Space-Time Plasma-Steering Source: Control of Microwave Plasmas in Overmoded Cavities

Recently, space-time plasma-steering source has been proposed as an innovative microwave plasma source to meet the challenge of controlling plasmas in overmoded cavities. This concept has been successfully demonstrated experimentally, allowing the space-time control of nanosecond microwave plasmas on initiators. This paper gives insights into the path that shall be taken to reach full space-time control of plasmas in overmoded cavities. To that end, a key criterion, namely the “plasma-steering criterion,” is introduced and verified with a numerical model. This criterion must be respected for an accurate space-time control of plasmas in overmoded cavities. The usefulness of the plasma density (depending on its value with respect to the critical plasma density) on the plasma-control capabilities is also highlighted.

Figure 1

Control of microwave plasmas in cavities at a central frequency $f_c$ as a function of the volume $V$ of the cavity. For small volumes of the cavity, one single resonant mode can be excited [microwave resonant plasma source (MRPS)]. For large volumes space and time control of the plasmas is possible [space-time plasma-steering source (STPSS)] by using transient signals.

Figure 2

Schematic of a space-time plasma control by STPSS. Illustration of the “plasma-steering criterion.”

Figure 3

Schematic of a space-time plasma control by STPSS based on TR. Illustration of the corresponding “plasma-steering criterion.”

Figure 4

Schematic of the two steps of the TR operation. The region where the TRM is located (in white) is at atmospheric pressure (no plasma can develop) and the plasma chamber (in purple) is at a pressure $p=1.5$ torr. (Left) Measure of the impulse responses $i^m(t)$ by a certain number of transducers in the TRM, $m\in [[0:N_{\mathrm{ant}}]]$. (Right) Emission of the time-reversed impulse responses $i^m(-t)$ by the TRM.

Figure 5

Example of a plasma ignition by TR with an initial plasma density $n_{e_0}={10}^6{\mathrm{m}}^{-3}$ and $N_{\mathrm{ant}}=1$. (a) Electric fields (without and with plasma) and plasma density measured at the focusing location. (b) Snapshots of the plasma density at different instants. Colorbar is settled with a minimal value equal to $n_{e_0}$ and a maximum value of ${10}^8{n}_{e_0}$.

Figure 6

Evolution of the electric fields $E_{\mathrm{par}}(t)$ without and with plasma and of the plasma density $n_{e_{\mathrm{par}}}(t)$, measured at location ${\mathbf{r}}_{\mathrm{par}}$.

Figure 7

Example of a plasma ignition by TR with an initial plasma density $n_{e_0}={10}^6{\mathrm{m}}^{-3}$ and $N_{\mathrm{ant}}=10$. (a) Electric fields (without and with plasma) and plasma density measured at the focusing location. (b) Snapshots of the plasma density at different instants. Colorbar is settled with a minimal value equal to $n_{e_0}$ and a maximum value of ${10}^8{n}_{e_0}$.

Figure 8

Focus on the TR focusing with an initial plasma density $n_{e_0}={10}^6{\mathrm{m}}^{-3}$. (a) Horizontal and vertical cuts at the focusing location, meaning along the $x$ axis for $y=0.7$ m and along the $y$ axis for $x=1.2$ m, respectively. In red is plotted the electric field at the focusing instant $t=300$ ns and in black is plotted the plasma density right after the focusing peak at $t=304$ ns. (b) Snapshots of the electric field and plasma density at these instants (meaning $t=300$ ns and $t=304$ ns, respectively).

Figure 9

Example of a plasma ignition by TR with an initial plasma density $n_{e_0}={10}^9{\mathrm{m}}^{-3}$ and $N_{\mathrm{ant}}=10$. (a) Electric fields (without and with plasma) and plasma density measured at the focusing location. (b) Snapshots of the plasma density at different instants. Colorbar is settled with a minimal value equal to $n_{e_0}$ and a maximum value of ${10}^8{n}_{e_0}$.