Moon}/(3\varepsilon_0 \phi_g)$$, $C_{\rm adh} = 3W R/(8\varepsilon_0\phi_g)$; $\phi_g$ is the floating potential. For grains liberated into the sheath, the apex and static hover heights are

$$h_{\rm ball}(a) = \frac{q \mathcal{E}}{m g_{\rm Moon}} = \frac{3\varepsilon_0 \phi_g \mathcal{E}}{\rho_p g_{\rm Moon} a^2}$$

$$h_*(a) = \lambda \ln\left( \frac{q E_0}{m g_{\rm Moon}} \right )$$

with sheath characteristics $\mathcal{E} = E_0 \lambda$, $E_0$ field at $z = 0$, $\lambda$ scale height (directly measured).

Transport flux is synthesized as:

$$J(z) = \int_{a_{\rm min}}^{a_{\rm max}} m(a)\, v_z(a, z)\, n_d(a, z)\, da$$

Practically, $J(z)$ is reconstructed from direct stereo inversion and counting statistics at measured $z$.

3. Validation, Surface Property Feedback, and Comparative Frameworks

SCALPSS results were validated using independent thermal observations from LRO Diviner, which constrain post-plume surface conductivity and the perturbation to the local thermophysical regime. The contact+radiative model form

$$k(T, \rho) = k_{\rm cond,0} (\rho/\rho_s)^\ell + A\, T^3$$

with empirically determined parameters ($\ell \approx 2.7$, $A \approx 2.5 \times 10^{-12}$ W/m/K⁴) accurately reproduced the observed cooling transient in the ∼10–30 cm SCALPSS-disturbed patch, confirming the impact of meso-scale surface modification on local heat flow.

Comparatively, SCALPSS design requirements and context draw on:

• Apollo-era photogrammetric results: required coverage of ejection angles ($\alpha \sim 1$–$3^\circ$), densities ($n \sim 10^8$–$10^{13}$/m³), resolved velocities, and large-rock ($\sim$10–15 cm) ejection for risk analysis (Immer et al., 2021).
• Laboratory/analytical cratering studies: Incorporation of geotechnical property dependencies (bulk density $P_m$, cohesion $C$, internal friction angle $\phi$) and production-based erosion models (Dotson et al., 9 Apr 2025).
• Plume–deposition models on icy satellites (e.g., Enceladus): Gravitational, velocity, and source-tilt parameter extraction, validating forward- and inverse-mapping pipelines for ejecta diagnostics (Southworth et al., 2018).
• Thermal models at plume sites on Europa: Discrimination of thermal-inertia-driven vs. endogenic heat-driven surface warming and related inferences for regolith and plume evolution (Trumbo et al., 2017).
• Boundary-layer plume analogs: Employed two-temperature toy and spectral models for cross-sectional area and vertical distribution diagnostics in turbulent surface layers (McNaughton et al., 2020).

4. Role of Geotechnical Properties in Erosion and Ejecta Kinematics

SCALPSS incorporates calibration and predictive modeling of plume erosion by explicitly measuring critical regolith parameters: bulk density (to ±0.05 g/cm³ via onboard γ-ray attenuation), cohesion (to ±100 Pa via vane or ring-shear), grain-size distribution (±10 µm), and internal friction angle (direct shear/penetrometer). The adopted modified viscous-erosion model,

$$\dot{V} = \frac{27\,\rho_f\,v^2\,A}{0.5\,P_m\,g\,D + C}$$

(where variables follow those in (Dotson et al., 9 Apr 2025)) provides agreement within 5–10% of observed crater and volume growth for $C<1000$ Pa and $P_m=0.9$–2.0 g/cm³.

Erosion rate is inversely sensitive to bulk density and cohesion, saturating or slightly increasing at very high $C$ (particle clumping). Particle-size effects appear through both direct dependence and via $\phi$: steeper friction angles inhibit crater wall collapse, reduce recirculation, and hence lower effective erosion. Model applicability is limited to subsonic, turbulent regimes with appropriate pressure correction for vacuum (to be derived via CFD).

5. Engineering Synthesis and Operational Implications

SCALPSS diagnostics directly inform system-level lander and rover hardware constraints. Design recommendations derived from IM-1 deployment include:

Parameter	Recommended Range	Rationale
Hover altitude	≥ 2 m	Sub-100 µm ejecta flux reduced >90%
Particle deflector angle	≥ 30° off-normal	Centerline flux reduction ~70%
Shielding thickness	3–5 mm Al/equiv.	Survives peak mass fluxes
Dust removal events	≥ 3 cycles/engine-off	Pre-loosens adhesion-dominated fines

Throat-skirt deflectors, leg/facet bumpers, and active dust-clearing mechanisms are recommended for mitigation. Real-time knowledge of dust density, particle-size flux, and sheath state enables adaptive hover and throttle control, hardware orientation, and informed scheduling of extravehicular activities or critical hardware exposures.

6. Limitations, Uncertainties, and Prospects for Further Research

Instrumentation and modeling uncertainties include (per (Turyshev, 11 Nov 2025) and (Dotson et al., 9 Apr 2025)):

• Counting/statistics uncertainty: ±15% on optical ejecta counts, ±5–8% on density via γ-techniques.
• Model bounds: calibration constants assume Earth-atmosphere lab to vacuum scaling extrapolations; vacuum expansion, diffused-gas eruption, and high-cohesion regimes remain poorly characterized for true lunar/Martian conditions.
• Onboard model validation requires mini-jet impingement at known $P_m, C$ prior to landing; coefficients can be empirically adjusted.
• SCALPSS capability is applicable for $n_d=10^4$–$10^6$/m³, $PSD(a=1$–$50\,\mu$m), $w(a)=20$–$200$ m/s; extension to Mars or denser atmospheres may require higher dynamic range and channel sensitivity.

A key operational caveat is the relevance of near-surface electric fields and pre-loosening mechanisms (vibration, acoustics), which set critical thresholds for dust liberation. The data and models do not yet resolve saltation and aggregate/fragment liftoff dynamics at the smallest scales in PSRs or ultrafine, highly cohesive regolith regimes.

This suggests robust predictive capability for plume–surface interaction is critically dependent on direct measurement and in-situ calibration of regolith geotechnics, combined with rapid-response, multi-modal particle monitoring as implemented in SCALPSS.

7. Cross-Disciplinary and Future Directions

SCALPSS methodology, integrating real-time photogrammetry, backscattering, piezoelectric impact diagnostics, and geotechnical feedback, establishes a new standard for plume-surface analysis in planetary landing contexts. Its architecture is extensible to Mars, asteroids, and icy satellites, providing diagnostic invariants and lookup structures for source-geometry and regime inversion (cf. Enceladus jet tilt, Europa thermal-inertia anomalies). Prospects include real-time model updating via onboard processors, implementation of adaptive hazard avoidance, and closed-loop integration with descent guidance systems.

Furthermore, SCALPSS-derived findings are already being employed for CLPS and Artemis mission risk posturing, informing guidelines for hardware shielding, landing sequencing, and off-nominal site selection, and they contribute directly to the construction of generalized PSI databases for extraplanetary operations.