Technical cutaway and architecture notes

These values describe an idealized experiment, not supplier-approved hardware. Identical round magnets are held at fixed antiparallel axial orientations. Both faces of both disks are included. The 1.31 T starting point comes from Arnold’s N42SH grade table; uniform magnetization M ≈ Bᵣ/μ₀ is an additional approximation.

Enable the electrical model using supplied device coupling and capacitance

Leave this off while CIPS device data are missing. Off means a mechanical spring–damper model with no electrical branch, not a validated open-circuit CIPS cartridge. When on, entered coefficients are assumptions unless characterized for the actual device. The circuit is an AC resistor—not a rectifier, regulated bus or battery.

With x positive into compression and y the driver’s vertical position: Fₓ = −∂Uₘ/∂x; m ẍ + c ẋ + kx − θV = Fₓ; Cₚ V̇ + V/R + θẋ = 0. The reciprocal θ terms include electrical reaction on motion. Preload is a balanced static bias: x = 0 is the mechanical equilibrium before magnetic loading, with an equal opposing fixture force. The calculation begins at rest with magnetic field energy already present. Off-axis force can become attractive; it is not clipped to repulsion.

Magnetic driver power is (∂Uₘ/∂y)ẏ, including negative power on return. Stored energy E = ½m ẋ² + ½kx² + ½CₚV² + Uₘ. Signed input work − resistor energy − damping heat − ΔE should approach zero as the time step is refined. Resistor energy is ∫V²/R dt, not separate peak voltage multiplied by peak current. Displayed means include startup and are not steady-state ratings.

This numerical face integral assumes hard, uniformly magnetized cylinders in nonmagnetic surroundings. A 36-patch-per-face model is spot-checked against 144 patches at 15 positions; differences above 3% block results. This checks resolution, not the true field or every point on the path. Demagnetization, eddy currents, hysteresis, guide friction, driver inertia/motor loss, nonlinear CIPS response, leakage, fatigue and temperature dependence are excluded. Returned work is ideal mechanical return, not guaranteed recovered electricity. Signed net work is not purchased drive energy. No electrical or facility efficiency is claimed.

• UT Austin: magnetic surface-density formulation — basis for the face integral.
• Vokoun et al. (2009): uniformly magnetized cylinders — finite-cylinder theory/experimental context, not validation of this discretization.
• Erturk & Inman (2008): coupled piezoelectric harvester modeling — reciprocal coupling, not CIPS coefficients.
• Io et al. (2022): CIPS nanogenerator — material research, not a complete cartridge parameter set.
• Arnold N42SH material table — magnet material starting point.

Ferromagnetism / Ferromagnetismus (H. P. J. Wijn, editor; Springer, 1966) provides historical context through Keffer’s spin waves, Carr’s secondary effects and Döring’s micromagnetics chapters. The review used accessible contents, chapter summaries and two-page previews, not a full-chapter derivation. This original diagram is a teaching construction informed by that context and the modern sources below; it does not reproduce a book figure or implement its full theory.

Historical Gaussian/CGS conventions require care before using formulas in an SI model: distinguish B from H and magnetization, and check the definition and units of every coefficient. The display above uses unitless directions. Its tilt decays with a chosen exponential envelope; no exchange equation, spin-wave dispersion, thermal noise or energy dissipation is solved.

A useful engineering next step is a bounded material model feeding the larger force, motion and load calculation. NIST distinguishes equilibrium minimization from time-dependent LLG evolution; its convenient default damping is not automatically appropriate for material dynamics. Neither a more detailed animation nor a published magnetoelectric voltage coefficient establishes device power, efficiency or net energy creation.

• Springer front matter and contents; Keffer: Spin Waves; Carr: Secondary Effects; Döring: Mikromagnetismus. Historical sources, not WegaWomb measurements.
• NIST OOMMF energy terms and time evolvers. Modern numerical methods and input definitions.
• Vansteenkiste et al., MuMax3 author manuscript (published DOI: 10.1063/1.4899186). Verified micromagnetic software; its material examples do not supply WegaWomb parameters.
• Zong et al., Cellulose-based magnetoelectric composites (DOI: 10.1038/s41467-017-00034-4). A bonded cellulose/Metglas laminate driven by applied alternating and static magnetic fields; measured voltage response with a lock-in amplifier. This is evidence for strain coupling, not loaded carousel output or CIPS device performance.