# Iodine plasmas for space propulsion and industrial applications

Trevor Lafleur, Benjamin Esteves, Cyril Drag, Anne Bourdon, Pascal Chabert, Javier Martínez Martínez, Luca Vialetto, George Bowden, Rawoof Shaik

► To cite this version:

Trevor Lafleur, Benjamin Esteves, Cyril Drag, Anne Bourdon, Pascal Chabert, et al. Iodine plasmas for space propulsion and industrial applications. Journal of Physics D: Applied Physics, 2025, 59 (2), pp.023001. 10.1088/1361-6463/ae2b7e. hal-05445110

HAL Id: hal-05445110

https://hal.science/hal-05445110v1

Submitted on 6 Jan 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
TOPICAL REVIEW • OPEN ACCESS

Iodine plasmas for space propulsion and industrial applications

To cite this article: Trevor Lafleur *et al* 2026 *J. Phys. D: Appl. Phys.* **59** 023001

View the [article online](#) for updates and enhancements.

You may also like

- *Biomolecular mass spectrometry in plasma medicine*

Zengyu Wang, Klaus-Dieter Weltmann,
Sander Bekeschus et al.

- *Angle-resolved polarization control of surface plasmon resonance in superimposed metallic gratings*

Alex Zettel, Yazan Bdour and Ribal
Georges Sabat

- *PIC/MCC simulation of post-arc plasma diffusion considering TRV, initial drift velocity and metal droplets*

Lijun Wang, Hongjian Wang, Zhuo Chen
et al.
<figure><img src="image_2.png" /></figure>

TOPICAL REVIEW

# Iodine plasmas for space propulsion and industrial applications

Trevor Lafleur<fnref n="1" />,*, Benjamin Esteves<fnref n="2" />,<fnref n="3" /> ID, Cyril Drag<fnref n="3" /> ID, Anne Bourdon<fnref n="3" /> ID, Pascal Chabert<fnref n="3" /> ID, Javier Martínez Martínez<fnref n="4" />, Luca Vialetto<fnref n="5" /> ID, George Bowden<fnref n="1" /> and Rawoof Shaik<fnref n="1" /> ID

E-mail: t.lafleur@unsw.edu.au

**Keywords:** iodine, electric propulsion, alternative propellant, plasma etching

OPEN ACCESS

RECEIVED

12 August 2025

REVISED

20 October 2025

ACCEPTED FOR PUBLICATION

10 December 2025

PUBLISHED

30 December 2025

Original content from
this work may be used
under the terms of the
Creative Commons
Attribution 4.0 licence.

Any further distribution
of this work must
maintain attribution to
the author(s) and the title
of the work, journal
citation and DOI.

<figure><img src="image_3.png" /></figure>

Abstract

With as many as 2000 satellites per year forecast to be launched over the next decade, onboard propulsion systems will become increasingly important for ensuring both mission success and a sustainable space environment. Plasma-based electric propulsion systems are particularly attractive because of their high fuel efficiency, but due to challenges with conventional propellants such as xenon, a strong interest in viable alternatives has emerged. One such alternative is iodine, which in addition to space-based applications, is also of use in a number of ground-based industrial applications such as plasma etching. With a lower cost, higher global production output, and a reduced ionization threshold compared with xenon, iodine has the potential to meet current and future space industry demand while also providing improved propulsion performance. Furthermore, iodine is a solid at typical ambient conditions with a high storage density. However, iodine is chemically reactive with many common materials and has a more complex plasma chemistry that includes molecular dissociation, attachment to form negative ions, and several ionization processes creating positive atomic and molecular ions. This topical review provides a comprehensive overview of iodine within the context of plasma applications and also serves as a useful data source for various thermodynamic properties, collision cross-sections, and iodine-surface interactions. In addition to discussing the physical and atomic/molecular properties of iodine, we also highlight important theoretical, numerical, and experimental work in the field and discuss the current state-of-the-art: including the space flight heritage of iodine-fueled propulsion systems and remaining research/-technical challenges.

1. Introduction

Iodine is a versatile substance that has a wide range of uses from wound dressings and disinfectants, to additives in common table salt [1]. However, within a plasma physics context it is still relatively new and has only received increased attention over the last ten years or so largely because of its possible viability as an alternative propellant for space propulsion [2]. High-performance electric propulsion systems such as gridded ion and Hall thrusters have successfully been used in space for more than 60 years [3]. While mercury propellant was chosen for the first gridded ion thrusters tested on the SERT-I spacecraft in 1964 [4], toxicity concerns eventually led to a shift towards xenon within the space community [5], and which has subsequently become the nominal propellant of choice.

As a propellant, xenon offers a number of strong advantages [3, 6]. Firstly, it is a noble gas that is nonreactive and compatible with most materials. It also has a high average atomic mass (131.3 u) and a relatively low ionization threshold energy (12.13 eV). A high atomic mass is usually favored for gridded ion and Hall thrusters as it yields a higher thrust-to-power ratio and thruster electrical efficiency [7]: important factors as most spacecraft are power limited and so a higher thrust can reduce maneuver

<footnote n="1">¹ School of Engineering and Technology, University of New South Wales Canberra, Canberra, ACT 2600, Australia</footnote>

<footnote n="2">² Safran Spacecraft Propulsion, 27200 Vernon, France</footnote>

<footnote n="3">³ LPP, CNRS, Ecole Polytechnique, Sorbonne Université, F-91128 Palaiseau, France</footnote>

<footnote n="4">⁴ Private address, Madrid, Spain</footnote>

<footnote n="5">⁵ Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, United States of America</footnote>

<footnote>* Author to whom any correspondence should be addressed.</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Mass density of xenon, krypton, and argon as a function of pressure at a temperature of 20 °C [8]. The black dashed line shows the expected density for xenon from the ideal gas law, while the solid red line shows the density of iodine under ambient conditions.</figcaption></figure>

duration. Xenon also exhibits very attractive storage properties, as illustrated in figure 1 which shows the mass density as a function of pressure at a temperature of 20 °C. For pressures above approximately 6 MPa, xenon undergoes a phase transition from a gas to a supercritical fluid and its density increases substantially (particularly when compared with that expected from the ideal gas law; black dashed line in figure 1). A higher density implies a smaller storage tank size, which is again an advantage for spacecraft.

Xenon however presents several challenges. It is a relatively rare gas and production is through fractional distillation of air: a process that is time consuming and energy intensive. For example, for every 1000 metric tons of oxygen produced, only 1.2 kg of xenon are obtained [9]. Consequently, xenon can be relatively expensive (of the order of $5000 per kg) and global production is limited to around 50–60 metric tons per year [10]. This creates several emerging problems for the space industry. The rise of satellite constellations [11] has resulted in many hundreds, or even thousands, of satellites requiring onboard propulsion systems, and while economies-of-scale can be used to reduce satellite production costs, such cost savings usually do not extend to the propellant [12]. With the trend towards smaller satellites [13], and with such satellites often being launched via ride-share options or in batches, many satellite operators are looking at further reducing satellite costs. This includes having stand-alone propulsion systems that can be delivered pre-fueled and without any expensive or highly specialized propellant loading equipment being needed: a disadvantage with xenon because of its high storage pressure. Aside from representing a general explosion risk, high-pressure propellant storage can also cause potential blo wout problems during launch (because of launch loads and intense vibrations), particularly for CubeSats launched via rideshare. Consequently, low-pressure propellant storage is ideally preferred where possible [14].

Cumulatively, between 17 000 and 300 000 satellites are forecast to be launched over the next 10 years [15, 16], and with the vast majority requiring onboard propulsion, space industry demand for xenon alone may outpace supply. Considering that the estimated average satellite mass is about 300 kg [16], and that the required propellant mass for missions in low-Earth orbit can represent as much as 11%–18% of the satellite mass [17], each satellite may require between 30 and 60 kg of propellant. Conservatively assuming 2000 satellites launched per year, the amount of xenon needed is between 60 and 120 metric tons per year: equal to or higher than current global production. Furthermore, this ignores the demand for xenon from other sectors such as the semiconductor, medical, and lighting industries, as well as large science experiments searching for dark matter [18]. While the above estimate is naturally very simplified and makes several assumptions, it nonetheless highlights the potential scale of the problem. Demand for xenon can also lead to strong market fluctuations, and for several deep-space science missions, xenon needs to be stockpiled in advance to prevent market collapse [10]. In the lead up to the war in Ukraine that broke out in 2022, the xenon market experienced a strong disruption (see figure 2) as Ukraine and Russia account for about 25%–30% of the world’s xenon and krypton supply. This disruption initially caused a surge in market prices because of the drop in supply, although prices later stabilized as many industries dipped into their rare-gas reserves, invested in gas recycling technolo-gies, or switched to alternatives.

The above challenges with xenon have provided a strong motivation to search for viable alternat-
ive propellants. Within the short term, krypton has emerged as an obvious candidate [12], and more
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Cost of xenon as a function of time indicating the strong market disruption caused by the war in Ukraine. Data taken from [19].</figcaption></figure>

recently, even argon [20]. However, while the cost of krypton and argon are approximately one and two orders of magnitude lower than xenon respectively, their physical properties are less attractive. For example, both gases have lower atomic masses of 83.7988 u and 39.948 u, and higher ionization threshold energies of 14 eV and 15.76 eV. Consequently, the thrust-to-power ratio and electrical efficiency of the propulsion system is lower, which implies that either more satellite power is required, or that maneuver duration increases. Furthermore, the mass density of krypton and argon are much lower than xenon (even at high pressures), as seen in figure 1. Thus, not only does the storage tank size increase, but also the tank mass. This can then affect satellite design and launch costs.

An emerging alternative propellant that can address current concerns is iodine [2, 21, 22], which is also of interest for several ground-based applications such as plasma etching [23]. Located just adjacent to xenon in the periodic table of elements, it has a similar atomic mass of 126.9 u, and a lower atomic ionization threshold of 10.45 eV [24]. As a result, similar or even higher performance to xenon can be obtained. Figure 3 shows a photograph of a typical iodine plasma discharge where its characteristic yellow color is seen. The cost of iodine is approximately two orders of magnitude lower than xenon (although the price can depend strongly on the required purity), and global production sits at about 30 000 metric tons per year [25]: i.e. almost 500–600 times higher than xenon. Chile is the largest supplier of iodine (which is extracted from caliche ore) and accounts for almost two-thirds of global production. Japan is the second largest producer contributing roughly 30%, followed by Turkmenistan and Iran with approximately 3% and 2% respectively. With such a large global output, iodine has the potential to more than satisfy current and future space industry demand. However, the advantages of iodine go further as it is typically a solid at ambient conditions. It therefore has a higher storage density (see figure 1) and does not require pressurization. This significantly reduces the size and mass of the storage tank and overall propulsion system. These cost reducing factors make iodine particularly attractive for satellite constellations.

Iodine does however present certain difficulties, which most likely explains why it is only now being seriously considered as a propellant. Firstly, being stored as a solid complicates propellant delivery and flow control to the thruster. Secondly, iodine is significantly more chemically reactive than xenon and can corrode many common materials such as iron or aluminum [27]. Finally, while xenon is an atomic gas with a relatively simple plasma chemistry, iodine is initially in a molecular state and has a complex chemistry that includes collisional reactions such as dissociation into atomic iodine, and the formation of negative ions because of its high electron affinity [26, 28]. Until quite recently [29–31], many of the electron impact cross-sections for these reactions were not known. Consequently, a significant amount of research work has since occurred to study basic and applied iodine plasmas. Nonetheless, despite this recent progress, large uncertainties in cross-section data and reaction mechanisms still remain.

This topical review is dedicated to a comprehensive overview of iodine within the context of low-temperature plasma physics, while also acting as a single source of useful fundamental data (such as reaction cross-sections). We begin with a brief discussion on the history of iodine and highlight its physical and thermodynamic properties in section 2. We then introduce relevant iodine plasma chemistry (including both atomic and molecular reactions) in section 3, and iodine-surface interactions in section 4. Section 5 is then devoted to iodine plasma applications and important theoretical, numerical, and experimental research that has been conducted. A discussion of iodine propulsion testing in space
<figure><img src="image_6.png" /><figcaption>Figure 3. Photograph of a low-pressure iodine plasma produced in the PEGASES thruster prototype. Reproduced with permission from [26].</figcaption></figure>

and possible emerging environmental considerations are presented in section 6. We then end by identifying remaining challenges and further required research in section 7, before providing a final outlook in section 8. Where possible, all fundamental data is either provided in the paper, or is available on the Zenodo repository [32].

## 2. Properties of iodine

### 2.1. Overview

Atomic iodine, I, is a non-metallic element of the halogen family that appears in Group 17 of the periodic table. The only stable isotope is iodine-127. Under standard conditions, iodine exists as a diatomic molecule, I₂, with two iodine atoms covalently bonded together. It is a bluish-black solid and has a glittering crystalline appearance. It has a moderate vapor pressure at room temperature, and in an open vessel, it slowly sublimates to a deep violet vapor that is irritating to the eyes, nose, and throat. Iodine melts at a relatively low temperature of 113.7 °C, and boils at 184.3 °C. The triple point temperature was recently determined to a high level of precision as 113.314 ± 0.005 °C [33]. Iodine was discovered by the French chemist Bernard Courtois in 1811 and was named two years later by Joseph Louis Gay-Lussac after the Ancient Greek word Ιώδης, which means ‘violet’. Atomic and molecular term symbols are described in appendices A and B, while important thermodynamic properties for the solid, liquid, and gas phases are given in table 1. Additional properties are provided in section 2.3.

### 2.2. Physical properties

#### 2.2.1. Vapor pressure

The evolution of iodine vapor pressure as a function of temperature is illustrated in figure 4. The earliest measurements, dating back to before 1926, were compiled from the International Critical Tables [34], noting significant uncertainties in pressures for temperatures below 0 °C. Several vapor pressure-temperature relationships can be employed, such as the common Dupré formula derived by integrating the Clausius–Clapeyron equation assuming that the heat of sublimation can be linearized. Gillespie and Fraser extended the vapor pressure measurements in 1936 and proposed the following empirical equation for the vapor pressure-temperature relationship [35]:

$$ \log_{10} p = -\frac{3512.830}{T} - 2.013\log_{10} T + 18.37972, \quad (1) $$

where p is the iodine vapor pressure in units of (Pa), and T is the temperature in (K).

Further measurements were conducted in the 1960s for temperatures between 43 °C and 80 °C, and which yielded values approximately 10% lower than previous measurements [36]. Dupré's law was slightly modified by Lindenberg [37], but the resulting values remained very similar to those given by the original relation. Additionally, the hyperfine transitions of molecular iodine in the visible spectrum
<table><caption>**Table 1.** Example thermodynamic properties of iodine.</caption><thead><tr><th>Property</th><th>Value</th></tr></thead><tbody><tr><td><em>Temperatures</em></td><td></td></tr><tr><td>Melting point (θ<sub>m</sub>)</td><td>386.85 K</td></tr><tr><td>Boiling point (θ<sub>b</sub>)</td><td>457.45 K</td></tr><tr><td>Triple point</td><td>386.464 K, 12.1 kPa</td></tr><tr><td><em>Solid phase</em></td><td></td></tr><tr><td>Density (298 K)</td><td>4.933 g cm<sup>-3</sup></td></tr><tr><td>Enthalpy of sublimation (298 K)</td><td>245.9 kJ kg<sup>-1</sup></td></tr><tr><td>Heat capacity (0.1 MPa, 298.15 K)</td><td>214.5 J kg<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td>Thermal conductivity (298 K)</td><td>0.449 W m<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td>Electrical conductivity</td><td>8 × 10<sup>-8</sup> S m<sup>-1</sup></td></tr><tr><td>Thermal diffusivity</td><td>4 × 10<sup>-7</sup> m<sup>2</sup> s<sup>-1</sup></td></tr><tr><td>Thermal effusivity</td><td>689.3 W s<sup>1/2</sup> m<sup>-2</sup> K<sup>-1</sup></td></tr><tr><td><em>Liquid phase</em></td><td></td></tr><tr><td>Enthalpy of fusion</td><td>61.1 kJ kg<sup>-1</sup></td></tr><tr><td>Heat capacity (0.1 MPa, 386.75 K)</td><td>313.4 J kg<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td><em>Gaseous phase</em></td><td></td></tr><tr><td>Enthalpy of vaporization</td><td>163.8 kJ kg<sup>-1</sup></td></tr><tr><td>Heat capacity (I<sub>2</sub>: 0.1 MPa, 298.15 K)</td><td>145.3 J kg<sup>-1</sup> K<sup>-1</sup></td></tr><tr><td>Heat capacity (I: 0.1 MPa, 298.15 K)</td><td>163.8 J kg<sup>-1</sup> K<sup>-1</sup></td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>**Figure 4.** Iodine vapor pressure curve. The data markers correspond to different experimental measurements: blue circles [34], orange squares [35], green up triangles [36], red left triangles [40], purple right triangles [39], and brown down triangles [41] for the liquid phase only. The variation of vapor pressure for solid iodine is determined from equation (1) and is represented by the black curve, while that for the liquid phase is obtained using equation (2) and is represented by the red curve. The red and blue dotted vertical lines represent the melting and boiling temperatures respectively.</figcaption></figure>

were recommended as standard frequencies by the Bureau International des Poids et Mesures (BIPM) [38–40]. In this high-resolution spectroscopy work, pressure effects leading to spectral broadening of laser absorption lines were measured with high precision. These pressure-dependent broadening measurements (for temperatures from 0 °C down to –22 °C), are consistent with Dupré's law to within an accuracy of the order of 4%.

In the liquid phase, the enthalpy of vaporization is lower than that of sublimation, resulting in a smaller slope in the vapor pressure-temperature variation. In addition to the data in [34], measurements published in 1979 [41] were fitted using a least-squares method to the Antoine equation with an average
<figure><img src="image_8.png" /><figcaption>Figure 5. Visible absorption spectrum of I₂. (a) Relevant potential energy curves. (b) Absorption cross-section for T = 300 K as a function of wavenumber taken from [57]. The I(²P°₃/₂) + I(²P°₃/₂) and I(²P°₃/₂) + I(²P°₁/₂) dissociation limits are indicated by horizontal dashed lines in (a) and (b).</figcaption></figure>

error of 0.66% for temperatures up to 263.2 °C:

$$ \log_{10} p = 9.24828 - \frac{1694.23}{T - 58.32}. \qquad (2) $$

The above equation yields pressures similar to those found in recent reference tables for gases and liquids (see for example [42]). Finally, it should be noted that when iodine is no longer in a controlled vacuum cell (where most vapor pressure-temperature measurements are performed), but rather at atmospheric pressure, the vapor pressure will be affected by the ambient pressure exerted on the solid or liquid surface. A vapor pressure correction was established by Poynting [43] but remains negligible (a difference of only 35 Pa at a temperature of 150 °C, for example).

### 2.2.2. Electronic spectroscopy of molecular iodine

Electronic spectroscopy of the iodine molecule was extensively performed in the second part of the 20th century. In 1978, an atlas of the absorption spectrum of molecular iodine in the energy range 1.83–2.48 eV was developed [44]. The study of the visible absorption spectrum of gaseous I₂ became a classic molecular spectroscopy experiment for undergraduate students in physical chemistry to determine spectroscopic constants [45]. Indeed, the vibrational-electronic spectrum of I₂ in the wavelength range between 500 and 640 nm displays a large number of well-defined bands. Near-ultraviolet (UV) and UV transitions were also well studied [46, 47]. Optical transitions of molecular iodine are also referenced as secondary frequency standards by the BIPM (around 515, 532, 543, 633, and 640 nm).

While known and studied for a century [48, 49], the visible spectrum of I₂ was carefully investigated by Tellinghuisen [50–53]. Three electronic transitions contribute to absorption in the visible region between 400 and 650 nm, and which is continuous below 500 nm (~2.48 eV) but shows pronounced rovibrational structures between 500 and 630 nm (approximately 1.55–2.48 eV). These transitions are from the ground state I₂(X ¹Σg) to the bound state I₂(B ³Π(0u)), correlated with the I(²P°₁/₂) + I(²P°₃/₂) dissociation limit, and the two Iu states I₂(A ³Π(1u)) and I₂(C ¹Π(1u)), correlated with the I(²P°₃/₂) + I(²P°₃/₂) dissociation limit. Potential energy curves (see also section 2.2.3) for the above molecular states are plotted in figure 5(a) which are taken from [54–56].

Recently, hyperfine spectroscopy studies have been carried out to develop an iodine atomic clock for wavelengths around 532 nm [58]. Beyond 2.48 eV, the diffuse part of the absorption spectrum leads exclusively to molecular photodissociation via the I₂(B ³Π(0u)) and I₂(C ¹Π(1u)) states. This region is very interesting, in different ways, for absorption-based density measurements between a bound state and the continuum, especially in a plasma where pressures and temperatures are different from what they are in the normal gas phase. Contrary to optical transitions between bound states, the resonance condition is independent of the gas velocity and there is no saturation related to the stimulated emission at high laser intensities. It is also possible to detect the population of different rotational and vibrational levels of molecular iodine without changing the laser wavelength. This peculiarity was used by Esteves et al [26, 59] to directly measure the dissociation rate in iodine plasmas.

The effective absorption cross-section is well known experimentally at room temperature (see figure 5(b)), thanks to the growing interest in the role that iodine chemistry plays in a number of
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Potential energy curve for the iodine ground state $I_2(X^1\Sigma_g^+)$ using the Morse approximation. Example vibrational wave functions (with an arbitrary amplitude) are also shown.</figcaption></figure>

atmospheric processes. The latest measurements of the absorption cross-section of iodine have been reviewed in a technical report from the Jet Propulsion Laboratory-Caltech committee on standards for atmospheric cross-sections [60] (see section 4H of the report). The recommended data are those computed by Saiz-Lopez and Plane [57].

### 2.2.3. Vibrational states of molecular iodine

For a diatomic molecule, an important property of an electronic state is its potential energy curve (energy as a function of the internuclear distance) as illustrated in figures 5(a) and 6. The curve can have a minimum thus leading to a bound state (such as the blue curve in figure 5(a) with an equilibrium internuclear distance of $r_e = 2.666$ Å [61] for the iodine ground state) or a repulsive state (such as the green curve in figure 5(a) monotonically decreasing and leading to dissociation). For high internuclear distances, the potential energy curve reaches an asymptotic value synonymous with dissociation. It has been found that the iodine ground state $I_2(X^1\Sigma_g^+)$ can be well approximated by a Morse potential at low internuclear distances [47, 62], as illustrated in figure 6 (where the ground state potential energy curve is repeated from figure 5).

Unlike atoms, diatomic molecules have two additional degrees of freedom which, until now, have largely been ignored in the study of iodine plasmas: vibration and rotation. A bound electronic state of a molecule is composed of several vibrational levels, which are quantized energy levels associated with the motion of the two iodine nuclei in the molecule. In the case of the iodine electronic ground state, over 60 vibrational levels are present. The first vibrational level, $v=0$, has an energy of approximately 0.0133 eV (relative to the minimum of the potential energy curve), and the energy gap between the first two levels ($E_1-E_0$) is about 0.0266 eV in the Morse potential approximation. The energy gap between higher consecutive levels ($E_{v+1}-E_v$ with $v > 0$) diminishes slightly with increasing vibrational level $v$ because the potential is anharmonic. Each vibrational level can be represented by a vibrational wave function, whose radial profile is schematically drawn in figure 6 for several example levels. Note that with the exception of $v=0$, the vibrational wavefunctions exhibit maxima around the turning points of the potential energy curve. The transition probability between two vibrational levels, according to the Frank-Condon principle, occurs at a fixed internuclear distance. As a result, the transition probability is higher when the overlap of the radial wave functions is maximized. This principle applies to both optical transitions and collision-induced phenomena.

