Arc-Corona: Diverse Phenomena in Science

• Arc-Corona is a term that indexes diverse phenomena, ranging from plasma discharges and solar arcades to protostellar bow shocks and digraph products.
• It covers applications such as laser-induced corona discharge for arc suppression, formation of solar arcade structures, and mapping protostellar feedback in star-forming regions.
• Additionally, it formalizes a novel digraph product in graph theory and supports industrial monitoring through advanced multimodal detection techniques.

Arc-Corona denotes several technically distinct constructs across plasma physics, solar and stellar astrophysics, industrial hazard monitoring, and algebraic graph theory. In the surveyed literature, the term is associated with corona discharge that suppresses streamer-to-arc transition near high-voltage electrodes, with arc-shaped and double-arc structures in the solar corona, with an arc-like molecular bow shock in the Corona Australis cluster, and with the arc-corona product of digraphs. The common lexical elements are “arc” and “corona,” but the underlying objects differ substantially in ontology: electrical discharges, magnetically structured plasma, protostellar feedback morphologies, and graph products (Schubert et al., 2015, Reva et al., 2015, Ishiguro et al., 2017, Scott et al., 2018, Sabatini et al., 2024, Lee et al., 8 Feb 2025, Cavers et al., 17 Sep 2025).

1. Domains of use and technical scope

The surveyed usage separates naturally into four domains.

Domain	Object	Defining feature
Electrical discharge physics	corona associated with arc suppression	glow discharge neutralizes a high-voltage electrode
Solar and stellar astrophysics	arcs, arcades, double arcs, high-Q arcs	magnetic or shock-structured plasma morphology
Industrial robotics	arc-discharge hazard classes	Corona, Surface, Floating discharges in multimodal detection
Digraph theory	arc-corona product	one copy of a digraph attached to each arc or underlying edge

In discharge physics, the relevant phenomenon is a corona discharge around a high-voltage electrode that prevents an electrical arc by screening the local field. In solar physics, “arc” refers both to loop arcades and to topological high-Q arcs at the open-closed flux boundary, while “double arc” designates a pre-eruptive current-loop geometry in the low corona. In star-formation studies, an arc-like molecular structure in Corona Australis is interpreted as a bow shock driven by a protostellar jet. In digraph theory, the arc-corona is a graph product defined through systematic attachment of copies of a second digraph to arcs or symmetric arc pairs of a first digraph (Cavers et al., 17 Sep 2025).

This distribution of meanings suggests that Arc-Corona is not a single standardized technical term across disciplines. Rather, it indexes a family of domain-specific objects in which arc-like geometry, coronal structure, or arc-associated attachment is central.

2. Electrical arc suppression and corona-mediated neutralization

In the context of remote laser-triggered arc suppression, Arc-Corona refers to the ultraviolet-filament-induced glow discharge around a high-voltage electrode and the way in which that glow neutralizes the electrode so effectively that no streamer-to-arc transition can occur. Schubert et al. investigate narrow plasma channels formed in the filamentation of ultrashort laser pulses interacting with a DC high voltage. A femtosecond pulse of 14.5 mJ in 80 fs at 800 nm forms filaments with on-axis intensity clamped at $\sim 5\times 10^{13}\ \mathrm{W/cm^2}$, over a diameter of $\sim 100\ \mu\mathrm{m}$, generating a plasma channel several tens of centimeters long. The instantaneous free-electron density can reach $\gtrsim 10^{21}\ \mathrm{m^{-3}}$ and persists for a few microseconds before recombining (Schubert et al., 2015).

