<figure><img src="image_50.png" /><figcaption>**Figure 47.** Spatial density distribution of electrons, I, and I⁻ species in an I₂-Xe ICP plasma operated at 400 W. Reproduced from [298]. CC BY 4.0.</figcaption></figure>

of iodine allows an extension of thruster operating parameters to lower mass flow rates and discharge powers. Xu *et al* [242] performed 2D simulations of an iodine-fueled Hall thruster and found that the dissociation zone overlaps with the near-anode region and the ionization zone. Andrews *et al* [295] have developed a model of the REGULUS ambipolar thruster. In contrast to gridded ion thrusters, Andrews *et al* found that iodine gives slightly lower performance than xenon, but predictions where again in reasonable agreement with experimental measurements. Iodine ambipolar thrusters have also separately been modeled by Saini and Ganesh [296]. Niu *et al* [297] performed 1D fluid simulations of an iodine HEMPT thruster. Low-frequency oscillations (around 25 kHz) were observed and the densities of I⁺ and I₂⁺ were found to be similar. Iodine was predicted to give enhanced performance compared with xenon. As with the iodine Hall thruster models above, the density of I⁻ is again predicted to be negligible, which is not surprising given the high electron temperatures present in these devices, and hence the importance of molecular dissociation and detachment processes.

Finally, the work of Gehring *et al* [298] is noteworthy as it is one of the only models not developed for propulsion applications. Here, the commercial package COMSOL was used to simulate iodine ICPs for the development of mercury-free UV radiation sources, and results were compared with experimental data. In particular, the model included a mixture of xenon and iodine. Figure 47 shows the predicted spatial density distribution of different particle species.

# 6. In-space testing

## 6.1. Flight heritage

Although development of the first iodine-fueled electric propulsion system occurred at least as early as 2011 by the US company Busek [153], the first known in-space demonstration was in November 2019 by the French company ThrustMe who tested the I2T5 cold/warm gas thruster [27]. The system flew aboard the 6U CubeSat, Xiaoxiang 1-08, operated by the Chinese company Spacety [299], and which was placed into a 500 km circular Sun-synchronous orbit (SSO). The first firings of the thruster were between 16 and 19 November and consisted of 4 h of cumulative burn time. While propulsion system telemetry indicated successful operation, the firing duration and thrust was too low for a clearly discernible orbit change from global positioning system (GPS) and space surveillance network (SSN) data. Despite slight variations in expected thermal behavior compared with ground-testing, the system functioned as expected and validated iodine storage and flow control/distribution hardware [27].

The first in-space demonstration of a plasma-based iodine electric propulsion system occurred in 2020. This system (the NPT30-I2; also developed by ThrustMe) flew aboard the 12U CubeSat, Beihangkongshi-1 (again operated by Spacety), launched on the 6 November 2020 into a 480 km SSO [300]. Figure 48 shows a photograph of the propulsion system integrated with the satellite at the assembly facility. After several initial system tests, the first firing campaign took place at the end of December 2020 and continued until the end of February 2021. During the campaign, a total of 11 separate firings were conducted, with the satellite attitude control system adjusting the thrust vector direction to be parallel, anti-parallel, or perpendicular to the satellite velocity vector. The time evolution of the satellite mean semi-major axis is shown in figure 49, together with the firing tests performed. The black line in figure 49 shows the planned/expected semi-major axis from a simplified analytical model including the planned firing maneuvers and their duration. The decay between maneuvers occurs because of residual atmospheric drag on the satellite. The blue circles show independent tracking data from the SSN
<figure><img src="image_51.png" /><figcaption>**Figure 48.** The NPT30-I2 propulsion system integrated with the Beihangkongshi-1 satellite before launch. Reproduced from [2].
CC BY 4.0.</figcaption></figure>

<figure><img src="image_52.png" /><figcaption>**Figure 49.** Mean semi-major axis of the Beihangkongshi-1 satellite with time. The black line shows predictions from theory, while the markers show data from the space surveillance network [301] (SSN; blue circles), onboard global positioning system receiver (GPS; orange squares), and high-fidelity numerical simulations using the general mission analysis tool [302] (GMAT; green up triangles). The arrows denote firing events. Reproduced from [2].
CC BY 4.0.</figcaption></figure>

managed by the US Space Force, while the orange squares show GPS data taken just before and after each firing. Finally, the green up triangles show high-fidelity orbital dynamics simulations accounting for the propulsion system performance and firing duration. The nominal thrust was 0.8 mN for a total operating power of approximately 55 W, and the burn duration was between 80 and 90 min for each firing (which included the 10–20 min time needed for initial propellant heating). This resulted in a satellite altitude change between about 200 and 400 m.

Overall, the agreement between theory, simulation, and GPS/SSN measurements in figure 49 is excellent and there is a clear altitude change correlated with each firing. The thrust vector direction was varied such that the altitude increased for firings labeled 1A, 1B, and 2B (simulating a drag compensation maneuver for example), and decreased for firings 2A, 2C, 2D, 2E, 2F, 2H, and 2I (simulating collision avoidance or initial de-orbiting). For firing 2G, the thrust vector direction was such that the altitude was not expected to change. In total, a cumulative altitude change of 3 km occurred over all firings. In addition to a clear orbit change, onboard telemetry confirmed successful thruster operation. Figure 50 shows various grid current measurements, subsystem temperatures, and the thrust/power evolution for firing 1B. As seen, telemetry is consistent with ground testing data, which indicates that the space environment can be well replicated during thruster qualification.
<figure><img src="image_53.png" /><figcaption>**Figure 50.** (a) Ion beam current ($I_b$), electron neutralizer current ($I_e$), and accel grid current ($I_a$), (b) propulsion subsystem temperatures, and (c) thrust and power evolution for firing 1B in figure 49. The symbols in (b) indicate the temperature of the MotherBoard ($T_{MB}$), the radio-frequency Generator ($T_{RFG}$), the accelerator grid supply unit ($T_{GSU}$), the neutralizer cathode supply unit ($T_{CSU}$), and the iodine flow control unit ($T_{FCU}$). Reproduced from [2]. CC BY 4.0.</figcaption></figure>

<figure><img src="image_54.png" /><figcaption>**Figure 51.** Average estimated thrust for each maneuver in figure 49 as determined by numerical modeling, and indirect/direct testing. From [288]. Reprinted by permission of the American Institute of Aeronautics and Astronautics, Inc.</figcaption></figure>

