ProtoDynamics LLC · Engineering Disclosure · Rev. 3 · Controlled Distribution

Bilateral Coupler Engine

A sealed, propellant-free electrostatic thrust cell with an integrated liquid-metal steering stage. Device architecture, materials stack, control-surface system, operating envelope, and build sequence.

NDA notice. This document is shared under a signed non-disclosure agreement. It discloses the device: what the parts are, what each part does, how the assembly is built, driven, protected, and steered. The materials-selection model, the ceramic deposition parameters, the alloy compositions, and the vortex drive scheme are intentionally withheld (Section 15).

Section 1

Scope of This Disclosure

This is a device document. It describes the Bilateral Coupler Engine (BCE) at the level a propulsion laboratory needs to evaluate it: geometry, materials by name and function, electrical envelope, failure modes, steering architecture, assembly sequence, and a staged validation plan with binary outcomes.

It deliberately does not describe the selection model that fixed the materials and the deposition parameters. Every choice in this document has a quantitative basis in a proprietary design method; that method is a separate disclosure tier under expanded NDA. Where a parameter derives from the withheld method, this document gives the parameter's role and, where safe, its as-built value — never its derivation.

How to read the numbers

All dimensions, ratios, and tolerances in this document are engineering reference values from the BCE-30 record and its drawing set. They are stated as bare numbers. Ratios are dimensionless build targets; the drawing set governs where an as-built value and a target value differ at the millimeter level.

Section 2

Device Overview

The BCE is a sealed lenticular vacuum cell built around an asymmetric high-voltage capacitor. A gently curved copper-aluminum dome forms the positive electrode. A thin, dense tungsten rim at the cell's outer edge forms the negative electrode and concentrates the field at a controlled cusp. Between them, the device adds four elements no flat-stack asymmetric capacitor has: a ferroelectric ceramic stratum bonded to the dome's underside, a rare-earth alloy cathode spine on the cell axis, a circulating liquid-metal torus (gallium-indium-tin eutectic) acting as a magnetohydrodynamic stage, and a terraced bismuth floor that terminates the internal field.

The device class traces to a decade of asymmetric-capacitor force measurements: real, repeatable micronewton-scale forces on analytical balances, persisting after power-off, surviving vacuum tests that eliminate ion wind and corona as explanations. The BCE is an engineered completion of that device class — closed geometry instead of open plates, purpose-selected materials instead of foil and tape, and an actuated steering system instead of a fixed thrust axis.

Operating voltage
100–200 kV
Design headroom
350 kV
Continuous power
< 3.5 W
Operating current
~10 µA
Environment
< 10⁻⁵ Torr
Predicted thrust
10–50 mN

Predicted thrust is for a multi-unit stacked configuration in vacuum. The single-unit flat-stack baseline the class is built on measures ~29 µN at 100 kV; multi-unit flat stacks reach 5–10 mN in atmosphere, where corona losses consume an estimated 30–60% of input field energy.

Section 3

Architecture & Cross-Section

The cell is a closed convex-concave shell: a hemispherical-arc dome above, a shallow bowl below, joined at an equatorial rim. Every component either feeds, shapes, converts, or terminates the internal field. The cross-section below is the full part inventory.

BCE cross-section Sectioned lenticular cell: copper-aluminum dome on top with a ceramic stratum on its underside, tungsten rim at the equator, axial cathode rod descending from the equator plane to a terraced bismuth floor, and a liquid-metal torus ring surrounding the rod. standoff 95 mm (vacuum — no contact) Cu-Al dome — anode (+HV) ceramic stratum (BaTiO₃) W rim — cathode edge (−HV) GaInSn torus (MHD stage) Bi terraces — field sink Er-Ho cathode spine bowl shell / hull floor contact: rod base → top terrace equator plane net thrust (rim → dome axis) SECTION A-A — schematic, not to scale. Sealed shell; interior < 10^-5 Torr.
Fig. 1 — BCE cross-section. Six functional materials in one sealed lenticular cell. The rod's upper tip faces the dome interior across a vacuum standoff; its base is in required mechanical contact with the top bismuth terrace.
Component inventory at a glance
  1. Lenticular shell — closed convex-concave hull; contains the internal field structure and holds vacuum.
  2. Cu-Al layered dome — positive HV electrode; large area, gentle curvature, low surface field.
  3. BaTiO₃ thin-film stratum — ferroelectric ceramic multilayer bonded to the dome's underside; the active dielectric.
  4. Tungsten rim — negative HV electrode; thin cusp edge where the field concentrates; segmented into quadrants for steering.
  5. Er-Ho cathode spine — axial rare-earth alloy rod from the equator plane to the floor; second field axis.
  6. GaInSn torus — circulating liquid-metal ring around the rod; magnetohydrodynamic converter and steering actuator.
  7. Bismuth terraces — three-step diamagnetic field sink at the bowl floor; terminates the internal field into the hull structure.

