Microwave Anapole Line-Jet Reactors

• Microwave anapole line-jet reactors are planar plasma sources that employ engineered anapole modes in hybrid metallo-dielectric structures to focus microwave energy and ionize process gases efficiently.
• They achieve high electron densities and uniform plasma jets at low gas temperatures through precise slot geometries, split-ring resonators, and scalable PCB-compatible fabrication.
• Near-field enhancement via destructive interference between electric and toroidal dipoles enables efficient plasma ignition and energy absorption efficiencies approaching unity.

Microwave anapole line-jet reactors are planar plasma sources that employ non-radiating electromagnetic resonances—specifically, anapole modes—within sub-wavelength dielectric resonators to generate spatially extended plasma jets. This approach leverages the suppression of far-field radiation via destructive interference between electric and toroidal dipoles, concentrating microwave fields at the plasma outlet to efficiently ionize process gases. Microwave anapole line-jet reactors deliver uniform, high-density plasma lines with low gas temperatures and high efficiency, and are amenable to compact, PCB-based fabrication and large-area integration (Akram et al., 2023, Akram et al., 25 Mar 2025).

1. Device Architecture and Fabrication

Microwave anapole line-jet reactors are realized using @@@@2@@@@ metallo-dielectric structures with slot and split-ring features engineered for anapole resonance. The dielectric resonator typically consists of a Rogers TMM13i cylinder (relative permittivity $\epsilon_r = 13.0$, $\tan\delta = 1.9 \times 10^{-3}$) with thickness $h \approx 3.81$ mm and radii $r = 11$–14 mm, copper-clad on top and bottom. The resonator is coupled to a planar feed board (Rogers TMM6, $\epsilon_r = 6.0$) via a 50 $\Omega$ microstrip that is slot-coupled to the dielectric disc. A key element is the formation of a gas-outlet valley (e.g., 20 mm $\times$ 0.1 mm slot) and the inclusion of split-ring resonator (SRR) copper islands, each shorted with vias to establish two anti-phase electric-dipole resonances (Akram et al., 2023, Akram et al., 25 Mar 2025).

Assembly employs lithographic patterning and precision-drilled vias; a 3D-printed high-temperature resin channel (inlet $\diameter = 5$ mm, outlet $20$ mm $\times$ $0.6$ mm, wall thickness $0.2$ mm) guides the process gas (He) to the exit slot. The result is a fully planar, PCB-compatible module with typical in-plane device dimensions of $40$ mm $\times$ $40$ mm.

Parameter	Dielectric Jet (Akram et al., 2023)	Line-Jet (Akram et al., 25 Mar 2025)
Disc material	TMM13i ($\epsilon_r=13$)	TMM13i ($\epsilon_r=13$)
Feed PCB	TMM6 ($\epsilon_r=6$)	TMM6 ($\epsilon_r=6$)
Slot length	8.83 mm	20 mm
SRR via separation	$s=1.2$ mm	$s=1.2$ mm

Fabrication exploits standard PCB technology and allows scaling to arrays by edge-joining modules and interlocking gas manifolds.

2. Anapole Resonance Physics

The distinctive feature of these reactors is excitation of an anapole mode—a non-radiating configuration achieved when two spatially coincident electric dipole moments oscillate out of phase, canceling their radiation fields in the far field yet enhancing local near fields. The anapole condition is written:

$\mathbf{P} + i k \mathbf{T} = 0$

with $\mathbf{P}$ the electric dipole moment and $\mathbf{T}$ the toroidal dipole moment:

$$\mathbf{P} = \frac{1}{-i\omega} \int \mathbf{J}(\mathbf{r}) d^3\mathbf{r}, \quad \mathbf{T} = \frac{1}{10c} \int [(\mathbf{r}\cdot\mathbf{J})\mathbf{r} - 2 r^2 \mathbf{J}] d^3\mathbf{r}$$

Engineering two nearly degenerate, anti-phase electric dipole resonances (via SRR for metallic and HE$_{11\delta}$ for the dielectric) suppresses radiative losses, trapping microwave energy in subwavelength volumes (Akram et al., 2023, Akram et al., 25 Mar 2025). Eigenmode simulations yield Q-factors $Q\approx256$ at 2.45 GHz for a disk jet (Akram et al., 2023), and experimentally 960 MHz resonance for a 20 mm line-jet (Akram et al., 25 Mar 2025). Power coupling efficiency $\eta_{\rm couple} = 1-|S_{11}|^2 \approx 99.9\%$ indicates nearly all source power is delivered to the anapole.