An important factor in validating new propulsion technologies is a rigorous performance audit conducted throughout the design and testing phases, as even slight variations in performance can lead to unacceptable differences in predicted and actual spacecraft positions during flight [303]. While this has been performed and publicly documented for some thrusters and missions, such as SERT-I and SERT-II [253, 304], performance audits of micropropulsion systems are far more limited [305, 306]. Based on numerical modeling (similar to that discussed in section 5.3 and which uses data from sections 3 and 4), indirect laboratory testing from diagnostic probes, indirect in-space testing from propulsion system telemetry, and direct in-space testing analyzing GPS data, a full thrust audit has been conducted of the NPT30-I2 [288]. Figure 51 shows a comparison of these different methods for the firings in figure 49, where excellent agreement and consistency is observed. Furthermore, the predicted thrust of all maneuvers is close to the nominal thrust level commanded by the satellite (black dashed line in figure 51). Such a thrust audit is an important step towards improving confidence in iodine propulsion technologies. The good agreement of the numerical model results with the various measurements also provides a strong indirect validation of the iodine plasma chemistry and cross-section data presented in section 3.

Since the in-space demonstration of the NPT30-I2 between 2020 and 2021, further flights of this technology have occurred with as many as 100 systems in space since July 2025 [307]. In addition, the BIT-3 gridded ion thruster developed by the US company Busek, and the iodine ambipolar thruster REGULUS developed by the Italian company T4i, have also subsequently flown [240, 308]. REGULUS was integrated with the Unisat-7 satellite and launched in March 2021, while the BIT-3 was included
onboard the LunaH-Map cubesat and launched as part of Artemis 1 in November 2022. Publicly available information is limited such that the status of these systems is not known, although there is some indication that a propellant valve became blocked during the LunaH-Map mission because of iodine deposition (resulting from an excessive launch delay) and the thruster was not able to fire [308].

## 6.2. Safety and environmental considerations

Iodine is an essential trace element for life. However, molecular iodine is toxic in cases of excessive exposure through inhalation or ingestion, with a mean lethal dose of 2–4 g [309]. For large doses of several grams, iodine can cause burning of the mouth and throat, chest tightness, and even headaches [310]. It is a skin irritant and can even lead to tissue damage. Since iodine readily sublimates to form a corrosive vapor, appropriate safety precautions must be taken when handling iodine: including when cleaning vacuum equipment such as chambers or pumps that have been exposed to iodine. Typical protective gear can include gloves, safety goggles, and respirator masks to prevent inhalation of iodine vapor or contaminated dust [310].

From an environmental perspective, depletion of stratospheric ozone has been proposed as a potential impact of iodine propulsion. Iodine can catalyze ozone destruction in a similar way to the other halogens chlorine and bromine [311]. Feng et al [312] modeled ozone depletion in a scenario with widespread use of iodine propulsion numerically using a general circulation model of the atmosphere. They initially assumed emission of 8 metric tons of $I_2$ per year (corresponding to an annual launch of 40 000 satellites each with 0.2 kg of propellant), resulting in a ~0.1 part per trillion volume increase in stratospheric iodine and 0.02% decrease in global average stratospheric ozone. However, iodine concentration increases were found to scale nearly linearly with 10 to 100-fold further increases in emissions, leading to significant stratospheric ozone depletion in the latter case. Such cases are currently however very far from being achieved or even projected within the space industry. Furthermore, iodine propulsion cannot conceivably alter iodine levels in the troposphere appreciably, with estimates of natural oceanic emissions ranging from 114 000 to 550 000 metric tons per year [313].

In their study, Feng et al assumed that iodine from electric propulsion in low-Earth orbit would ultimately descend to lower layers of the atmosphere rather than escape to space. The question of which possibility dominates has been explored for other propellants, such as mercury, by Fourie et al [314]. Depending on the thruster orientation and specific impulse, ions may or may not achieve escape velocity. For example, for orbit raising at 800 km, ions with an exhaust velocity less than $1.8 \times 10^4$ m s$^{-1}$ remain gravitationally bound to the Earth. Even where they exceed the escape velocity, ions are typically trapped by the geomagnetic field, bouncing between polar magnetic mirror points. Repeating the calculation in appendix A.2 of Fourie et al for iodine gives a maximum gyroradius of 1.4 km (much smaller than the Earth's radius). Ions are likely to be neutralized on reaching lower altitudes near the poles, limiting the chance that they will retain sufficient energy to escape. This likelihood contrasts with that of iodine originating in the troposphere reaching the stratosphere; this iodine is contained within short-lived gases severely limiting transport to higher altitudes [311, 313].

# 7. Future research and remaining challenges

## 7.1. Material compatibility

As highlighted in section 4.1, iodine can react with many common materials. While a number of recent works have been dedicated to the study of iodine-material compatibility, it is clear that further research is still needed. In particular, three main research directions can be identified. Firstly, there is a lack of uniformity of results in the literature which makes it challenging to extract general conclusions for certain substances (e.g. gold). Similarly, there is a strong discrepancy between corrosion rates for some substances, which implies that test conditions are not identical (e.g. the state of the test material surface, the background pressure and temperature, the quality of measurements, etc).

Secondly, there is a lack of tests and data for high-temperature iodine exposure. Even if some materials may be compatible with iodine at low temperatures, this can change at elevated temperatures where reaction rates can increase exponentially. This may be particularly relevant to many iodine applications, since as discussed in section 7.6 below, measurements in low-pressure iodine discharges indicate strong gas heating with temperatures reaching as high as 1500 K in some cases. Furthermore, vibrationally excited iodine, electronically excited iodine, and even positive or negative iodine ions, may increase reaction rates further or even promote new reaction pathways: as is well-known with other molecular substances such as hydrogen used for reducing iron ores (see for example [315]). While there is some
information on high-temperature corrosion of iodine in the context of nuclear applications, this is usu-
ally limited to only a few materials (e.g. stainless steel, zirconium alloys, refractory metals, and some
ceramics).

Finally, it should be noted that most previous research has only considered a few standard materials with little innovation regarding novel material options. While this is natural for pure metals and their alloys, there are many possible ceramics, ceramic coatings, or polymer coatings that could be tested and very little, if any, existing literature on their iodine compatibility. This point is also of specific relevance to electric propulsion, since thermionic insert materials (such as barium oxide, BaO) for hollow cathodes (see section 7.2) have thus far failed to demonstrate long-term stable operation with iodine [257]. Since the number of possible materials that could be studied is potentially vast, it may be useful to consider several practical or regulatory constraints to narrow the solution space. For example, some materials, such as refractory metals or their compounds, may survive reentry and pose a collision risk on the ground [316], whereas other materials, such as platinum or palladium, have a strong cost barrier.