Section 4

Reference Geometry

The BCE-30 is the reference build. Its proportions are fixed build targets — the design holds specific aspect ratios and axial stations, each with a tight tolerance band. The values below are the engineering record; their derivation belongs to the withheld design method.

Table 1 — BCE-30 reference geometry. The drawing set governs conflicts between target and as-built values.
ParameterValueToleranceNote
Principal lens aspect (dome height : bowl diameter)1.21 : 1±0.1%Sets the lens profile itself
Cathode rod aspect (length : diameter)3 : 1±0.1%Fixed integer aspect; machined, not trimmed
Rod axial spanequator plane → floor—Rod occupies the full bowl depth
Rod-tip axial station45.2% of internal height, from floor±0.1%Upper tip sits exactly on the equator plane
Internal axial extent (BCE-30)165 mmper drawingReference build
Dome arc height / rod-tip standoff (BCE-30)95 mm±0.08 mmVacuum gap, dome interior to rod tip
Cathode rod, next-prototype target74.6 mm × 24.9 mm±0.1%~6× cross-section vs. original 30 × 10 mm rod
Dielectric stack, total thickness~0.2 mmprocess-controlled~2,000 layers × 100 nm, thin-film deposition
Electrode edge radius≥ 2 mm—Everywhere except designed field cusps

Two geometric facts carry most of the device's behavior. First, the rod tip terminates exactly at the equator plane — the plane where the dome meets the rim — and faces the dome's interior across a 95 mm vacuum standoff. Second, the rod base is in mechanical contact with the bismuth floor. One interface must never touch; one must always touch. Section 7 specifies both.

The original BCE-30 rod (30 mm × 10 mm) was undersized relative to the design targets above; the 74.6 × 24.9 mm rod is the corrected next-prototype spec. Expected force scales with rod cross-section.

Section 5

The Materials Stack

Six materials, six functions. Each entry below states what the material does in the device — its electrical role, its physical properties that the design exploits, and its interfaces. The selection logic that fixed this specific set is part of the withheld design method; what is disclosed here is sufficient to build, drive, and test the stack.

#Element / LayerMaterialElectrical roleEngineering function
1DomeCu-Al layered alloyAnode (+HV)Large-area charge reservoir; low surface field via gentle curvature; structural upper hull
2Dome undersideBaTiO₃ thin-film multilayerActive dielectricFerroelectric stratum; its polarization field spans the interior standoff to the rod tip
3RimTungstenCathode (−HV)Field-shaping cusp edge; current return; survives sustained edge-field conditions
4Axial spineEr-Ho alloy rodCathode bias axisSecond field axis intersecting the dome-rim field; hazmat-free rare-earth alloy
5TorusGaInSn eutecticConducting fluidMHD converter; Lorentz (v × B) boost and steering authority; replaces mercury
6Floor stepsBismuthField terminationStrongly diamagnetic sink; disperses residual field into the hull floor

5.1 — Cu-Al layered dome (anode)

The dome is the device's charge reservoir. Its job is to present the largest practical electrode area at the lowest practical surface field: electrostatic surface pressure scales as E² × A, and the dome wins on area while its gentle curvature (large local radius) keeps E low everywhere on its face. The layered copper-aluminum construction pairs copper's surface conductivity and charge-distribution behavior with aluminum's structural mass savings — the dome is also the upper pressure hull of the vacuum cell. All dome edges blend at ≥ 2 mm radius; there are no designed cusps on the anode side.

5.2 — BaTiO₃ ferroelectric stratum (active dielectric)

Barium titanate is a ferroelectric perovskite: below its Curie point the crystal carries a spontaneous electric polarization along a preferred crystal axis (the c-axis). In the BCE it is not a passive insulator — it is the component that makes the interior vacuum gap electrically active. The stratum is deposited on the dome's underside as a thin-film multilayer, and its polarization field extends down through the standoff to terminate on the cathode rod's tip. The gap stays a mechanical void; the ceramic makes it a dielectric link.