The distribution of iodine vibrational levels is plotted in figure 7 for three different temperatures (300 K, 900 K, and 1500 K) assuming a Boltzmann distribution and using spectroscopic data for the energy of each vibrational level taken from [63]. At room temperature, the $v=0$ level is by far the most populated (>60%) and the first three $v$-levels are enough to account for more than 90% of the total population. At 1500 K however, the distribution is much more homogeneous and 11 $v$-levels are necessary to account for 90% of the population. In iodine plasmas where gas temperatures above 1000 K have been measured [26], the first ten $v$-levels are therefore expected to be populated to a significant extent.

The iodine molecule can also be excited rotationally, and has a rotational constant of $4.67 \times 10^{-6}$ eV [61]. At 300 K, the mean number of rotational levels for each $v$-level is 67. As of now, the
<figure><img src="image_10.png" /><figcaption>Figure 7. Distribution of the I₂ vibrational state population (assuming Boltzmann statistics) for the first 10 levels at temperatures of 300 K, 900 K, and 1500 K. Data for the energy of each vibrational level is taken from Herzberg [63].</figcaption></figure>

effect of rotational excitation has been neglected in all iodine plasma studies. Additionally, no cross-section data for electron impact rotational excitation of I₂ is available. In the absence of such cross-section data, approximate theoretical expressions for diatomic molecules can be used instead (see for example [64, 65]).

## 2.3. Thermochemistry properties

While example thermodynamic and thermochemistry properties were given in table 1, these properties naturally vary with temperature and pressure, and this can be important for the operation of an iodine-fed plasma system. In particular, properties such as the gas phase thermal conductivity, specific heat at constant pressure, specific enthalpy, and viscosity, can be relevant to iodine gas flow, heating, and plasma discharge modeling. The variation of thermal conductivity with temperature for both atomic and molecular iodine is available from several sources based on experimental measurements or theoretical calculations. Example data from [66–68] is presented in figure 8 for the thermal conductivity and viscosity. In the temperature range illustrated, the thermal conductivity of atomic, $κ_I$, and molecular, $κ_{I₂}$, iodine are well described by the following best-fit empirical expressions

$$κ_I = 5.307 \times 10^{-5} T_I^{0.804}, \quad (3)$$

$$κ_{I₂} = 1.167 \times 10^{-5} T_{I₂}^{0.969}, \quad (4)$$

with $T_I$ and $T_{I₂}$ the atomic and molecular iodine temperatures respectively in units of (K), and where the thermal conductivity is in units of (W m⁻¹ K⁻¹). The empirical relation for $I₂$ is similar to that independently obtained in [69]. As seen in figure 8, the empirical relations are in excellent agreement with available theoretical and experimental data in the indicated temperature range. Figure 8(b) shows a comparison of the viscosity where similar good agreement is observed. Best-fit empirical expressions of the atomic, $μ_I$, and molecular, $μ_{I₂}$, viscosity can be obtained using Sutherland's law

$$μ_I = 3.252 \times 10^{-5} \left( \frac{T_I}{233} \right)^{3/2} \left( \frac{233}{233 + T_I} \right), \quad (5)$$

$$μ_{I₂} = 4.424 \times 10^{-5} \left( \frac{T_{I₂}}{473} \right)^{3/2} \left( \frac{473}{473 + T_{I₂}} \right). \quad (6)$$

Here the temperature is again in units of (K), while viscosity is in units of (Pa s). Note that thermal conductivity and viscosity may also vary with pressure, but many experiments or databases only provide values at a certain reference pressure (typically about 0.1 MPa). The experimental data for the thermal conductivity in figure 8(a) however corresponds to pressures between 26 and 59 kPa. Comparison with the theoretical calculations performed at 0.1 MPa show negligible differences in this temperature range. Properties also naturally depend on the phase. Figure 9 provides a convenient summary of the phase and temperature dependence of the thermal conductivity for $I₂$ [70].
<figure><img src="image_11.png" /><figcaption>Figure 8. (a) Thermal conductivity and (b) viscosity as a function of temperature for I and I₂. The data markers correspond to different theoretical or experimental measurements: green circles [68], purple up triangles [68], red squares [66], and red down triangles [67].</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 9. Thermal conductivity of I₂ in various states as a function of temperature. Data compiled by Ho et al [70].</figcaption></figure>

Iodine plasmas operating at conditions where local thermodynamic equilibrium (LTE), or near-LTE, is satisfied have so far been of limited interest, and so other transport properties, such as the electrical conductivity, have not been required. Such properties are anyway more directly and accurately obtained from non-equilibrium plasma discharge models (see for example [26, 28, 71] as well as section 5.3). Other properties, such as the specific heat at constant pressure, cₚ, the specific enthalpy, h, and the specific entropy, s, may however be useful for understanding iodine gas flow dynamics or designing gas flow systems. Such properties can be directly obtained from various databases (such as the JANAF tables [72]), or approximated by the NASA Glenn 9-coefficient polynomials

$$ \frac{c_p(T)}{R} = a_1 T^{-2} + a_2 T^{-1} + a_3 + a_4 T + a_5 T^2 + a_6 T^3 + a_7 T^4, \qquad (7) $$

$$ \frac{h^0(T)}{RT} = -a_1 T^{-2} + \frac{a_2 \ln T}{T} + a_3 + \frac{a_4 T}{2} + \frac{a_5 T^2}{3} + \frac{a_6 T^3}{4} + \frac{a_7 T^4}{5} + \frac{b_1}{T}, \qquad (8) $$

$$ \frac{s^0(T)}{R} = -\frac{a_1 T^{-2}}{2} - a_2 T^{-1} + a_3 \ln T + a_4 T + \frac{a_5 T^2}{2} + \frac{a_6 T^3}{3} + \frac{a_7 T^4}{4} + b_2, \qquad (9) $$

where h⁰ is a standard enthalpy relative to that at 298.15 K, and s⁰ is a reference entropy at a standard pressure of 1 atm. The corresponding polynomial coefficients (i.e. a₁, a₂, etc) can be retrieved for I and
<table><caption>**Table 2.** NASA Glenn coefficients for I and I₂ for temperatures between 200–1000 K and 1000–6000 K.</caption><thead><tr><th rowspan="2">Coefficient</th><th colspan="2">Temperature range</th></tr><tr><th>200–1000 K</th><th>1000–6000 K</th></tr></thead><tbody><tr><td colspan="3"><strong>Atomic iodine, I</strong></td></tr><tr><td>a<sub>1</sub></td><td>1.698×10<sup>2</sup></td><td>-7.786 × 10<sup>5</sup></td></tr><tr><td>a<sub>2</sub></td><td>-2.716×10<sup>0</sup></td><td>2.303 × 10<sup>3</sup></td></tr><tr><td>a<sub>3</sub></td><td>2.517×10<sup>0</sup></td><td>2.887 × 10<sup>-3</sup></td></tr><tr><td>a<sub>4</sub></td><td>-5.731×10<sup>-5</sup></td><td>1.181 × 10<sup>-3</sup></td></tr><tr><td>a<sub>5</sub></td><td>1.032×10<sup>-7</sup></td><td>-2.264 × 10<sup>-7</sup></td></tr><tr><td>a<sub>6</sub></td><td>-9.671×10<sup>-11</sup></td><td>1.964 × 10<sup>-11</sup></td></tr><tr><td>a<sub>7</sub></td><td>3.706×10<sup>-14</sup></td><td>-6.244 × 10<sup>-16</sup></td></tr><tr><td>b<sub>1</sub></td><td>1.211×10<sup>4</sup></td><td>-2.617 × 10<sup>3</sup></td></tr><tr><td>b<sub>2</sub></td><td>7.406×10<sup>0</sup></td><td>2.559 × 10<sup>1</sup></td></tr><tr><td colspan="3"><strong>Molecular iodine, I<sub>2</sub></strong></td></tr><tr><td>a<sub>1</sub></td><td>-5.088×10<sup>3</sup></td><td>-5.633 × 10<sup>6</sup></td></tr><tr><td>a<sub>2</sub></td><td>-1.250×10<sup>1</sup></td><td>1.794 × 10<sup>4</sup></td></tr><tr><td>a<sub>3</sub></td><td>4.504×10<sup>0</sup></td><td>-1.723 × 10<sup>1</sup></td></tr><tr><td>a<sub>4</sub></td><td>1.371×10<sup>-4</sup></td><td>1.244 × 10<sup>-2</sup></td></tr><tr><td>a<sub>5</sub></td><td>-1.391×10<sup>-7</sup></td><td>-3.333 × 10<sup>-6</sup></td></tr><tr><td>a<sub>6</sub></td><td>1.175×10<sup>-10</sup></td><td>4.125 × 10<sup>-10</sup></td></tr><tr><td>a<sub>7</sub></td><td>-2.338×10<sup>-14</sup></td><td>-1.960 × 10<sup>-14</sup></td></tr><tr><td>b<sub>1</sub></td><td>6.213×10<sup>3</sup></td><td>-1.069 × 10<sup>5</sup></td></tr><tr><td>b<sub>2</sub></td><td>5.584×10<sup>0</sup></td><td>1.601 × 10<sup>2</sup></td></tr></tbody></table>

<figure><img src="image_13.png" /><figcaption>**Figure 10.** Specific heat at constant pressure for I and I₂. The black dashed line shows the theoretical value for a monatomic gas: $c_p = 5R/2$.</figcaption></figure>

I₂ from various sources, such as the NASA ThermoBuild software [73, 74], and are tabulated in table 2 for temperature ranges between 200–1000 K and 1000–6000 K. Once $c_p$ is known, the specific heat at constant pressure, $c_v$, can be found from the relation $c_v = c_p - R$, where R is the specific gas constant (equal to 65.52 J kg⁻¹ K⁻¹ for I and 32.76 J kg⁻¹ K⁻¹ for I₂). Figure 10 shows the specific heat as a function of temperature for pure I and I₂. While there is some minor variation for I₂, the specific heat is effectively constant for I below 1000 K, and is well approximated by the theoretical value for a monatomic gas: i.e. $c_p = 5R/2$.

If thermal dissociation occurs (see section 2.4), both I and I₂ species may be present in a general iodine gas flow. In this case, the total specific enthalpy and entropy can be computed from

$$h(T) = \sum_{j} h_{j}^{0}(T) x_{j}, \qquad (10)$$

$$s(T,p) = \sum_{j} \left[ s_{j}^{0}(T) - R_{j} \ln \left( \frac{p_{j}}{p_{\text{ref}}} \right) \right] x_{j}, \qquad (11)$$
<figure><img src="image_14.png" /><figcaption>Figure 11. Measured dissociation fraction (data markers) from [78] as a function of pressure for various temperatures. The solid lines show predicted fractions obtained using equations (13) and (14).</figcaption></figure>

where the sum is over I and $I_2$ species, $p_{ref} = 1$ atm is a reference pressure, and $x_j$ is the mass fraction of species j.

## 2.4. Dissociation

Thermal dissociation of $I_2$ leads to the formation of I according to the reaction: $I_2 \rightarrow 2I$. The equilibrium constant for partial pressures of this reaction, $K_p$, is a function of temperature only and is defined as:

$$K_p = \frac{p_1^2}{p_{12}} = k_B T \frac{n_1^2}{n_{12}}, \qquad (12)$$

where $p_1$ and $p_{12}$ are the atomic and molecular partial pressures respectively, and $n_1$ and $n_{12}$ are the corresponding number densities. By considering statistical physics and mass action laws, the equilibrium constant can be expressed in terms of the partition function of atoms and molecules [75]. Using the rigid rotator and harmonic oscillator approximation, and considering only the fundamental molecular potential energy curve, the equilibrium constant is given by [76]:

$$K_p = K_0 T^{3/2} \left(1 - e^{-T_v/T}\right) e^{-D/T}, \qquad (13)$$

with $K_0 = 2.26 \times 10^6$ Pa K$^{-3/2}$, D the binding energy of the molecules (1.54 eV = 17 855 K), and $T_v$ the vibrational temperature (313 K). For temperatures above 1500 K, the partition functions must be corrected to account for excited electronic states and anharmonic spectroscopic constants [77].

The equilibrium constant allows the dissociation fraction, $\alpha = n_1/(2n_{12} + n_1)$, to be determined from

$$\alpha = \sqrt{\frac{K_p}{4p + K_p}}, \qquad (14)$$

where $p$ is the total pressure. Dissociation measurements [78] at different pressures and temperatures are shown in figure 11, together with the predicted dissociation fraction from equations (13) and (14). Despite the simplifying assumptions, the agreement is excellent.

In many plasma systems, the pressure is relatively low such that the predicted thermal dissociation degree may be significant. Figure 12 shows the dissociation fraction as a function of temperature for different representative pressures. For some electric propulsion systems, such as gridded ion or Hall thrusters, the operating pressure can be less than 1 Pa, indicating that thermal dissociation may be substantial. However, it should be noted that equations (13) and (14) are strictly valid only for conditions where thermodynamic equilibrium is satisfied, which is often not true for conditions relevant to electric propulsion systems. In this case, plasma dissociation (such as via electron impact dissociation processes; see section 3.3) may be more prevalent. The importance of thermal dissociation relative to plasma dissociation has been compared in controlled capacitively coupled radio-frequency (RF) discharges [59]. At low pressures, plasma dissociation dominates, but at higher pressures, thermal and plasma dissociation appears similar.
<figure><img src="image_15.png" /><figcaption>Figure 12. Thermal dissociation fraction as a function of temperature for different pressures.</figcaption></figure>

If thermodynamic equilibrium is not satisfied, the thermal dissociation fraction may differ from that predicted by equations (13) and (14). In this case, dissociation and recombination processes may need to be directly treated from a more fundamental microscopic perspective. The relevant reactions are

$$A + I_2 (X^1\Sigma_g^+) \rightarrow A + 2I (^2P_{3/2}^\circ), \quad (15)$$

$$A + 2I(^2P_{3/2}^\circ) \rightarrow A + I_2 (X^1\Sigma_g^+), \quad (16)$$

where A represents either I or $I_2$ (or indeed any heavy particle species that may be present, including ions). The thermal dissociation and recombination rates are then given by $n_A n_{I_2} K_{th,diss}$ and $n_A n_I^2 K_{th,recom}$ with $n_A$ the number density of species A, and $K_{th,diss}$ and $K_{th,recom}$ the thermal dissociation and recombination rate coefficients. Several works have measured or compiled such rate coefficients as a function of temperature for different species A including Baulch et al [79] and Ip and Burns [80]. Following Baulch et al:

$$K_{th,diss} = 1.37 \times 10^{-16} \exp\left(-\frac{15250}{T}\right) \text{m}^3\text{s}^{-1}, \quad (17)$$

$$K_{th,recom} = 6.51 \times 10^{-46} \exp\left(\frac{754}{T}\right) \text{m}^6\text{s}^{-1}. \quad (18)$$

Here the recommended values are based on various experimental measurements in the temperature range 800–2000 K (dissociation) and 290–1250 K (recombination), and with A = Ar (argon) or A = $N_2$ (molecular nitrogen) for dissociation, and A = Ar for recombination. In the absence of further data, it seems practical to extend the validity of the above rate coefficients to A = I and A = $I_2$.

# 3. Iodine plasma chemistry

## 3.1. Discharge composition

A wide range of neutral and charged particle species contribute to the overall dynamics of an iodine plasma discharge, including atomic iodine (I), molecular iodine ($I_2$), electrons ($e^-$), positive and negative atomic ions ($I^+$, $I^-$), and positive and negative molecular ions ($I_2^+$, $I_3^+$, $I_2^-$, $I_3^-$). These species can exist not only in their respective ground states, but also in excited electronic states, and in the case of molecules, excited vibrational and rotational states.

The foundation of ionization and molecular ion formation in halogen plasmas was established in the early 20th century. In 1925, Mohler [81] provided some of the first systematic measurements of electron impact ionization, while Hogness and Harkness [82] demonstrated the formation of molecular ions through charge-exchange and dissociative ionization processes, thus highlighting the importance of molecular species in plasma environments. Further refinements in understanding negative ion formation came from the work of Frost and McDowell [83], who investigated electron attachment processes in halogens, emphasizing iodine's strong electron affinity (3.06 eV) and its ability to form stable negative ions. Iodine is very electronegative as studied in several pioneering works such as those of Healey [84],
<table><caption>**Table 3.** Electron impact scattering processes for I. Here I\* represents an excited state above the I(²P°₃/₂) and I(²P°₁/₂) states, while n ≥ 1 is an integer.</caption><thead><tr><th>ID</th><th>Reaction</th><th>Process</th><th>Threshold energy (eV)</th></tr></thead><tbody><tr><td>B1</td><td>I(²P°₃/₂) + e⁻ → I(²P°₃/₂) + e⁻</td><td>Elastic scattering</td><td>—</td></tr><tr><td>B2</td><td>I(²P°₁/₂) + e⁻ → I(²P°₁/₂) + e⁻</td><td>Elastic scattering</td><td>—</td></tr><tr><td>B3</td><td>I(²P°₃/₂) + e⁻ → I⁺ + 2 e⁻</td><td>Ionization</td><td>10.451</td></tr><tr><td>B4</td><td>I(²P°₁/₂) + e⁻ → I⁺ + 2 e⁻</td><td>Ionization</td><td>9.5084</td></tr><tr><td>B5</td><td>I(²P°₃/₂) + e⁻ → Iⁿ⁺ + (n + 1) e⁻</td><td>Multiple ionization</td><td>See table 4</td></tr><tr><td>B6</td><td>I(²P°₃/₂) + e⁻ → I(²P°₁/₂) + e⁻</td><td>Electronic excitation</td><td>0.9426</td></tr><tr><td>B7</td><td>I(²P°₃/₂) + e⁻ → I\* + e⁻</td><td>Electronic excitation</td><td>See table 5</td></tr><tr><td>B8</td><td>I(²P°₁/₂) + e⁻ → I\* + e⁻</td><td>Electronic excitation</td><td>See table 5</td></tr></tbody></table>

Buchdahl [85], Biondi and Fox [86–88], Truby [89, 90], Woolsey et al [91] or Emeleus and Coulter [92], and can readily form negative ions (I⁻) via electron attachment, while negative molecular ions (I₂⁻, I₃⁻) emerge through subsequent clustering reactions. However, at higher electron temperatures, such as those encountered in many electric propulsion systems, multiple ionization pathways can become significant. Successive ionization thresholds at 10.45 eV (I⁺), 29.58 eV (I²⁺), 59.15 eV (I³⁺), and 99.51 eV (I⁴⁺) can lead to the formation of highly charged species, which dominate in high-energy environments. In contrast, molecular ions (I₂⁺, I₃⁺) tend to dissociate at elevated temperatures due to electron-impact fragmentation, while negative ions undergo detachment and collisional destruction. The interplay between these species governs key plasma properties such as particle transport, ionization-loss balance, and recombination kinetics. Within the context of electric propulsion or materials processing applications, sophisticated mathematical models are needed to understand these complex interactions, and to aid system design and optimization. Such models require a broad range of input data that includes important species (both neutral and charged), collisional reaction processes, and collision cross-sections. This section focuses on the underlying plasma chemistry relevant to iodine discharges, and which is required not only for theoretical and numerical plasma models, but also the interpretation and analysis of certain diagnostics. A further discussion of mathematical models making use of this data is provided in section 5.3.

## 3.2. Electron impact scattering: atomic iodine

For electrons colliding with atomic iodine, the main processes are elastic scattering (which primarily changes the electron momentum) and inelastic processes such as ionization and electronic excitation. Each of these reaction types are discussed further in the subsections below, and are summarized in table 3. The spin-orbit coupling degeneracy of the atomic ground state results in the presence of an 'excited' state I(²P°₁/₂) only 0.9426 eV [93] above the ground state I(²P°₃/₂). Further details on the term symbols for atomic iodine are given in appendix A (and for molecular iodine in appendix B). When thermal dissociation occurs due to gas heating (see section 2.4), the I(²P°₁/₂) state is always much less populated than the ground state, which can easily be seen by considering the system to be in LTE. At an example temperature of 1000 K ≈ 0.086 eV (and assuming Boltzmann statistics), the population density ratio of the first excited state to the ground state is approximately 8.7 × 10⁻⁶. For most applications of current interest however, LTE is not satisfied and the electron temperature is much higher than both the ion and neutral temperatures. Consequently, dissociation due to electron impact processes dominates and can be significant. Since the electron temperature in many plasmas is of the order of 5 eV or higher, the I(²P°₁/₂) state may be highly populated and strictly speaking should be treated as a separate species in any mathematical model. That being said, experiments in capacitive iodine discharges [94] have shown that the density of I(²P°₁/₂) states may be relatively low under some conditions due to collisional quenching (see section 3.6).

### 3.2.1. Elastic scattering

Elastic scattering processes are indicated by reactions B1 and B2 in table 3. Total elastic scattering cross-sections for I(²P°₃/₂) and I(²P°₁/₂) have been calculated by Ambalampitiya et al [31] up to electron energies of 100 eV. Data for I(²P°₃/₂) is shown in figure 13. While the cross-section for I(²P°₁/₂)
<figure><img src="image_16.png" /><figcaption>**Figure 13.** (Reaction B1 in table 3) Comparison of electron impact total elastic scattering cross-sections for $I(^{2}P^{\circ}_{3/2})$ from available theoretical/numerical data in the literature. The orange circles show experimental data from Zatsarinny et al [96].</figcaption></figure>

(not shown in figure 13) had not previously been calculated, the cross-section for $I(^{2}P^{\circ}_{3/2})$ can be compared to earlier calculations (see figure 13). In 2007, Wu and Yuan [95] performed an 11-state close-coupling calculation for the interaction between a slow electron and ground state atomic iodine using the fully relativistic R-matrix method, although their study was limited to energies up to 8 eV. In 2011, Zatsarinny et al [96] expanded this work by performing a combined experimental and theoretical study. Experimental data was obtained by subtracting known cross-sections from measured data of a pyrolyzed mixed beam containing various atomic and molecular species. The calculations were conducted using both the fully relativistic Dirac B-Spline R-matrix (BSR) method and an optical model potential approach. Despite the complexity of the problem, the agreement between the theoretical predictions and experimental data for angle-differential and angle-integrated elastic cross-sections at 40 eV and 50 eV was found to be satisfactory.

Hamilton [29] also calculated total scattering cross-sections for $I(^{2}P^{\circ}_{3/2})$, providing valuable data that was used in subsequent mathematical models by Grondein et al [71], Lucken [97], and Marmuse [98]. Lucken extrapolated the cross-section data at high energies using a log-linear law, while Marmuse used a power law at high energies and a quadratic law at low energies (see figure 13). While most calculations are in close agreement for electron energies between 3 and 50 eV, there are significant discrepancies below 3 eV. In particular, results differ by almost two orders of magnitude at 0.1 eV and the Ramsauer minima occurs at different energies. Currently, no known data exists for the elastic momentum transfer cross-sections (MTCSs) of either $I(^{2}P^{\circ}_{3/2})$ or $I(^{2}P^{\circ}_{1/2})$.