**7.2. Hollow cathodes**

While several iodine hollow cathode prototypes have been developed and tested, most, if not all, have failed to achieve stable long-term operation [257, 317–319]. This currently represents one of the greatest challenges facing wide-spread adoption of iodine as an alternative propellant within the space industry. Previous work with iodine Hall thrusters has shown that although thruster and neutralizer structural materials can be found or designed for iodine compatibility, the thermionic insert material in hollow cathodes is not compatible [320]. Similarly, several subsequent research studies focused on iodine neutralizers have encountered problems associated with depletion or degradation of the insert due to chemical reactions or sputtering. Insert materials tested include lanthanum hexaboride (LaB₆) [321], dodecacalcium hepta-aluminate electride (C12A7) [322–324], tungsten doped with La₂O₃ (WL20) [325], and tungsten matrix inserts impregnated with BaO–CaO–Al₂O₃ (see for example [320]). Overall, the longest duration operation observed was less than 100 h [257]. It is therefore clear that further research is needed in this area. As a short-term alternative however, the use of a noble gas hollow cathode (e.g. xenon or krypton) with an iodine thruster has been demonstrated [320].

There is also a more subtle challenge that some iodine hollow cathodes may encounter: negat-
ive atomic iodine ions (I⁻; see also section 7.5 below and [319]). Previous experiments [286] have
shown that at sufficiently high pressures (above about 1 Pa), significant quantities of negative ions can
be formed and the plasma discharge becomes electronegative. This occurs not only because the elec-
tron affinity of atomic iodine is very high, but also because dissociative electron attachment reactions
are favored at higher pressures where the electron temperature is lower (see section 3.7). As the pres-
sure inside hollow cathodes can be between 100 and 2000 Pa, negative ion production could therefore
strongly reduce electron extraction capability. Thus, even if iodine-compatible insert materials can be
found or developed, the unique iodine plasma chemistry may anyway limit or affect hollow cathode
operation. At present, it is difficult to assess the impact negative ion formation may have, since both
electron and heavy species impact collisional detachment would also occur (see section 3.5). Therefore,
additional research is needed to study the underlying iodine plasma chemistry in neutralizer-relevant
conditions.

**7.3. Lifetime testing**

Aside from neutralizer degradation (see section 7.2), general lifetime testing of complete iodine electric propulsion systems presents several practical challenges, some of which have recently been summarized in [217, 326]. For example, iodine can react with vacuum chamber wall materials leading to deposition or even chemical reactions (such as the formation of metal iodide layers). Similarly, iodine can react with other vacuum equipment and even corrode pump components. Typically, a special filter system is needed to prevent this, while periodic vacuum chamber cleaning and maintenance may be necessary. Cold heads or traps can be used to achieve low base pressures by forcing iodine to deposit, but again, this may require periodic cleaning. These factors make testing with iodine significantly more difficult than inert gases like xenon, and since some high-performance electric propulsion systems are required to operate for more than 10 000 h, lifetime testing or qualification of iodine thrusters is a costly and time-consuming process.

Other testing challenges noted in [217, 326] are not necessarily unique to iodine, but may be exacer-
bated by it. For example, a high level of back-sputtered vacuum chamber material was observed which
caused degradation and increased erosion of propulsion system components. Furthermore, the frequent
vacuum chamber maintenance cycles introduced other unexpected facility effects, such as an increased
exposure to water vapor or oxygen which can chemically react with some thruster components, deposited iodine, or even sputtered material. Because of the high-energy ion beam produced by most electric propulsion systems, a beam dump is needed to prevent direct impingement and damage to vacuum chamber walls. However, sputtering rates with carbon-carbon (which typically has a very low sputter yield) beam dumps exhibited volatility with irregular sputtering patterns. By comparison, molybdenum was found to be a more reliable material, although strong sputtering still occurred.

As iodine is still an emerging propellant, there is limited available information on lifetime testing, with the most detailed investigation described in [217] for the NPT30-I2 gridded ion thruster. This study found that thruster life was limited only by the amount of system propellant, followed by the filament neutralizers which are currently the most life-limiting component (each having an expected operating duration of about 1260 h). Failure of the neutralizer occurs predominantly due to material evaporation that is exacerbated by ion sputtering (a hypothesis confirmed with a simplified model). The filament also reacted with atmospheric oxygen and changes in lifetime (indicated by increased filament resistance: a useful proxy measurement for filament cross-sectional area) were correlated with each scheduled vacuum chamber maintenance cycle. Consequently, future testing should aim to use a partitioned vacuum chamber with a gate valve such that the thruster can remain under vacuum while cleaning of the main chamber is performed. For gridded ion thrusters, grid erosion (see also section 4.4) is also of importance. The testing campaign in [217] indicates that grid lifetime is at least 5000 h, and metrology measurements show that the maximum increase in grid aperture size (due to ‘barrel erosion’) is less than 5%: inline with sputter model predictions. All other subsystems (such as propellant storage and flow control/distribution) are predicted to have a lifetime of at least 8000 h.

Testing of the BHT-600-I Hall thruster was conducted in [320], where a lifetime of at least 1174 h was demonstrated. Because of difficulties with operating an iodine hollow cathode (see section 7.2), a xenon-fueled cathode was used instead. Similar thruster performance was found for both iodine and xenon thruster propellants over long firing durations, but again, several facility effects were identified and specific precautions implemented. For example, grafoil was attached to the vacuum chamber walls with graphite nuts. This not only decreased back-sputtered material, but also reduced the interaction of atomic and molecular iodine with the chamber wall material, since iodine can sputter the natural oxide layer of the walls and lead to direct corrosion.

Aside from challenges with iodine testing in terms of the vacuum equipment, there are also associated testing challenges since measurement equipment/diagnostics compatible with iodine are not always available. This includes mass flow rate controllers, pressure gauges, and even electrostatic probes such as Langmuir probes, retarding field energy analyzers, or ion flux probes. For example, Habl et al [196] developed an ion flux probe enabling spatial iodine ion beam measurements to be performed. To protect the system from iodine, the electrical measurement board was coated in urethane polymer, isolating its tracks and components from contamination. Connectors were covered in disposable metallic foil after placement in the chamber, and PTFE-based grease was used on the stepper motor bearings. After operation with iodine, the whole instrument was cleaned with alcohol and the probe collecting surfaces were polished to remove any possible thin film deposits. This latter point is important since as discussed in section 4.3, probe current-voltage characteristics can change due to SEE from any deposited iodides [199]. It should be noted though that optical methods would not suffer the same challenges and may be a valuable alternative or complementary tool for diagnosing iodine plasmas (see for example [26, 98, 227]).