5.3 — Tungsten rim (cathode edge)

The rim is where the device's field concentrates. Local field pressure scales as (V/r)² with r the local radius of curvature: the dome's r is large, the rim's edge r is deliberately small, and the resulting field intensity at the rim edge runs 100×–1000× higher than anywhere on the dome face. That edge volume is where the thrust-producing field asymmetry lives — so the rim material must survive it. Three simultaneous constraints select tungsten:

  1. Density. A concentrated rim mass in a thin disc edge wants the densest stable metal available at production scale. Tungsten, 19.25 g/cm³, is it — osmium and iridium are denser but supply-impossible at volume.
  2. Conductivity. The rim is the negative electrode's return path. Tungsten's 1.89 × 10⁷ S/m carries the field-shaping current without meaningful resistive penalty; resistive loss at the edge would dissipate the field structure as heat.
  3. Thermal endurance. The rim edge is where corona, arc, and field-emission risk concentrate. Aluminum melts at 660 °C, copper at 1085 °C, steels near 1500 °C — all fail at sustained edge-field conditions. Tungsten's 3422 °C melting point, the highest of any stable metal, is what survives prolonged operation at the edge under load.

The rim is fabricated as independent segments — a minimum of four quadrant buses — rather than one continuous ring. Segmentation serves two functions: it limits the energy available to any single arc path (Section 10), and it is the primary electrostatic steering actuator (Section 11).

5.4 — Er-Ho cathode spine

The axial rod is one of the two most tightly specified components in the device (the ceramic stratum is the other). Functionally it is the cathode's second field axis: biased relative to dome and rim, it establishes an axial field profile that intersects the dome-rim field, couples into the surrounding liquid-metal torus, and delivers the internal field down to the bismuth termination at its base. Segmented contacts along its length allow a gradient bias — the basis of Class 4 steering (Section 11).

5.5 — GaInSn liquid-metal torus (MHD stage)

A torus of gallium-indium-tin eutectic surrounds the rod. GaInSn is liquid at room temperature, electrically conductive, and non-toxic — it replaces the mercury of the original concept and removes the entire hazmat envelope with it. A conducting fluid circulating through a magnetic field experiences a Lorentz force (F = qv × B); driven in a closed loop around the rod, the torus becomes a magnetohydrodynamic stage with two jobs:

The mechanism that drives the circulation, and the closed-loop bias scheme coordinating coils and flow for vector control, are part of the engineering specification held under expanded NDA. What is disclosed: the stage exists, it uses the torus as its actuator, and its containment loop is compatible with standard liquid-metal handling practice (inert-gas fill, wetted-surface compatibility control).

5.6 — Bismuth terraces (field sink)

Three stacked terraces of bismuth form the bowl floor beneath the rod. Bismuth is the most strongly diamagnetic stable metal (volume susceptibility χ ≈ −1.66 × 10⁻⁴ SI): it repels magnetic field lines and pushes them outward. The graduated three-step geometry creates a termination volume — each terrace pushes the residual field a little further outward and downward into the hull floor structure, rather than letting it loop back up into the cavity. The rod's base must be in continuous mechanical contact with the top terrace; the field transfers from the conducting rod into the diamagnetic sink at that interface (Section 7.2).

Section 6

Why the Shape Is Lenticular

The lens shape is a consequence, not a styling choice. Read the materials table as a flat parts list and you miss the load-bearing fact: the outer edge of the tungsten rim is the device's power center, and everything else exists to feed, shape, or terminate the field that lives at that edge.

Where the power consolidates

The dome and rim form an asymmetric capacitor. Local field pressure goes as E² = (V/r)²: a thin edge (small r) sees very high E; a broad face (large r) sees low E. The dome's curvature is gentle; the rim's edge is thin. All else equal, field intensity at the rim edge runs 100×–1000× above any point on the dome surface, set by edge thinness. The radial field gradient peaks there, and the thrust vector pointing from rim toward dome originates in that concentrated edge volume. The dome pushes; the rim pulls.

Given that, the architecture demands four things simultaneously:

The unique geometry satisfying all four at once is a hemispherical-arc dome on a shallow bowl with an extending equatorial rim — a lenticular enclosure. A sphere has no rim concentration. A cylinder has no anode-to-cathode geometric asymmetry. A flat plate stack produces a partial version of the effect through stack asymmetry but is open — it has no rim consolidation, no axial cavity, and it radiates what a closed shell would contain. The lens is the minimal closed shape with a concentrated edge and an axial gradient. The rim edge is, literally, where the engine's power lives; the craft surrounds it.

