Reactive Near Field

Reactive Near-Field

Audience

Difficulty	Intermediate

Notation on this page

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:

$ 0<r<0.62\,{\sqrt {D^{3}/\lambda }} $

— with D the largest antenna dimension and λ = c/f the operating wavelength. This is the dominant operating regime for HelmKit and other 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:

$ \mathbf {B} (r)={\frac {\mu _{0}}{4\pi }}\,{\frac {3(\mathbf {m} \cdot {\hat {\mathbf {r} }})\,{\hat {\mathbf {r} }}-\mathbf {m} }{r^{3}}} $

— 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 u_B = 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 (ε_r ~ 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 F_μνF^μν = (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:

1. High local field per watt — stored energy gives large E and B amplitudes for a given input power.
2. Low far-field radiation — reduces RF interference and regulatory compliance burden.
3. Confined coupling region — the field is localised to within a few cm of the coil.
4. 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 J_ψ 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.