### 7.4. Flow control and long-term storage

Since iodine is a solid under typical ambient conditions (see section 2), an immediate challenge is flow control. At a temperature of 300 K, the sublimation rate of iodine is very low and the vapor pressure is less than 100 Pa, making it difficult to achieve the mass flow rates required by most electric propulsion systems. The flow control solution to emerge is controlled heating of iodine to increase the sublimation rate and vapor pressure [2, 153]. Typically, heaters are placed on the propellant storage tank together with a temperature sensor. A thermal control algorithm then controls the heater so that the desired temperature can be reached/maintained. If the propulsion system is correctly designed, waste heat from the thruster and power electronics can be used to provide partial heating [2]. However, care needs to be taken to ensure that the temperature does not exceed 113.7 °C as iodine undergoes a phase transition to a liquid above this value. As the tank is directly heated rather than the iodine itself, the tank and iodine temperatures may not be equal. This is particularly true if solid iodine crystals are loaded into
the tank, as thermal contact could be unreliable and nonuniform. While not a serious issue for ground-based experiments, it can pose potential problems in space.

The use of solid iodine crystals can also create other possible problems. For example, due to launch vibrations or spacecraft motion in orbit, iodine crystals can break or move around, possibly causing damage to the propulsion system or a variation in thermal contact with the tank walls. One proposed solution is to embed the iodine into a porous ceramic block that is then placed inside the tank [2]. In this way, the iodine is strongly fixed and the ceramic block facilitates more consistent and uniform heat transfer. Together with controlled sublimation, the issue of propellant flow control and storage is therefore largely solved: with the exception perhaps of on/off flow control to prevent iodine leakage. Some propulsion systems have made use of a flow control valve, but as this includes moving parts, iodine deposition can potentially cause valve sticking. This was the problem thought to have occurred on the LunaH-Map spacecraft and which consequently prevented the onboard iodine thruster from firing [308].

An alternative solution for on/off flow control already successfully demonstrated in space [2] is a passive thermal control valve. Here, a short flow distribution line containing a small orifice (<1 mm in diameter) connects the propellant storage tank with the downstream plasma source. When the thruster fires, the orifice becomes hot and iodine deposition is prevented, allowing propellant to flow freely. When the thruster is off though, the orifice is cooler and iodine deposits blocking further flow. One problem with this approach however, is that even when the thruster is not firing, the sublimation rate of iodine in the orifice is not zero. Nonetheless, ground experiments with the NPT30-I2 estimated an iodine leakage rate of less than 3 g per year [2]. While low, this may cause challenges with long-term propellant storage in space: particularly if the satellite temperature rises and causes the sublimation rate to increase.

For micropropulsion systems, sufficiently high mass flow rates can easily be produced with moderate propellant heating to temperatures below the melting point of iodine. However, for larger propulsion systems (such as kW-class Hall or cusp field thrusters) this may be insufficient to achieve the required flow rates and overcome various pressure drops in the flow distribution system, particularly as the vapor pressure just before melting is only about 12 kPa. Consequently, higher temperatures are needed implying that iodine may be present in solid, liquid, and gaseous phases. Additional research is needed to investigate this in more detail.

Further research is also needed to develop viable solutions to enable in-space refueling, which is an area attracting increased attention. For example, Ponti et al [252] have recently proposed a novel rechargeable iodine propulsion concept. Here, the use of special iodine propellant cartridges are envisioned which could be removed and replaced via in-orbit satellite servicing, hence allowing mission extension.

### 7.5. Negative ion formation and loss

As early as in 1925, Mohler [81] observed that in an iodine discharge, $I^-$ is created through Dissociative Electron Attachment (DEA) ($I_2 + e^- \rightarrow I + I^-$) rather than through dissociation into positive and negative ions, and that DEA occurs even at very low electron energies. This peculiarity is explained by the fact that the electron affinity of atomic iodine is 3.059 eV [135], which is almost double the dissociation energy of the iodine molecular ground state (1.542 eV [61]). In this configuration, the threshold energy for the production of negative ion fragments via DEA is lower that that for pure dissociation processes [124]. The potential energy curves of the $I_2(X^1\Sigma_g^+)$ ground state, the anionic molecular ground state $I_2^-$, and an anionic excited state $I_2^{*-}$ are schematically illustrated in figure 52.

DEA is a two step process whereby the molecule is first placed into an intermediate repulsive excited ionic state ($I_2 + e^- \rightarrow I_2^{*-}$) which subsequently dissociates into $I^-(^1S_0)$ and $I(^2P_{3/2}^0)$. The lowest crossing point between $I_2$ and $I_2^{*-}$ potentials is only a few hundredths of an eV high [131] which explains the magnitude of the DEA cross-section for iodine, the resonances being caused by several $I_2^{*-}$ potentials crossing the $I_2$ ground state for different energies (only one has been represented in figure 52). A better understanding of the $I_2^-$ electronic potentials would help to clarify the observed discrepancies between all of the DEA cross-section data plotted in figure 21. Note that Ambalampitiya et al [31] assumed that the atomic state created was $I(^2P_{1/2}^0)$, but this is in contradiction with most works on electron attachment in other halogens (see for example Ayala et al [131]).

As highlighted in recent experiments by Esteves et al [286], negative ion formation can be important even at low pressures. For example, the electronegativity ($\alpha = n_n/n_e$ where $n_n$ and $n_e$ are the negative ion and electron densities respectively) of an iodine ICP was observed to surpass 1 in some regions of the discharge for pressures above about 1 Pa. This indicates that negative ion creation and loss processes
<figure><img src="image_55.png" /><figcaption>**Figure 52.** Schematic representation of various iodine potential energy curves and their respective dissociation limits: I₂ is the molecular ground state, I₂⁻ is the anionic molecular ground state, and I₂⁻* is the first electronically excited state of I₂⁻. Here ε<sub>diss,I₂</sub> = 1.542 eV is the dissociation energy of I₂, ε<sub>a,1</sub> = 3.059 eV is the electron affinity of I, and ε<sub>a,I₂</sub> = 2.52 eV is the electron affinity of I₂.</figcaption></figure>

need to be included when modeling such systems, and that care must be taken with the pressure level when operating an iodine thruster.