The physical mechanism is framed as a laser analogue of an ultra-corona generator. Each filament pulse deposits a high density of free electrons along its 20 cm length. Under the DC field $E_0$, electrons and then positive ions drift and expand laterally, forming a quasi-steady space-charge distribution $\rho(r)$ that reduces the peak field at the electrode surface below the streamer-initiation threshold of $\sim 30\ \mathrm{kV/cm}$ for a 1 cm sphere. The minimal mathematical picture includes electron continuity,

$$\frac{\partial n_e}{\partial t} + \nabla\cdot(n_e v_e) = S_i(E) - \alpha_{\rm att} n_e - \beta_{\rm rec} n_e n_i,$$

Poisson’s equation,

$$\nabla\cdot[\epsilon_0 \nabla \phi(r)] = \rho(r) = e[n_i(r)-n_e(r)],$$

and a resistance estimate

$$R_{\rm plasma} \simeq \frac{1}{e\mu_e}\int_0^L \frac{dr}{S\,\rho_e(r)}.$$

With $L=0.1\ \mathrm{m}$, $\sim 100\ \mu\mathrm{m}$0, $\sim 100\ \mu\mathrm{m}$1, and $\sim 100\ \mu\mathrm{m}$2, the resulting $\sim 100\ \mu\mathrm{m}$3 for a single pulse becomes $\sim 100\ \mu\mathrm{m}$4 at 1 kHz repetition, matching effective resistances deduced from experiment.

Experimentally, two stainless-steel spheres of 1.2 cm diameter were separated by gaps $\sim 100\ \mu\mathrm{m}$5 from 12 cm to 40 cm, with filament-to-electrode distances $\sim 100\ \mu\mathrm{m}$6 from 0.2 cm to 30 cm. At 100 kV across 12 cm, a few arcing events per second ceased immediately when the laser was turned on, replaced by a glow connecting electrode to filament. A 10 nF capacitor charged to $\sim 100\ \mu\mathrm{m}$7 kV unloaded exponentially with $\sim 100\ \mu\mathrm{m}$8 when $\sim 100\ \mu\mathrm{m}$9, corresponding to $\gtrsim 10^{21}\ \mathrm{m^{-3}}$0, rising linearly with $\gtrsim 10^{21}\ \mathrm{m^{-3}}$1 to $\gtrsim 10^{21}\ \mathrm{m^{-3}}$2 at 30 cm. Even at $\gtrsim 10^{21}\ \mathrm{m^{-3}}$3 cm, the neutralization time was $\gtrsim 10^{21}\ \mathrm{m^{-3}}$4, still an order of magnitude faster than the natural leakage. A common misconception is that a laser filament necessarily triggers discharges; these measurements show the opposite operational regime, namely arc prevention by corona-induced neutralization (Schubert et al., 2015).

3. Solar-coronal arcades and double-arc instability

In solar physics, one major usage concerns hot loop arcades observed in monochromatic Mg XII 8.42 Å imaging. Reva et al. report four arcade-formation episodes above the same polarity-inversion line between AR 09847 and AR 09848, on 28 February 2002 at 09:18, 14:13, and 22:28 UT, and on 1 March 2002 at 00:40 UT. The Mg XII line forms only at $\gtrsim 10^{21}\ \mathrm{m^{-3}}$5 MK, giving essentially zero cold-plasma background. The cadence was $\gtrsim 10^{21}\ \mathrm{m^{-3}}$6 s and the nominal spatial resolution was $\gtrsim 10^{21}\ \mathrm{m^{-3}}$7 with a small instrumental elongation in one axis. Each episode followed the same sequence: a compact hot precursor appeared near the edge of the future arcade, successive loops brightened one by one along the polarity inversion line, and the arcade then faded over approximately one hour. The total arcade length was $\gtrsim 10^{21}\ \mathrm{m^{-3}}$8 Mm, with 3–5 loops spaced by $\gtrsim 10^{21}\ \mathrm{m^{-3}}$9 Mm, and the filling of the full arcade took $E_0$0 min, implying

$E_0$1

Maximum loop intensity falls off roughly exponentially with distance from the precursor,

$E_0$2

Loop intensities decay over $E_0$3–35 min, and the overall arcade becomes invisible in Mg XII after $E_0$4 h (Reva et al., 2015).

The interpretation advanced there is that the arcades formed without visible changes in their magnetic structure and were probably heated by instabilities of a current sheet above the arcade, caused by an MHD wave excited by the precursor. Using the group-speed estimate

$E_0$5

with $E_0$6, $E_0$7 Mm, $E_0$8, and $E_0$9, the inferred vertical current-sheet scale is $\rho(r)$0 Mm. The absence of detectable photospheric field changes is therefore not evidence against reconnection; in this interpretation, the energy release is confined to a coronal current sheet above a stable bipolar region (Reva et al., 2015).