### 3.2.2. Ionization

Figure 14 shows electron impact ionization cross-sections for $I(^{2}P^{\circ}_{3/2})$ taken from the literature. The threshold energy is 10.451 eV, which is a value measured more than sixty years ago [24] and commonly included in ionization energy tables of chemistry and physics handbooks. The only experimental data dates back to 1987 with the work of Hayes et al [99], where measurements were obtained using a crossed electron-beam fast-atom-beam method with an uncertainty of ±12%. Since then, at least nine different works have provided theoretical or semi-empirical cross-sections. Margreiter et al [100] applied the semi-classical Deutsch-Märk (DM) formalism, a semi-empirical method that fits parameters to experimental data. Later, Huo and Kim [101] utilized an effective core potential orbital approach, while Joshipura and Limbachiya [102] introduced the spherical complex optical potential (SCOP) model for ionization calculations. Bartlett and Stelbovics [103] improved calculations based on the Born approximation by incorporating orthogonalized plane waves that enhanced the accuracy of cross-section predictions. The Binary-Encounter-Bethe (BEB) model, originally formulated by Kim and Rudd [104], was later employed by Ali and Kim [105], Hamilton [29], and Ambalampitiya et al [31], the latter integrating effective-core potentials within Quantemol electron collisions (QECs) calculations. Vinodkumar et al [106] and Naghma et al [107] expanded on the SCOP method by introducing the Complex Scattering Potential-ionization contribution (CSP-ic) approach, which dynamically extracts the ionization cross-section from the total inelastic cross-section. The most recent calculations from Hamilton [29] and Ambalampitiya et al [31] appear the least consistent with experimental measurements (aside from the work of Bartlett et al which overestimates the cross-section as the method used is expected to be accurate
<figure><img src="image_17.png" /><figcaption>Figure 14. (Reaction B3 in table 3) Comparison of electron impact ionization cross-sections for I($^2$P°$_{3/2}$) from available data in the literature.</figcaption></figure>

mostly at high electron energies). However, this discrepancy is expected as the BSR calculations include more coupled states which lead to a drop in the cross-section. As indicated in the zoomed region in figure 14, the ionization cross-sections show a fairly significant spread in values (as high as a factor of about two) for electron energies below 30 eV. Since the electron temperature in many iodine discharges is of the order of 5 eV, these differences naturally lead to important variations in the corresponding ionization rate coefficient (see section 3.7) which is crucial for plasma modeling.

Ionization from the I($^2$P°$_{1/2}$) state may also be important, and which would effectively represent a two-step ionization process involving excitation followed by ionization:

$$I(^2P^\circ_{1/2}) + e^- \rightarrow I^+ + 2e^- \quad (19)$$

No data is available for the above ionization reaction, however, since the ionization cross-section for I($^2$P°$_{3/2}$) is known, several approaches can be employed to estimate it. For example, a common approach involves applying scaling laws based on the difference in ionization threshold energies and using the following empirical relation

$$\sigma_{iz,I}(^2P^\circ_{1/2}) (\varepsilon) \approx \sigma_{iz,I}(\varepsilon + \varepsilon_{exc1,I}) \left[ \frac{\varepsilon_{iz,I}}{\varepsilon_{iz,I}(^2P^\circ_{1/2})} \right]^2, \quad (20)$$

where $\varepsilon$ is the electron kinetic energy, $\sigma_{iz,I}$ and $\sigma_{iz,I}(^2P^\circ_{1/2})$ are the ionization cross-sections of the I($^2$P°$_{3/2}$) and I($^2$P°$_{1/2}$) states respectively, and $\varepsilon_{iz,I}$ and $\varepsilon_{iz,I}(^2P^\circ_{1/2}) = \varepsilon_{iz,I} - \varepsilon_{exc1,I}$ are the corresponding ionization threshold energies with $\varepsilon_{exc1,I}$ the excitation energy of I($^2$P°$_{1/2}$). Here, the ionization threshold of I($^2$P°$_{1/2}$) is shifted relative to that of I($^2$P°$_{3/2}$) as the minimum energy required for ionization is reduced accordingly by the excitation threshold energy. As an alternative approach, extrapolations of ionization cross-sections from chemically or electronically similar species may also provide reasonable estimates (e.g. chlorine, bromine, or fluorine).

In many iodine discharges, single ionization is usually sufficient for modeling and diagnostics purposes. However, in specific domains such as electric propulsion, where electron temperatures can reach several tens of electron volts in some devices (such as Hall thrusters), multiple ionization processes may become significant and should be considered to more accurately describe the plasma composition and dynamics. Only three known studies provide data for multiple ionization [99, 103, 105]. Table 4 lists the energy thresholds of the first four ionization processes with the corresponding cross-sections plotted in figure 15. Hayes et al [99] again remains the sole experimental reference, reporting single, double, and triple ionization cross-sections. Bartlett and Stelbovics [103] extended theoretical calculations up to
<table><caption>**Table 4.** Threshold energies for electron impact multiple ionization: I($^{2}\text{P}_{3/2}^{\circ}$) + e⁻ → Iⁿ⁺ + (n + 1)e⁻, for n ∈ {1, 2, 3, 4}.</caption><thead><tr><th>Process</th><th>Threshold energy (eV)</th></tr></thead><tbody><tr><td>Single ionization</td><td>10.451</td></tr><tr><td>Double ionization</td><td>29.58</td></tr><tr><td>Triple ionization</td><td>59.15</td></tr><tr><td>Quadruple ionization</td><td>99.51</td></tr></tbody></table>

<figure><img src="image_18.png" /><figcaption>**Figure 15.** (Reaction B5 in table 3) Comparison of direct electron impact multiple ionization cross-sections from available data in the literature: I($^{2}\text{P}_{3/2}^{\circ}$) + e⁻ → Iⁿ⁺ + (n + 1)e⁻, for n ∈ {1, 2, 3, 4}.</figcaption></figure>

quadruple ionization, while Ali and Kim [105] calculated indirect double ionization cross-sections (not shown).

### 3.2.3. Electronic excitation and de-excitation

No experimental measurements of electronic excitation cross-sections for atomic iodine are known, and additionally, there are few available theoretical calculations. Indeed, some early iodine plasma models neglected excitation reaction processes because of this (see for example [108]). The earliest known theoretical calculation was performed by Hamilton [29] in 2015, and was subsequently used in several iodine plasma models [71, 97, 98, 109]. In Hamilton's work, excitation was treated as a single process given by the following reaction:

$$I(^{2}\text{P}_{3/2}^{\circ}) + e^{-} \rightarrow I^{*} + e^{-}, \qquad (21)$$

where I* is an effective lumped excited state accounting for all possible excitation levels above the ground state and with an excitation threshold set to 0.9426 eV: i.e. the energy gap between the I($^{2}\text{P}_{3/2}^{\circ}$) and I($^{2}\text{P}_{1/2}^{\circ}$) states. The calculation used the BSR method of Zatsarinny and Bartschat [110], together with a close-coupling expansion and non-orthogonal bound and continuum orbitals. A plot of the computed cross-section is shown in figure 16. As noted in [28], a challenge with this cross-section is that it strongly underestimates electron energy losses in iodine plasmas at typical electron temperatures of relevance to electric propulsion. This is because the threshold energy is roughly an order of magnitude lower than the threshold energies of excited states above the first level (see table 5).

More detailed cross-sections were computed in 2021 by Ambalampitiya et al [31] who resolved individual levels due to excitation from both the I($^{2}\text{P}_{3/2}^{\circ}$) and I($^{2}\text{P}_{1/2}^{\circ}$) states. A semi-relativistic Breit-Pauli BSR (BPBSR) method was used [111–114] with either 10 or 25 target states in the close-coupling expansion considered, and which are referred to as BPBSR-10 or BPBSR-25 respectively. This work was also later extended to treat 29 target states (BPBSR-29). These new excitation cross-sections allow more sophisticated iodine plasma models to be built, and as shown in [26, 28], including the correct excitation thresholds of the individual levels can be important. These plasma models have been validated with experimental data and indicate that the theoretical cross-sections appear reasonable. Figure 16 shows a comparison of the total excitation cross-sections, while figure 17 shows excitation cross-sections for I($^{2}\text{P}_{3/2}^{\circ}$) and I($^{2}\text{P}_{1/2}^{\circ}$) to several higher states. The corresponding atomic configuration, term, and level energy are summarized in table 5, where it is seen that the level energies are in reasonable agreement
with those from the National Institute of Standards and Technology (NIST) [93], although the predicted energy is slightly higher and two levels appear missing.

In many plasma models, detailed information on the evolution and dynamics of higher excited states is not usually needed as the density of these states is typically much lower than the $I(^2P^°_{3/2})$ ground state. However, as noted in section 3.1, it can be important to account for the $I(^2P^°_{1/2})$ state because of its low threshold energy. This state is also metastable with a very weak radiative decay probability. Higher excited state densities are usually very low in most plasma systems of current interest, but we note that if this is not the case, or if modeling of emission spectra is required, then radiative processes can become important. This was recently considered by Agrawl et al [115] who developed a collisional-radiative model to study the atomic iodine emission spectra produced in a low-pressure inductive plasma discharge.

In addition to excitation, electron impact de-excitation of the $I(^2P^°_{1/2})$ state should also be considered. While de-excitation cross-sections can easily be determined using the principle of detailed balance (see appendix C), for convenience we explicitly calculate this cross-section, and which is shown in figure 17(a).

More recently, Agrawl et al [115] have computed excitation cross-sections of 340 fine-structure levels for electron energies up to 500 eV. This work represents the largest known data set of excitation cross-sections that spans most levels likely to be of interest in the near future. Cross-sections were calculated using a fully relativistic distorted wave theory [116, 117], which is derived from a first-order perturbation theory. Example cross-sections obtained with this method are compared with those from Ambalampitiya et al [31] in figure 17, where reasonable agreement is found. Table 5 also lists the computed level energies for the first 31 (and the last 3) excited states. Overall, the agreement with NIST appears better than that of the BPBSR-29 model, although there are still slight differences and the energies of some states are higher than those from NIST. For convenience, the data in table 5 has been listed in energy ordered format using the results from Agrawl et al [115]. As data for 340 levels was calculated (and which is too large to list in this review paper), the reader is referred to [115] for information on excited states above number 31. Similarly, as there are too many cross-sections to individually plot, we only show some of the first levels in figure 17, while figure 16 shows the total excitation cross-section summed over all levels.

Although [115] and table 5 provides many individual excitation levels which may be required in some cases (such as collisional radiative models [115]), for many other models, such fine-grained detail is not needed. Therefore, having to directly deal with tens or hundreds of excitation levels can be cumbersome, and so making use of a fewer number of lumped excitation levels can often be more practical and convenient. Esteves [26] proposed a series of effective lumped levels based on the BPBSR-29 data, and which are summarized in table 6. Here, the zeroth and first levels correspond to the individual $I(^2P^°_{3/2})$ and $I(^2P^°_{1/2})$ states. However, higher excited states are grouped together into effective lumped levels that consists of individual states summed together. The level energy is then set equal to the threshold energy (based on the more accurate NIST values) of the lowest excited state included in that lumped level. Based on the detailed individual cross-sections, the effective cross-section for the lumped levels in table 6 can easily be obtained from the sum of individual levels. Similarly, rate coefficient can be calculated based on these cross-sections, as discussed in section 3.7.

### 3.2.4. Other processes

Aside from electron impact excitation of the $I(^2P^°_{3/2})$ and $I(^2P^°_{1/2})$ states, excitation of higher states can also occur, although no known cross-sections are available and such reactions have been of limited interest thus far.

## 3.3. Electron impact scattering: molecular iodine

In addition to electron impact elastic scattering, electronic excitation, and ionization, new reactions emerge in collisions with molecular iodine including vibrational excitation and various dissociation processes. Each of these reaction types are again highlighted in the subsections below and summarized in table 7. The molecular ground state is $I_2(X^1\Sigma^+_g)$, with a further discussion of term symbols provided in appendix B. Since all available scattering data is based on electron impact of the molecular ground state, the term symbol will be omitted for convenience where possible and the ground state will simply be denoted as $I_2$.

### 3.3.1. Elastic scattering

Total elastic scattering and MTCSS for molecular iodine obtained from the literature are plotted in figure 18. The first known calculation of the total elastic scattering cross-section was performed by
<table><caption>**Table 5.** Energy ordered list of the first 31 (and last 3), excitation energy levels of atomic iodine following Agrawal *et al* [115]. Also shown are the corresponding level energies from Ambalampitiya *et al* [31] and NIST [93], as well as the total angular momentum quantum number, *J*, and level degeneracy, *g*.</caption><thead><tr><th rowspan="2">No.</th><th rowspan="2">Configuration</th><th rowspan="2">Term</th><th rowspan="2">J</th><th rowspan="2">g</th><th colspan="3">Level energy (eV)</th></tr><tr><th>[115]</th><th>[31]</th><th>NIST</th></tr></thead><tbody><tr><td>0</td><td>5p<sup>5</sup></td><td>2P°</td><td>3/2</td><td>4</td><td>—</td><td>—</td><td>—</td></tr><tr><td>1</td><td>5p<sup>5</sup></td><td>2P°</td><td>1/2</td><td>2</td><td>0.9687</td><td>0.9529</td><td>0.9426</td></tr><tr><td>2</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)6s</td><td>2[2]</td><td>5/2</td><td>6</td><td>6.7655</td><td>7.2015</td><td>6.7737</td></tr><tr><td>3</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)6s</td><td>2[2]</td><td>3/2</td><td>4</td><td>6.9881</td><td>7.3939</td><td>6.9546</td></tr><tr><td>4</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>0</sub>)6s</td><td>2[0]</td><td>1/2</td><td>2</td><td>7.5365</td><td>8.1898</td><td>7.5502</td></tr><tr><td>5</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>1</sub>)6s</td><td>2[1]</td><td>3/2</td><td>4</td><td>7.5878</td><td>7.9452</td><td>7.6647</td></tr><tr><td>6</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)6p</td><td>2[2]°</td><td>5/2</td><td>6</td><td>7.7717</td><td>8.1850</td><td>8.0473</td></tr><tr><td>7</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)6p</td><td>2[2]°</td><td>3/2</td><td>4</td><td>7.8121</td><td>8.2217</td><td>8.0577</td></tr><tr><td>8</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>1</sub>)6s</td><td>2[1]</td><td>1/2</td><td>2</td><td>7.8292</td><td>8.0447</td><td>7.8341</td></tr><tr><td>9</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)6p</td><td>2[3]°</td><td>7/2</td><td>8</td><td>7.8763</td><td>8.3228</td><td>8.1420</td></tr><tr><td>10</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)6p</td><td>2[3]°</td><td>5/2</td><td>6</td><td>7.9007</td><td>8.3373</td><td>8.1389</td></tr><tr><td>11</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)6p</td><td>2[1]°</td><td>7/2</td><td>8</td><td>7.9358</td><td>8.3503</td><td>8.1652</td></tr><tr><td>12</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)5d</td><td>2[3]</td><td>7/2</td><td>8</td><td>7.9699</td><td>8.3758</td><td>8.1848</td></tr><tr><td>13</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)5d</td><td>2[3]</td><td>5/2</td><td>6</td><td>8.0081</td><td>8.3867</td><td>8.1855</td></tr><tr><td>14</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)5d</td><td>2[1]</td><td>3/2</td><td>4</td><td>8.0784</td><td>8.4546</td><td>8.2270</td></tr><tr><td>15</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)6p</td><td>2[1]°</td><td>3/2</td><td>4</td><td>8.1305</td><td>8.4810</td><td>8.3146</td></tr><tr><td>16</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)5d</td><td>2[1]</td><td>1/2</td><td>2</td><td>8.1748</td><td>8.5757</td><td>8.3439</td></tr><tr><td>17</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)5d</td><td>2[4]</td><td>9/2</td><td>10</td><td>8.1923</td><td>8.6837</td><td>8.3970</td></tr><tr><td>18</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)5d</td><td>2[4]</td><td>7/2</td><td>8</td><td>8.3158</td><td>8.7887</td><td>8.5003</td></tr><tr><td>19</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)5d</td><td>2[2]</td><td>3/2</td><td>4</td><td>8.4002</td><td>9.0054</td><td>8.7229</td></tr><tr><td>20</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)5d</td><td>2[0]</td><td>1/2</td><td>2</td><td>8.4069</td><td>8.8971</td><td>8.5073</td></tr><tr><td>21</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)5d</td><td>2[2]</td><td>5/2</td><td>6</td><td>8.4185</td><td>9.0064</td><td>8.6976</td></tr><tr><td>22</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>1</sub>)6p</td><td>2[0]°</td><td>1/2</td><td>2</td><td>8.5620</td><td>8.9594</td><td>8.8650</td></tr><tr><td>23</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)7s</td><td>2[2]</td><td>5/2</td><td>6</td><td>8.6100</td><td>9.0545</td><td>8.9149</td></tr><tr><td>24</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>0</sub>)6p</td><td>2[1]°</td><td>3/2</td><td>4</td><td>8.6426</td><td>9.0841</td><td>8.9240</td></tr><tr><td>25</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>1</sub>)6p</td><td>2[2]°</td><td>5/2</td><td>6</td><td>8.6432</td><td>—</td><td>8.9925</td></tr><tr><td>26</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>0</sub>)6p</td><td>2[1]°</td><td>1/2</td><td>2</td><td>8.6491</td><td>9.0330</td><td>8.9038</td></tr><tr><td>27</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>2</sub>)7s</td><td>2[2]</td><td>3/2</td><td>4</td><td>8.6901</td><td>9.1104</td><td>8.9634</td></tr><tr><td>28</td><td>5p<sup>4</sup>(<sup>3</sup>P<sub>1</sub>)6p</td><td>2[2]°</td><td>3/2</td><td>4</td><td>8.7178</td><td>—</td><td>9.0269</td></tr><tr><td>29</td><td>5p<sup>4</sup>(<sup>1</sup>D<sub>2</sub>)6s</td><td>2[2]</td><td>5/2</td><td>6</td><td>8.7409</td><td>8.8837</td><td>8.5038</td></tr><tr><td>30</td><td>5p<sup>4</sup>(<sup>1</sup>D<sub>2</sub>)6s</td><td>2[2]</td><td>3/2</td><td>4</td><td>8.7567</td><td>8.8700</td><td>8.4991</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>337</td><td>5p<sup>4</sup>(<sup>1</sup>S<sub>0</sub>)9s</td><td>2[0]</td><td>1/2</td><td>2</td><td>13.7140</td><td>—</td><td>—</td></tr><tr><td>338</td><td>5p<sup>4</sup>(<sup>1</sup>S<sub>0</sub>)7d</td><td>2[2]</td><td>5/2</td><td>6</td><td>13.8221</td><td>—</td><td>—</td></tr><tr><td>339</td><td>5p<sup>4</sup>(<sup>1</sup>S<sub>0</sub>)5d</td><td>2[1]</td><td>3/2</td><td>4</td><td>14.5976</td><td>—</td><td>—</td></tr></tbody></table>

<figure><img src="image_19.png" /><figcaption>**Figure 16.** (Reaction B7 in table 3) Comparison of the total atomic iodine excitation cross-section for I(<sup>2</sup>P°<sub>3/2</sub>) from available data in the literature.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Figure 17.** (Reactions B6–B8 in table 3) Comparison of the excitation cross-sections from Ambalampitiya *et al* [31] (blue lines) and Agrawal *et al* [115] (orange lines) for the first two transitions from the $I(^2P_{1/2}^°)$ ground state (top row), and the first two transitions from the $I(^2P_{1/2}^°)$ excited state (bottom row). Also shown is the de-excitation cross-section (dashed line; top left) computed using the principle of detailed balance (see appendix C).</figcaption></figure>

<table><caption>**Table 6.** Energy ordered list of effective lumped excitation levels based on the BPBSR-29 model [26]. The last column lists the number of individual levels included in each effective level.</caption><thead><tr><th>No.</th><th>g</th><th>Energy (eV)</th><th>No. Levels</th></tr></thead><tbody><tr><td>0</td><td>4</td><td>—</td><td>1</td></tr><tr><td>1</td><td>2</td><td>0.9426</td><td>1</td></tr><tr><td>2</td><td>18</td><td>6.7736</td><td>5</td></tr><tr><td>3</td><td>26</td><td>8.0473</td><td>5</td></tr><tr><td>4</td><td>82</td><td>8.1848</td><td>17</td></tr></tbody></table>

Hamilton [29] in 2015, and which was adopted—along with various extrapolations—by Grondein *et al* [71], Lucken [97], and Marmuse [98]. Ambalampitiya *et al* [31] later provided new calculations for both total elastic scattering and MTCSs covering a broad range of electron energies. This data was subsequently used by Esteves [26], who extrapolated the data at both low (assuming a constant value) and high (assuming an inverse power law) energies. This extrapolation procedure follows the methodology introduced by Marmuse [98] and is consistent with the approach suggested by Tallents [118]. In 2020, Yadav *et al* [119] introduced new cross-section calculations using the *R*-matrix method with two different models: the static exchange plus polarization method and the configuration interaction technique [120]. While these cross-sections align reasonably well with those of Ambalampitiya *et al* [31], the MTCS is approximately five times larger. The magnitude of the MTCSs from both Ambalampitiya *et al* and Yadav are significant and suggest that elastic backward scattering plays an important role for electrons in $I_2$. However, similar elastic angular scattering has not been observed in other halogen gases, such as chlorine. Hence, further work is needed to clarify the role of electron momentum transfer during collisions with $I_2$.
<table><caption>**Table 7.** Electron impact scattering processes for I₂. Here I₂\* represents an electronically excited state above the I₂(X¹Σ<sup>+</sup>g) ground state (denoted simply as I₂ for convenience), while *ν* labels the vibrational level. Note that although the threshold energy for reaction C4 is set equal to the dissociation energy of the molecular ground state, the actual energy may vary depending on the specific dissociation pathway (see section 3.3.3).</caption><thead><tr><th>ID</th><th>Reaction</th><th>Process</th><th>Threshold energy (eV)</th></tr></thead><tbody><tr><td>C1</td><td>I<sub>2</sub> + e<sup>-</sup> → I<sub>2</sub> + e<sup>-</sup></td><td>Elastic scattering</td><td>—</td></tr><tr><td>C2</td><td>I<sub>2</sub> + e<sup>-</sup> → I<sub>2</sub><sup>+</sup> + 2 e<sup>-</sup></td><td>Ionization</td><td>9.31</td></tr><tr><td>C3</td><td>I<sub>2</sub> + e<sup>-</sup> → I(<sup>2</sup>P<sub>3/2</sub>) + I<sup>+</sup> + 2 e<sup>-</sup></td><td>Dissociative ionization</td><td>11.63</td></tr><tr><td>C4</td><td>I<sub>2</sub> + e<sup>-</sup> → 2I(<sup>2</sup>P<sub>3/2</sub>) + e<sup>-</sup></td><td>Dissociation</td><td>1.542</td></tr><tr><td>C5</td><td>I<sub>2</sub> + e<sup>-</sup> → I(<sup>2</sup>P<sub>1/2</sub>) + I<sup>-</sup></td><td>Dissociative attachment</td><td>—</td></tr><tr><td>C6</td><td>I<sub>2</sub> + e<sup>-</sup> → I<sub>2</sub><sup>*</sup> + e<sup>-</sup></td><td>Electronic excitation</td><td>See table 8</td></tr><tr><td>C7</td><td>I<sub>2</sub>(ν=0) + e<sup>-</sup> → I<sub>2</sub>(ν > 0) + e<sup>-</sup></td><td>Vibrational excitation</td><td>~0.0266 per level</td></tr></tbody></table>

<figure><img src="image_21.png" /><figcaption>**Figure 18.** (Reaction C1 in table 7) Comparison of the total elastic scattering and momentum transfer cross-sections (MTCS) for I₂ from available data in the literature.</figcaption></figure>

### 3.3.2. Ionization

No known experimental data is available for electron impact ionization of I₂, although the ionization threshold energy is well established at 9.31 eV (as experimentally determined by Cockett et al [121], for example). In the absence of direct measurements, several theoretical and semi-empirical approaches have been developed to estimate the ionization cross-section, and which are highlighted in figure 19. Among them, Deutsch et al [122] introduced the defect concept method, while Probst et al [123] applied the DM formalism, relying on semi-classical parameter fitting. Joshipura and Limbachiya [102] extended the SCOP model, and the BEB model (initially formulated by Kim and Rudd [104]), was again later employed by Ali et al [105] and Hamilton [29], with Ali et al incorporating the screening effect potential method for improved accuracy. Yadav et al [119] refined the SCOP model further through the CSP-ic approach, while Ambalampitiya et al [31] integrated effective-core potential effects within QEC calculations. In several of the above works, only the total ionization cross-section is determined, which is the sum of direct and dissociative ionization processes

$$I_2 + e^- \rightarrow I_2^+ + 2e^-, \qquad (22)$$

$$I_2 + e^- \rightarrow I(^2P_{3/2}) + I^+ + 2e^-. \qquad (23)$$

Ionization cross-sections for each individual process are then established by assuming a constant, energy-independent, branching ratio. For example, Ambalampitiya et al [31] assumed a ratio of 0.9 and 0.1 for each process respectively. Thus, the assumed iodine branching ratio represents an additional uncertainty.