When the pressure increases, molecular negative ions I₂⁻ and I₃⁻ are known to be created by clus-
tering reactions between I⁻ and atomic or molecular iodine [82, 327]. For example, Woolsey et al [91]
used a Langmuir probe together with orbital motion limited theory and found an electronegativity above
2000 resulting in a nearly electron-free ion–ion plasma (I₂⁺–I₃⁻; produced by allowing the plasma in
the Faraday dark space of a DC glow discharge to diffuse into a side-arm at pressures between 27 and
133 Pa). However, no cross-section data is available for these creation processes and, furthermore, hol-
low cathodes typically operate at pressures between approximately 100 and 2000 Pa, which suggests that
molecular negative ion formation may be particularly relevant to such discharges (a fact largely ignored
so far).

Finally, as mentioned above and in section 3, large uncertainties remain regarding not only the form-
ation processes of negative ions, but also their destruction mechanisms (e.g. ion–ion recombination,
charge-exchange, or detachment) in the plasma volume.

**7.6. Anomalous gas heating**

During the operation of most electric propulsion systems, there is inevitable thruster heating due to plasma-wall heat transfer. For example, the discharge chamber temperature measured in the NPT30-I2 gridded ion thruster is 443 K [2], while the channel temperature in Hall thrusters routinely reaches 700–900 K [328, 329]. Because of either heat transfer from the thruster walls, and/or plasma-gas collisional processes, the neutral propellant gas temperature increases above its input value. For noble gases such as xenon, this temperature increase may be similar to that of the thruster walls, and relevant collisional processes include electron-neutral elastic scattering, ion-neutral collisions, collisional quenching of excited states, and the formation of high-energy neutrals due to wall recombination. With iodine however, the measured gas temperature in some experiments can be much higher than the wall temperature and even exceed 1500 K [26, 94]. Furthermore, the temperature of I and I₂ species may be different [26], particularly at low pressures where the collision frequency is too low to ensure thermodynamic equilibrium.

In [26, 94], two-photon laser induced fluorescence (TALIF) was used to measure the temperature of neutral atomic iodine in an RF reference cell and a gridded ICP source. In both cases, atomic iodine temperatures were observed to increase with power level and operating pressure, and attained values between 300 and 1800 K. The consequence of high neutral temperatures can easily be seen by considering a simple model of neutral gas flow through a plasma system

$$
\dot{m} = \frac{1}{4} M n_g \bar{v}_g A_{\text{eff}}, \qquad (52)
$$

where *ṁ* is the input mass flow rate, *M* is the propellant atomic/molecular mass, *n*<sub>g</sub> is the average system gas density, *v̄*<sub>g</sub> = √(8*k*<sub>B</sub>*T*<sub>g</sub>/(π*M̄)) is the gas thermal speed with *T*<sub>g</sub> the gas temperature, and *A*<sub>eff</sub> is an effective loss area (accounting for any reduced flow conductance due to the thruster geometry). For a
<figure><img src="image_56.png" /><figcaption>Figure 53. Illustration of example electron impact dissociation pathways of molecular iodine. Here $ε_{12}$ and $ε_{13}$ represent energies transferred to the iodine molecule and which initially take it to either the repulsive state labeled 2, or the bound state labeled 3.</figcaption></figure>

fixed mass flow rate, $n_g \propto 1/\sqrt{T_g}$. Thus, gas heating leads to neutral depletion inside the thruster (see also [330] for a more detailed model). Since many important collisional reaction rates are proportional to the neutral density (such as ionization or dissociation), depletion can cause a change in system performance. In particular, as the neutral density decreases, the electron temperature in the discharge usually increases, which then leads to a larger plasma sheath potential, higher plasma kinetic energy losses to the walls, and therefore increased power consumption to achieve a target thrust level.

At present, these anomalously high gas temperatures are not well understood, but are thought to occur because of the unique iodine plasma chemistry. Initial calculations suggest that energy transfer during electron-neutral elastic scattering is far too small to explain the elevated temperatures observed, but rather kinetic energy release (KER) in several dissociation and neutralization reactions may be responsible [292]. For example, consider the general electron impact dissociation reaction given by

$$I_2 + e^- \rightarrow I + I^* + e^-, \qquad (53)$$

where $I^*$ represents a possible excited state because of the various reaction pathways and resulting dissociation products that could be produced (see figure 53). Although the threshold energy for dissociation, $ε_{diss}$, of $I_2$ is 1.542 eV, electrons can initially transfer more energy (typically known as the vertical excitation energy), $ε_e$, to the iodine molecule and place it into a bound state, or a repulsive state where the energy exceeds the molecular dissociation energy. The molecule then splits and releases the energy difference, $Δε = ε_e - ε_{diss}$, which either goes to excite one of the atomic iodine atoms, and/or is shared as kinetic energy amongst the products ($ε_{ker}$, referred to as KER). As the KER can be of the order of a few eV [124], hot neutral dissociation fragments are created that can subsequently lead to gas heating via heavy particle collisions. Indeed, energy release during dissociation has been implicated in gas heating in hydrogen [124, 331], oxygen [332], and chlorine discharges [333]. The exact KER is difficult to establish because of missing information associated with the initial electron energy transfer, and the different subsequent dissociation pathways. Nonetheless, for $ε_e > ε_{diss}$, and assuming that no dissociation products are formed in an excited state, one would expect $ε_{ker} > 0$ eV.

Initial unpublished calculations of KER due to electron-impact dissociation have been performed by Nicolas Sisourat and his team at LCPMR for different iodine gas temperatures. The KER has an energy distribution that depends on the specific intermediate excitation state and subsequent dissociation products. Although gas temperature is found to have little effect, the dissociation pathway strongly influences the resulting energy release. KER distributions typically show a spread between 0 and 1 eV per atom, with distribution-averaged values as low as 0.1 eV, and as high as 0.5 eV, depending on the specific dissociation pathway.

