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= Reactive Near-Field =

{{Audience_Sidebar
| difficulty = Intermediate
| reading_time = 5 minutes
| prerequisites = [[Near_Field_Electromagnetics]]; Maxwell's equations.
| if_too_advanced_see = [[Near_Field_Electromagnetics]]
| if_you_want_the_math_see = This page
}}

{{Notation
| signature = Non-relativistic; SI.
| units = E (V/m); H (A/m); D = largest antenna dimension (m); λ = wavelength (m).
}}

The '''reactive near-field''' is the innermost EM zone surrounding an antenna or radiating element — the region where electromagnetic energy is '''stored''' rather than radiated. It is defined by:

:<math>0 < r < 0.62\,\sqrt{D^3/\lambda}</math>

— with D the largest antenna dimension and λ = c/f the operating wavelength. This is the dominant operating regime for [[HelmKit]] and other [[Psionic_Device_Overview|psionic devices]] designed to couple strongly to nearby biological tissue.

== Field structure ==

In the reactive near-field:

* '''E and H are ~90° out of phase''' — energy oscillates between electric and magnetic stores, like the resonance of an LC circuit rather than propagating as a wave.
* '''Spatial decay is r−3 for dipoles''' (electrostatic-like and magnetostatic-like terms), faster than the r−1 decay of the far-field.
* '''The Poynting vector P = E × H is reactive (imaginary)''' — no net energy flux outward; energy circulates.
* The fields are large in amplitude relative to the far-field for the same input power, because energy is not lost to radiation.

== Dominant coupling mechanism ==

The reactive zone is where '''inductive/capacitive coupling to matter is strongest'''. A coil in this zone behaves more like the primary of a transformer than like a radiator: nearby conductive or polarisable matter (the brain) absorbs energy via mutual-inductance and dielectric coupling.

For an electrically-small coil with magnetic moment '''m''', the near-zone magnetic field at distance r is:

:<math>\mathbf{B}(r) = \frac{\mu_0}{4\pi}\,\frac{3(\mathbf{m}\cdot\hat{\mathbf{r}})\,\hat{\mathbf{r}} - \mathbf{m}}{r^3}</math>

— the same form as a static magnetic dipole. This is the quasi-static limit of the radiating dipole, valid in the reactive zone.

== Energy storage ==

The reactive zone stores energy in the field. For a single-turn loop with current I, magnetic moment m = NIA (N turns, area A), the stored energy density is uB = B2/(2μ0). Integrating over the near-field volume gives the inductive stored energy:

W = (1/2) L I2

— where L is the coil's self-inductance. In the reactive zone, this stored energy '''does not radiate away''' — it cycles back and forth between the source and the field at every cycle.

For a 5 cm coil at 2.45 GHz, the stored energy per cycle can be 100×–1000× larger than the radiated energy per cycle, depending on the antenna's radiation Q (see [[Antenna_Theory_for_Psionic_Devices]] §Chu-Harrington bound).

== Penetration into biological tissue ==

For a coil placed against a human head:

* Magnetic field penetrates with little attenuation — H continues across tissue boundaries (the magnetic susceptibility of tissue is ~ 1, so μ ≈ μ0).
* Electric field is reduced by the tissue's dielectric constant (εr ~ 40 for brain at 2.45 GHz) and ohmically dissipated via σ|E|2/ρ — see [[SAR_Calculation_for_Psionic_Devices]].
* The induced eddy currents create local heating (the SAR concern) and a complex internal E-field distribution.

For ψ-coupling the relevant quantity is the local FμνFμν = (E2 − c2B2)/2 inside the tissue, '''not the externally applied E or B'''.

== Engineering implications ==

For [[HelmKit]] design, the reactive-near-field regime is preferred because:

# '''High local field per watt''' — stored energy gives large E and B amplitudes for a given input power.
# '''Low far-field radiation''' — reduces RF interference and regulatory compliance burden.
# '''Confined coupling region''' — the field is localised to within a few cm of the coil.
# '''Direct inductive coupling''' — bypasses the radiation impedance mismatch of free-space EM.

The cost: '''near-field exposure is also the regime of highest SAR'''. Compliance requires strict E-amplitude limits (≲ 30 V/m rms in brain tissue). See [[Psionic_Device_Safety]].

== Coupling to ψ ==

The reactive near-field is the framework's preferred ψ-source regime:

* High local F2 → high Jψ per unit volume.
* The stored (rather than radiated) energy state means '''each oscillation cycle has another chance to couple to ψ''' rather than losing energy to outgoing radiation.
* The volume of coupling is sub-wavelength — well-matched to mm-scale microtubule networks and nanometer-scale exciton arrays in tubulin.

== Sanity checks ==

* '''r → 0''' (very close to source) → standard near-field dipole formulas apply. ✓
* '''r ≫ 2D2/λ''' → energy stored vanishes; only radiated energy remains. ✓
* '''ψ → 0''' (in framework) → reactive near-field is standard EM; no extra coupling. ✓ ([[Sanity_Check_Limits]] §6.)

== See Also ==

* [[Near_Field_Electromagnetics]]
* [[Antenna_Theory_for_Psionic_Devices]]
* [[Caduceus_Coil]]
* [[Bifilar_Coil]]
* [[Psionic_Device_Safety]]
* [[SAR_Calculation_for_Psionic_Devices]]

== References ==

* Balanis, C. A. (2016). ''Antenna Theory: Analysis and Design.'' 4th ed., Wiley.
* Pozar, D. M. (2011). ''Microwave Engineering.'' 4th ed., Wiley.
* Jackson, J. D. (1999). ''Classical Electrodynamics.'' 3rd ed., Wiley.

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

Reactive Near Field - Revision history

JonoThora: Phase N (01b): LaTeX restoration — promote Unicode display-math to ; lint-clean per tools/wiki_latex_lint.py

JonoThora: Phase N (01b): LaTeX restoration — promote Unicode display-math to $; lint-clean per tools/wiki_latex_lint.py$