### 3.3.3. Dissociative processes

Aside from thermal dissociation discussed in section 2.4, electron impact dissociation is an important process that tends to dominate at low pressures. The only known dissociation cross-section is from Hamilton [29], which is plotted in figure 20. The reaction threshold energy was fixed to 1.542 eV, which corresponds to the dissociation limit of the molecular ground state [61]. The atomic dissociation
<figure><img src="image_22.png" /><figcaption>**Figure 19.** (Reactions C2–C3 in table 7) Comparison of ionization cross-sections for I₂ from available data in the literature.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>**Figure 20.** (Reaction C4 in table 7) Dissociation cross-section for I₂ from available data in the literature.</figcaption></figure>

products were assumed to be in the I(²P°₃/₂) ground state. Unfortunately, data is only available for electron energies below 10 eV, which is typically insufficient for an accurate description of most iodine discharges. Several previous models have therefore extrapolated the data at high energy using either a log-linear or inverse power law [26, 28, 97, 98]. Dissociation can be viewed as a multi-step process whereby an electron first transfers energy to the molecule placing it into one of a number of possible bound or repulsive excited states. Repulsive states can subsequently dissociate into a combination of different I(²P°₃/₂) or I(²P°₁/₂) atomic states, or even ionic states [124]. Information on these dissociation pathways is not well known.

Dissociative electron attachment is a reaction whereby the incident electron initially becomes attached to the molecule. The molecule then dissociates and the electron remains bound to one of the resulting atoms to form a negative ion (I⁻). This reaction is particularly important in low-pressure iodine discharges as it is the main process leading to the creation of negative ions. Figure 21 shows a comparison of the dissociative electron attachment cross-sections from data available in the literature (obtained either experimentally, theoretically or with numerical simulations) spanning a wide energy range from 0.01 to 100 eV. This includes early works by Healey [84], Buchdahl [85], Biondi and Fox [86–88], and Frost and McDowell [83] (where the data were normalized to Buchdahl’s maximum cross-section), subsequent works by Tam and Wong [125], Brooks et al [126], Kurepa et al [127] and Pozdneev [128], as well as more recent evaluations by Hamilton [29] and Ambalampitiya et al [31]. The cross-sections from Tam et al and Kurepa et al were normalized by setting the total attachment rate coefficient at room temperature (obtained by integrating over a Maxwellian distribution) equal to the value of Truby [89] (the I₂ attachment rate coefficient has been measured several times and its dependence on the gas temperature discussed in different works; see for example [84, 89, 90, 127, 129–132]). For energies below 1 eV, there is significant disagreement across all data sources. Caledonia et al [133] and Ayala
<figure><img src="image_24.png" /><figcaption>**Figure 21.** (Reaction C5 in table 7) Comparison of dissociative electron attachment cross-sections for I₂ from available data in the literature.</figcaption></figure>

et al [131] had already highlighted these discrepancies stating that the Biondi and Fox experiments [86–88] were conducted in the presence of hydrogen iodide (HI), which is known to exhibit a large thermal electron attachment cross-section. The presence of HI impurities may therefore account for the discrepancies between their findings and those of other published works [83, 85, 89, 90]. Gallagher et al [132] also heavily disregarded Healey’s results because of their disagreement with Brook’s data. As noted by Ambalampitiya et al, the neutral atomic dissociation product is predicted to be the I(²P°₁/₂) state, which has largely been ignored in previous plasma modeling work (with the notable exception of [26]) and which seems to be in contradiction with other works (see section 7.5).

Finally, dissociative ionization is another important dissociation reaction that was already highlighted in section 3.3.2. From Ambalampitiya et al [31], the neutral atomic dissociation product is assumed to be the I(²P°₃/₂) ground state. The calculated threshold energy of 11.94 eV is similar to the sum of the photoionization energy (about 8.9 eV; see [134]) and the electron affinity of atomic iodine (approximately 3.06 eV; see [135]). This is also close to the experimentally measured value of 11.63 ±0.05 eV [136]. Differences with the dissociative ionization cross-section originally calculated by Hamilton [29] are very minor, although as noted in section 3.3.2, an assumption is made on the branching ratio of the different ionization pathways.

### 3.3.4. Electronic excitation

The first known calculations of electron impact electronic excitation of I₂ were performed by Yadav et al [119], who considered six excited states: ³Π<sub>u</sub>, ¹Π<sub>u</sub>, ³Σ<sup>-</sup><sub>g</sub>, ¹Σ<sup>+</sup> (two states), and ¹Σ<sup>-</sup><sub>g</sub>. In 2021, Ambalampitiya et al [31] performed similar calculations with four excited states: ³Π<sub>u</sub>, ¹Π<sub>u</sub>, ³Σ<sup>-</sup><sub>g</sub>, and ¹Σ<sup>+</sup><sub>g</sub>. Before these works, iodine plasma models did not account for molecular electronic excitation as no cross-sections were available, and because the dissociation threshold energy is lower than the excitation threshold energies such that excited states were assumed to become dissociated [97].

The levels and notations of molecular excited states used by Ambalampitiya et al [31] and Yadav et al [119] differ from that used by other authors (see for example [137]). This is related to whether relativistic effects are accounted for in the molecular potential calculations. The notation used by spectroscopists [61, 138] is much closer to that used by Poline et al [137]. It is not easy to exactly match the states obtained by relativistic and non-relativistic calculations. Moreover, the threshold energies depend on the calculation method used, which not only differs between authors, but also with precise spectroscopic measurements. This largely explains the discrepancies in table 8 which summarizes several excitation reactions.

The sum of all molecular excitation cross-sections are plotted in figure 22. While the trends agree quite well, the total cross-section from Yadav et al is about two times higher than that from Ambalampitiya et al. As mentioned previously in section 3.2.3, if the density of excited states is important, or if emission spectra are needed (such as for diagnostic purposes), radiative processes need to be considered. No known collisional-radiative models accounting for emission from molecular iodine exist, although Prince et al [139, 140] have performed measurements to enable the development of such models, particularly within the context of diagnosing iodine thruster plumes. Prince et al have measured apparent excitation cross-sections for photoemission from iodine plasmas for wavelengths between 300 and 1050 nm. Emission was observed from I*, I₂, I⁺*, and I₂⁺* species produced during various electron
<table><caption>**Table 8.** List of molecular electronic excitation reactions available from the literature. In the work by Yadav *et al* [119], two $^1\Sigma_g^+$ states are considered with different excitation cross-sections.</caption><thead><tr><th rowspan="2">ID</th><th rowspan="2">Reaction</th><th colspan="3">Threshold energy (eV)</th></tr><tr><th>Calculation [31, 119]</th><th>Theory [138]</th><th>Experiment [139, 141]</th></tr></thead><tbody><tr><td>C6-1</td><td>I<sub>2</sub> + e<sup>-</sup> → I<sub>2</sub> (<sup>3</sup>Π<sub>u</sub>) + e<sup>-</sup></td><td>2.18 ; 2.18</td><td>2.37</td><td>1.25 ; 1.95</td></tr><tr><td>C6-2</td><td>I<sub>2</sub> + e<sup>-</sup> → I<sub>2</sub> (<sup>1</sup>Π<sub>u</sub>) + e<sup>-</sup></td><td>3.00 ; 2.99</td><td>2.38</td><td>—</td></tr><tr><td>C6-3</td><td>I<sub>2</sub> + e<sup>-</sup> → I<sub>2</sub> (<sup>3</sup>Σ<sub>g</sub><sup>-</sup>) + e<sup>-</sup></td><td>5.18 ; 5.44</td><td>3.90</td><td>5.04</td></tr><tr><td>C6-4</td><td>I<sub>2</sub> + e<sup>-</sup> → I<sub>2</sub> (<sup>1</sup>Σ<sub>g</sub><sup>-</sup>) + e<sup>-</sup></td><td>— ; 6.26</td><td>4.4</td><td>—</td></tr><tr><td>C6-5</td><td>I<sub>2</sub> + e<sup>-</sup> → I<sub>2</sub> (<sup>1</sup>Σ<sub>g</sub><sup>+</sup>) + e<sup>-</sup></td><td>5.70 ; 6.80</td><td>—</td><td>—</td></tr></tbody></table>

<figure><img src="image_25.png" /><figcaption>**Figure 22.** (Reaction C6 in table 7) Total electronic excitation cross-sections for I₂ from available data in the literature.</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>**Figure 23.** (Reaction C7 in table 7) Example electron impact vibrational excitation cross-sections of molecular iodine for $v=0$ to $v=1$, $v=0$ to $v=10$, and the combined sum of $v=0$ to $v=k$ for $k \in \{1, \dots, 10\}$.</figcaption></figure>

impact collisions of I₂ for electron energies between about 4 and 100 eV. The authors note however that interpretation of the results is limited by several factors including a constrained spectral range, cascading processes from higher excited states, and congested spectral data.

### 3.3.5. Vibrational excitation

The only known electron impact vibrational excitation cross-sections were calculated by Ambalampitiya *et al* [31] up to electron energies of approximately 6 eV. These calculations treat vibrational excitation from the molecular ground state I₂(X $^1\Sigma_g^+$, $v=0$) to the first ten vibrational levels, and approximate I₂ as a harmonic oscillator. The energy difference between successive vibrational levels corresponds to 0.0266 eV. Figure 23 shows example cross-sections for the first transition (from $v=0$ to $v=1$) and the last (from $v=0$ to $v=10$), as well as the sum of all ten contributions. Two peaks are observed and which are centered around 0.5 eV (due to the $^2\Pi_g$ resonance) and 2 eV (due to the $^2\Pi_u$ resonance).
<table><caption>**Table 9.** Example ion-neutral collisional processes. A negative threshold energy indicates an exothermic reaction with energy release.</caption><thead><tr><th>ID</th><th>Reaction</th><th>Process</th><th>Threshold energy (eV)</th></tr></thead><tbody><tr><td>D1</td><td>I(<sup>2</sup>P<sub>3/2</sub>) + I<sup>+</sup> → I<sup>+</sup> + I(<sup>2</sup>P<sub>3/2</sub>)</td><td>Charge-exchange</td><td>—</td></tr><tr><td>D2</td><td>I<sub>2</sub> + I<sup>+</sup> → I<sub>2</sub><sup>+</sup> + I(<sup>2</sup>P<sub>3/2</sub>)</td><td>Charge-exchange</td><td>-1.14</td></tr><tr><td>D3</td><td>I<sub>2</sub> + I<sub>2</sub><sup>+</sup> → I<sub>2</sub><sup>+</sup> + I<sub>2</sub></td><td>Charge-exchange</td><td>—</td></tr><tr><td>D4</td><td>I<sub>2</sub> + I<sup>+</sup> → 2I(<sup>2</sup>P<sub>3/2</sub>) + I<sup>+</sup></td><td>Dissociation</td><td>1.542</td></tr><tr><td>D5</td><td>I<sub>2</sub> + I<sub>2</sub><sup>+</sup> → I<sub>2</sub> + I(<sup>2</sup>P<sub>3/2</sub>) + I<sup>+</sup></td><td>Dissociation</td><td>2.68</td></tr></tbody></table>

<figure><img src="image_27.png" /><figcaption>**Figure 24.** (Reactions D1–D5 in table 9) Ion-neutral collision cross-sections as a function of the lab frame energy for (a) I + I⁺ and (b) I₂ + I⁺ and I₂⁺. Data taken from [21, 146]. The dashed line in (a) shows the empirical cross-section from Sakabe et al [147], while the dashed line in (b) shows the empirical cross-section from equation (24) for I₂ + I⁺.</figcaption></figure>

Compared with other electron impact processes, the contribution of vibrational excitation appears small. Nonetheless, it may be important in some plasma discharges to correctly account for electron energy losses or neutral gas heating. For example, in addition to electron impact vibrational excitation and de-excitation, relaxation of vibrationally excited states can also occur via collisions with I or I₂ (see for example [142, 143]).

### 3.4. Collisional processes between ions and neutrals

Following Phelps [144], ion-neutral elastic collisions can be considered to consist of isotropic and backward (or charge-exchange) scattering processes. We note however that for collisions between particles which have a different mass (such as I₂ and I⁺ or I₂⁺ and I), charge-exchange is no longer an elastic process as the ionization energy of the species differs. Thus, the reaction may be inelastic or even superelastic. Of the many possible ion-neutral collisional processes that exist in iodine plasmas, only a small number have been studied experimentally or theoretically, as summarized in table 9. Figure 24 shows the cross-sections for these processes as a function of the lab frame energy.

Various works, such as the book by Smirnov [145], provide approximate methods for calculating the charge-exchange cross-section from first principles quantum mechanics. Smirnov also provides representative cross-sections for many atomic elements in the periodic table, including iodine, where the reaction I + I⁺ → I⁺ + I has a cross-section between about 10 and 20 × 10⁻¹⁹ m² and a threshold energy of 0 eV. Dressler et al [21] calculated charge-exchange cross-sections for I + I⁺ → I⁺ + I at lab frame
<table><caption>**Table 10.** Example charged particle collisional processes. A negative threshold energy indicates an exothermic reaction with energy release.</caption><thead><tr><th>ID</th><th>Reaction</th><th>Process</th><th>Threshold energy (eV)</th></tr></thead><tbody><tr><td>E1</td><td>I<sup>n+</sup> + e<sup>-</sup> → I<sup>(n+1)+</sup> + 2 e<sup>-</sup></td><td>Ion ionization</td><td>—</td></tr><tr><td>E2</td><td>I<sup>+</sup> + I<sup>-</sup> → 2 I<sup>(2P<sub>3/2</sub>)</sup></td><td>Recombination</td><td>-7.39</td></tr><tr><td>E3</td><td>I<sub>2</sub><sup>+</sup> + I<sup>-</sup> → 3 I<sup>(2P<sub>3/2</sub>)</sup></td><td>Recombination</td><td>-4.71</td></tr><tr><td>E4</td><td>I<sub>2</sub><sup>+</sup> + e<sup>-</sup> → I<sup>(2P<sub>3/2</sub>)</sup> + I<sup>+</sup> + e<sup>-</sup></td><td>Ion dissociation</td><td>2.68</td></tr><tr><td>E5</td><td>I<sub>2</sub><sup>+</sup> + e<sup>-</sup> → 2I<sup>(2P<sub>3/2</sub>)</sup></td><td>Dissociative recombination</td><td>-8.27</td></tr><tr><td>E6</td><td>I<sup>-</sup> + e<sup>-</sup> → I<sup>(2P<sub>3/2</sub>)</sup> + 2 e<sup>-</sup></td><td>Detachment</td><td>3.059</td></tr></tbody></table>

energies between 10 and 1000 eV using a corrected one-electron treatment based on a linear combination of atomic orbitals model. These cross-sections are compared with those from Smirnov in figure 24 where reasonable agreement is seen.

Hause *et al* [146] measured cross-sections for the charge-exchange reaction $I_2 + I^+ \rightarrow I_2^+ + I$ (which is an exothermic reaction releasing 1.14 eV of energy), as well as total cross-sections for the sum of this reaction and $I_2 + I^+ \rightarrow 2I + I^+$ (with a threshold energy of 1.542 eV), using a guided-ion beam technique. In particular, cross-sections were estimated using a beam attenuation method (expected to provide an upper cross-section limit) and a time-of-flight method (expected to give a lower cross-section limit). Experiments were performed for lab frame energies from around 0.67 eV to almost 300 eV. Individual cross-sections were also measured for the charge-exchange reaction $I_2 + I_2^+ \rightarrow I_2^+ + I_2$ (with a threshold energy of 0 eV) and the collision induced dissociation reaction $I_2 + I_2^+ \rightarrow I^+ + I + I_2$ (with a threshold energy of 2.68 eV). Measured cross-sections for the above reactions are provided in figure 24(b). All atomic and molecular iodine products are in their respective ground states. An empirical cross-section was proposed by Hause *et al* for the reaction $I_2 + I^+$ at high energies (above about 100 eV) and which is given by

$$ \sigma_{I_2-I^+} = A - B \ln \varepsilon, \qquad (24) $$

where $A = 66.0 \times 10^{-20} \text{ m}^2$, $B = 4.7 \times 10^{-20} \text{ m}^2$, and $\varepsilon$ is the lab frame energy in units of (eV). The above empirical cross-section is similar in form to the Sakabe-type cross-section [147] which was used by Choi [148] to fit the cross-sections by Hause *et al* at high energies.

For ion-neutral collisional processes where no information is available, one may reasonably refer to approaches used for other diatomic gases such as chlorine [149, 150] and oxygen [151]. Here, the scattering cross-section is typically assumed to be half the value of the charge-exchange cross-section. Due to a lack of data, cross-sections for the scattering of negative ions with iodine atoms and molecules is assumed to be the same as those for positive ion scattering. However, as highlighted by Karmohapatro [152] in chlorine plasmas, the resonant charge-exchange cross-section is in fact higher for negative ions than for positive ions, so this simplified approach requires care.

### 3.5. Collisional processes between charged particles

In addition to collisions between charged particles and neutrals, there can also be collisions between charged particles themselves. Aside from Coulomb collisions (which are not specific to iodine), relevant collisional processes include electron impact excitation and ionization of ions (see also section 3.2), as well as recombination of positive and negative ions. Table 10 lists possible charged particle reactions with several important reactions subsequently discussed in further detail in the subsections below. For convenience (and due to a lack of data), we do not treat electron-ion excitation/de-excitation, nor ion-ion excitation/de-excitation or ionization.

#### 3.5.1. Ion ionization

While direct multiple ionization processes were discussed in section 3.2.2, ionization processes involving electron impact ionization of ions themselves may also be relevant

$$ I^{n+} + e^{-} \rightarrow I^{(n+1)+} + 2e^{-}, \qquad (25) $$

where $n \ge 1$ with $n$ an integer. Since the electron temperature in some electric propulsion systems can be above 10 eV, ionization leading to $I^{2+}$ and $I^{3+}$ may be significant in some discharges. Indeed, experimental measurements in the plume of an iodine-fueled Hall thruster [153] have observed small fractions of $I^{2+}$. Experimental measurements or theoretical calculations of ionization cross-sections of ionic states are however not known.
### 3.5.2. Ion-ion recombination

In several previous works, such as Grondein et al [71], the only reaction process considered for the loss of $I^-$ was via recombination with $I^+$ (to produce two iodine atoms) or $I_2^+$ (to produce an iodine atom and a molecule). Rate coefficients were respectively obtained from Yeung [154] and Greaves [155] and were assumed to be constant:

$$K_{\text{rec},I^+ - I^-} = 9.311 \times 10^{-15} \text{ m}^3 \text{ s}^{-1},$$

$$K_{\text{rec},I_2^+ - I^-} = 1.22 \times 10^{-13} \text{ m}^3 \text{ s}^{-1}.$$

The above rate coefficients were also later used by Lucken [97] and Marmuse [98]. However, subsequent investigations have shown that these values are likely not correct for several reasons. Firstly, Yeung [154] did not explicitly mention which recombination process was being studied and both positive and negative iodine ions were assumed to be molecular (i.e. $I_2^+$ and $I_2^-$): as suggested by Spencer-Smith's early work on iodine discharges in 1935 [156] where $I_2^+$ and $I_2^-$ were found to be the most dominant ions. Secondly, Greaves [155] later repeated the experiment of Yeung and concluded that there may have been a fault with one of the amplifiers originally used resulting in an underestimation by a factor of 10. Mass spectrometry measurements also determined that the dominant ion species were $I_2^+$ and $I^-$ (which had also been demonstrated in 1928 by Hogness and Harkness [82]). Greaves also measured rate coefficients for pressures between 4 and 133 Pa, and gas temperatures between 296 and 338 K. Overall, the rate coefficient increases with pressure and the measured value at 4 Pa and 296 K is $K_{\text{rec},I_2^+ - I^-} = 5.8 \times 10^{-14} \text{ m}^3 \text{ s}^{-1}$: a value roughly half of that used by Grondein et al. Based on the above factors, and considering similar recombination reactions used in chlorine plasma models [150], reasonable empirical rate coefficients are

$$K_{\text{rec},I^+ - I^-} = K_{\text{rec},I_2^+ - I^-} = 5 \times 10^{-14} \sqrt{\frac{300}{T_g}} \text{ m}^3 \text{ s}^{-1}, \qquad (26)$$

where $T_g$ is the gas temperature in units of (K) and the rate coefficients for both recombination reactions are assumed equal. The dependence on gas temperature is an assumption informed by theoretical considerations related to the integration of a cross-section proportional to $1/\epsilon$ over a Maxwellian distribution [157]. Again in analogy with chlorine plasmas [150], the reaction products depend on the reaction type: i.e. $I^+ + I^-$ leads to two iodine atoms, while $I_2^+ + I^-$ leads to three iodine atoms (as opposed to one atom and one molecule; see table 10). This hypothesis has been confirmed in private discussions with Nicolas Sisourat and his team at the Laboratory of Physical Chemistry-Matter and Radiation (LCPMR) in France who carried out preliminary experiments at the Double ElectroStatic Ion Ring ExpEriment (DESIREE) at Stockholm University in Sweden.