A second solar-coronal usage is the “double arc” of Ishiguro and Kusano. Here the sigmoidal pre-eruptive core field is modeled as a thin current loop made of two circular arcs rooted at $\rho(r)$1 and joined at $\rho(r)$2. The magnetic energy is

$\rho(r)$3

with equilibrium determined by

$\rho(r)$4

For three idealized external fields, the numerically found critical height is $\rho(r)$5, nearly independent of the decay of the overlying field. The resulting Double Arc Instability is therefore distinct from torus instability, which requires decay index $\rho(r)$6 for a thin torus. DAI can occur even in a uniform field. Its sufficient condition is expressed through

$\rho(r)$7

with $\rho(r)$8 for type 1, $\rho(r)$9 for type 2 with $\sim 30\ \mathrm{kV/cm}$0, and $\sim 30\ \mathrm{kV/cm}$1 for type 3. This formulation makes explicit that twist and tether-cutting reconnection act complementarily in destabilizing the pre-eruptive double arc (Ishiguro et al., 2017).

4. High-Q arcs and magnetic topology at the boundary of the closed corona

A different coronal usage concerns the S-web, the pattern of high-squashing-factor structures that separates open and closed flux in the solar corona. Global coronal field models, such as PFSS extrapolations, reveal high-Q volumes whose intersections with the outer boundary appear as narrow one-dimensional bands of very large $\sim 30\ \mathrm{kV/cm}$2, termed high-Q arcs. The squashing factor is defined from the field-line mapping Jacobian $\sim 30\ \mathrm{kV/cm}$3 by

$\sim 30\ \mathrm{kV/cm}$4

In practice, $\sim 30\ \mathrm{kV/cm}$5 is used, but the qualitative interpretation is the same: large $\sim 30\ \mathrm{kV/cm}$6 indicates strong divergence in magnetic connectivity (Scott et al., 2018).

Simple arc segments arise from hyperbolic flux tubes associated with narrow open-flux corridors; both ends of such arcs meet the global helmet-streamer polarity-inversion line. Detached or terminating arcs arise in a topologically different way, when a separatrix dome intersects the open-closed boundary and the dome footprint maps to a null whose outer spine reaches the open corona away from the helmet streamer apex. In that case, a finite segment of the open-closed boundary collapses to a single point on the source surface, and the high-Q arc terminates there. If several dome-related structures share the same null-spine footpoint, several high-Q arcs intersect at a vertex away from the helmet-streamer apex (Scott et al., 2018).

This topological distinction matters for interchange reconnection. Corridor-type structures support slipping-type transfer of closed-corona plasma into the wind, whereas null-fan geometries provide routes by which plasma on the inner spine can be expelled along the outer spine into the heliosphere. The proposed implication is that high-Q arc vertices identify locations preferential for the appearance of solar energetic particles or slow solar wind plasma with particular compositional signatures.

5. Arc morphology in the Corona Australis cluster

In the Corona Australis star-forming region, the relevant arc is not a coronal magnetic arcade but a molecular arc associated with protostellar feedback. High-resolution ALMA observations at 1.3 mm and 3 mm toward IRS7B reveal two elongated continuum structures defining a conical cavity with opening angle $\sim 30\ \mathrm{kV/cm}$7, together with a $\sim 30\ \mathrm{kV/cm}$8 au-long arc in CH$\sim 30\ \mathrm{kV/cm}$9OH at a projected $$\frac{\partial n_e}{\partial t} + \nabla\cdot(n_e v_e) = S_i(E) - \alpha_{\rm att} n_e - \beta_{\rm rec} n_e n_i,$$0 au from IRS7B. H$$\frac{\partial n_e}{\partial t} + \nabla\cdot(n_e v_e) = S_i(E) - \alpha_{\rm att} n_e - \beta_{\rm rec} n_e n_i,$$1CO emits both along the arc and inside the cone, while SiO peaks sharply on the eastern flank of the arc, identified as “wall B” at $$\frac{\partial n_e}{\partial t} + \nabla\cdot(n_e v_e) = S_i(E) - \alpha_{\rm att} n_e - \beta_{\rm rec} n_e n_i,$$2 au. Taking into account the association with a previously detected radio jet, the molecular arc is interpreted as the first revealed bow shock driven by IRS7B and the continuum strands as a two-sided dust cavity opened by the mass-loss process (Sabatini et al., 2024).