Section 7

Cathode Interface Specification

The rod has two critical interfaces. One must never make mechanical contact; one must always make mechanical contact. Reversing either destroys the device or its output. This is the part of the build most often gotten wrong, so it gets its own section.

7.1 — Rod tip ↔ dome interior: NO mechanical contact (95 mm vacuum standoff)

Why no contact. The dome is the anode at +HV (100–350 kV); the rod is cathode-side at −HV or ground. The two carry the device's entire potential difference. Touching them together drops the full operating voltage across zero resistance: instant short, arc plasma, electrode vaporization. The mechanical standoff is mandatory and non-negotiable.

Why the gap is active, not dead. The ceramic stratum on the dome's underside is ferroelectric — its spontaneous polarization projects a dielectric field down through the standoff, terminating on the rod's polished tip. The gap is a mechanical void but an electrical link: the standoff is the dielectric, and the oriented ceramic is what makes it active rather than passive insulation.

Why it doesn't arc at 350 kV. Operation is at < 10⁻⁵ Torr. Vacuum breakdown strength with polished electrodes at gaps ≥ 10 mm sits comfortably above 350 kV; the 95 mm standoff clears the envelope with wide margin. No solid insulator is needed in the gap — and none is permitted, since a solid spanning the gap would both short the field structure and create a tracking path.

Drift consequences. Too narrow: the gap approaches breakdown threshold and arcs — device destruction. Too wide: the ceramic's projected polarization arrives at the rod tip with insufficient amplitude, the dielectric link weakens, and thrust drops sharply. The 95 mm value equals the dome arc height and places the rod tip exactly on the equator plane; build tolerance is ±0.08 mm.

7.2 — Rod base ↔ top bismuth terrace: REQUIRED contact (field termination)

Why. The rod delivers the axial field down its length to its base. At the rod-bismuth interface the field transfers from conductor into the diamagnetic sink, whose response repels the residual magnetic component outward through the three terraces and disperses it into the hull floor. That transfer requires a continuous physical interface.

Failure mode. Suspend the rod base even a few millimeters above the top terrace and the field has no termination. Two things follow: (a) the field loops back up through the cavity to the dome, creating a circulating current that subtracts from thrust and dissipates as heat; or (b) it leaks through the hull floor into the environment. Either way the output collapses. The bismuth contact is the field's exit valve — without it the cell leaks instead of thrusts.

Build rule — the two-interface check

Before first power-up, verify with a meter and a feeler set: open circuit between rod tip and dome (and standoff at 95 ± 0.08 mm), continuity between rod base and bismuth stack. Any inversion of this pattern is a no-go.

Section 8

Operating Sequence

  1. HVDC is applied between dome (+) and rim (−). The asymmetric electrode pair creates an asymmetric field: large-area, low-field dome versus small-area, concentrated-field rim edge. The net differential in E² × A field pressure defines the thrust axis, from rim toward dome.
  2. The ferroelectric stratum activates the interior gap. The oriented BaTiO₃ multilayer on the dome underside projects its polarization field across the 95 mm standoff to the rod tip, converting the vacuum gap from passive insulation into a dielectric link between the dome-side stack and the cathode spine.
  3. The cathode spine is biased on its own axis. The rod's potential and current profile — adjustable along its length via segmented contacts — establishes a second field axis intersecting the dome-rim field, and couples into the surrounding torus.
  4. The GaInSn torus circulates. Conducting fluid moving through the local magnetic field experiences Lorentz forces (v × B); the driven circulation adds boost along the axis and, when biased asymmetrically, deflects the net reaction vector. The circulation drive and closed-loop bias scheme are withheld (Section 15).
  5. The bismuth terraces terminate the field. The diamagnetic floor repels the residual field outward and downward into the hull structure, preventing recirculation into the cavity.
  6. The sealed hull contains the field structure. Operation is in vacuum: no corona, no ion wind, no gas-phase arcing below the field-emission threshold. The thrust mechanism is the same anomalous-force effect measured in flat-stack asymmetric capacitors for a decade — engineered, contained, and steered. No spacetime-curvature or warp-drive claim is made; conservation accounting is the standard energy/momentum balance that applies to any asymmetric-capacitor force measurement, with the propellant-free regime requiring vacuum operation to eliminate ion-wind and corona contributions.