Recently, Poline et al [137] studied the recombination of $I^+$ and $I^-$ at the DESIREE facility and showed that the reaction products are two iodine atoms either in the $I(^2P_{3/2}^\circ)$ ground state (40%), or with one of the atoms in the $I(6s^2[2])$ excited state (60%). No significant variation of the branching ratio was observed over the studied energy range between 0.1 and 0.8 eV. The total recombination cross-section (including all reaction pathways) is estimated to be of the order of $10^{-17} \text{ m}^2$ at an energy of 0.1 eV. Initial cross-section calculations have been performed at LCPMR and are presented in figure 25(a). Here, the cross-section depends on the reaction products with $I(^2P_{3/2}^\circ) + I(6s)$ being the most probable, and where I(6s) designates a highly excited 6s Rydberg state. The corresponding rate coefficients (assuming a Maxwellian distribution) are shown in figure 25(b). The sum of individual rate coefficients is given by the dashed line which is seen to be in quite close agreement with the empirical relation from equation (26) between 0.1 and 1 eV. While different reaction products are possible, the broad assumption of only ground-state atomic iodine (as in table 10) seems practical and reasonable if excited states are not of interest or being tracked in a given plasma model.

### 3.5.3. Electron-ion scattering

Aside from electron impact ionization of ions (see section 3.2), three additional reaction processes may be important in iodine plasmas: electron impact dissociation of $I_2^+$, electron impact dissociative recombination of $I_2^+$, and electron impact detachment of $I^-$. No known data for dissociative recombination exists, but cross-sections have been calculated by Hamilton [30] for ion dissociation and detachment and are shown in figure 26. No other data is available and these cross-sections have previously been used by Lucken [97] and Marmuse [98]. The dissociation threshold energy is estimated to be 2.68 eV. The energy resolution of the detachment cross-section is only 1 eV and the first non-zero value occurs at 4 eV. The
<figure><img src="image_28.png" /><figcaption>**Figure 25.** (Generalization of reaction E2 in table 10 accounting for several possible atomic products; see main text) (a) cross-sections and (b) rate coefficients for the recombination of $I^+$ and $I^-$ as a function of energy. I(6s) designates a highly excited 6s Rydberg state. In (b), the dashed line denotes the sum of the individual rate coefficients, while the black line shows the empirical relation from equation (26).</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>**Figure 26.** (Reactions E4 and E6 in table 10) Cross-sections for the electron impact dissociation of $I_2^+$, and the electron impact detachment of $I^-$.</figcaption></figure>

electron affinity of iodine has however been precisely measured as 3.059 0463 eV [135]. Some uncertainty exists with the detachment cross-section as it is roughly an order of magnitude higher than that for chlorine [158], yet the photodetachment cross-section is of a similar magnitude. Plasma modeling by Esteves [26] noted that better agreement with experiment was obtained if detachment was ignored, again suggesting that the detachment cross-section may be too high.
<table><caption>**Table 11.** Example neutral-neutral collisional processes. A negative threshold energy indicates an exothermic reaction with energy release.</caption><thead><tr><th>ID</th><th>Reaction</th><th>Process</th><th>Threshold energy (eV)</th></tr></thead><tbody><tr><td>F1</td><td>I<sub>2</sub> + I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>) → I<sub>2</sub> + I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>)</td><td>Elastic scattering</td><td>—</td></tr><tr><td>F2</td><td>I<sub>2</sub> + I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>) → I<sub>2</sub> + I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>)</td><td>Elastic scattering</td><td>—</td></tr><tr><td>F3</td><td>I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>) + I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>) → 2 I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>)</td><td>Quenching</td><td>-0.9426</td></tr><tr><td>F4</td><td>I<sub>2</sub> + I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>) → I<sub>2</sub> + I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>)</td><td>Quenching</td><td>-0.9426</td></tr></tbody></table>

### 3.6. Collisional processes between neutral particles

Aside from thermal dissociation reactions (see section 2.4), other important collisional processes between neutral particles include elastic scattering and quenching of excited states, which are illustrated in table 11. While elastic scattering of neutrals is not typically included or required in many plasma models, it can be important for iodine as it represents an energy exchange mechanism between atoms and molecules that is relevant to gas heating. At the low pressures of interest for several propulsion and industrial applications, elastic collisions appear insufficient for thermalization to a common temperature. Consequently, iodine atoms and molecules can have very different temperatures with the atomic temperature typically higher than the molecular temperature [26]. Similarly, while collisional quenching of excited states can occur in any plasma discharge, it may be more important in iodine because of the low excitation threshold energy of the I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>) excited state. As this state is metastable, collisional quenching represents an important depopulating process.

#### 3.6.1. Elastic scattering

Elastic collisions between neutral particles can be approximated with a binary collision model accounting for the relative velocity between colliding species. Following Benilov [159, 160], particles are treated as hard spheres with a MTCS for collisions of I with I₂ given by

$$ \sigma_{I-I_2} = \frac{\pi}{4} (d_1 + d_{I_2})^2, \qquad (27) $$

where $d_1 \approx 280$ pm and $d_{I_2} \approx 560$ pm are the atom and molecule diameters respectively, which gives $\sigma_{I-I_2} \approx 5.5 \times 10^{-19}$ m². Integrating over an assumed Maxwellian distribution, the rate coefficient is

$$ K_{I-I_2} = \sigma_{I-I_2} \sqrt{\frac{k_B T_{I-I_2}}{2\pi m_{I-I_2}}}, \qquad (28) $$

with

$$ T_{I-I_2} = \frac{m_{I_2} T_1 + m_1 T_{I_2}}{m_1 + m_{I_2}}, \qquad (29) $$

$$ m_{I-I_2} = \frac{m_1 m_{I_2}}{m_1 + m_{I_2}}, \qquad (30) $$

the reduced temperature and mass respectively. The diffusion coefficient, which is relevant to the transport of atomic iodine to any surface bounding the plasma discharge, can be determined from

$$ D_{I-I_2} = \frac{3\pi}{8} \lambda_{I-I_2} v_{I-I_2}, \qquad (31) $$

where $\lambda_{I-I_2} = 1/(n_{I_2} \sigma_{I-I_2})$ is the collisional mean free path of I with $n_{I_2}$ the I₂ density, and $v_{I-I_2} = \sqrt{2k_B T_{I-I_2}/(\pi m_{I-I_2})}$. Following the above reasoning, a similar diffusion coefficient can be defined for elastic collisions between I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>) and I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>).

The diffusion coefficient of atomic iodine was estimated by Brewer and Tellinghuisen [161] approximately fifty years ago using an atomic fluorescence technique. Assuming a constant *sticking probability* ($\gamma$; see section 4.2), Brewer *et al* proposed a value of $C = pD = 0.01$ Pa m² s⁻¹. This estimation leads to $\sigma_{I-I_2} \approx 1.06 \times 10^{-18}$ m² at room temperature. More recent measurements obtained by investigating the evolution of the atomic density generated by laser photodissociation of molecular iodine (for pressures between 3 and 30 Pa [162]) have instead yielded $C = 0.047 \pm 0.007$ Pa m² s⁻¹. This corresponds to $\sigma_{I-I_2} \approx 2.2 \times 10^{-19}$ m².
<figure><img src="image_30.png" /><figcaption>Figure 27. (Reaction F4 in table 11) Quenching rate coefficients of I($^{2}$P°$_{1/2}$) by I$_{2}$ as a function of gas temperature from Chichinin [163] (and references therein).</figcaption></figure>

### 3.6.2. Quenching

The rate coefficients for the quenching of I($^{2}$P°$_{1/2}$) by I$_{2}$ have been compiled in a detailed work by Chichinin [163] and are shown in figure 27 (note that some of the data and temperature dependencies appear incorrect and were therefore retrieved directly from the original cited works [164–167]). At a temperature of 300 K, the quenching rate coefficient is measured to be between 3.3 × 10⁻¹⁸ and 7.07 × 10⁻¹⁷ m³ s⁻¹, taking into account experimental uncertainties. The dependence on temperature is not clear and so until new data becomes available, assuming a constant rate coefficient seems practical. Performing a statistical analysis of the data around 300 K gives a mean rate coefficient of K$_{quench}$ = 3.13 × 10⁻¹⁷ m³ s⁻¹ with a standard deviation of 1.08 × 10⁻¹⁷ m³ s⁻¹. Quenching of I($^{2}$P°$_{1/2}$) by I$_{2}$ results in vibrationally excited I*$_{2}$(X, 25 ≤ v ≤ 43) [168]. Quenching of I($^{2}$P°$_{1/2}$) by I($^{2}$P°$_{3/2}$) is also discussed by Chichinin, but is found to be three orders of magnitude smaller than quenching with I$_{2}$, and so may be negligible in most cases.

### 3.7. Rate coefficients

While the reaction cross-sections provided in the sections above are directly usable for certain theoretical or numerical models (such as particle-in-cell (PIC) simulations), many fluid-based models instead require reaction rate coefficients. In this case, the cross-section data can be averaged over the particle distribution function. If this is not known, a Maxwellian distribution can be assumed, and for the electron impact processes in sections 3.2 and 3.3, the rate coefficient can be computed from

$$K_j = \frac{\bar{v}_e}{T_e^2} \int_0^\infty \sigma_j(\varepsilon) \varepsilon e^{-\varepsilon/T_e} d\varepsilon, \quad (32)$$

where $\bar{v}_e = \sqrt{8eT_e/(\pi m_e)}$ is the electron thermal speed with e and m$_{e}$ the elementary charge and electron mass respectively, T$_{e}$ is the electron temperature, and σ$_{j}$ is the energy-dependent cross-section for reaction j. If required, cross-sections can be extrapolated at low and high energies to compensate for any missing data.

Using equation (32), rate coefficients for the main electron impact scattering processes can be determined for I and I$_{2}$ and are displayed in figure 28. Here, the different rate coefficient subscripts in the labels correspond to: total elastic scattering (el), elastic momentum transfer (elm), electronic excitation (exc), ionization (iz), dissociative ionization (dissiz), dissociation (diss), dissociative electron attachment (dissatt), and vibrational excitation (vibexc). For convenience, the correspondence of rate coefficient symbols and processes is provided in table 12, while atomic excitation processes have been grouped together using the lumped method discussed in section 3.2.3. Similarly, all molecular electronic and vibrational excitation processes have been grouped together into separate effective rate coefficients. The rate coefficients in figure 28 are also provided as supplementary data on the Zenodo repository [32]. Additionally, empirical fits for the main processes are provided in tables 13 and 14 using equations (33) and (34):

$$K(T_e) = A \left[ \ln \left( 1 + BT_e + CT_e^2 \right) \right]^D \exp \left( -\frac{\mathcal{E}}{T_e} \right), \quad (33)$$
<table><caption>**Table 12.** Correspondence between rate coefficient symbols and processes. The lumped electronic excitation processes correspond to those listed in table 6.</caption><thead><tr><th>Rate coefficient</th><th>Process</th></tr></thead><tbody><tr><td colspan="2"><em>Electron impact scattering: atomic iodine</em></td></tr><tr><td>K<sub>el,1</sub></td><td>Total elastic scattering</td></tr><tr><td>K<sub>el,1</sub>(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>)</td><td>Total elastic scattering—I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>)</td></tr><tr><td>K<sub>iz,1</sub></td><td>Ionization</td></tr><tr><td>K<sub>iz,1</sub>(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>)</td><td>Ionization—I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>)</td></tr><tr><td>K<sub>dexc</sub></td><td>De-excitation</td></tr><tr><td>K<sub>exc<sub>1</sub>,1</sub></td><td>Lumped electronic excitation 1</td></tr><tr><td>K<sub>exc<sub>2</sub>,1</sub></td><td>Lumped electronic excitation 2</td></tr><tr><td>K<sub>exc<sub>3</sub>,1</sub></td><td>Lumped electronic excitation 3</td></tr><tr><td>K<sub>exc<sub>4</sub>,1</sub></td><td>Lumped electronic excitation 4</td></tr><tr><td colspan="2"><em>Electron impact scattering: molecular iodine</em></td></tr><tr><td>K<sub>el,1<sub>2</sub></sub></td><td>Total elastic scattering</td></tr><tr><td>K<sub>elm,1<sub>2</sub></sub></td><td>Elastic momentum transfer</td></tr><tr><td>K<sub>iz,1<sub>2</sub></sub></td><td>Ionization</td></tr><tr><td>K<sub>diss,1<sub>2</sub></sub></td><td>Dissociation</td></tr><tr><td>K<sub>exc,1<sub>2</sub></sub></td><td>Electronic excitation</td></tr><tr><td>K<sub>dissatt,1<sub>2</sub></sub></td><td>Dissociative attachment</td></tr><tr><td>K<sub>dissiz,1<sub>2</sub></sub></td><td>Dissociative ionization</td></tr><tr><td>K<sub>vibexc,1<sub>2</sub></sub></td><td>Vibrational excitation</td></tr><tr><td>K<sub>rotexc,1<sub>2</sub></sub></td><td>Rotational excitation</td></tr></tbody></table>

$$K(T_e) = A \exp\left(-\frac{B}{T_e} + \frac{C}{T_e^2} - \frac{D}{T_e^3} + \frac{E}{T_e^4}\right) T_e^{-F} \quad (34)$$

Rate coefficients for other processes, such as ion-ion recombination, are already provided in sections 3.5 and 3.6.

### 3.8. Collisional energy cost

A common and useful metric used to assess collisional power loss in plasma discharges is the collisional energy loss, $\mathcal{E}_c$. This effectively represents the average energy expended to produce an electron-ion pair when considering relevant collisional processes (here only electron impact reactions). For molecular gases like iodine, a true energy loss is difficult to establish outside of a complete and comprehensive simulation where the balance between different species is accounted for. Nonetheless, an approximate order of magnitude computation can be made when assuming fully atomic or fully molecular iodine plasmas. For atomic iodine, the collisional energy loss can be defined by

$$\mathcal{E}_{c,I} = \frac{1}{K_{iz,I}} \left[ K_{iz,I} \varepsilon_{iz,I} + \sum_{j} K_{exc_{j},I} \varepsilon_{exc_{j,I}} + \frac{3m_e k_B}{m_I} (T_e - T_I) K_{el,I} \right], \quad (35)$$

which accounts for all collisional energy loss processes associated with ionization, excitation, and elastic scattering. Here, it is assumed that ground state atoms are the only species present. Similarly, the collisional energy loss for molecular iodine is

$$\mathcal{E}_{c,I_2} = \frac{1}{K_{iz,I_2} + K_{dissiz,I_2}} \left[ \begin{aligned} & K_{iz,I_2} \varepsilon_{iz,I_2} + K_{dissiz,I_2} \varepsilon_{dissiz,I_2} + \sum_j K_{exc_{j,I_2}} \varepsilon_{exc_{j,I_2}} + \sum_j K_{vibexc_{j,I_2}} \varepsilon_{vibexc_{j,I_2}} \\ & + \sum_j K_{rotexc_{j,I_2}} \varepsilon_{rotexc_{j,I_2}} + \sum_j K_{diss_{j,I_2}} \varepsilon_{diss_{j,I_2}} \\ & + \frac{3m_e k_B}{m_{I_2}} (T_e - T_{I_2}) K_{el,I_2} \end{aligned} \right]. \quad (36)$$

Collisional energy loss processes include direct and dissociative ionization, electronic, vibrational, and rotational excitation, dissociation, and elastic scattering. Because of a lack of data, we assume that the electron dissociation energy loss is equal to the dissociation threshold energy of the molecular ground state, and rotational excitation processes are ignored. Equations (35) and (36) are plotted in figure 29
<table><caption>Table 13. Best-fit rate coefficients for various electron impact reaction processes for I and I₂ based on equation (33).</caption><thead><tr><th>Rate Coef.</th><th>A (m<sup>3</sup> s<sup>-1</sup>)</th><th>B (eV<sup>-1</sup>)</th><th>C (eV<sup>-2</sup>)</th><th>D</th><th>E (eV)</th><th>T<sub>e</sub> (eV)</th><th>Error (%)</th></tr></thead><tbody><tr><td>K<sub>iz,I2</sub></td><td>1.20694 &times; 10<sup>-13</sup></td><td>-2.05557 &times; 10<sup>-3</sup></td><td>8.10106 &times; 10<sup>-2</sup></td><td>7.95734 &times; 10<sup>-1</sup></td><td>9.31000 &times; 10<sup>0</sup></td><td>[1; 50]</td><td>4.16</td></tr><tr><td>K<sub>diss,I2</sub></td><td>1.94272 &times; 10<sup>-14</sup></td><td>1.65161 &times; 10<sup>-5</sup></td><td>-1.36170 &times; 10<sup>-7</sup></td><td>-6.05364 &times; 10<sup>-2</sup></td><td>2.92201 &times; 10<sup>0</sup></td><td>[1; 50]</td><td>8.91</td></tr><tr><td>K<sub>dissiz,I2</sub></td><td>2.73612 &times; 10<sup>-14</sup></td><td>1.62507 &times; 10<sup>-1</sup></td><td>-9.69904 &times; 10<sup>-4</sup></td><td>9.41764 &times; 10<sup>-1</sup></td><td>1.19400 &times; 10<sup>1</sup></td><td>[0.5; 50]</td><td>6.74</td></tr><tr><td>K<sub>dissatt,I2</sub></td><td>8.51271 &times; 10<sup>-18</sup></td><td>5.26610 &times; 10<sup>-6</sup></td><td>1.94777 &times; 10<sup>-7</sup></td><td>-5.57411 &times; 10<sup>-1</sup></td><td>2.94075 &times; 10<sup>0</sup></td><td>[2; 50]</td><td>17.22</td></tr><tr><td>K<sub>exc,I2</sub></td><td>6.94179 &times; 10<sup>-18</sup></td><td>2.07908 &times; 10<sup>-6</sup></td><td>2.83839 &times; 10<sup>-9</sup></td><td>-6.91696 &times; 10<sup>-1</sup></td><td>4.63389 &times; 10<sup>0</sup></td><td>[1.5; 50]</td><td>3.48</td></tr><tr><td>K<sub>vibexc,I2</sub></td><td>1.68131 &times; 10<sup>-19</sup></td><td>3.04258 &times; 10<sup>-4</sup></td><td>1.57137 &times; 10<sup>-4</sup></td><td>-8.01979 &times; 10<sup>-1</sup></td><td>1.41568 &times; 10<sup>0</sup></td><td>[0.5; 50]</td><td>3.46</td></tr><tr><td>K<sub>iz,I</sub></td><td>1.00526 &times; 10<sup>-13</sup></td><td>3.04247 &times; 10<sup>-1</sup></td><td>-1.87150 &times; 10<sup>-3</sup></td><td>1.02720 &times; 10<sup>0</sup></td><td>1.04500 &times; 10<sup>1</sup></td><td>[0.5; 50]</td><td>7.16</td></tr><tr><td>K<sub>exc2,I</sub></td><td>9.91412 &times; 10<sup>-16</sup></td><td>7.39500 &times; 10<sup>-9</sup></td><td>1.81077 &times; 10<sup>-10</sup></td><td>-2.18520 &times; 10<sup>-1</sup></td><td>1.01082 &times; 10<sup>1</sup></td><td>[4; 50]</td><td>8.61</td></tr><tr><td>K<sub>exc3,I</sub></td><td>1.10016 &times; 10<sup>-17</sup></td><td>-4.81093 &times; 10<sup>-10</sup></td><td>3.15998 &times; 10<sup>-9</sup></td><td>-4.89424 &times; 10<sup>-1</sup></td><td>1.17398 &times; 10<sup>1</sup></td><td>[2.5; 50]</td><td>8.93</td></tr><tr><td>K<sub>exc4,I</sub></td><td>1.61045 &times; 10<sup>-16</sup></td><td>1.80686 &times; 10<sup>-9</sup></td><td>9.69122 &times; 10<sup>-11</sup></td><td>-3.49321 &times; 10<sup>-1</sup></td><td>1.09391 &times; 10<sup>1</sup></td><td>[2.5; 50]</td><td>13.34</td></tr><tr><td>K<sub>iz,I</sub>(2P<sup>+</sup><sub>1/2</sub>)</td><td>2.21512 &times; 10<sup>-13</sup></td><td>2.82764 &times; 10<sup>-1</sup></td><td>-1.72072 &times; 10<sup>-3</sup></td><td>1.03783 &times; 10<sup>0</sup></td><td>9.50740 &times; 10<sup>0</sup></td><td>[0.5; 50]</td><td>7.74</td></tr><tr><td>K<sub>dexc</sub></td><td>4.65222 &times; 10<sup>-16</sup></td><td>1.33736 &times; 10<sup>-8</sup></td><td>8.85358 &times; 10<sup>-10</sup></td><td>-2.72591 &times; 10<sup>-1</sup></td><td>1.56932 &times; 10<sup>-1</sup></td><td>[0.5; 50]</td><td>16.50</td></tr></tbody></table>
<table><caption>**Table 14.** Best-fit rate coefficients for various electron impact reaction processes for I and I₂ based on equation (34).</caption><thead><tr><th>Rate Coef.</th><th>A (m<sup>3</sup> s<sup>-1</sup>)</th><th>B (eV)</th><th>C (eV<sup>2</sup>)</th><th>D (eV<sup>3</sup>)</th><th>E (eV<sup>4</sup>)</th><th>F</th><th>T<sub>e</sub> (eV)</th><th>Error (%)</th></tr></thead><tbody><tr><td>K<sub>el,I<sub>2</sub></sub></td><td>4.13224 &times; 10<sup>-13</sup></td><td>2.57431 &times; 10<sup>-1</sup></td><td>4.18501 &times; 10<sup>-2</sup></td><td>2.82420 &times; 10<sup>-3</sup></td><td>6.56031 &times; 10<sup>-5</sup></td><td>-3.70209 &times; 10<sup>-1</sup></td><td>[0.5;50]</td><td>6.28</td></tr><tr><td>K<sub>elm,I<sub>2</sub></sub></td><td>4.35460 &times; 10<sup>-13</sup></td><td>-4.36057 &times; 10<sup>0</sup></td><td>-1.32992 &times; 10<sup>1</sup></td><td>-1.11529 &times; 10<sup>1</sup></td><td>-2.92094 &times; 10<sup>0</sup></td><td>-4.88306 &times; 10<sup>-1</sup></td><td>[1.5;50]</td><td>8.06</td></tr><tr><td>K<sub>el,I</sub></td><td>3.54863 &times; 10<sup>-12</sup></td><td>5.50332 &times; 10<sup>0</sup></td><td>6.21721 &times; 10<sup>0</sup></td><td>2.87360 &times; 10<sup>0</sup></td><td>4.67478 &times; 10<sup>-1</sup></td><td>6.06788 &times; 10<sup>-1</sup></td><td>[0.5;50]</td><td>7.51</td></tr><tr><td>K<sub>exc<sub>1</sub>,I</sub></td><td>8.99640 &times; 10<sup>-14</sup></td><td>3.34729 &times; 10<sup>0</sup></td><td>1.38934 &times; 10<sup>0</sup></td><td>2.84949 &times; 10<sup>-1</sup></td><td>7.48700 &times; 10<sup>-3</sup></td><td>6.55418 &times; 10<sup>-1</sup></td><td>[0.5;50]</td><td>8.87</td></tr><tr><td>K<sub>el,I</sub>(2P<sup>o</sup><sub>1/2</sub>)</td><td>6.71548 &times; 10<sup>-12</sup></td><td>8.96192 &times; 10<sup>0</sup></td><td>8.42273 &times; 10<sup>0</sup></td><td>3.60817 &times; 10<sup>0</sup></td><td>5.73389 &times; 10<sup>-1</sup></td><td>7.62752 &times; 10<sup>-1</sup></td><td>[0.5;50]</td><td>6.28</td></tr></tbody></table>
<figure><img src="image_31.png" /><figcaption>**Figure 28.** Rate coefficients as a function of electron temperature (assuming a Maxwellian distribution) for various collisional processes for (a) I and (b) I₂.</figcaption></figure>

as a function of electron temperature (assuming a Maxwellian distribution function). For comparative purposes, results are also shown for the noble gases argon, krypton, and xenon. Here we see that the collisional energy loss in iodine is lower than the noble gases for temperature above about 4 eV. This important result indicates that iodine discharges are expected to be more energy efficient at sufficiently high temperatures. However, below 4 eV, the energy loss increases rapidly and far surpasses that of the noble gases. This is largely due to the very low threshold energy for excitation of the I(²P°₁/₂) state.

