---
title: Microwave Anapole Line-Jet Reactors
url: https://www.emergentmind.com/topics/microwave-anapole-line-jet-reactors
type: topic
---

# Microwave Anapole Line-Jet Reactors

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 [2311.00572, 2503.20059].

## 1. Device Architecture and Fabrication

Microwave anapole line-jet reactors are realized using hybrid 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 [2311.00572, 2503.20059].

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 [2311.00572]     | Line-Jet [2503.20059]  |
|---------------------|---------------------------------|------------------------|
| 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 [2311.00572, 2503.20059]. Eigenmode simulations yield Q-factors $Q\approx256$ at 2.45 GHz for a disk jet [2311.00572], and experimentally 960 MHz resonance for a 20 mm line-jet [2503.20059]. 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 [2503.20059]. 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 [2311.00572]. 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, 2311.00572) or $P_{\rm in}\approx4$ W (line-jet, 2503.20059). 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 [2311.00572]. 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 ($\rm{Re} > 2000$) [2503.20059]. 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 [2503.20059].

| Metric         | Disk-Jet [2311.00572] | Line-Jet [2503.20059]           |
|----------------|-----------------------|----------------------------------|
| $n_e$ [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 [2311.00572, 2503.20059].

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 [2503.20059].
- 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 [2311.00572].

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 [2311.00572, 2503.20059]. 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 [2503.20059]. 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 [2311.00572, 2503.20059].

Source: https://www.emergentmind.com/topics/microwave-anapole-line-jet-reactors