Section 9

Electrical & Vacuum Envelope

ParameterValueNote
Operating voltage100–200 kV DCDome-rim principal supply
Design headroom350 kVField-emission managed; surface finish < 0.1 µm
Operating current~10 µAContinuous
Supply protection≤ 1 mA current tripPlus series resistance against runaway discharge
Continuous power< 3.5 WAll stages, steady state
Vacuum< 10⁻⁵ TorrEliminates corona, ion wind, gas-phase arcing
Rim drive4+ independent quadrant busesSmall ΔV offsets for steering; arc-energy limiting
Coil drive4+ independent quadrantsΔI offsets for MHD steering

The supply architecture matters as much as the voltage rating. A voltage-regulated source with no current limiting will happily feed an arc until something melts; the BCE spec calls for a current-limited supply with a ≤ 1 mA trip and series resistance, so a breakdown event is starved before it does structural damage. The segmented rim additionally caps the energy any single arc path can draw.

Section 10

Failure Regimes & Design Rules

More voltage does not always mean more thrust. Three failure regimes bracket the operating window; a working engine is one designed against all three.

Regime 1 — Corona onset (30–60 kV in air)

What happens: the field at sharp edges exceeds ~3 kV/mm (air breakdown threshold). Visible purple glow at points and edges; audible hissing.

Physics: air molecules ionize at high-field points; freed electrons accelerate and liberate more (Townsend avalanche), forming a conducting plasma sheath around sharp features.

Impact: corona is noise, not signal. It consumes power without contributing to output, and the plasma sheath shorts out the very field geometry that creates the asymmetry. More corona, less usable thrust per watt.

Mitigation: round all electrode edges (≥ 2 mm radius) except designed cusps; operate in vacuum (or SF₆ if atmospheric testing is unavoidable). Flat-stack test rigs deliberately use sharp tips to maximize field concentration — acceptable for proving a force exists, unacceptable in a production cell.

Regime 2 — Arc breakdown (60–120 kV)

What happens: corona channels bridge the full electrode gap. A single bright arc forms — a short circuit through ionized air — and all stored energy dumps through it in microseconds. This is what melts hardware.

Physics: streamer propagation — a corona filament extends far enough that the field at its tip ionizes the next segment of gas, until the channel closes the gap and resistance collapses.

What it destroys: electrode surfaces (pitting, melting), the ceramic multilayer (thermal-shock cracking), insulation (charring). The deposited film's crystal orientation — achieved through careful deposition — is lost in a single arc event; the film must be redeposited.

Mitigation: current-limited supply (≤ 1 mA trip), series resistance, vacuum operation (eliminates gas-phase arcing entirely), and segmented rim electrodes so no single arc path can draw the full stored energy.

Regime 3 — Dielectric breakdown (material-limited)

What happens: even in perfect vacuum, the solid dielectric itself can fail. Bulk BaTiO₃ breaks down at ~10–15 kV/mm; 100 kV across a 5 mm bulk layer is 20 kV/mm — already above the bulk limit.

Physics: electrons tunnel through lattice defects; once a conducting channel forms through the ceramic it is permanent. This is catastrophic — the stratum is a core functional element, and losing it kills the device.

Mitigation: stacked thin-film deposition instead of bulk ceramic. Thin films withstand ~500 kV/mm, so ~0.2 mm total thickness carries 100 kV with margin — roughly 2,000 layers at 100 nm by standard PVD/sputter process, the film's crystal orientation maintained across layers by epitaxial growth.

The operating window

Design rules — flat-stack rig vs. BCE

ParameterFlat-stack rig (typical)BCE (engineered)
EnvironmentAir, 1 atmVacuum, < 10⁻⁵ Torr
Max safe voltage~30–50 kV100–200 kV
DielectricBulk PTFE / tapeThin-film BaTiO₃ multilayer (~0.2 mm)
Edge radiusSharp everywhere≥ 2 mm except designed cusps
Power supplyVoltage-regulatedCurrent-limited (≤ 1 mA trip; ~10 µA operating)
Corona losses30–60% of input0% (vacuum)
Recoverable from arc?No — rebuilt each timeYes — segmented rim limits damage
The limit is engineering, not physics

Meltdown at 100 kV in air is a hardware limit, not a mechanism limit. Vacuum removes the gas-phase failure modes; thin-film stacking removes the dielectric limit at operating voltage; current limiting removes the destructive-arc energy; segmentation contains what remains. Corona losses in atmospheric operation typically consume 30–60% of input field energy above 30 kV (standard high-voltage engineering estimate — Kuffel & Zaengl, High Voltage Engineering Fundamentals, 2nd ed., §5). Redirecting that loss into useful output is where the 10–50 mN vacuum projection for multi-unit configurations comes from; the ceiling above that is set by the dielectric stack, not by the mechanism.