Similar results are obtained for molecular iodine, where above a temperature of about 2 eV, the energy cost is lower than both atomic iodine and the noble gases. However, care is needed here as rotational excitation has been neglected, and the electron energy loss during dissociation is typically much higher than the dissociation threshold energy (being equal to the so called vertical excitation energy). Depending on the composition of an iodine discharge, the true energy cost is expected to lie somewhere between that for I and I₂. Regardless, we can already make a strong statement about iodine plasmas: for high-efficiency operation, conditions must be such that the electron temperature is higher than about 4 eV.

## 3.9. Electron swarm parameters

Due to the high reactivity of halogen gases (such as I₂), experimental investigations of electron swarm parameters are scarce. Most available studies have been conducted in gas mixtures where the halogen is diluted with a non-reactive, non-electronegative buffer gas. In such cases, the concentration of the electronegative component is typically low enough that the electron energy distribution and drift velocity are effectively assumed to be equal to those of the pure buffer gas.

To date, the only available data on the electron drift velocity in I₂ are the indirect measurements reported by Healey in 1938 [84], using a diffusion apparatus constructed from brass and platinum. As noted by Gallagher et al [132], these results are subject to significant uncertainty as the drift velocities were not measured directly but rather inferred from measurements in gas mixtures. The inferred values for I₂ are presented in figure 30 and compared with those for other halogens, such as chlorine (Cl₂).
<figure><img src="image_32.png" /><figcaption>**Figure 29.** Average collisional energy cost per electron-ion pair as a function of electron temperature for atomic iodine, molecular iodine, argon, krypton, and xenon. In all cases, the gas temperature is 300 K.</figcaption></figure>

<figure><img src="image_33.png" /><figcaption>**Figure 30.** Drift velocity of electrons in Cl₂ (blue squares) [169], Br₂ (orange triangles) [170], and I₂ (green circles) [84] as function of the reduced electric field (E/N).</figcaption></figure>

and bromine (Br₂), reported by Bailey *et al* [169, 170]. More recently, González-Magaña and De Urquijo [171] measured electron drift velocities in Cl₂ and found fair agreement with the data of Bailey *et al* to within about 12% for reduced electric fields (E/N, where E is the electric field magnitude, N is the gas density, and typical units are the Townsend (Td) with 1 Td = 10⁻²¹ V m²) between 120 and 220 Td (not shown). It is important to emphasize that Healey's data, being the only measurements available for I₂, should be regarded as approximate.

The only reported data for the electron characteristic energy *D*<sub>T</sub>/μ (i.e. the ratio of the transverse diffusion coefficient, *D*<sub>T</sub>, to the mobility, μ) in I<sub>2</sub> also originate from Healey and Bailey *et al* [84, 169, 170], who employed a combined electric and magnetic field technique. Figure 31 presents the inferred values of *D*<sub>T</sub>/μ as a function of the reduced electric field *E*/*N* in the range 0–250 Td. As noted by Gallagher *et al* [132], significant challenges were encountered in handling these highly reactive gases, which further complicate the interpretation of the results. Given the absence of additional measurements, this data should also be regarded as approximate.

Brooks *et al* [126] investigated the temperature dependence of the reduced electron attachment coefficient (η/*N* with η the attachment coefficient) in a mixture of 1% I₂ and 99% N₂ at 6.7 kPa using an electron swarm experiment, as a function of the reduced electric field *E*/*N*. This data, shown in figure 32, demonstrates a significant increase in the attachment coefficient with gas temperature, attributed to the thermal population of vibrationally excited states. In figure 32, it is important to note that while the attachment coefficient is referenced to the iodine partial density (i.e. *N* = *N*<sub>I₂</sub>), the reduced electric field *E*/*N* corresponds to the density of the entire gas mixture. By varying the reduced electric field between 1 and 50 Td, Brooks *et al* modulated the mean electron energy between approximately 0.5 and 2.5 eV. Their results reveal a clear minimum in the attachment coefficient near 4 Td, suggesting the involvement of multiple resonant states for dissociative electron attachment.
<figure><img src="image_34.png" /><figcaption>**Figure 31.** Characteristic energy of electrons in Cl₂ (blue squares) [169], Br₂ (orange triangles) [170], and I₂ (green circles) [84] as function of the reduced electric field (E/N).</figcaption></figure>

<figure><img src="image_35.png" /><figcaption>**Figure 32.** Reduced attachment coefficient ($\eta/N_{I_2}$) for 1% I₂ and 99% N₂ measured at different gas temperatures as a function of the reduced electric field (E/N) by Brooks et al [126]. The gas pressure is 6.7 kPa.</figcaption></figure>

It should be highlighted that to date, no known studies have been reported in the literature on electron swarm analysis in pure atomic or molecular iodine. Nevertheless, such studies would be very valuable to reduce the large uncertainties in the electron impact total momentum transfer and dissociative electron attachment cross-sections as discussed above in sections 3.3.1 and 3.3.3.

# 4. Iodine-surface interactions

## 4.1. Material compatibility

As a halogen, iodine is quite reactive with many other substances. Having an electronic configuration of [Kr] 4d¹⁰ 5s² 5p⁵, it lacks only a single electron to achieve a noble gas like stable configuration with a full valence shell. Although its electronegativity is lower than the lighter halogens (i.e. fluorine, chlorine, and bromine), it is still very high (2.66 on the Pauling scale). The iodine-iodine dissociation energy (1.54 eV) is also weak compared to that of other diatomic molecules which exist in stable states in nature (e.g. 9.79 eV for molecular nitrogen and 5.15 eV for molecular oxygen), which implies that less energy is required to chemically break the bond.

Iodine-material compatibility can be generally discussed by considering a reduced list of transition and post-transition metals, as well as certain non-metallic substances, for two main reasons. Firstly, cost and availability are important factors when selecting materials for space applications [172]. Secondly, structural rigidity and integrity are often of interest in design: particularly for containers, tanks, or fluidic elements in direct contact with iodine. Therefore certain metallic elements and their alloys are ignored here as they are extremely scarce or expensive. This includes, for example, ruthenium (Ru), dubnium (Db), seaborgium (Sg), bohrium (Bh), hassium (Hs), thallium (Tl), astatine (At), as well as the lanthanides and actinides. Similarly, metalloids and their alloys are also ignored, such as germanium
<table><caption>**Table 15.** Compatibility of iodine with various materials [173, 174].</caption><thead><tr><th>Material</th><th>Reactivity</th></tr></thead><tbody><tr><td><em>Metals</em></td><td></td></tr><tr><td>Aluminum (6061)</td><td>Medium</td></tr><tr><td>Aluminum (7075)</td><td>Medium</td></tr><tr><td>Aluminum (anodized 7075)</td><td>Low</td></tr><tr><td>Chromium</td><td>Low</td></tr><tr><td>Copper (110)</td><td>High</td></tr><tr><td>Copper (C260 brass)</td><td>High</td></tr><tr><td>Gold</td><td>Low</td></tr><tr><td>Iron (4130 alloy steel)</td><td>High</td></tr><tr><td>Iron (304 stainless steel)</td><td>High</td></tr><tr><td>Iron (316 stainless steel)</td><td>Medium</td></tr><tr><td>Nickel (Hastelloy B-3)</td><td>Low</td></tr><tr><td>Nickel (Hastelloy C-22)</td><td>Low</td></tr><tr><td>Nickel (Hastelloy C-276)</td><td>Low</td></tr><tr><td>Nickel (Hastelloy C-2000)</td><td>Low</td></tr><tr><td>Platinum</td><td>Low</td></tr><tr><td>Titanium (pure)</td><td>Low</td></tr><tr><td>Titanium (Ti-6Al-4V)</td><td>Low</td></tr><tr><td>Tungsten</td><td>Low</td></tr><tr><td><em>Non-metals</em></td><td></td></tr><tr><td>Boron nitride</td><td>Low</td></tr><tr><td>Silicon carbide</td><td>Low</td></tr><tr><td>Silicon nitride</td><td>Low</td></tr><tr><td>Zirconium oxide</td><td>Low</td></tr></tbody></table>

(Ge), arsenic (As), antimony (Sb), and tellurium (Te), with the exception of boron (B) and silicon (Si). Certain non-metallic substances, such as the noble gases, do not react under normal conditions with iodine, which is useful for some applications (e.g. to extend the lifetime of halogen lamps). These elements do not usually form solid compounds due to their chemical stability, and typically have very high saturation and melting temperature-pressure phase diagram characteristics.

Remaining substances can be divided into three main material categories: metallic pure elements and alloys (e.g. high-strength aluminum alloys like Al2024), ceramics (e.g. zirconium oxide, ZrO2) and polymers (e.g. polytetrafluoroethylene, PTFE). Establishing the chemical compatibility of iodine with every chemical compound is a complex task as the behavior of compound components (i.e. alloying elements) often differs from the behavior of the base elements. Nonetheless, an overview can be provided based on the existing literature, with table 15 providing a summary indicating the typical level of reactivity between iodine and various materials.

Naturally, alkali metals, which display a s¹ valence electron configuration (i.e. lithium to francium), are perfect electron donors for halogens and therefore show a strong chemical affinity with iodine. When reacting with iodine, alkali metals form metal iodides in a highly exothermic reaction, particularly between iodine and the heavier alkali metals like potassium (K), rubidium (Rb), and cesium (Cs). Similarly, alkaline Earth metals (beryllium to radium), which have a s² valence electron configuration, also display a strong affinity with halogens, although at a reduced level compared with the alkali metals.

Note however that the corrosion behavior of a substance does not solely depend on the chemical affinity of the material with iodine. Environmental conditions are equally important and can accelerate the corrosion and failure of the material. Notable factors which influence corrosion behavior include: (a) the phase of iodine (e.g. solid, liquid, or gas), (b) the temperature conditions (with higher temperatures typically causing higher corrosion), (c) the vapor pressure (in the case of corrosion by iodine gas, with higher gas densities typically leading to accelerated corrosion damage), (d) the state of the surface (pits or localized previous attack can remove the protective layer of certain materials, such as aluminum oxides), and (e) the presence of external ambient substances (e.g. water) or pollutant particles (e.g. metallic particles left from the machining/manufacturing process).

Aluminum, typically alloyed with other metallic substances like copper (Cu), zinc (Zn), or magnesium (Mg), generally offers poor resistance to continuous iodine exposure. While Craig and Anderson [175] note its resistance to solid iodine at ambient temperatures, Zschätzsch et al [176] and Martínez
Martínez and Rafalskyi [174] have reported localized attack that can easily be perceived under microscope observations.

Stainless steel suffers pitting even at ambient conditions [175], with apparent surface degradation and the formation of iron iodides. The corrosion of iron (Fe) and its alloys is particularly fast. Jerman [173] studied the corrosion of various substances under a 7 day 200°C iodine flow test, measuring a corrosion rate of 1.055 mm yr⁻¹ for A304 stainless steel, which was 3.7 times higher than that of an aluminum alloy (non-anodized Al7075), 25 times higher than that of a nickel alloy (Hastelloy C-276), and 28 times higher than that of pure titanium (Ti). Even if iron suffers strong corrosion, the remaining stainless steel constituents, such as manganese (Mn), chromium (Cr), and nickel (Ni) are also subject to iodine corrosion [177]. Copper similarly displays a strong chemical affinity for iodine, with a corrosion rate of 0.606 mm yr⁻¹. Other works note similar corrosion rates, but also report changes in the core properties of the metal, such as the thermal conductivity, as well as a 42% increase in DC resistance after the tests [174]. Tin (Sn) is also observed to be very susceptible to iodine corrosion [174].

Titanium is reported as moderately resistant at ambient temperatures and may offer certain protection to cold iodine, but is subject to stress corrosion cracking in hot iodine-rich environments [178]. Titanium alloys commonly used in aerospace applications (e.g. Ti6Al4V) may offer worse behavior than the base metal due to corrosion of some of the alloy constituents [173]. Zirconium (Zr) and its alloys, which are used in nuclear power reactors [179], are also subject to iodine corrosion and may suffer from stress corrosion cracking [178].

Iodine reacts with nickel largely to form $NiI_2$, which has a melting point of about 780 °C. Up to moderately high temperatures (around 100 °C), nickel offers a moderate resistance to iodine and displays limited chemical interaction [176], although it does already display moderate pitting. Fontana and Staehle [180] note that some Ni–Cr alloys (e.g. Inconel 600, Inconel 625, Inconel X-750, and Hastelloy C-276) are generally resistant to iodine [180], although Martínez Martínez and Rafalskyi [174] have highlighted that chromium and iron are present in these alloys and may be subject to localized pitting [174].

Refractory metals (e.g. molybdenum, Mo) offer satisfactory resistance to iodine corrosion and display very limited chemical reactivity at ambient or moderate temperatures [174, 176, 181]. Jerman [173] has however observed non-negligible corrosion of these metals under certain test conditions. For example, the corrosion rate of tantalum under iodine bath exposure at 200 °C was measured as 0.834 mm yr⁻¹ [173]. This contradicts other research where corrosion rates of 0.004 mm yr⁻¹ at 300 °C, and 0.88 mm yr⁻¹ at 450 °C were observed. This again emphasizes the need to carefully set and control the test conditions to replicate the expected operating environment for a given application.

Literature on the corrosion of noble metals and silver (Ag) by iodine is more scarce. Silver and gold (Au) are reported to have a poor resistance to dry iodine by Craig et al [175], but these results appear to disagree with later work by Lai [182]. Platinum (Pt) has been used for iodine corrosion applications [183], with some information on measured corrosion rates: 0 mm yr⁻¹ at 300 °C and 0.0055 mm yr⁻¹ at 450 °C [182]). Iridium (Ir) and ruthenium (Ru) have low corrosion rates (less than 0.003 mm yr⁻¹ [175]), but this has only been measured at ambient temperatures (approximately 22 °C). Craig and Anderson [175] also report extended corrosion for osmium (Os). No corrosion rates are given for palladium (Pd) or rhodium (Rh).

Ceramic materials are typically stable and do not display pitting damage. Boron nitride (BN) shows good compatibility with iodine and no evidence of surface attack [174]. Other ceramic materials, such as silicon carbides/nitrides (SiC and $Si_3N_4$), zirconium oxide (ZrO₂), mica, or Macor show no growth of defects or changes in weight after iodine exposure [174]. Silicate or borosilicate glasses, as amorphous, ceramic-like substances, display very little chemical interaction with iodine, with no surface etching or pitting under extended exposure [173].

Polymeric materials, such as Teflon, Viton, or Kapton, typically have stable corrosion behavior, but may become subject to weakening or changes in volume under certain test conditions, with evidence of shrink or swell. Jerman [173] has reported non-negligible corrosion rates for Teflon (0.219 mm yr⁻¹), Viton (0.24 mm yr⁻¹), and Kapton (0.125 mm yr⁻¹) under a 7 day 200 °C iodine bath test.

Finally, some ceramic coatings (e.g. tantalum pentoxide, $Ta_2O_5$) have been found to protect metallic surfaces exposed to iodine [174]. However, it is noted that iodine can grow on surface defects, or attack the base material, causing the ceramic protective layer to crack and expose further sections of the underlying element. Care needs to be taken when handling iodine with ceramics, glasses, polymeric materials, or in general substances with a low thermal conductivity, as iodine flows may deposit. Even if corrosion is not observed, lack of heating may lead to blockages or other issues [27].

A further discussion exploring the compatibility of materials with iodine is available across a range of relevant studies. For example, a foundational investigation is the 1990 doctoral thesis of Mathieu and
<table><caption>**Table 16.** List of measured or inferred surface recombination coefficients obtained from the literature.</caption><thead><tr><td>γ<sub>wall</sub></td><td>Surface</td><td>Comments</td></tr></thead><tbody><tr><td>0.001–0.01</td><td>Acid-coated surfaces [188]</td><td>With plasma</td></tr><tr><td>0.07</td><td>Alumina [28]</td><td>With plasma</td></tr><tr><td>0.05–0.2</td><td>Aluminum [26]</td><td>With plasma</td></tr><tr><td>0.001–0.065</td><td>Quartz [26, 161]</td><td>With plasma</td></tr><tr><td>0.05–0.25</td><td>Quartz [162]</td><td>Without plasma</td></tr><tr><td>0.14</td><td>BK7 glass [189]</td><td>Without plasma</td></tr><tr><td>0.014</td><td>Dimethyldichlorosilane [189]</td><td>Without plasma</td></tr></tbody></table>

references therein [184], which, although focused on the behavior of iodine in nuclear reactor environments, provides valuable baseline data on iodine-induced corrosion phenomena. For similar applications, but at the molecular level, Beck et al [185] investigated iodine interactions with Fe, Ni, Cr, and stainless steel alloys, offering mechanistic insight into material degradation. In the aerospace context, Guidi et al [181] recently examined the reactivity of iodine with various materials commonly used in spacecraft. Complementing this, Costa et al [186] reported chemical, structural, and microstructural changes in metallic and silicon-based coatings exposed to iodine vapor. Holste et al [187] have also identified material compatibility as a central challenge in advancing iodine-based ion thruster technologies. Finally, Zschatzsch et al [176] proposed an accelerated testing methodology based on the constant $pΔt$ concept, whereby increased iodine vapor pressure over short durations replicates long-term exposure by maintaining a constant product of pressure and time (proportional to the total number of iodine-material interactions).

Interestingly, despite iodine's well-known corrosive properties described above, its use under vacuum conditions appears to pose a somewhat limited risk of severe degradation for many materials initially considered poorly compatible (e.g. stainless steel or aluminum). In the absence of moisture and at low partial pressures, the reactivity of iodine is significantly reduced, and observed material damage is often superficial or self-limiting. This suggests that, for a wide range of aerospace-relevant substrates, iodine can be safely handled in vacuum environments without inducing critical structural or functional failure.

## 4.2. Surface recombination of atomic iodine

As discussed in sections 2.4 and 3.3, thermal and electron impact dissociation processes lead to the formation of atomic iodine, which can later recombine via the following general surface reaction (applicable to both ground and excited atomic states)

$$I + I \rightarrow I_2. \qquad (37)$$

The recombination probability can be described by the *sticking probability* or *surface recombination coefficient*, $γ_{wall}$, which varies between 0 and 1. The flux of atomic iodine to a surface can then be expressed as

$$\Gamma_{\text{wall,I}} = \frac{1}{4} n_I v_I \left( \frac{2\gamma_{\text{wall}}}{2 - \gamma_{\text{wall}}} \right), \qquad (38)$$

where $n_I$ and $v_I = \sqrt{8k_B T_I/(\pi m_I)}$ are the atomic iodine density and thermal speed respectively. The surface recombination coefficient plays a key role in most, if not all, iodine discharges because it directly affects the balance between collisional volume dissociation and surface recombination processes. In general, the surface recombination coefficient depends on the surface material, state (e.g. surface roughness, concentration of chemisorbed or physiosorbed contaminant atoms, surface defect structures, etc), and temperature, and thus is not in general a constant but can vary with discharge conditions. Indeed, recent measurements with atoms produced by photodissociation [162] have shown a variation of the recombination coefficient between 0.25 and 0.05 (for a quartz surface) when the pressure varies from 3 to 30 Pa. For other more well-studied molecular gases, such as chlorine, the recombination coefficient can vary from as low as 0.01 for silicon surfaces at room temperature, to as high as 0.85 for stainless steel. Detailed and accurate data for iodine is sparse, although several experiments have previously measured the surface recombination coefficient for various materials, as summarized in table 16.

For numerical modeling (see section 5.3), the surface recombination coefficient plays a role in diffusional loss processes to any bounding surfaces, which can be described by an effective rate coefficient
given by

$$K_{s-s'} = \left[ \frac{\Lambda_0^2}{D_{s-s'}} + \frac{4V}{\bar{v}_{s-s'}} A_s \left( \frac{2 - \gamma_{\text{wall}}}{2\gamma_{\text{wall}}} \right) \right]^{-1} \quad (39)$$

Here V is the plasma volume, A_s is the surface area bounding the plasma, $\bar{v}_{s-s'} = \sqrt{8k_B T_{s-s'}/(\pi m_{s-s'})}$ is the thermal speed with the s and s' subscripts indicating either atomic or molecular iodine species, $D_{s-s'}$ is the relevant diffusion coefficient (see section 3.6), and for a cylindrical discharge, the diffusion length is given by [124]

$$\Lambda_0 = \left[ \left( \frac{\pi}{L} \right)^2 + \left( \frac{\chi_{01}}{R} \right)^2 \right]^{-1/2}, \quad (40)$$

with L and R the length and radius of the discharge, and $\chi_{01} \approx 2.405$ the first zero of the zeroth order Bessel function of the first kind.

### 4.3. Secondary electron emission (SEE)

An important plasma-surface process is the emission of electrons due to bombardment by photons and neutral/charged particle species [190]. Referred to as SEE, this process plays a critical role in sustaining DC discharges [191, 192], can influence plasma-wall losses in Hall thrusters [193], modifies electron heating and ionization dynamics in capacitively coupled plasmas (CCPs) [194, 195], and can even affect the operation of electrostatic probe diagnostics [196–198]. Electron- and photon-induced SEE are expected to remain similar in iodine plasmas (although the surface state may change due to deposition and specific photon energies will depend on the various excited iodine states), while neutral- and ion-induced SEE will be a function of the different atomic and molecular species present, and their energy. The current of emitted electrons is quantified by the emission yield, $\gamma_{see}$, which is defined as

$$\gamma_{\text{see}} = \frac{I_{\text{see}}}{I_i}, \quad (41)$$

where $I_i$ is the ion beam (or equivalent neutral beam) current incident on the surface, and $I_{see}$ is the current of secondary electrons emitted. Emission yield data for iodine ion and neutral bombardment is very sparse in the literature. In addition, the molecular nature of iodine complicates experimental measurements as multiple positive ion species (primarily $I^+$ and $I_2^+$) are typically formed in iodine discharges (see section 3). A further complication is the chemical reactivity of iodine, which can lead to the deposition of iodine or the formation of iodide layers. Thus, the effective emission yield may change in time and differ from that for atomically clean surfaces.

Dedicated measurements of ion-induced SEE yields have been performed by Habl et al [199] for energies between 0.6 and 1.4 keV (a range relevant to many electric propulsion systems) and for different target materials including: aluminum (Al), carbon-carbon (CC), copper (Cu), molybdenum (Mo), steel, titanium (Ti), and tungsten (W). Experiments were performed with an iodine-fueled gridded ion thruster that was repurposed to act as an ion source, and the fraction of atomic and molecular ions in the beam was determined using time-of-flight spectrometry. By varying the input power to the ion source, the ratio of atomic-to-molecular ion beam current could be varied. Although filtering of neutral iodine species was not possible, the collisional mean free path was estimated to be about 7 m, such that fast neutrals should only account for a small fraction (~7%) of the incident beam. Emission yields were inferred from the current-voltage characteristics of an electrostatic probe placed downstream of the ion source, and whose collector surface was composed of the target material. Because of the polarity of the probe, both electrons and negative ions are reflected and prevented from entering the probe. Results are shown in figure 33 for two different ion source power levels (which give atomic-to-molecular ion beam current ratios of approximately 50:50 and 75:25 respectively).