The quantitative derivations are based on optically thin dust continuum. With $$\frac{\partial n_e}{\partial t} + \nabla\cdot(n_e v_e) = S_i(E) - \alpha_{\rm att} n_e - \beta_{\rm rec} n_e n_i,$$3, gas-to-dust ratio $$\frac{\partial n_e}{\partial t} + \nabla\cdot(n_e v_e) = S_i(E) - \alpha_{\rm att} n_e - \beta_{\rm rec} n_e n_i,$$4, mean molecular weight $$\frac{\partial n_e}{\partial t} + \nabla\cdot(n_e v_e) = S_i(E) - \alpha_{\rm att} n_e - \beta_{\rm rec} n_e n_i,$$5 per H$$\frac{\partial n_e}{\partial t} + \nabla\cdot(n_e v_e) = S_i(E) - \alpha_{\rm att} n_e - \beta_{\rm rec} n_e n_i,$$6, and $$\frac{\partial n_e}{\partial t} + \nabla\cdot(n_e v_e) = S_i(E) - \alpha_{\rm att} n_e - \beta_{\rm rec} n_e n_i,$$7 K, the H$$\frac{\partial n_e}{\partial t} + \nabla\cdot(n_e v_e) = S_i(E) - \alpha_{\rm att} n_e - \beta_{\rm rec} n_e n_i,$$8 column density is estimated from

$$\frac{\partial n_e}{\partial t} + \nabla\cdot(n_e v_e) = S_i(E) - \alpha_{\rm att} n_e - \beta_{\rm rec} n_e n_i,$$9

yielding $$\nabla\cdot[\epsilon_0 \nabla \phi(r)] = \rho(r) = e[n_i(r)-n_e(r)],$$0 for the cavity walls. Summing surface density over the mapped area gives a mass of $$\nabla\cdot[\epsilon_0 \nabla \phi(r)] = \rho(r) = e[n_i(r)-n_e(r)],$$1 for each cavity wall. From the 1.3 mm to 3 mm flux ratio, and the 3 mm non-detection at $$\nabla\cdot[\epsilon_0 \nabla \phi(r)] = \rho(r) = e[n_i(r)-n_e(r)],$$2, the inferred lower limit on the dust spectral index is $$\nabla\cdot[\epsilon_0 \nabla \phi(r)] = \rho(r) = e[n_i(r)-n_e(r)],$$3. SiO is detected at blueshifted velocities $$\nabla\cdot[\epsilon_0 \nabla \phi(r)] = \rho(r) = e[n_i(r)-n_e(r)],$$4 to $$\nabla\cdot[\epsilon_0 \nabla \phi(r)] = \rho(r) = e[n_i(r)-n_e(r)],$$5 with broader profiles of FWHM $$\nabla\cdot[\epsilon_0 \nabla \phi(r)] = \rho(r) = e[n_i(r)-n_e(r)],$$6, while the arc component in CH$$\nabla\cdot[\epsilon_0 \nabla \phi(r)] = \rho(r) = e[n_i(r)-n_e(r)],$$7OH and H$$\nabla\cdot[\epsilon_0 \nabla \phi(r)] = \rho(r) = e[n_i(r)-n_e(r)],$$8CO has FWHM $$\nabla\cdot[\epsilon_0 \nabla \phi(r)] = \rho(r) = e[n_i(r)-n_e(r)],$$9. Abundance ratios in the arc, $$R_{\rm plasma} \simeq \frac{1}{e\mu_e}\int_0^L \frac{dr}{S\,\rho_e(r)}.$$0–600 and $$R_{\rm plasma} \simeq \frac{1}{e\mu_e}\int_0^L \frac{dr}{S\,\rho_e(r)}.$$1–130, are reported as typical of low-mass protostellar shocks (Sabatini et al., 2024).

