#
On the Temperature and Plasma Distribution of an Inductively Driven Xe-I_{2}-Discharge

^{1}

^{2}

^{*}

## Abstract

**:**

^{®}. The included species and the used reactions are presented in this paper. To verify the simulation in relation to the plasma distribution, the results were compared with measurements from literature. The temperature of the lamp vessel was measured in relation to the temperature distribution and also compared with the results of the simulation. It could be shown that the simulation reproduces the plasma distribution with a maximal deviation of ≈6.5% to the measured values and that the temperature distribution in the examined area can be predicted with deviations of up to ≈24% for long vessel dimensions and ≈3% for shorter dimensions. However, despite the deviating absolute values, the general plasma behaviour is reproduced by the simulation. The simulation thus offers a fast and cost-effective method to estimate an effective geometrical range of iodine-containing ICPs.

## 1. Introduction

^{®}was used [10]. This software includes a module for ICP simulations. The simulation results were compared with the work of Barnes et al. [11] in relation to the plasma distribution. Furthermore, the results of the temperature distribution for the glass vessel were also compared with measurements on a lab system. The simulation model presented in the following shows a useful approximation of the plasma behaviour for future research.

## 2. Materials and Methods

^{®}uses the approach:

## 3. Results and Discussion

#### 3.1. Plasma Distribution

#### 3.2. Temperature Distribution

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Pressure curve over the temperature of a discharge with 100 Pa of Xe as well as 1 mg of I${}_{2}$. The green marked area corresponds to the area of an unsaturated discharge.

**Figure 2.**Comparison of the electron density distribution at 400 W input power with 3 MHz and an initial pressure of 190 Pa.

**Left**: Xe discharge.

**Right**: I${}_{2}$-Xe-discharge.

**Figure 3.**Comparison of different particle density distributions of the I${}_{2}$-Xe plasma at 400 W input power.

**Left**: Electron density.

**Center**: Atomic iodine density.

**Right**: I${}^{-}$-density.

**Figure 4.**I${}_{2}$-particle density distribution along the lamp radius in the middle of the vessel. Comparison of the measurements of Barnes et al. [11], indicated with ${n}_{{B}_{m}}$; a simulation using the same parameters and geometry, indicated with ${n}_{{B}_{s}}$; and the simulation with the geometry and parameters presented in this paper, indicated as ${n}_{s}$.

**Figure 5.**Comparison of the plasma distribution of pure gas- to halide-filled lamp systems at 400 W input power.

**Left**: Xe-filled lamp system.

**Right**: Xe-I${}_{2}$-filled lamp system.

**Figure 6.**Measurement of the temperature distributions for different lamp lengths. The zero was set at the hottest point.

**Figure 8.**Comparison of plasma temperature distribution with different lamp lengths. Here, a coil with 15 windings was simulated to reproduce the real system for the measurement.

Xenon Collision Reactions | ||||||
---|---|---|---|---|---|---|

No. | Process | Reaction | $\mathsf{\Delta}\mathbf{\epsilon}\phantom{\rule{0.166667em}{0ex}}\left[\mathbf{eV}\right]$ | Source | ||

1 | Elastic | $\mathrm{Xe}+e$ | ⟶ | $\mathrm{Xe}+e$ | [14] | |

2 | Excitation | $\mathrm{Xe}+e$ | ⟶ | $\mathrm{Xe}\left(6{s}_{2}\right)+e$ | 8.31 | [15] |

3 | Excitation | $\mathrm{Xe}+e$ | ⟶ | $\mathrm{Xe}\left(6{s}_{1}\right)+e$ | 8.43 | [16] |

4 | Ionisation | $\mathrm{Xe}+e$ | ⟶ | ${\mathrm{Xe}}^{+}+2e$ | 12.12 | [17] |

5 | Stepwise ionisation | $\mathrm{Xe}\left(6{s}_{2}\right)+e$ | ⟶ | ${\mathrm{Xe}}^{+}+2e$ | 3.44 | [18] |