The highest emission yields are obtained with Al and Cu, while CC, Mo, and W give the lowest yields. Since the emission yield varies linearly for some materials (such as Al and Ti), kinetic emission processes likely dominate over Auger emission [124]. Overall, ion beam composition only plays a minor role for SEE from Al, CC, Mo, Ti, and W, but appears to play a significant role for Cu and steel: most likely due to the formation of a thin iodide layer as these materials are known to be reactive with iodine (see section 4.1). Although detailed surface modification studies were not conducted, previous work with oxygen and nitrogen beams have demonstrated that the formation of oxide and nitride layers affects the emission yield [200–203]. As these layers are continually formed and sputtered, the SEE yield obtained is therefore an effective value representative of the original surface material and the compound layer. As
<figure><img src="image_36.png" /><figcaption>Figure 33. Secondary electron emission yields for iodine ion bombardment of different target surfaces and for two atomic-to-molecular ion beam current ratios (blue circles or green up triangles for 50:50 and orange squares or red down triangles for 75:25). The horizontal solid and dashed lines show the emission yield from equation (42) for I⁺ and I⁺₂ respectively. Data taken from [199]. Error bars have been omitted for clarity but are typically less than ±20%.</figcaption></figure>

surface modification is expected to anyway occur in any real device, the effective emission yield obtained may well be more accurate than that obtained for a ‘clean’ surface.

As no measurements were performed at low energies, and in the absence of any other available data, the approximate empirical expression from Raizer [204] can be used to obtain an estimate of the SEE yield due to Auger emission

$$ \gamma_{\text{see}} \approx 0.016(\varepsilon_{\text{iz}} - 2\varepsilon_{\phi}), \qquad (42) $$

with εᵢᵦ the ionization threshold of the ion and εᵦ the work function of the target material, with both in units of (eV). Comparison with more detailed theoretical emission models show that equation (42) is quite reasonable [205]. As an example, equation (42) is applied to the target materials in figure 33 and predicted emission yields are shown as the horizontal solid and dashed lines, and given in table 17. As seen, the estimated SEE yield is mostly consistent with the low energy values obtained experimentally.

### 4.4. Sputter erosion

An important consideration in both electric propulsion and materials processing is sputter erosion of materials or components. Here, high-energy ions striking a target can physically remove atoms leading to gradual surface erosion with time. For example, ion-neutral collisions in gridded ion thrusters can lead to a loss of ion focusing through the acceleration grids, and the generation of a backstreaming ion current [3]. This causes high-energy ions to strike the downstream acceleration grid (typically referred to as the accel grid) leading to sputter erosion of grid surfaces (so called ‘pits and grooves’ erosion), or enlargement of the grid apertures (known as ‘barrel’ erosion). This erosion produces a degradation in thruster performance and eventually complete failure. Similarly, erosion of neutralizers is a concern, while sputter erosion rates are typically important in certain plasma etching applications. For ions incid-ent on a flat surface, the erosion rate is given by

$$ \frac{dh}{dt} = \frac{m_s \Gamma_i f_c Y}{\rho_s}, \qquad (43) $$
<table><caption>**Table 17.** Representative secondary electron emission yields due to Auger emission obtained from equation (42). Here $\epsilon_{iz,1} = 10.451$ eV and $\epsilon_{iz,2} = 9.31$ eV.</caption><thead><tr><th>Target</th><th>ε<sub>φ</sub> (eV)</th><th>Ion</th><th>γ<sub>see</sub></th></tr></thead><tbody><tr><td rowspan="2">Al</td><td rowspan="2">4.28</td><td>I<sup>+</sup></td><td>0.030</td></tr><tr><td>I<sub>2</sub><sup>+</sup></td><td>0.012</td></tr><tr><td rowspan="2">CC</td><td rowspan="2">4.81</td><td>I<sup>+</sup></td><td>0.013</td></tr><tr><td>I<sub>2</sub><sup>+</sup></td><td>≈0</td></tr><tr><td rowspan="2">Cu</td><td rowspan="2">4.65</td><td>I<sup>+</sup></td><td>0.018</td></tr><tr><td>I<sub>2</sub><sup>+</sup></td><td>≈0</td></tr><tr><td rowspan="2">Mo</td><td rowspan="2">4.60</td><td>I<sup>+</sup></td><td>0.020</td></tr><tr><td>I<sub>2</sub><sup>+</sup></td><td>0.002</td></tr><tr><td rowspan="2">Steel</td><td rowspan="2">4.40</td><td>I<sup>+</sup></td><td>0.026</td></tr><tr><td>I<sub>2</sub><sup>+</sup></td><td>0.008</td></tr><tr><td rowspan="2">Ti</td><td rowspan="2">3.96</td><td>I<sup>+</sup></td><td>0.040</td></tr><tr><td>I<sub>2</sub><sup>+</sup></td><td>0.022</td></tr><tr><td rowspan="2">W</td><td rowspan="2">4.55</td><td>I<sup>+</sup></td><td>0.022</td></tr><tr><td>I<sub>2</sub><sup>+</sup></td><td>0.003</td></tr></tbody></table>

where *h* is the dimension perpendicular to the surface, *m*<sub>s</sub> is the atomic/molecular mass of the surface material, *ρ*<sub>s</sub> is the mass density of the surface material, Γ<sub>i</sub> is the incident ion flux, *Y* = *Y*(*ε*<sub>i</sub>) is the sputter yield at perpendicular incident and which is a function of the ion bombarding energy *ε*<sub>i</sub>, and *f*<sub>c</sub> is a correction factor accounting for ions that strike the surface at an oblique angle. The sputter yield can be defined as

$$Y = \frac{\Gamma_a}{\Gamma_i}, \qquad (44)$$

with Γ<sub>a</sub> the flux of atoms removed. Sputter yields have been calculated or measured for many different bombarding ion and target elements [206–208], including for oblique ion incidence [209, 210]. Within an electric propulsion context, xenon ions striking metal surfaces like molybdenum have been particularly well studied [211–213], as molybdenum has a low sputter yield compared with other materials (such as copper for example) and so is well-suited for acceleration grids. Figure 34 shows a range of experimental data for perpendicular incidence of singly-charged xenon ions striking a molybdenum surface [214], together with an empirical fit based on Eckstein’s formulation [214, 215]

$$Y = Qs_n \left[ \frac{\left( \frac{\epsilon_i}{\epsilon_{th}} - 1 \right)^{\mu}}{\frac{\lambda}{w} + \left( \frac{\epsilon_i}{\epsilon_{th}} - 1 \right)^{\mu}} \right], \qquad (45)$$

where $Q = 18.4$, $\epsilon_{th} = 14.2$ eV, $\mu = 2.2$, $\lambda = 1.7$, and

$$s_n = \frac{0.5 \ln(1 + 1.2288\beta)}{\beta + 0.1728\sqrt{\beta} + 0.008\beta^{0.1504}}, \qquad (46)$$

$$w = \beta + 0.1728\sqrt{\beta} + 0.008\beta^{0.1504}, \qquad (47)$$

$$\beta = \frac{a_L}{Z_i Z_s} \frac{4\pi\epsilon_0}{e^2} \frac{m_s}{m_i + m_s} \epsilon_i, \qquad (48)$$

$$a_L = \left( \frac{9\pi^2}{128} \right)^{1/3} a_0 \left( Z_i^{2/3} + Z_s^{2/3} \right)^{-1/2}. \qquad (49)$$

Here $Z_s = 42$ is the molybdenum charge number, $Z_i = 54$ is the xenon charge number, $a_0$ is the Bohr radius, and $m_i$ is the ion mass. By contrast, very little data is available for iodine ions (either atomic or molecular) striking any surfaces, nor has there been any significant research to develop iodine sputter codes. The lack of sputter yield data for other specific ion-surface element combinations is also a challenge for the materials processing community, and which was partially addressed in [216] by using a machine learning (ML) model based on Gaussian process regression to estimate unknown sputter yields. Previous lifetime testing studies [217] of an iodine-fueled gridded ion thruster have used sputter yields predicted from this model, and which are compared with those for xenon in figure 34. As seen, the
<figure><img src="image_37.png" /><figcaption>**Figure 34.** Sputter yields for singly-charged atomic xenon and iodine ions striking a molybdenum surface. Xenon data is taken from [214]. The black curve shows the empirical fit from equation (45), while the orange curve shows machine learning (ML) predictions from [216] (with the shaded orange region denoting model prediction uncertainty).</figcaption></figure>

sputter yield for singly-charged atomic iodine ions is noticeably higher than that of xenon (although the majority of xenon data still falls within the shaded lower uncertainty region). However, comparing erosion rate predictions with measurements obtained through high-resolution metrology suggests that iodine sputter yields may be overestimated by roughly a factor of 2 [217]. By comparison, measurements correlated reasonably well when xenon sputter yield data was used instead. As almost no known experimental iodine sputter yield data is available for validation, the ML predictions in [216] should be viewed as an upper estimate with xenon sputter yield data a reasonable interim substitute until further data becomes available.

# 5. Applications and modeling of iodine plasmas

## 5.1. Space propulsion

### 5.1.1. Thrusters

The first proposal to use iodine within the context of space propulsion occurred at least as early as 1960 when Gilleo and Kash [218] introduced a propulsion concept using composite beams of positive and negative ions to achieve mutual neutralization. The idea was to generate negative ions via surface ionization processes from low work function materials, which was already widely being used at the time for positive ion formation (such as in cesium gridded ion thrusters) [7]. A strong motivation for this work was connected with neutralization of the positive ion beam generated by electrostatic propulsion systems, and concerns over whether electron emission for neutralization was viable. In particular, it was unclear if electrons would be able to provide space-charge compensation of the ion beam in the plume due to their small mass. Negative ions could potentially avoid this problem, and because of its high electronegativity, iodine was identified as a possible propellant. A similar concept was proposed in 1963 by Bussi and Filippi [219]. Around the same time, several other works emerged associated with negative ion formation. For example, in 1962 Dong et al [220] performed experiments to generate $I^-$ with the aim of producing a negative ion beam source. Experiments were performed to create negative ions on lanthanum or gadolinium hexaboride surfaces via surface ionization processes. The maximum current density measured was $15 \text{ mA cm}^{-2}$ and the technique was concluded to be technically viable with no iodine surface contamination observed. A schematic of the original experiment is shown in figure 35.

The use of iodine for producing negative ions for neutralization then appears to have 'vanished' from the literature, possibly because of the successful SERT-1 mission launched in 1964, which tested two mercury-fueled gridded ion thrusters. Neutralization was achieved using thermionic filament neutralizers, which conclusively demonstrated that electrons were able to achieve ion beam neutralization. As electron emission is simpler and easier than negative ion emission, neutralization using electrons subsequently became commonplace and is now used in virtually all electrostatic propulsion systems (with the notable exception of electrospray or colloid thrusters which use ionic liquid propellants [221], and micro-cathode arc thrusters which use a solid metal propellant [222]). Additionally, with the advent of hollow cathode neutralizers which are extremely energy efficient [3], the need for negative ion neutralization effectively disappeared.
<figure><img src="image_38.png" /><figcaption>**Figure 35.** Schematic of the experimental apparatus used by Dong *et al* to produce I⁻. Reprinted from [220], Copyright (1962), with permission from Elsevier.</figcaption></figure>

<figure><img src="image_39.png" /><figcaption>**Figure 36.** Photograph showing the BHT-200 Hall thruster operating with iodine. The discharge voltage is 250 V and the discharge power is 500 W. From [225]. Reprinted by permission of the American Institute of Aeronautics and Astronautics, Inc.</figcaption></figure>

Iodine did not receive significant consideration again for space propulsion until the early 2000's when Dressler *et al* [21] proposed iodine as an alternative propellant to xenon in the context of general positive ion formation. After the first gridded ion thruster tests which used mercury and cesium propellants, xenon later emerged as the preferred propellant of choice, in large part because of its low reactivity and toxicity. However, based on space industry trends and long-term projections, Dressler *et al* noted that cost and availability problems with xenon were likely to occur in the near future and that alternative propellants would be needed. Iodine was identified as an attractive propellant option because its atomic mass is similar to xenon, the ionization threshold energies of both I and I₂ are low, and iodine can be stored unpressurized as a solid with a high density. Dressler *et al* concluded that iodine was potentially a feasible alternative to xenon, but that further investigation was required.

Around the same time, Tverdokhlebov and Semenkin [22] considered several alternative condensable propellants for Hall thrusters, including iodine. It was again noted that the availability of xenon (due to a low global production output) was a restriction that could cause challenges for the space industry in the future. After considering several alternatives, iodine was discussed as an attractive option as world production is several orders of magnitude higher than xenon, and iodine can be stored as a solid with a low temperature required for sublimation. Several potential reactivity and toxicity concerns were however noted.

Several patents for iodine electric propulsion systems were subsequently filed, first by Dressler *et al* [223] in 2003 and then by Chabert [224] in 2006. However, the first known iodine electric propulsion system was only developed and tested in 2011 by Szabo *et al* [225] at the US company Busek. Ground experiments consisted of an iodine-fed Hall thruster, an iodine propellant storage and feed system, and a prototype power processing unit. Neutralization was provided with a xenon-fueled hollow cathode. Operation was found to be stable and performance was comparable with xenon. Figure 36 shows a photograph of the thruster operating with iodine, while figure 37 shows a performance comparison between iodine and xenon propellants. Solid iodine crystals were stored in a reservoir and then sublimated using a thermal control system to vary the pressure and achieve target mass flow rates. For mass flow rates of the order of 1 mg s⁻¹, and a discharge voltage of 300 V, the thrust-to-power ratio observed was about 60 mN kW⁻¹ with an anode specific impulse and anode thruster efficiency of approximately 1500 s and 45%–50% respectively. The ion beam plume was found to be well-collimated and contained small fractions of I⁺, I²⁺, and I³⁺ [226], with the dominant ion being I⁺. This was confirmed in subsequent work by Chiu and Prince [227] who performed optical emission spectroscopy of the thruster plume.
<figure><img src="image_40.png" /><figcaption>**Figure 37.** Thrust as a function of power for the BHT-200 Hall thruster operating with xenon and iodine. The propellant mass flow rate is between 0.58 and 1.04 mg s⁻¹. Data taken from [225].</figcaption></figure>

Following successful ground-testing, Busek performed an extensive set of additional experiments with different Hall thruster variants, and power levels ranging from below 200 W to around 10 kW [228, 229]. As a general conclusion, iodine was found to be a viable alternative propellant that can provide superior performance to xenon for various space missions. Furthermore, a strong reduction in propulsion system size, mass, and cost is possible, and iodine deposition on spacecraft components was predicted to be negligible. Some of the above tests were supported by NASA, which began to invest in further advancing iodine propulsion technology [230, 231]. In particular, a CubeSat-sized iodine Hall thruster demonstrator mission was proposed in 2012 [232] based on the Busek BHT-200 Hall thruster and which led to the Iodine Satellite (iSAT) mission. Although iodine Hall thrusters were developed and delivered as part of the mission, it did not fly. Scheduled for launch in 2018, the mission was stopped in 2017 because of concerns related to propulsion system maturity: particularly operational challenges with the iodine hol-low cathode [231] (see also sections 5.1.2 and 7.2).

Several other research groups also began seriously investigating iodine around this time. This included Tsay *et al* [233] (also at Busek) who developed a gridded ion thruster (the BIT-3) based on RF inductively coupled plasma (ICP) technology. This propulsion system also included an RF neutralizer (see section 5.1.2 below). Similarly, Holste *et al* [234] developed an iodine-fueled gridded ion thruster based on the existing RIT-10. Results were found to be broadly comparable with xenon, although iodine exhibited higher performance at low mass flow rates, while at higher mass flow rates (and hence pressures), there was a strong decrease in performance: consistent with the collisional energy loss arguments discussed in section 3.8. Holste *et al* concluded that iodine appears to be a feasible alternative propellant to xenon, although neutralization was achieved using a heated tungsten filament. Shortly after however, Dietz *et al* [109] developed and tested an iodine-fueled RF neutralizer to replace the thermionic filament (see section 5.1.2).

In parallel to the above studies, work on iodine electric propulsion also began in France at Ecole Polytechnique and which was largely motivated by the plasma propulsion using electronegative GASES (PEGASES) propulsion concept [235]. PEGASES was a proposed dual-beam propulsion system that alternatively extracts and accelerates positive and negative ions (somewhat similar to the original iodine propulsion concepts; see [218, 219]). A primary requirement of this concept was a propellant with a strong electron affinity to enable negative ion formation, and iodine was quickly identified as an ideal propellant. Several experimental prototypes were developed demonstrating the basic idea and validating the alternate ion beam extraction concept [236–238]. In 2016, the French company ThrustMe spun out of Ecole Polytechnique and began pioneering the use of iodine in the space industry. To partially validate several iodine technologies (such as the propellant storage and flow control systems) the I2T5 cold/warm gas propulsion system was developed [27], and which is illustrated in figure 38. Here, solid iodine is stored unpressurized and then sublimated using a temperature-controlled feedback loop. The iodine vapor is then expanded through a small nozzle to generate thrust. The high storage density of iodine, and the simple flow control hardware required, enabled a compact propulsion system design with a 0.5-Unit (0.5U) form factor and a total wet mass of 0.9 kg. Concurrently, ThrustMe also developed the NPT30-I2, which is an iodine-fueled RF gridded ion thruster [2], a cut-away view of which is shown in figure 39. The use of iodine enabled a high impulse density system with a wet mass
<figure><img src="image_41.png" /><figcaption>**Figure 38.** Photograph of the I2T5 cold/warm gas propulsion system. Reproduced with permission from [27].</figcaption></figure>

<figure><img src="image_42.png" /><figcaption>**Figure 39.** Cutaway schematic of the NPT30-I2 propulsion system. Reproduced from [2]. CC BY 4.0.</figcaption></figure>

of 1.2 kg, and a form factor of only 1U: almost half that needed for a similar xenon version. To promote further propulsion system miniaturization, electron-emitting thermionic filaments were used for ion beam neutralization.

Following the successful in-space demonstration of the NPT30-I2 in 2020, several other organizations have developed iodine electric propulsion systems. This includes the IRIT4 gridded ion thruster by Yang *et al* [239], as well as the REGULUS ambipolar thruster developed by the Italian company T4i [240], and the electron cyclotron resonance ambipolar thruster ECRA developed by ONERA. In the REGULUS system, plasma is created using an RF antenna and is then expanded through a magnetic nozzle. This creates an internal electric field (called an ambipolar field) that then accelerates ions to generate thrust. A strong advantage of such ambipolar acceleration is that the thruster is inherently current balanced, and so no neutralizer is needed. More recently, ThrustMe has developed the prototype iodine Hall thruster JPT-150 [241], while Busek offers several Hall thruster variants that are compatible with iodine [228]. Iodine Hall thrusters have also been developed by Xu *et al* [242], Paganucci *et al* [243] in collaboration with the Italian company SITAEL, and more recently by Esteves *et al* [244] in collaboration with Safran Spacecraft Propulsion. A recent review by Tirila *et al* [245] has compiled Hall thruster performance data for a number of propellants. Iodine gives similar, or even superior, performance to xenon over a wide power range from 100 W to 10 kW, and is found to be one of the best alternative propellants available: nicely validating the original proposals by Dressler *et al* [21] and Tverdokhlebov and Semenkin [22]. Finally, a consortium led by Airbus is developing several iodine-fueled thrusters as part of the iFACT project (iodine Fed Advanced Cusp Field Thruster), which are based on a cusp magnetic
<table><caption>**Table 18.** Example commercial iodine, or iodine-compatible, electric propulsion systems and the number of systems in space (with respect to iodine). Here, power, thrust, and specific impulse ($I_{sp} = F/(\dot{m}g_0)$) where F is the thrust, $\dot{m}$ is the input propellant mass flow rate, and $g_0$ is the gravitational acceleration at sea level) represent nominal or maximum values depending on available data [27, 247–251].</caption><thead><tr><th>Name</th><th>Organization</th><th>Power (W)</th><th>Thrust (mN)</th><th>I<sub>sp</sub> (s)</th><th>Number in space</th></tr></thead><tbody><tr><td colspan="6"><strong>Cold/warm gas thrusters</strong></td></tr><tr><td>I2T5</td><td>ThrustMe</td><td>5</td><td>0.35</td><td>—</td><td>11</td></tr><tr><td colspan="6"><strong>Gridded ion thrusters</strong></td></tr><tr><td>BIT-3</td><td>Busek</td><td>80</td><td>1.25</td><td>2300</td><td>At least 2</td></tr><tr><td>NPT30-I2-1U</td><td>ThrustMe</td><td>65</td><td>1.1</td><td>2400</td><td>96</td></tr><tr><td>NPT30-I2-1.5U</td><td>ThrustMe</td><td>65</td><td>1.1</td><td>2400</td><td>4</td></tr><tr><td colspan="6"><strong>Hall thrusters</strong></td></tr><tr><td>BHT-100</td><td>Busek</td><td>100</td><td>7</td><td>1000</td><td>Unknown</td></tr><tr><td>BHT-200</td><td>Busek</td><td>200</td><td>13</td><td>1390</td><td>Unknown</td></tr><tr><td>BHT-350</td><td>Busek</td><td>300</td><td>17</td><td>1244</td><td>Unknown</td></tr><tr><td>BHT-600</td><td>Busek</td><td>600</td><td>39</td><td>1500</td><td>Unknown</td></tr><tr><td>BHT-1500</td><td>Busek</td><td>1500</td><td>101</td><td>1710</td><td>Unknown</td></tr><tr><td>BHT-6000</td><td>Busek</td><td>6000</td><td>325</td><td>2700</td><td>Unknown</td></tr><tr><td>BHT-20K</td><td>Busek</td><td>20 000</td><td>1005</td><td>2515</td><td>Unknown</td></tr><tr><td>JPT-150</td><td>ThrustMe</td><td>300</td><td>10</td><td>1600</td><td>-(R&D stage)</td></tr><tr><td>PPS®X00</td><td>Safran</td><td>1000</td><td>—</td><td>—</td><td>-(R&D stage)</td></tr><tr><td colspan="6"><strong>Ambipolar thrusters</strong></td></tr><tr><td>REGULUS-50-I2</td><td>T4i</td><td>50</td><td>0.55</td><td>550</td><td>At least 1</td></tr><tr><td>ECRA-30</td><td>ONERA</td><td>30</td><td>—</td><td>—</td><td>-(R&D stage)</td></tr><tr><td>ECRA-150</td><td>ONERA</td><td>150</td><td>—</td><td>—</td><td>-(R&D stage)</td></tr><tr><td colspan="6"><strong>Cusp field thrusters</strong></td></tr><tr><td>Alberich</td><td>Airbus</td><td>20</td><td>0.63</td><td>900</td><td>-(R&D stage)</td></tr><tr><td>MkI</td><td>Airbus</td><td>300</td><td>—</td><td>—</td><td>-(R&D stage)</td></tr><tr><td>Linear CFT</td><td>Airbus</td><td>1000</td><td>—</td><td>—</td><td>-(R&D stage)</td></tr></tbody></table>

field thruster somewhat similar to Hall thrusters [246]. A summary of several commercial iodine-fueled electric propulsion systems is listed in table 18.