Section 11

Vector Control System

A fixed-thrust cell is a demonstration; a steerable cell is a vehicle. The BCE steers electrically and magnetically — no fins, no gimbals, no swiveling nozzles. Steering comes from vectoring the field and the vortex: you deliberately unbalance the cell so the net thrust points where you want it.

11.1 — Four classes of control surface

Class 1 — Segmented rim electrodes (electrostatic vectoring)

Drive rim segments at slightly different voltages instead of busing them together. The local field under the dome leans toward the hotter segment, deflecting the effective thrust axis toward it — thrust vectoring done purely electrostatically.

Class 2 — Multiple engine cells (differential thrust)

A vehicle carries several cells around its center of mass. Throttle one side up and the other down for pitch, roll, and yaw — the same control law multirotor drones use with motor thrust.

Class 3 — GaInSn vortex shaping (MHD steering)

Bias coil currents or local circulation speed around the torus so the vortex is slightly stronger on one side. The skewed internal Lorentz forces nudge the net reaction vector sideways — steering with a fluid actuator that has no moving solid parts.

Class 4 — Cathode rod biasing (off-axis centerline)

Independently control the potential and current profile along the rod (segmented contacts, gradient bias) to shift where the strongest coupling into the vortex and bismuth stack occurs — moving the effect's apparent centerline off the geometric axis.

11.2 — Single-cell steering

Rim quadrants. Group the rim into at least four quadrant buses (front, rear, left, right). Slightly raise the voltage on the quadrant you want thrust to lean toward and lower the opposite quadrant, holding the average constant. The field under the dome leans toward the hottest segment and the thrust axis follows.

Coil and vortex asymmetry. Divide the coil system into four independently driven quadrants. Slightly higher current — or slightly higher local GaInSn speed — in a quadrant biases the MHD forces so the internal reaction is stronger on that side, pushing the net vector laterally.

On a torsion balance, steering shows up as a sideways twist or a shift in force direction when these small asymmetries are introduced against a symmetric, straight-up baseline. Single-cell vectoring authority is bounded — on the order of 15–20° from the cell axis in the reference design. Larger commanded angles are flown with multi-cell differential thrust.

Top-down steering diagram Top view of one cell: four rim quadrant buses and four coil quadrants around a central dome, with a commanded thrust vector leaning toward the raised-voltage quadrant. +ΔI coil quadrant (raised) +ΔV rim bus (raised) −ΔV rim bus (lowered) rod dome (top view) net thrust leans toward hot quadrant TOP VIEW — rim quadrant buses (inner ring), coil quadrants (outer ring)
Fig. 2 — Single-cell steering, top view. Raising one rim bus and its coil quadrant while lowering the opposite pair deflects the net thrust vector toward the raised side; total average drive is held constant.

11.3 — Vehicle-scale steering

A flight computer continuously adjusts dome-rim voltages (per cell and per rim quadrant), rod biases, coil currents, and vortex speeds (per cell and per quadrant) to produce the commanded combination of total thrust and vector angles.

11.4 — Master control-surface table

Control elementWhat you changePrimary effectSteering / attitude role
Dome-rim HV supplyVoltage between dome and rimMain lift magnitude (engine throttle)Symmetric across cells: climb/descent. Differential between cells: pitch/roll authority
Er-Ho rod biasRod potential and current profile vs. dome/rimAdjusts the axial field profile and the spine's coupling into the vortex stageCell-by-cell trim; biases which cell contributes more to a maneuver
Rim segments (quadrants)Small ΔV offsets between front/rear/left/right busesLeans the local electrostatic field under the domeDirect electrical thrust vectoring — more voltage on one side leans thrust toward it (pitch/roll/yaw by quadrant choice)
Coil quadrantsCurrent in each coil quadrantLocal magnetic-field strength through the GaInSnAsymmetric drive skews MHD forces — lateral vector nudge or yaw torque
GaInSn vortex driveCirculation speed and direction, segmentableOverall strength and handedness of the vortexGlobal change modulates engine gain; small side-to-side asymmetries assist steering and stability
Engine-cell throttle (per cell)Combined HV + rod + vortex + coil command for that cellNet thrust of that cellDifferential thrust between cells: coarse pitch/roll/yaw, multirotor-style

11.5 — Coordinate entry → actuator commands

Spatial targeting reduces to a deterministic decomposition — there is no black-box "thrust direction" knob. Every steering decision factorizes into rim, coil, rod, and vortex commands through five steps:

  1. Target to acceleration. Commanded displacement (Δx, Δy, Δz) over time Δt, flown accelerate-then-decelerate, requires a = 4d/Δt² on each axis.
  2. Acceleration to thrust vector. F = m(a + ĝ) — the vertical channel carries weight plus commanded vertical acceleration; horizontal channels carry their accelerations directly.
  3. Magnitude to throttle. |F| maps to the symmetric dome-rim voltage command across all cells.
  4. Direction to deflection. The vector's angle off vertical decomposes into per-cell deflection while it remains inside single-cell authority (~15–20°); beyond that, the controller allocates the excess to multi-cell differential thrust and flags the required cell count.
  5. Deflection to actuators. Per-cell deflection maps to rim quadrant ΔV and coil quadrant ΔI; yaw commands map to antisymmetric lateral deflections across the array.

Actual flight-control loops run at sub-millisecond cadence with sensor feedback, cell-cell coupling terms, and the closed-loop vortex/coil bias scheme held under expanded NDA. The disclosed point is the architecture: targeting is vector arithmetic over a known actuator set.

11.6 — Lab proof protocol: vector control

Bench demonstration — one afternoon, binary outcome

Setup: give the rim four independently driven buses (front, rear, left, right); give the coils four independently driven quadrants; mount the assembly on a torsion balance that measures torque about more than one axis.

  1. Run a symmetric, straight-up configuration; record the baseline vertical force.
  2. Slightly raise the front rim bus and lower the rear bus, holding average voltage constant. Observe fore-aft torque.
  3. Repeat with left/right rim bias, then separately with coil-quadrant bias, demonstrating deliberate vector rotation about both horizontal axes.

Reliable, repeatable vector deflection under electrical command in the lab is the whole demonstration: the same control laws scale to a multi-cell vehicle, where steering is coordinated small asymmetries in voltages and currents across the array.

Section 12

Assembly & Manufacturing Sequence

  1. Hull fabrication. Spin-form or machine the Cu-Al dome and bowl shells to the drawing profile (lens aspect 1.21:1, ±0.1%). Blend all edges to ≥ 2 mm radius except the rim interface. Surface-finish interior faces to < 0.1 µm where they see high field.
  2. Ceramic deposition. Deposit the BaTiO₃ multilayer on the dome's interior face by PVD/sputter: ~2,000 layers at ~100 nm, ~0.2 mm total, with the film's c-axis orientation set per the deposition spec and carried layer-to-layer by epitaxial growth. This step is the longest-lead and highest-skill operation in the build; an arc event at any later stage that damages the film sends the dome back to this step.
  3. Rim fabrication and segmentation. Machine the tungsten rim as four (or more) electrically isolated segments with the specified cusp-edge profile. Fit segment buses with independent HV feedthrough paths.
  4. Cathode rod. Arc-melt the erbium-holmium alloy to the composition specification (certificate retained); cast and machine the rod to 3:1 aspect (next-prototype: 74.6 mm × 24.9 mm). Polish the upper tip flat (< 0.1 µm); finish the base for full-face terrace contact. Install segmented bias contacts along the length.
  5. Bismuth terraces. Cast or machine the three-step terrace stack; install at the bowl floor with continuous mechanical and electrical contact to the hull-floor structure.
  6. Torus loop. Install the torus containment ring and coil quadrants around the rod station. Verify wetted-surface compatibility (gallium alloys aggressively attack aluminum — barrier coatings or compatible liner materials are mandatory on any Al-bearing surface the eutectic can reach). Fill with GaInSn under inert gas.
  7. Rod installation. Mount the rod on the terrace stack: base in verified continuous contact with the top terrace, tip at the equator plane, standoff to the dome interior at 95 ± 0.08 mm. Run the two-interface check (Section 7).
  8. Closure and pump-down. Mate dome and bowl at the rim, seal, and evacuate to < 10⁻⁵ Torr. Bake out per vacuum practice; verify leak-tightness.
  9. Electrical fit-out. Connect the current-limited HV supply (≤ 1 mA trip, series resistance), quadrant buses, rod bias channels, and coil drives. Verify isolation between all independently driven channels.
  10. Conditioning. Ramp voltage slowly on first power-up (standard HV conditioning): step, hold, watch for micro-discharge, proceed. Field-emission sites burn in during conditioning; do not skip to operating voltage.

Section 13

Validation Pathway

The full BCE is not the first experiment. The pathway is staged so that each tier is cheap, binary, and decisive — pass proceeds, fail stops and diagnoses. No tier requires building the sealed cell until the materials thesis has already survived two independent tests on existing flat-stack hardware.