The juxtaposition of “arc” and “Corona” here is therefore geographic rather than solar-physical: the arc lies in the Corona Australis cluster. A plausible implication is that lexical overlap with solar-coronal terminology can obscure the fact that the object is a bow shock in a protostellar envelope.

6. Industrial arc-hazard detection and the arc-corona product in digraphs

In industrial monitoring, arc-related “Corona” appears as a discharge class within a multimodal robotic detection system. A 2025 system integrates a BATCAM FX ultrasonic camera with 112 MEMS microphones at 96 kHz, a 640×480 RGB camera, onboard ROS computation, YOLOv5, delay-and-sum beamforming, STFT, Gamma Correction, and an Inception-style CNN. The classification task spans five classes: Corona, Surface, Floating discharges, Gas leak, and Background noise. Beamforming uses

$$R_{\rm plasma} \simeq \frac{1}{e\mu_e}\int_0^L \frac{dr}{S\,\rho_e(r)}.$$2

and the STFT employs a Hamming window with frame length $$R_{\rm plasma} \simeq \frac{1}{e\mu_e}\int_0^L \frac{dr}{S\,\rho_e(r)}.$$3 samples and hop $$R_{\rm plasma} \simeq \frac{1}{e\mu_e}\int_0^L \frac{dr}{S\,\rho_e(r)}.$$4, producing spectrogram blocks of size $$R_{\rm plasma} \simeq \frac{1}{e\mu_e}\int_0^L \frac{dr}{S\,\rho_e(r)}.$$5 after sliding-window segmentation. Gamma correction is applied as

$$R_{\rm plasma} \simeq \frac{1}{e\mu_e}\int_0^L \frac{dr}{S\,\rho_e(r)}.$$6

with $$R_{\rm plasma} \simeq \frac{1}{e\mu_e}\int_0^L \frac{dr}{S\,\rho_e(r)}.$$7 chosen experimentally. The Inception-style CNN has approximately 21,810 parameters and is trained with categorical crossentropy over the five classes. Reported performance includes 99% gas-leak detection accuracy, Corona discharge classification with F1-score $$R_{\rm plasma} \simeq \frac{1}{e\mu_e}\int_0^L \frac{dr}{S\,\rho_e(r)}.$$8, up to $$R_{\rm plasma} \simeq \frac{1}{e\mu_e}\int_0^L \frac{dr}{S\,\rho_e(r)}.$$9 percentage-point improvement over raw-waveform and prior spectrogram baselines in noisy or reverberant tests, and onboard inference time of 2.1 s per task (Lee et al., 8 Feb 2025).

In graph theory, the arc-corona is a formal product of digraphs. For the symmetric-arc-corona $L=0.1\ \mathrm{m}$0, one introduces a fresh copy of $L=0.1\ \mathrm{m}$1 for each undirected edge $L=0.1\ \mathrm{m}$2, where $L=0.1\ \mathrm{m}$3 is the underlying graph of $L=0.1\ \mathrm{m}$4, and joins both $L=0.1\ \mathrm{m}$5 and $L=0.1\ \mathrm{m}$6 bidirectionally to every vertex in that copy. The adjacency matrix has the block form

$L=0.1\ \mathrm{m}$7

and the corresponding characteristic polynomial factorization is

$L=0.1\ \mathrm{m}$8

where the digraph coronal is

$L=0.1\ \mathrm{m}$9

Parallel Schur-complement formulas are given for the Laplacian and signless Laplacian. For example, when $\sim 100\ \mu\mathrm{m}$00, the forward-arc-corona satisfies

$\sim 100\ \mu\mathrm{m}$01

This is a purely combinatorial use of the expression, unrelated to plasma or astrophysical coronae, and it formalizes “arc-corona” as an attachment operation indexed by arcs or symmetric arc pairs (Cavers et al., 17 Sep 2025).