Streamer self-focusing in an external longitudinal magnetic field

The numerical simulation of the development of a streamer discharge in a gap with an external longitudinal magnetic field was used to demonstrate the self-focusing of such discharges. Self-focusing is caused by a sharp deceleration of the radial ionization wave due to a change in the electron energy distribution function, a decrease in the average electron energy, the rate of gas ionization, and the electron mobility in crossed electric and magnetic fields as compared to the case of the discharge development without a magnetic field. The self-focusing effect of a streamer discharge in an external longitudinal magnetic field is observed for both positive and negative pulse polarities. The paper proposes an estimate of the critical value of the magnetic field, which makes it possible to control the development of pulsed high-voltage discharges at various gas pressures.

Figure 1

Discharge gap geometry (left) and adaptive computational mesh (right). Left: The plane high-voltage electrode had a radius of $R=100$ mm and was located at $Z=8$ mm (marked by red). The tip of the high-voltage electrode needle was located at $Z=20$ mm. The grounded plane electrode (black) was located at $Z=150$ mm. The computational domain had a size of $150\times 150\mathrm{m}{\mathrm{m}}^2$ above $Z$ axis (gray mesh). Right top: The contours of the electric field of the positive streamer 40 ns after the start of the high-voltage pulse. $P=50$ Torr, $T=293$ K, $U=+20$ kV, $\mathrm{C}{\mathrm{O}}_2$. Right bottom: The adaptive computational mesh (every 10th cell is shown).

Figure 2

Electron momentum cross section and Hall parameter versus electron energy for $\mathrm{C}{\mathrm{O}}_2$ at $P=50$ Torr and $B=1$ T.

Figure 3

Electron energy distribution functions in $\mathrm{C}{\mathrm{O}}_2$ for $E/n=300$ Td, $P=50$ Torr, and various values of magnetic field. The electric and magnetic fields are perpendicular to each other.

Figure 4

(a) Mean electron energy versus $E$/$n$ for $\cos \left(\alpha \right)=0$ and different $B$. (b)–(d) Ionization rate coefficient $k_i$ and electron mobility along the magnetic field vector (${\mu }_Z$) and across the magnetic field vector (${\mu }_R$) versus $\cos \left(\alpha \right)$ for $B=3$ T and different $E$/$n$ (scales in Td).

Figure 5

Spatial electric field distribution during the development of a positive streamer for $B=0$ (left) and $B=3$ T (right). Left scale: 0–0.85 MV/m. Right scale: 0–1.7 MV/m. $P=50$ Torr, $\mathrm{C}{\mathrm{O}}_2$, $U=+20$ kV. Numbers are time in nanoseconds.

Figure 6

Temporal evolution of the axial profiles of the electron density (upper row) and electric field (bottom row) during positive streamer development for $B=0$ (left) and $B=3$ T (right). Calculations are for $P=50$ Torr, $\mathrm{C}{\mathrm{O}}_2$, and $U=+20$ kV. The legend shows time from the discharge start in nanoseconds.

Figure 7

Temporal evolution of the propagation velocity (a), channel radius (b), and discharge current (c) for a positive streamer propagating $\mathrm{C}{\mathrm{O}}_2$. $P=50$ Torr, $U=+20$ kV.

Figure 8

Temporal evolutions of the spatial distributions of the Hall parameter (upper part of the image) and electron mean energy (lower part of the image) for a positive streamer developing in a magnetic field of $B=3$ T. Scale for Hall parameter: 1.5–2.8. Scale for $\langle \varepsilon \rangle$: 0–16 eV. $P=50$ Torr, $\mathrm{C}{\mathrm{O}}_2$, $U=+20$ kV. Numbers are time in nanoseconds.

Figure 9

Spatial distributions of the electric field (upper part of the image) and electron density (lower part of the image) for the positive streamer propagation in different magnetic fields. $P=50$ Torr, $\mathrm{C}{\mathrm{O}}_2$, $t=7.0$ ns after high-voltage pulse start, $U=+20$ kV.

Figure 10

Spatial distributions of the electric field (upper part of the image) and electron density (lower part of the image) for the negative streamer propagation in different magnetic fields. $P=50$ Torr, $\mathrm{C}{\mathrm{O}}_2$, $t=4.2$ ns after high-voltage pulse start, $U=-20$ kV.

Figure 11

Axial profiles of the electron density and electric field for different discharge polarities and magnetic fields. Top: Positive polarity, $t=7.0$ ns. Bottom: Negative polarity, $t=4.2$ ns. $P=50$ Torr, $\mathrm{C}{\mathrm{O}}_2$, $U=20$ kV.

Figure 12

Streamer velocity (a), discharge current (b), and channel radius (c) versus magnetic field for different voltage polarities. Positive polarity, $t=7.0$ ns. Negative polarity, $t=4.2$ ns. $P=50$ Torr, $\mathrm{C}{\mathrm{O}}_2$, $U=20$ kV.