TierChange under testHardwareOutcome sought
0None — baselineExisting flat-stack unit, vacuum, 100 kVReference force (~29 µN single unit); noise floor characterized
1Single-variable cathode substitution: a commercially available pure rare-earth rod replaces the stock cathode; a light-metal control rod runs as counter-caseSame rig, same supply, same dielectricThe withheld selection model predicts a specific force ordering across the three cathodes. Ordering observed → pass. Ordering absent → model falsified at the first gate
2Engineered binary Er-Ho alloy cathode (arc-melted to the withheld composition spec)Same rigStep-change beyond Tier 1 predicted by the model; confirms the alloy spec, not just the direction
3Add the oriented ferroelectric multilayer dielectricFlat geometry, both engineered materialsMaximum force available in an open flat stack; last stop before closed geometry
4Full sealed lenticular BCE with MHD stage and quadrant steeringNew build per Section 1210–50 mN class output; vector-control demonstration per Section 11.6
Why Tier 1 is the right first test

No new geometry. The flat-stack form factor stays; only the cathode material changes — a single isolated variable.

No new infrastructure. Same 100 kV supply, same current limits, same vacuum chamber, same balance.

No hazmat. The substitution rod is a standard catalog rare-earth item (machined rod, lab-grade, roughly $200–500); the control rod is trivial.

Binary outcome. Either the predicted force ordering appears or it does not. A clean null is publishable; a confirmed ordering makes Tier 2 the obvious next afternoon. The control rod exists specifically to eliminate "any new material helps" as an alternative explanation.

Section 14

Heritage & Positioning

The BCE's device class was not invented on paper. Exodus Propulsion Technologies (Charles Buhler's NASA-alumni team) has measured anomalous forces in asymmetric capacitors since 2014 — hundreds of device configurations, forces on analytical balances, no ion wind, no measurable propellant, results that persist after power-off and survive vacuum testing. Roughly 2,000 configurations of electrodes, dielectrics, and geometries were explored by systematic trial. That body of work established, empirically, that the force class is real, repeatable, scales with voltage squared and electrode area, and stacks additively — 5–10 mN across multi-unit configurations in atmosphere.

Sourcing note — reconstruction

ProtoDynamics does not hold Exodus's proprietary specifications. All references to their hardware here derive from the public record — recorded presentations, interviews, and published photographs — and describe our best reconstruction of the device class, not their design files.

What the flat-stack work proved

What the flat stack lacks — and the BCE adds

AspectFlat-stack rigBCE
GeometryOpen plate stack — internal field structure radiates awaySealed lenticular shell — field structure contained
ElectrodesCopper foilCu-Al dome + segmented tungsten rim
DielectricGeneric PTFE/tape; no crystal-orientation controlOriented BaTiO₃ thin-film multilayer
Axial elementNoneEr-Ho cathode spine with gradient bias
Conversion stageNoneGaInSn MHD torus (boost + steering)
Field terminationNone — open returnThree-step bismuth diamagnetic sink
SteeringFixed thrust axis, set by geometryFour actuator classes, three-axis authority
Materials selectionTrial and error (~2,000 configs)Model-selected (method withheld)
EnvironmentMostly atmospheric — corona losses 30–60%Vacuum-native — zero corona loss

The geometric insight the flat stack stumbled into is worth naming: a large-area anode plane crossed by a narrower cathode at a right angle. That T-shape is a flat unfolding of the BCE's dome-and-rod architecture — the same load-bearing relationship, opened out into plates. Wrap the anode plane into a dome, run the cathode through the center as an axial rod, close the shell: that is the BCE. The flat stack proves the force exists; the BCE is what you build to capture, contain, scale, and steer it. A flat stack is a flashlight. The BCE is a laser.

Proposed engagement

The shortest path from this document to a peer-defensible result is Tier 1 of Section 13: a single-cathode substitution on an existing rig, in vacuum, one afternoon, binary outcome — followed by Tier 2 if the predicted ordering holds. We expect critique and invite it; the staged pathway is designed so that every claim meets an instrument before any capital is committed. Collaboration preserves the experimental team's priority and credits each contribution.

Contact: Cory Graves · protodynamics01@gmail.com · ProtoDynamics LLC

Section 15

What This Document Withholds

For clarity between the parties, the following are deliberately excluded from this disclosure tier and are available only under expanded NDA:

Everything else in this document — geometry, materials by name and function, interfaces, envelope, failure design, steering architecture, build sequence, and validation plan — is disclosed to the full depth of the engineering record.