KER can also occur in other dissociation reactions, such as dissociative electron attachment (see reaction C5 in table 7). As iodine has an electron affinity of $ε_{a,1} = 3.059$ eV that is higher than the molecular dissociation energy, a transient $I_2^*$ repulsive state can initially be produced even for low electron collision energies, before it dissociates. Since the electron is captured by one of the atomic iodine products, it cannot carry away any excess collision energy. Consequently, very hot neutral and negative ion fragments
<table><caption>**Table 20.** Example collisional processes that may produce hot fragments, together with an estimate of the kinetic energy release (see also [292]).</caption><thead><tr><th>Reaction</th><th>ε<sub>ker</sub> (eV)</th></tr></thead><tbody><tr><td>I<sub>2</sub> + e<sup>-</sup> → 2I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>) + e<sup>-</sup></td><td>>0</td></tr><tr><td>I<sub>2</sub> + e<sup>-</sup> → I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>) + I<sup>-</sup></td><td>>0.5</td></tr><tr><td>I<sub>2</sub> + e<sup>-</sup> → I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>) + I<sup>+</sup> + e<sup>-</sup></td><td>>0</td></tr><tr><td>I<sub>2</sub><sup>+</sup> + e<sup>-</sup> → 2I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>)</td><td>8.27</td></tr><tr><td>I<sup>+</sup> + I<sup>-</sup> → 2I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>)</td><td>7.39</td></tr><tr><td>I<sub>2</sub><sup>+</sup> + I<sup>-</sup> → 3I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>)</td><td>4.71</td></tr><tr><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>) → 2I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>)</td><td>0.94</td></tr><tr><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>0.94</td></tr></tbody></table>

can be produced. The KER can be estimated by performing a collision energy balance

$$ \epsilon_e + \epsilon_{I_2} + U_{I_2} = \epsilon_I + \epsilon_{I-} + U_I + U_{I-}, \qquad (54) $$

where $\epsilon_{I_2} \approx 0$ is the kinetic energy of the molecule, $\epsilon_I$ and $\epsilon_{I-}$ are the kinetic energies of the neutral and negative ion fragments, and $U_{I_2}$, $U_I$, and $U_{I-}$ are the internal energies of the molecule, neutral, and negative ion. Calculations suggest that the neutral fragment is in the excited $^2P_{1/2}^o$ state (with a threshold energy $\epsilon_{exc_1}$) [31], and thus $U_{I_2} - U_I - U_{I-} = \epsilon_{a,I} - \epsilon_{diss} - \epsilon_{exc_1}$. Using this in equation (54) and rearranging, we find

$$ \epsilon_I + \epsilon_{I-} \approx \epsilon_e + \epsilon_{a,I} - \epsilon_{diss} - \epsilon_{exc_1} = \epsilon_e + 0.574. \qquad (55) $$

Thus, even if the initial electron energy is zero, the resulting KER is above 0.5 eV. Considering a typical electron temperature of 5 eV, and assuming an upper limit case where all kinetic energy is initially transferred to the molecule (i.e. $\frac{3}{2}T_e$ on average), the KER could be as high as 8.074 eV. Similarly, consider the dissociative ionization reaction

$$ I_2 + e^- \rightarrow I + I^+ + 2e^- \qquad (56) $$

Assuming that both neutral and ion fragments are in the ground state, and again performing a collision energy balance, the KER is estimated to be at least $\epsilon_{ker} = \epsilon_{diss,I_2} - \epsilon_{diss} - \epsilon_{Iz,I} > 0$ eV.

Table 20 summarizes KER from the above reactions, together with several other reactions including: recombination between $I^+$ and $I^-$, recombination between $I_2^+$ and $I^-$, and collisional quenching of $I(^2P_{1/2}^o)$ with either $I$ and $I_2$. Not included in Table 20 are vibrational-vibrational and vibrational-translational collisional relaxation processes, which are known to be important in some molecular plasmas [334]. Further research is needed to better understand which processes are responsible for anomalous gas heating, and how this affects system performance.

### 7.7. Missing collision cross-section and surface data

While we have provided a detailed iodine reaction set in section 3, there are a number of reactions still missing and for which little or no reliable cross-section or rate coefficient data exists (or for which there are strong inconsistencies). Similarly, and as already highlighted in section 4, iodine-surface data (such as sputter/SEE yields and surface recombination coefficients) is very sparse in the literature. It should also be noted that most cross-sections have only been computed theoretically/numerically and there is very little available experimental cross-section or swarm parameter data for validation. Table 21 summarizes some of the main iodine reactions for which data is missing or inconsistent.

While recent research has calculated and proposed cross-sections for various electron impact processes [31, 115], there is only a single set of known data for dissociation of molecular iodine, and this is only for energies below 10 eV which is insufficient (hence requiring extrapolation for higher energies; see also section 3.3.3). In addition, information on the specific dissociation pathways and reaction products, as well as the KER, is not known.

Another important process for which incomplete and inconsistent data exists is elastic collisions between electrons and atomic iodine. Firstly, only the total elastic scattering cross-section is known [31], while the elastic MTCS (which is important for calculating collisional drag and momentum exchange) is missing. Secondly, total elastic scattering cross-sections calculated with different theoretical methods disagree by as much as an order of magnitude below about 3 eV (see figure 13). Consequently, the electron-neutral total elastic scattering collision frequency may be over or underestimated depending on the data
<table><caption>**Table 21.** Important iodine reaction processes for which cross-section or rate coefficient data is either unknown, missing, or inconsistent. Here *J* and *J'* denote rotational excitation levels of *I*₂ such that *J'* > *J*.</caption><thead><tr><th>Reaction</th><th>Process</th><th>Comment</th></tr></thead><tbody><tr><td colspan="3"><strong>Electron impact scattering: atomic iodine</strong></td></tr><tr><td>I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>) + e<sup>-</sup> → I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>) + e<sup>-</sup></td><td>Total elastic scattering</td><td>Disagreement between calculations below 3 eV</td></tr><tr><td>I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>) + e<sup>-</sup> → I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>) + e<sup>-</sup></td><td>Elastic momentum transfer</td><td>No data</td></tr><tr><td>I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>) + e<sup>-</sup> → I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>) + e<sup>-</sup></td><td>Elastic momentum transfer</td><td>No data</td></tr><tr><td>I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>) + e<sup>-</sup> → I<sup>+</sup> + 2e<sup>-</sup></td><td>Ionization</td><td>Empirical estimate only</td></tr><tr><td>I<sup>+</sup> + e<sup>-</sup> → I<sup>2+</sup> + 2e<sup>-</sup></td><td>Double ionization</td><td>No data</td></tr><tr><td>I<sup>-</sup> + e<sup>-</sup> → I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>) + 2e<sup>-</sup></td><td>Detachment</td><td>Only one calculation with a high cross-section</td></tr><tr><td colspan="3"><strong>Electron impact scattering: molecular iodine</strong></td></tr><tr><td>I<sub>2</sub>(J) + e<sup>-</sup> → I<sub>2</sub>(J' > J) + e<sup>-</sup></td><td>Rotational excitation</td><td>No data</td></tr><tr><td>I<sub>2</sub> + e<sup>-</sup> → 2I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>) + e<sup>-</sup></td><td>Dissociation</td><td>No data above 10 eV</td></tr><tr><td>I<sub>2</sub> + e<sup>-</sup> → I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>) + I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>) + e<sup>-</sup></td><td>Dissociation</td><td>No data</td></tr><tr><td>I<sub>2</sub> + e<sup>-</sup> → 2I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>) + e<sup>-</sup></td><td>Dissociation</td><td>No data</td></tr><tr><td>I<sub>2</sub> + e<sup>-</sup> → I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>) + I<sup>-</sup></td><td>Dissociative attachment</td><td>Disagreement between calculations<br>Uncertainty in the resulting<br>neutral atomic state</td></tr><tr><td colspan="3"><strong>Ion-neutral collisions</strong></td></tr><tr><td>I + I<sup>+</sup><sub>2</sub> → I<sup>+</sup> + I<sub>2</sub></td><td>Charge-exchange</td><td>Data only for the reverse reaction</td></tr><tr><td>I + I<sup>2+</sup> → I<sup>+</sup> + I<sup>+</sup></td><td>Charge-exchange</td><td>No data</td></tr><tr><td>I<sub>2</sub> + I<sup>2+</sup> → I<sup>+</sup><sub>2</sub> + I<sup>+</sup></td><td>Charge-exchange</td><td>No data</td></tr><tr><td>I + I<sup>-</sup> → I<sub>2</sub><sup>-</sup></td><td>Clustering</td><td>No data</td></tr><tr><td>I<sub>2</sub> + I<sup>-</sup> → I<sub>3</sub><sup>-</sup></td><td>Clustering</td><td>No data</td></tr></tbody></table>

