JonoThora: Psionics expansion (01a + 01b): content authored / LaTeX-restored per local submodule; lint-clean.

2026-05-11T20:51:02Z

Psionics expansion (01a + 01b): content authored / LaTeX-restored per local submodule; lint-clean.

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= Near-Field Electromagnetics =

{{Audience_Sidebar
| difficulty = Intermediate
| reading_time = 7 minutes
| prerequisites = Maxwell's equations; basic antenna concepts; wavelength and frequency.
| if_too_advanced_see = [[Psionic_Device_Overview]]
| if_you_want_the_math_see = This page; [[Reactive_Near_Field]]; [[Antenna_Theory_for_Psionic_Devices]]
}}

{{Notation
| signature = Non-relativistic; SI units throughout.
| units = E (V/m); H (A/m); B (T); λ (m); D = largest antenna dimension (m); k = 2π/λ.
}}

'''Near-field electromagnetics''' is the branch of electromagnetic theory concerned with the fields near an antenna or radiating element — distances comparable to or smaller than a wavelength. In contrast to '''far-field''' (radiation-zone) behaviour, near-field fields exhibit:

* Strong stored (non-radiated) energy.
* E and H mutually out of phase.
* Faster than r−1 spatial decay (r−2, r−3 terms).
* Direct inductive/capacitive coupling to nearby matter.

These properties make the near field the operational regime for [[Psionic_Device_Overview|psionic devices]] such as [[HelmKit]] — devices that must couple strongly to nearby biological tissue (a few cm distant) while minimising far-field radiative exposure.

== Field-zone boundaries ==

For an antenna of largest dimension D operating at wavelength λ = c / f, the EM field is conventionally divided into three zones:

| Zone | Range | Field character | Energy state |
|---|---|---|---|
| Reactive near-field | 0 < r < 0.62·√(D3/λ) | E and H ~90° out of phase; r−3 behavior | Stored |
| Radiating near-field (Fresnel) | 0.62·√(D3/λ) ≤ r < 2D2/λ | E and H phase-aligning; r−2 | Mix |
| Far-field (Fraunhofer) | r ≥ 2D2/λ | E ⊥ H ⊥ propagation; plane wave; r−1 | Radiated |

The transition wavelength-distance r = 2D2/λ defines the boundary at which the antenna's emitted wave can be treated as a plane wave — the standard far-field idealisation.

== Worked examples at 2.45 GHz ==

The 2.45 GHz ISM band is the standard operating frequency for many [[HelmKit]]-class devices (chosen because of regulatory allowance and the availability of standard hardware).

At f = 2.45 GHz: λ = c/f = 0.1224 m = 12.24 cm.

=== D = 5 cm coil (HelmKit-typical) ===

* Reactive boundary: 0.62 · √(0.053/0.1224) ≈ 6.3 cm.
* Fresnel boundary: 2 · 0.052/0.1224 ≈ 4.1 cm.

The Fresnel boundary is '''smaller''' than the reactive boundary — a sign that the antenna is '''electrically small''' (D ≪ λ) and the standard boundary formulas no longer cleanly separate the zones. Essentially the entire local field is reactive.

=== D = 10 cm coil ===

* Reactive: ~ 5.6 cm.
* Fresnel: ~ 16.3 cm.
* Far-field begins at r ≈ 16 cm.

=== D = 50 cm dish ===

* Reactive: ~ 63 cm.
* Fresnel: ~ 4.1 m.
* Far-field begins at r ≈ 4 m — a real beam emerges at this scale.

== Why the reactive zone matters ==

The reactive near-field is where:

# '''Inductive/capacitive coupling''' to nearby matter is strongest. For a coil near a brain, the coil's stored magnetic energy couples directly into the brain tissue via mutual inductance.
# '''EM energy is stored, not radiated'''. High field amplitudes can be achieved per unit input power. A 100 mW source can produce locally large E-fields without significant radiated power.
# '''Field can be spatially shaped''' with higher precision than the diffraction-limited far-field. Sub-wavelength field structures are easily made in the reactive zone.

For psionic-device design, '''operate in the reactive zone''' to maximise coupling to biological tissue while minimising radiative loss and far-field exposure (which would otherwise expand the regulatory compliance burden).

== Electrically small antennas ==

When D ≪ λ — the regime of compact wearable devices — the antenna is '''electrically small''' and obeys different scaling laws. See [[Antenna_Theory_for_Psionic_Devices]] for the Chu-Harrington bound, Wheeler radiation resistance, and related limits.

For a 5 cm coil at 2.45 GHz (ka ≈ 1.28), the antenna sits at the boundary between electrically small and resonant. For deeper near-field operation, lower the operating frequency to ~ 300-500 MHz (or larger coils at 2.45 GHz).

== Coupling to ψ in the near field ==

In the [[Psionics|framework]]:

* The ψ-source Jψ = α FμνFμν is proportional to E2 − c2B2 locally.
* In the reactive near-field, both E and B are large; their product FμνFμν ≠ 0.
* Per-volume ψ-source density can exceed far-field by '''factors of 102-104''' at typical near-field amplitudes.
* This is the rationale for near-field operation of psionic devices: high-efficiency ψ-source per watt of input power.

== Safety ==

The reactive near-field is also the regime of highest [[Psionic_Device_Safety|biological exposure risk]]. See [[SAR_Calculation_for_Psionic_Devices]] for the ICNIRP/IEEE compliance framework: the localised SAR limit (2.0 W/kg over 10 g of head tissue) demands strict control of near-field E-amplitudes.

== Sanity checks ==

* '''r ≫ 2D2/λ''' → recovers standard far-field plane-wave radiation. ✓
* '''Static limit (f → 0)''' → reactive near-field becomes pure inductive/electrostatic. ✓
* '''ψ → 0''' (in framework) → standard near-field EM intact; no ψ-coupling. ✓ ([[Sanity_Check_Limits]] §6.)

== See Also ==

* [[Reactive_Near_Field]]
* [[Antenna_Theory_for_Psionic_Devices]]
* [[Caduceus_Coil]]
* [[Bifilar_Coil]]
* [[Double-Helix_Antenna]]
* [[Psionic_Device_Overview]]
* [[HelmKit]]
* [[Psionic_Device_Safety]]

== References ==

* Balanis, C. A. (2016). ''Antenna Theory: Analysis and Design.'' 4th ed., Wiley.
* Pozar, D. M. (2011). ''Microwave Engineering.'' 4th ed., Wiley.
* Kraus, J. D. (1988). ''Antennas.'' 2nd ed., McGraw-Hill.

[[Category:Psionics]]
[[Category:Electromagnetism]]
[[Category:Antenna Theory]]

Near Field Electromagnetics - Revision history

JonoThora: Psionics expansion (01a + 01b): content authored / LaTeX-restored per local submodule; lint-clean.