Xenon Relaxation and Surface Reactions | ||||||

No. | Process | Reaction | $\mathsf{\Delta}\mathbf{\epsilon}\phantom{\rule{0.166667em}{0ex}}\left[\mathbf{eV}\right]$ | Source | ||

6 | Relaxation ${}^{1}$ | $\mathrm{Xe}\left(6{s}_{1}\right)$ | ⟶ | $\mathrm{Xe}+h\nu $ | −8.43 | [19] |

7 | Recombination | ${\mathrm{Xe}}^{+}$ | ⟶ | $\mathrm{Xe}$ | ||

8 | Relaxation | $\mathrm{Xe}\left(6{s}_{1}\right)$ | ⟶ | $\mathrm{Xe}$ | ||

9 | Relaxation | $\mathrm{Xe}\left(6{s}_{2}\right)$ | ⟶ | $\mathrm{Xe}$ | ||

Iodine Collision Reactions | ||||||

No. | Process | Reaction | $\mathsf{\Delta}\mathbf{\epsilon}\phantom{\rule{0.166667em}{0ex}}\left[\mathbf{eV}\right]$ | Source | ||

10 | Dissociative attachment | ${\mathrm{I}}_{2}+e$ | ⟶ | ${\mathrm{I}}^{-}+\mathrm{I}$ | [20] | |

11 | Elastic | $\mathrm{I}+e$ | ⟶ | $\mathrm{I}+e$ | [21] | |

12 | Ionisation | $\mathrm{I}+e$ | ⟶ | ${\mathrm{I}}^{+}+2e$ | 10.45 | [22] |

Iodine Surface Reactions | ||||||

No. | Process | Reaction | $\mathsf{\Delta}\mathbf{\epsilon}\phantom{\rule{0.166667em}{0ex}}\left[\mathbf{eV}\right]$ | Source | ||

13 | Recombination | ${\mathrm{I}}^{+}$ | ⟶ | I | ||

14 | Decay | ${\mathrm{I}}^{-}$ | ⟶ | I | ||

15 | Recombination | $\mathrm{I}+\mathrm{I}$ | ⟶ | ${\mathrm{I}}_{2}$ |

^{1}For this reaction the reaction rate of k

_{j}= 2.73 · 10

^{8}s

^{−1}was used.

Lamp Geometry | Unit | Value | Coil Geometry | Unit | Value |
---|---|---|---|---|---|

Inner diameter | [mm] | 54 | Inner diameter | [mm] | 59 |

Outer diameter | [mm] | 56 | Outer diameter | [mm] | 67 |

Length | [mm] | 78 | Length | [mm] | 75 |

Volume | [cm${}^{3}$] | 111 | Frequency | [MHz] | 3 |

Filling pressure | [Pa] | 100 | Windings | 8 | |

Starting gas | Xe | ||||

Filling material | I${}_{2}$ | ||||

Amount of solid | [mg] | 1.0 | |||

Calculated initial pressure | [Pa] | 190 |

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**MDPI and ACS Style**

Gehring, T.; Eizaguirre, S.; Jin, Q.; Dycke, J.; Renschler, M.; Kling, R.
On the Temperature and Plasma Distribution of an Inductively Driven Xe-I_{2}-Discharge. *Plasma* **2021**, *4*, 745-754.
https://doi.org/10.3390/plasma4040037

**AMA Style**

Gehring T, Eizaguirre S, Jin Q, Dycke J, Renschler M, Kling R.
On the Temperature and Plasma Distribution of an Inductively Driven Xe-I_{2}-Discharge. *Plasma*. 2021; 4(4):745-754.
https://doi.org/10.3390/plasma4040037

**Chicago/Turabian Style**

Gehring, Tim, Santiago Eizaguirre, Qihao Jin, Jan Dycke, Manuel Renschler, and Rainer Kling.
2021. "On the Temperature and Plasma Distribution of an Inductively Driven Xe-I_{2}-Discharge" *Plasma* 4, no. 4: 745-754.
https://doi.org/10.3390/plasma4040037