set used. Furthermore, below 2 eV, the total elastic scattering cross-section for atomic iodine is much higher even than that for molecular iodine.

## 8. Conclusions

Despite being proposed for space propulsion applications as early as 1960 [218], iodine was only seriously considered as a propellant several decades later in 2000 when it became apparent that xenon may not be able to meet growing space industry demand in the future [21, 22]. Consequently, it is only within the last 15 years or so that strong research interest has emerged. While a significant amount of work has been performed during this time, there are still several difficulties that must be overcome before iodine becomes a widespread propellant option within the space community. Although several challenges were identified in section 7, it is worth emphasizing that these challenges do not appear to represent physical or technical barriers to iodine usage: with the exception perhaps of iodine-material compatibility. Appropriate materials for the thruster subsystem itself have been found or developed [2, 174, 176], but iodine-compatible hollow cathode neutralizers remain a strong concern [257, 317]. Furthermore, the high gas temperatures observed in several iodine plasmas [26, 59, 94] may increase chemical reaction rates with some materials and alter the conclusions of previous iodine-material studies [174].

It is worth reiterating that iodine electric propulsion systems have been successfully developed and continuously flown in space since 2020 [2]. Thus, until feasible iodine-fueled hollow cathodes are developed, we note that thermionic filament and RF neutralizer solutions already exist [2, 109, 233, 257]. For some propulsion technologies, such as ambipolar thrusters [240], no neutralizer is required and so this problem is avoided altogether. For high-performance propulsion technologies that require large neutralizer currents, such as Hall thrusters, a short-term solution is the use of an iodine-fueled thruster and a xenon- or krypton-fueled hollow cathode. Since the mass flow rate required to operate a hollow
cathode is typically between 5% and 10% of the main thruster mass flow rate [3], this still offers significant advantages over a full xenon system. For example, less xenon (or krypton) is needed, and both the size and mass of the propellant tanks is reduced [172]: important considerations for small satellites and satellite constellations.

While much of the recent research with iodine plasmas has been driven by space propulsion applications, there are several ground-based industrial applications of importance that can leverage many of these developments. For example, atomic and molecular plasma chemistry data is relevant to the operation and numerical modeling of iodine etching reactors [23, 270, 335]. Furthermore, lifetime testing and iodine-material compatibility studies provide important information for understanding iodine plasma-surface interactions, long term operation of vacuum systems, and the appropriate design of plasma processing reactors. Likewise, materials processing studies can benefit the propulsion sector through the development or discovery of novel materials that are resistant to iodine.

As noted previously in several other topical reviews [187, 257, 336], electric propulsion systems, as well as plasma processing reactors, are complex devices and development requires a multi-disciplinary approach that not only considers plasma physics and gas dynamics, but also material science. A collaborative approach is therefore needed to advance iodine plasma technology further and address some of the challenges highlighted in this review. Iodine has the potential to be a game-changing propellant for the space industry and to both enable new missions, while ensuring a sustainable space environment around the Earth. Iodine has a low cost, a high global production output, is easier to handle and transport than xenon, and can provide a higher plasma discharge efficiency. Solutions currently exist for iodine delivery and flow control, and a number of compatible materials have been found. Furthermore, a reasonable iodine plasma chemistry reaction set with known collision cross-sections exists and has been validated with several experiments [26, 28, 287, 288]. In closing, we note that iodine plasma research could also serve as a model for the development of other alternative propellants currently being investigated such as water [337–339], bismuth [245], and even air [340].

## Data availability statement

The data that support the findings of this study are openly available at the following URL/DOI: https://doi.org/10.5281/zenodo.17348832 [32].

## Acknowledgments

The authors would like to thank Dmytro Rafalskyi, Lui Habl, Oliver Jia-Richards, Kristof Holste, Rainer Dressler, Akhiro Matsutani, Harin Ambalampitiya, Klaus Bartschat, Ayushi Agrawal, Mirko Magarotto, Weizong Wang, Victor Desangles, Nicolas Sisourat, and Max Vaupel for several useful discussions on iodine plasmas and for providing valuable feedback on this review paper. The authors also thank Ayushi Agrawal and Nicolas Sisourat for providing supplementary data.

## Appendix A. Term symbols for atomic iodine

### Overview

The ground state of atomic iodine has an electron configuration of [Kr] 4d¹⁰ 5s² 5p⁵, with the seven valence electrons in the outermost (fifth) shell. Like the other halogens, iodine is one electron short of a full octet and is hence an oxidising agent that easily reacts with many other elements. Table 22 provides several fundamental properties.

