Add open question: bulk plasma motion inside spark channel
Catalogs what is known (radial expansion, buoyancy, electron/ion drift,
ion wind) vs unknown (net axial flow under AC drive, tip gas dynamics,
acoustic signatures). Prompted by external reviewer question.
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
@ -114,6 +117,26 @@ I_branch proportional to d_branch^1.5
```
This follows from the assumption that current density scales with cross-sectional area and conductivity scales with temperature (which scales with diameter for a given total power). The exponent 1.5 is intermediate between the area scaling (exponent 2) and the linear scaling. This model has not been validated against measurements.
### 1.5 Bulk Plasma Motion Inside the Channel
The framework models the spark channel as a stationary conductor with time-varying resistance. It does not address the motion of the plasma itself — either the charged particle drift or the bulk neutral gas flow. Several distinct motions are known or expected:
**What we know:**
- **Radial expansion** [T1]: When the channel heats rapidly, the gas expands outward against surrounding cold air. Bazelyan measured initial expansion rate ~100 m/s, dropping to ~2 m/s at pressure equilibrium. The channel reaches pressure balance within microseconds; after that, hot gas is less dense but at ambient pressure. For lightning return strokes, this expansion launches a cylindrical shock wave (thunder). [Bazelyan & Raizer 2000, Ch 4, p. 167]
- **Buoyancy-driven convection** [T1]: Hot channel gas rises. This is the primary mechanism extending leader persistence beyond pure thermal diffusion (see [[thermal-physics]] Section 1). Vertical or upward-angled sparks maintain a hot column for seconds; horizontal sparks lose coherence as the column rises and disconnects.
- **Electron and ion drift** [T0]: Electrons drift toward the positive end of the field, ions toward the negative end. In a TC's AC field, directions reverse every half-cycle. Electron mobility is ~400x higher than ion mobility (mu_e = 600 cm^2/(V*s) vs mu_i = 1.5 cm^2/(V*s) [Bazelyan & Raizer 2000]). On the RF timescale (1-10 us half-period), ions are essentially stationary while electrons carry the current.
- **Ion wind / electric wind** [T1 general; T4 for TC channels]: Ions colliding with neutrals transfer momentum, driving bulk gas flow at ~100 m/s in the drift direction. Well-documented in corona/ESP applications [Becker et al. 2005, Ch 9, pp. 581-583]. In a TC streamer crown, positive ions left behind by the fast-moving electron front drive neutral gas outward from the topload.
**What we do not know:**
- **Net axial bulk flow in a leader channel during AC operation** [T4]: The AC reversal complicates the picture. Ion wind reverses every half-cycle — does it cancel to zero net axial flow, or does some asymmetry (positive vs negative streamer dynamics, polarity-dependent attachment rates) create a net drift? No measurements or models address this for TC sparks.
- **Gas flow at the propagating tip** [T3]: As each new streamer segment heats and expands to become leader, the expansion should displace gas forward (outward from the topload). This creates a transient outward flow at the leader-streamer boundary. Whether this contributes meaningfully to propagation or is negligible compared to the photoionization-driven advance is unknown.
- **Acoustic effects of channel motion** [T3]: The radial expansion produces acoustic signatures. Whether axial flows (if any) contribute to the characteristic sound of different operating modes is unexplored.
- **Effect on channel straightness** [T4]: If there is net axial gas flow, it could contribute to (or detract from) the straightness of QCW sword sparks by stabilizing (or destabilizing) the thermal column.
**Why this matters:** If significant bulk gas motion exists inside the channel, it could affect heat transport (convective enhancement of axial thermal conduction), mass transport (fresh gas swept into hot regions), and channel stability. The current framework implicitly assumes the gas is stationary except for radial diffusion and buoyancy, which may miss important physics.