3. Near-Field Enhancement and Plasma Ignition

At resonance, the E-field near the gas-exit slot is sharply intensified—simulations and experiment demonstrate $|E(x)|\sim10^6$ V/m for 1 W input along a 2 cm line (Akram et al., 25 Mar 2025). For the dielectric jet, $|E|_{\rm max} \sim 1.4 \times 10^5$ V/m is observed at the aperture at 1 W, scaling up with input power and Q-factor (Akram et al., 2023). This large near-field amplification—factor $10^2$–$10^3$ relative to the feed—enables breakdown of helium at atmospheric pressure, requiring only $E_{\rm breakdown}\approx 3 \times 10^5$ V/m over 0.5 mm gaps.

Plasma ignition is observed at $P_{\rm in}\approx2.7$ W (disk-jet, (Akram et al., 2023)) or $P_{\rm in}\approx4$ W (line-jet, (Akram et al., 25 Mar 2025)). After ignition, plasma conductivity shifts the resonant response, and sustaining power can drop as low as 1 W. Under laminar flow conditions, plasma length and stability are maintained with input power and flow as tunable parameters.

4. Plasma Jet Properties and Operational Metrics

Electron density ($n_e$) is measured using Stark broadening of the H$\alpha$ line (656.28 nm):

$$n_e~(\textrm{cm}^{-3}) = 10^{17} \left(\frac{\Delta\lambda_{\rm Stark}}{1.098}\right)^{1.47135}$$

In the disk-jet, $n_e \approx 1.55 \times 10^{16}$ cm$^{-3}$ at 15 W, 5 slpm He (Akram et al., 2023). For the 20 mm line-jet, $n_e \approx 1.2 \times 10^{16}$ cm$^{-3}$ at 5.5 W, 1 slpm He; peak $n_e$ is sustained even at high flows (up to 30 slpm) before dropping in the turbulent regime ($\rm{Re} > 2000$) (Akram et al., 25 Mar 2025). Jet length scales with flow: at 2.7 W, 1 slpm helium, length is $5$–$7$ mm (disk-jet); for the line-jet, a continuous 20 mm plasma line forms for flows $>20$ slpm.

Gas temperature ($T_g$), estimated from N$_2^+$ rotational bands, is $300$–$350$ K, supporting a cold plasma regime at 1–40 slpm and up to 30 W input (Akram et al., 25 Mar 2025).

Metric	Disk-Jet (Akram et al., 2023)	Line-Jet (Akram et al., 25 Mar 2025)
$n_e$ [cm$^{-3}$]	$1.6\times10^{16}$	$1.2\times10^{16}$ (20 mm line)
$T_g$ [K]	$315$–$350$	$300$–$350$
Ignition Power [W]	$2.7$	$4$ (20 mm slot)

Power absorption efficiency $$\eta = (P_{\rm in} - P_{\rm refl} - P_{\rm rad}) / P_{\rm in}$$ reaches $94\%$ at 1.5 W for disk jets, and approaches unity for line-jets (Akram et al., 2023, Akram et al., 25 Mar 2025).

Compared to conventional cavity-based plasma jets (P$_{\rm in} \gtrsim 15$–100 W, $n_e \sim 10^{14}$–$10^{16}$ cm$^{-3}$, point/needle plasma), the anapole line-jet achieves $n_e \sim 10^{16}$ cm$^{-3}$ at $4$–$27$ W over 20 mm, with low $T_g$ and without need for metallic enclosures or non-planar assemblies.