To conclude, Building bioOcks for iodine thrusters [252], a research initiative funded by the European Union, was recently launched with the primary goal of advancing and promoting iodine electric propulsion technology as a key enabler for the small satellite market; overcoming the current low technological maturity through a modular approach focused on developing essential building blocks for future commercialization.

### 5.1.2. Neutralizers

The majority of iodine electric propulsion systems developed to date are classed as electrostatic systems (such as gridded ion or Hall thrusters), which require an electron-emitting neutralizer [3]. Not only is this needed to ensure overall current balance of the propulsion system and spacecraft, but it is also necessary for charge compensation to prevent ion-beam stalling [7]. In the case of Hall thrusters, the neutralizer also serves as an electron source for initiating and sustaining the plasma discharge.

Currently, there are three main types of neutralizer technology which includes: a heated wire filament, a miniature RF or microwave plasma discharge, and a thermionic hollow cathode. A filament neutralizer is the simplest and consists of a metal wire (such as thoriated tungsten or tantalum) that is heated by flowing a sufficiently high current through it. Ohmic heating of the wire causes a temperature increase that can lead to thermionic electron emission. Although filament neutralizers have flown in space [2, 253], they are not widely used because the wire can evaporate at typical operating temperatures and/or is very susceptible to damage (such as from sputter erosion due to ion bombardment)
<table><caption>**Table 19.** Common neutralizer technologies and their typical efficiencies (representative data taken from [257]).</caption><thead><tr><td>Neutralizer</td><td>ε<sub>e</sub> (eV)</td><td>η<sub>g</sub></td></tr></thead><tbody><tr><td>Filament</td><td>1000–2000</td><td>—</td></tr><tr><td>RF/microwave</td><td>100–300</td><td>1–10</td></tr><tr><td>Hollow cathode</td><td>15–50</td><td>1–100</td></tr></tbody></table>

[217]. There is also a limit to the maximum electron current density that can be extracted because of both Richardson's law [3], and the Child–Langmuir law associated with space-charge effects [124]. By contrast, RF neutralizers make use of an ICP discharge and then extract a quasi-neutral plasma (but with a net electron current) through an orifice [109, 233, 252, 254]. Microwave neutralizers operate in a similar manner [255, 256]. As the discharge is essentially quasi-neutral and electrodeless, a higher electron current density can be extracted and erosion is reduced or eliminated. Finally, hollow cathodes create a high-density plasma discharge inside a hollow cylindrical geometry via electron emission from a special heated insert material (such as lanthanum hexaboride, LaB<sub>6</sub>, or barium oxide, BaO [3, 257]; see also section 7.2) and a quasi-neutral plasma is again extracted through an orifice. Care is needed when operating and handling hollow cathodes however, as the insert material is susceptible to poisoning or chemical reactions with some substances [3]. Despite this, hollow cathodes are by far the most efficient and dominant neutralizer technology to date.

Neutralizer power efficiency can be expressed in terms of an electron energy cost given by

$$ \varepsilon_e = \frac{P_{\text{neut}}}{I_e}, \qquad (50) $$

where $I_e$ is the net extracted electron current and $P_{\text{neut}}$ is the total power needed to operate the neutralizer. A typical design objective is to minimize the energy cost. While RF, microwave, and hollow cathode neutralizers can achieve a lower energy cost than filament neutralizers, they require a small amount of propellant flow (approximately 5%–10% of the main thruster mass flow rate) to operate [3]. Consequently, a propellant gas utilization efficiency can also be defined by

$$ \eta_g = \frac{M I_e}{e \dot{m}}, \qquad (51) $$

with M the atomic/molecular mass of the propellant, $\dot{m}$ the neutralizer propellant mass flow rate, and e the elementary charge. Table 19 provides representative efficiency values for the different neutralizer technologies, where it is seen that hollow cathodes have the lowest electron energy cost.

At present, the only known technology demonstrated in space for iodine-fueled electric propulsion systems is a filament neutralizer, which is used by the NPT30-I2 thruster [2]. While such neutralizers are simple and do not require any propellant flow, their electron energy cost is very high. Thus, they are only appropriate for low currents (for reference, the ion beam current produced by the NPT30-I2 is between about 10 and 20 mA [2, 28]). For higher currents, and in particular for Hall thrusters, the electron energy cost of filament neutralizers is too high to be feasible. For example, consider a 1 kW Hall thruster generating a nominal ion beam current of 4 A. If a filament neutralizer is to be used, and assuming an aggressive design with an electron energy cost of 1000 eV, the power consumption required is 4 kW. Another challenge with filament neutralizers is that they are easily damaged. Recent testing suggests that the maximum lifetime may be limited to just above 1260 h [217]: a value that may be insufficient for many space missions.

RF/microwave neutralizers have an electron energy cost almost an order of magnitude lower than filaments, and are less prone to erosion or degradation. They are therefore well-suited for long-duration missions and flight models operating with iodine have already been successfully developed [257]. Indeed, an RF neutralizer (the BRFC-1; see figure 40) is used by the BIT-3 thruster [233], although publicly available information on flight heritage is not known. The status of iodine neutralizers have recently been thoroughly discussed in the review paper by Becke et al [257], who have identified various organizations developing iodine neutralizers. Becke et al note that while there does not appear to be any technical barrier for RF neutralizers, as of 2025 there has been no known stable, long-term operation of a hollow cathode using iodine (see also section 7.2). The electron energy cost for RF neutralizers may however still be too high for some thrusters. Using the Hall thruster example from before, and assuming an electron energy cost of 100 eV, the power consumption is about 400 W: a significant fraction of the total propulsion system power. By contrast, the power consumption of a hollow cathode for this example could be as low as 60 W.
<figure><img src="image_43.png" /><figcaption>**Figure 40.** Photograph of the BIT-3 ion thruster (bottom discharge) and BRFC-1 RF neutralizer (top discharge) operating with iodine. From [233]. Reprinted by permission of the American Institute of Aeronautics and Astronautics, Inc.</figcaption></figure>

<figure><img src="image_44.png" /><figcaption>**Figure 41.** Scanning electron microscope image of InP cylindrical array patterns produced using iodine plasma etching. Reproduced from [23]. © IOP Publishing Ltd. All rights reserved.</figcaption></figure>

## 5.2. Industrial applications

Although interest in iodine plasmas has largely been driven by space propulsion needs in recent years, there are also a number of potential ground-based applications including dry etching [23, 258], material surface treatment or modification [259, 260], lasers [261–263], and UV light sources [264]. Unlike for propulsion, a mixture of different gases (such as xenon and iodine), or even iodine compounds (such as boron triiodide; $BI_3$), are typically used instead of pure iodine. While this adds further reaction processes beyond those explicitly treated in this review article, various atomic and molecular neutral and ionic iodine species are nonetheless expected to form such that much of the volume and surface plasma chemistry is still relevant.

Low-temperature dry etching of III–V semiconductors is often desired for preserving fine resist masks during fabrication. An important requirement for dry etching is that the product of the reaction between radicals in the plasma and atoms of the material surface must be volatile. The use of iodine plasmas has been proposed for the etching of certain semiconductor materials [23] such as indium phosphide (InP), gallium arsenide (GaAs), and silicon dioxide ($SiO_2$). As the volatilization temperature of indium iodide (InI) is much lower than indium chloride (InCl), a lower temperature etching process can be realized. For example, [23, 265] describe an etching process for micro/nano-optical or electron device fabrication, as well as photonic crystals. Solid iodine crystals are placed on a heated substrate that causes sublimation and the resulting iodine vapor is then distributed within the processing chamber. Controlling the substrate temperature allows the iodine vapor pressure (and hence mass flow rate) to be adjusted. An ICP discharge is created above the substrate using xenon as the main feed gas, although reactive iodine ions are also generated from the iodine vapor. By applying an RF bias to the substrate, the ion energy can be controlled and a smooth vertical etch of the substrate material obtained. For the etching of InP, a low process temperature of only 90 °C is required and a reasonable etch rate of $0.4 \ \mu m \ min^{-1}$ can be achieved. By comparison, etching with chlorine requires process temperatures as high as 250 °C. Figure 41 shows a scanning electron microscope image of optical waveguides fabricated using this technique.
<figure><img src="image_45.png" /><figcaption>**Figure 42.** Etching rate of InP as a function of pressure. The ICP power is 300 W, the substrate bias power is 20 W, and the process temperature is 90 °C. Data taken from [23].</figcaption></figure>

Other sources of iodine have included HI for use in neutral beam etching of gallium nitride (GaN) and indium gallium nitride (InGaN) for micro light-emitting diodes [266]. Compared with chlorine neutral beam etching, a higher etch rate is observed when using HI, together with a lower surface roughness and significantly lower etching residues. These results are consistent with those obtained earlier by Pearton *et al* [267], who also showed that HI is a universal etchant for III–V semiconductors enabling very anisotropic etch features. It should be noted though that in some cases, non-hydrogen etchants are preferred as they can result in simpler etch processes and equipment requirements [268]. Solid iodine is therefore an attractive etchant, which also allows more precision in the etching process to be achieved by finely controlling the amount of iodine placed in the processing chamber. Although argon is often used as a feed gas in semiconductor manufacturing, xenon was chosen for iodine etchants because it has a similar mass to atomic iodine [23, 265]. With the use of iodine in the process, the etch rate increases by a factor of almost two compared with that observed for xenon alone. This is thought to result from the higher chemical reactivity of iodine and the higher volatility of the etch products. Figure 42 shows the measured etching rate with pure xenon and xenon/iodine chemistries. Iodine can also have other advantages. For example, when etching indium gallium arsenide phosphide (GaInAsP) structures [268], although indium iodide (InI₃) has a high volatility, other iodide etching products can form a passivation layer protecting etch structure sidewalls. As an alternative to solid iodine crystals, iodine trichloride (ICl₃) powder has been used to etch GaAs [265]. The main etching mechanism depends on the process pressure with sputtering by positive ions dominating at pressures around 0.1 Pa, while chemical etching dominates at 1 Pa.

The etching process described above has also been investigated for the dry etching of silicon (Si) [269], and is very simple as it is free of any carbon, carbon fluoride, or hydrogen reaction products. This is potentially attractive as such products can lead to the deposition of a polymeric layer on etched surfaces. While xenon fluoride ($XeF_2$) as been used as an alternative etchant, the etching profile is very rough and isotropic which affects device performance. Similarly, although HI has been demonstrated as an etchant, the presence of hydrogen can induce damage to the substrate. Thus, solid iodine etching again offers potential advantages as it avoids these issues. Since deep vertical etches with smooth profiles can be produced (typically with a surface roughness of 6 nm: i.e. smaller than the wavelength of light which satisfies optical device requirements) and with reasonable etching rates of up to 90 nm min⁻¹, solid iodine could be useful for fabricating micro-electromechanical system devices. For the etching of silicon, the use of iodine has been found to increase the etch rate by a factor of 3–4 over pure xenon depending on the process pressure and substrate bias power [269]. Since pure xenon etching is due to sputter erosion, it is thought that iodine etching is again of a chemical nature. This demonstrates that although iodine reactivity may be a disadvantage for some applications (see section 4.1), it can in fact be beneficial for other applications.

The use of iodine for etching is not however always useful. For example, [270] studied the etching of zinc oxide (ZnO) and indium-zinc-oxide (IZO) films with iodine bromide (IBr) and BI₃ chemistries where little benefit was observed. The etching rates found were similar to those for physical sputtering
from pure argon. Similarly, $BI_3$ was used to etch lanthanum manganite perovskite ($LaCaMnO_3$) for magnetic memories and sensors in [271]. While some chemical etching enhancement was observed (amounting to a few tens of percent), above a certain gas flow rate the etch rate in fact decreased due to the adsorption of iodine on the substrate surface. Iodine was also found to be impractical for the etching of silicon carbide (SiC) in [272] because the resulting etch products are not sufficiently volatile.

Several studies have investigated the use of iodofluorocarbon substances (such as iodotrifluoroethylene and 1-iodoheptafluoropropane) for etching dielectric films as an alternative to perfluoro compounds currently used and which have a strong global warming potential [273]. Promising results have been found for the etching of $SiO_2$ and silicon nitride ($SiN_2$) films. Global warming concerns with perfluorinated compounds have also led to research with trifluoroiodomethane ($CF_3I$) for atomic layer etching [274, 275], which is a type of etching that has received increased interest in recent years as it allows atomic-level control of etch thickness and exhibits self-limiting characteristics [276, 277].

Focused ion-beam etching has been proposed as a technique enabling rapid prototyping of new micro-/nano devices and has been applied to the etching of silicon for photonic applications [278, 279]. Optical losses due to crystal damage and ion implantation can make the manufacture of some optical devices impractical or challenging. However, such damage can be reduced by etching with iodine gas enhancement, followed by thermal post-treatment to desorb any silicon-iodine bonds from the surface. Using a 30 keV gallium focused ion beam, [278, 279] injected iodine vapor from a gas nozzle positioned near the etch site. The nozzle contained a crucible with solid iodine heated to 42 °C causing sublimation and adsorption on the silicon surface. Measurements indicated that optical losses were reduced from $3520 \text{ dB cm}^{-1}$ for a direct gallium ion beam etch, to approximately $196 \text{ dB cm}^{-1}$ when iodine was added (followed by thermal post-treatment).

Aside from etching, there are also other uses for iodine, such as in surface modification/treatment. For example, in [259] carbon nanospheres were impregnated with iodine and iron-nitrogen (Fe-Nx) dopants using a solution plasma process to improve electrocatalytic activity. Iodine dopants have a large atomic radius that can induce defects and distortions in the carbon lattice and positively affect oxygen reduction reactions for fuel cells. In this sense, such novel dopants can act as alternative catalysts to platinum. Iodine can also promote improved electron conductivity and enable high current densities to be achieved. In [280], a low-temperature CCP iodine plasma was used to treat activated carbon for use as an electrode in electrochemical capacitors. Iodine-doped carbon leads to samples that are much rougher compared with untreated carbon (see figure 43), and electrochemical measurements indicate superior performance. This is potentially useful for supercapacitors because of the reversible reduction-oxidation (redox) reactions of iodide species at the carbon/electrolyte interface. Other applications include the manufacture of catalysts for water splitting and hydrogen generation applications [281]. Inspired by observations that iodine addition to some lamps can increase filament lifetime (by binding to evaporated tungsten atoms and promoting re-deposition onto the surface of the filament), [281] used an atmospheric pressure iodine dielectric barrier discharge to create three-dimensional copper sulfide ($Cu_2S$) nanosheet arrays for the low-cost fabrication of novel oxygen evolution reaction catalysts. Finally, iodine-based substances, such as iodophor and povidone-iodine, have been used to create antiseptic nano-scale coatings via plasma polymerization for medical devices and wound dressings [260]. Such coatings have been shown to exhibit broad spectrum anti-bacterial activity against microbes responsible for wound infections: including drug resistant strains.

Iodine plasmas can also indirectly be formed in several other applications. For example, determination of iodine content in food or geological samples is often conducted using ICP mass or optical spectrometry [282–284]. Knowledge of the relevant iodine plasma chemistry, surface reactions, and different species formed can therefore aid the understanding and interpretation of measurements obtained. Similarly, the purification of iodine for semiconductor production has been studied in [285] to reduce carbon or metal impurities. Here, an oxygen-argon ICP plasma interacts with iodine vapors to form diiodine oxides ($I_2O_5$). Thermal decomposition then produces oxygen and high-purity iodine: a process that could also be relevant to the production of high-purity iodine propellant for space propulsion applications.

### 5.3. Theoretical and numerical modeling

Sections 2–4 provided a comprehensive set of data associated with general iodine properties, collision reactions and plasma chemistry, and plasma-surface interactions. Aside from being useful in understanding the basic underlying processes relevant to iodine plasmas, this information is important for the design of practical devices (such as propulsion or processing systems as discussed in sections 5.1
<figure><img src="image_46.png" /><figcaption>**Figure 43.** Scanning electron microscope images of (a) unmodified carbon, (b) iodine treated carbon (20 W for 10 min), and (c) iodine treated carbon (80 W for 10 min). Reprinted from [280], Copyright (2016), with permission from Elsevier.</figcaption></figure>

and 5.2), is needed to help interpret or analyze several diagnostics (such as optical emission spectroscopy), or is a critical input to theoretical/numerical models. This last point is particularly relevant as iodine plasmas are significantly more complex than noble gas plasmas like argon or xenon.

The majority of modeling efforts to date have focused on electric propulsion applications. The first known model of an iodine plasma was developed by Grondein *et al* in 2016 [71] using electron impact cross-section data largely obtained from Hamilton [29]. In this work, Grondein *et al* developed a model of an RF gridded ion thruster and studied system performance when using xenon or iodine. Overall, comparable performance was obtained and iodine was found to be a viable alternative propellant. However, at low mass flow rates, the performance with iodine was predicted to be higher than with xenon: consistent with experimental measurements performed several years later by Holste *et al* [234] and Esteves *et al* [286]. The work by Grondein *et al* helped to create an initial iodine reference reaction set that was subsequently leveraged in several previous works: first by Lucken [97] and Marmuse [98], and more recently by Lafleur *et al* [28] and Esteves [26, 287]. The model of Grondein *et al* also appears to have been adapted by Dietz *et al* [109] to model iodine RF neutralizers. While the general trends were consistent with experiment, the predicted neutralizer current was approximately two times higher than that measured experimentally.
<figure><img src="image_47.png" /><figcaption>**Figure 44.** Thrust of the NPT30-I2 as a function of total propulsion system power for mass flow rates of (a) 38 µg s⁻¹, (b) 58 µg s⁻¹, and (c) 99 µg s⁻¹. Data markers show experimental measurements while shaded regions indicate model predictions. Data taken from [288].</figcaption></figure>

Lafleur *et al* [28] and Esteves [26, 287] developed more sophisticated models than Grondein *et al* by including additional reaction processes and using updated electron scattering cross-sections provided by Ambalampitiya *et al* [31]. The model of Esteves was compared with experimental measurements performed in an RF ICP plasma source showing good agreement. Similarly, the model of Lafleur *et al* was validated with measurements of the ion beam current and propellant utilization efficiency ($\eta_m = \dot{m}_i/\dot{m}_{in}$ where $\dot{m}_i$ is the ion mass flow rate and $\dot{m}_{in}$ is the propellant inlet mass flow rate) obtained with the NPT30-I2 propulsion system (see section 5.1). Further work by Jia-Richards and Lafleur [288] then compared the predicted and measured thrust where excellent agreement was obtained, as demonstrated in figure 44 (see also section 6.1). Overall, the above works indicate that although there are missing collisional processes and cross-section data, current reaction sets appear reasonable and can be used to predict realistic system performance. Results also confirm that performance with iodine is higher than xenon at low mass flow rates, and that it appears to be a promising alternative propellant. Furthermore, the higher elastic scattering cross-section of atomic iodine, and the shallower Ramsauer minimum (see section 3.2.1), may enhance electron momentum transfer leading to a higher RF power coupling efficiency in low-pressure ICPs [28]. However, both Lafleur *et al* and Esteves noted that there is still uncertainty in the validity of available elastic scattering cross-sections for atomic iodine at low electron energies and that further research is needed.

The works above use volume-averaged models focused on iodine reaction kinetics and global system performance. Several studies have however investigated discharge spatial variations. This includes the 2D model by Levko and Raja [108] who simulated an iodine ICP, Esteves [26] who developed a 1D model of iodine gas flow in an ICP (including a limited set of plasma collisional processes), and Liu *et al* [289] who developed a 2D fluid model of an iodine-fed hollow cathode discharge. This last model underwent partial validation against experimental electrical measurements, revealing the critical importance of molecular iodine dissociation due to electron impact and thermal processes, which results in atomic iodine as the dominant neutral species. While the simulated discharge behavior shared some similarities with xenon, significant differences were also observed. Simulations illustrate that including I⁻ results in a higher ionization degree, discharge power, and electron and gas temperatures compared to cases where I⁻ was not considered. These findings underscore the necessity of thoroughly understanding the more complex iodine plasma chemistry to help optimize the design and operation of iodine neutralizers. As an illustration, figure 45 presents example 2D contour maps of key plasma properties within the hollow cathode, as simulated by Liu *et al*.

Other multi-dimensional models include the work of Saifutdinova *et al* [290] who simulated an iodine ICP with a more sophisticated plasma chemistry than that originally used by Levko and Raja [108]. An interesting finding of this work is that for short initial simulation times, the discharge is an ion-ion plasma dominated by $I_2^+$ and I⁻ charged species, and that it only transitions to an electron-ion plasma (dominated by $I^+$ and e⁻) after several milliseconds. This was also studied by the same authors
<figure><img src="image_48.png" /><figcaption>**Figure 45.** Spatial density distribution of (a) electrons, (b) $I^+$, (c) $I_2^+$, and (d) $I^-$ in an iodine hollow cathode, with a 1D profile along the hollow cathode axis shown in (e). Reproduced from [289]. © IOP Publishing Ltd. All rights reserved.</figcaption></figure>

<figure><img src="image_49.png" /><figcaption>**Figure 46.** (a) Velocity of $I^+$ and $I_2^+$ species and (b) electric field (E) and ionization rate ($S_{iz,1+}$ for $I^+$ and $S_{iz,12+}$ for $I_2^+$) profiles as a function of axial position along the channel of an iodine-fueled Hall thruster. Reprinted from [294], with the permission of AIP Publishing.</figcaption></figure>

using an earlier volume-averaged model [291], where it was found that an ion-ion plasma could be produced at low powers and for pressures above 3 Pa. As the power is increased, electron impact dissociation of molecular iodine starts to become more significant and a transition to a conventional electron-ion plasma is observed. Lequette [292] developed a quasi-2D iodine PIC model (which was 1D in the axial direction with approximate transverse boundaries) to simulate inductive discharges. This PIC model was coupled to a fluid model describing the evolution of neutral species and represents one of the only known iodine PIC codes developed to date. Lequette noted that at low pressures, the discharge is electro-positive and similar to a typical noble gas discharge. However, at higher pressures, the plasma becomes electronegative with a significant negative ion density. Strong gas heating is also observed, which is consistent with previous experimental measurements [26], and the atomic iodine temperature is higher than the molecular temperature. Gas heating appears to result from electron impact dissociation processes, although recombination reactions were also found to be relevant in some cases. The work of Lequette provides an important step towards high-fidelity 2D modeling of various iodine electric propulsion systems.

While many models have focused on gridded plasma sources, work has also been done to model Hall thrusters, ambipolar thrusters, and cusp magnetic field thrusters based on the high efficiency multistage plasma thruster (HEMPT) concept. Bianchi et al [293] developed a volume-averaged model of an iodine Hall thruster segmented into two separate zones (a dissociation zone and a combined acceleration and ionization zone). Results suggest that the density of negative ions is expected to be negligible, while an appreciable fraction of $I_2^+$ (as high as 30%) is predicted. Model results were found to be in reasonable agreement with the JPT-150 thruster prototype. Chabert et al [294] developed a 1D simulation of an iodine-fed Hall thruster and showed that there are two distinct ionization zones (see figure 46): one near the anode and associated with the ionization of molecular iodine, and a second downstream associated with the ionization of atomic iodine. A significant fraction of $I_2^+$ was predicted, and the use