5. Tunability, Arrays, and Scaling Laws

Frequency tuning is achieved by modifying geometric and material parameters of the dielectric disk and SRR:

• Varying the disk radius $r$, thickness $h$, and slot length directly tunes the anapole frequency $f_0$. Empirically, $f_0 \propto 1/L_{\rm eff}\sqrt{\epsilon_r}$, with $L_{\rm eff}$ the effective slot length (Akram et al., 25 Mar 2025).
• Changing the SRR configuration adjusts the dipole mode overlap and thus the bandwidth for anapole excitation.
• Swap-in of substrates with different $\epsilon_r$ enables additional tuning (shift by tens of MHz).
• Lumped capacitors ($0.3$–$0.7$ pF, at slot edges) permit $1.6$–$2.5$ GHz tuning range in disk-jets (Akram et al., 2023).

Integration into arrays requires element spacing $d_{\rm array} \leq 0.5\lambda_{\rm res}$ (yet $\geq 0.3\lambda$ to avoid destructive coupling) to ensure overlapping near fields merge, producing continuous plasma curtains. Electrical feed is distributed via planar microstrip splitters with matched electrical paths.

The near-field sum for $N$ jets governs field uniformity:

$$E_{\rm total}(x) \approx \sum_n E_n \exp(-|x-x_n|/\delta)$$

with $\delta \sim 1$–$2$ mm the near-field decay length. Line length scaling requires disc/ring geometry supporting higher-order HE$_{1n\delta}$ modes.

6. Applications and Future Directions

The spatially extended, uniform plasma output of anapole line-jet reactors is suited to large-area surface treatment, rapid material processing, plasma-enabled disinfection, and low-temperature etching in ambient air (Akram et al., 2023, Akram et al., 25 Mar 2025). Uniform jet flux, low operating temperature, and scalable integration support roll-to-roll processing and large-pattern plasma treatment in thin-film manufacturing, microfluidic catalysis, and polymer activation.

Biomedical uses include wound disinfection over extended regions with uniform, low-temperature plasma, free of localized hot spots. The high-gradient E-field ($10^6$ V/m) presents opportunities for direct electron injection in accelerator plasma wakefield staging. Arrays are suitable for in situ micro-thrusters for satellite propulsion (He/Xe mixtures), and local chemical synthesis (e.g., NO, O$_3$ generation).

Future development opportunities include:

• Higher Q-cylinder design and low-loss dielectrics ($\epsilon_r \sim 20$, $\tan\delta < 10^{-3}$) for miniaturization and higher fields.
• Active, real-time frequency tuning via varactor or MEMS capacitors.
• Fabrication of sub-$100\,\mu$m slots via laser patterning for high-resolution plasma lines.
• Higher-order anapole modes for mm-scale line arrays and contiguous plasma sheets.
• Integration with fluidic channels for on-chip gas mixtures and modular array assembly.

7. Performance Comparison and Limitations

Microwave anapole line-jet reactors present a twofold increase in electron density per watt compared to conventional cavity jets ($n_e / P_{\rm in} \approx 2 \times 10^{15}$ cm$^{-3}/$W for line-jets), with energy per unit length as low as $0.2$ W/mm for 20 mm jets (Akram et al., 25 Mar 2025). Power efficiency approaches unity at low power; temperature rise is limited to $\sim50$ K even over $30$ W. The open, PCB-compatible architecture is unique, providing operation free from metallic cavity constraints.

Limitations include: necessity for precise slot and disc dimensions to maintain uniform fields along extended slots; plasma uniformity is sensitive to gas flow profile and turbulence (onset near Re $= 2000$); and scalability to longer lines is restricted by the dielectric’s ability to support higher-order modes without modal disruption.

Overall, microwave anapole line-jet reactors represent a significant advance in the generation of cold, uniform, and energy-efficient plasma jets within a compact, scalable format (Akram et al., 2023, Akram et al., 25 Mar 2025).