### Ground state and first excited state

The iodine atom has a transition from the fundamental state 5s²5p⁵ ²P°₃/₂ towards the first excited state 5s²5p⁵ ²P°₁/₂ at 7602.9762(2) cm⁻¹ (approximately 0.9426 eV) [341], or around 1.3149 µm in the infrared (IR). The splitting between both states is due to spin-orbit coupling. The transition between these states is forbidden with respect to electric dipole radiation but allowed mainly by magnetic dipole radiation. This transition has been studied by Luc-Koenig et al [342] by using Fourier transform spectrometry and by Ha et al [343] by measuring the absorption spectra of the transition with a tunable near-IR diode laser. This latter technique has also recently been used as a novel optical diagnostic in iodine CCPs [26, 59].
<table><caption>**Table 22.** Iodine atom and ion properties.</caption><tr><td>Mass</td><td>126.904 47(3) u</td></tr><tr><td>Atomic number</td><td>53</td></tr><tr><td>Stable isotope</td><td>127</td></tr><tr><td>Nuclear spin</td><td>5/2</td></tr><tr><td>Electron configuration</td><td>[Kr] 4d<sup>10</sup> 5s<sup>2</sup> 5p<sup>5</sup></td></tr><tr><td>Enthalpy of formation</td><td>106.76(4) kJ mol<sup>-1</sup></td></tr><tr><td>First ionization energy</td><td>10.451 26 eV</td></tr><tr><td>Electron affinity</td><td>3.059 0465(37) eV</td></tr><tr><td>Polarizability</td><td>32.9 ± 1.3 a.u</td></tr><tr><td>Pauling electronegativity</td><td>2.66</td></tr><tr><td>Van der Waals radius</td><td>198 pm</td></tr><tr><td>Ionic radius (I<sup>-</sup>)</td><td>206 pm</td></tr></table>

## Higher excited states

The excited levels of the $5s^25p^4nl$ type configuration of I are divided into several groups, each of which corresponds to a level of the $5s^25p^4$ ion: $^3P_{2,1,0}$, $^1D_0$ or $^1S_0$ (with $nl \in \{6s, 7s, 6p, 7p, 5d, 6d, 4f\}$). In 1962, Minnhagen [24] interpreted the set of known levels through the pairwise coupling scheme

$$ \langle (\{p^4 (S_c, L_c) J_c l\} K_s) J \rangle, \qquad (57) $$

which is the most appropriate to describe the level distribution in some configurations of the iodine spectrum [344]. Except for the degenerated upper level of the ground state (see previous subsection), a general excited level of atomic iodine can be written as

$$ 5s^25p^4 (2S_c+1) L_{cJ_c} \quad nl \ 2s+1 [K]_J, \quad \text{if even,} \qquad (58) $$

$$ 5s^25p^4 (2S_c+1) L_{cJ_c} \quad nl \ 2s+1 [K]_J^\circ, \quad \text{if odd,} \qquad (59) $$

where $S_c$, $J_c$, and $L_c$ are the total spin, total angular momentum, and total orbital quantum numbers of the core electrons respectively, while $K = J_c + l$ and $J = K + s$ are quantum numbers built by using the orbital momentum, $l$, and spin, $s$, of the outer electrons.

Using Fourier transform spectrometry, Luc-Koenig et al [344] observed 440 structures and analyzed 130 hyperfine structures, giving the magnetic dipole and the electric quadrupole hyperfine structure constants for 37 even levels and 42 odd levels. Recently, absolute positions of atomic levels were revised after new energy measurements of two iodine excited levels using TALIF measurements by Esteves et al [94]. The atomic configurations, terms, and level energies from NIST are compared with those obtained in recent theoretical works by Ambalampitiya et al [31] and Agrawal et al [115] in section 3.2.3.

## Hyperfine structure

The nuclear spin number of iodine is $I = 5/2$, meaning that any of the atomic levels of quantum number $J$ is divided into several hyperfine sub-levels from $F = |I - J|$ to $F = I + J$. The positions of the hyperfine components, with respect to the fine structure energy level, are calculated as a function of the hyperfine structure constants $A$ and $B$ of the 2 levels, according to the Casimir formula [344]:

$$ \Delta E = \frac{1}{2}AC + B \left[ \frac{3C(C+1) - 4I(I+1)J(J+1)}{8I(2I-1)J(2J-1)} \right], \qquad (60) $$

with $C = F(F+1) - I(I+1) - J(J+1)$.

## Appendix B. Term symbols for molecular iodine

In a diatomic molecule, the rotational symmetry around the line connecting the two nuclei (the internuclear axis) acts as the quantization axis. The projections of the various electronic angular momenta onto this axis have well-defined values that are characteristic of the electronic state of the molecule. Each individual electron, described by a molecular orbital, is characterized by four quantum numbers: $n, l, \lambda$, and $m_s$, which respectively characterize the energy, the magnitude of the orbital angular momentum, the spin component, and the projection of these moments onto the quantization axis. The quantum number $\lambda$ measures, in units of $\hbar$, the component of the orbital angular momentum on the nuclear axis and can
<table><caption>**Table 23.** Summary of selected low-lying electronic states of I₂ plotted in figure 5.</caption><thead><tr><th>State</th><th>S</th><th>Λ</th><th>Ω</th><th>Parity</th><th>Dissociation limit</th></tr></thead><tbody><tr><td>X <sup>1</sup>Σ<sup>+</sup><sub>g</sub></td><td>0</td><td>0</td><td>0</td><td>g<sup>+</sup></td><td>I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>) + I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>)</td></tr><tr><td>A <sup>3</sup>Π(<sup>1</sup>u)</td><td>1</td><td>1</td><td>1</td><td>u</td><td>I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>) + I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>)</td></tr><tr><td>C <sup>1</sup>Π(<sup>1</sup>u)</td><td>0</td><td>1</td><td>1</td><td>u</td><td>I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>) + I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>)</td></tr><tr><td>B <sup>3</sup>Π(<sup>0</sup>u<sup>+</sup>)</td><td>1</td><td>1</td><td>0</td><td>u<sup>+</sup></td><td>I(<sup>2</sup>P<sup>o</sup><sub>1/2</sub>) + I(<sup>2</sup>P<sup>o</sup><sub>3/2</sub>)</td></tr></tbody></table>

take any integer value, positive, negative, or zero, between $-l$ and $l$. Its absolute value is symbolized analogously to that of atoms, but with a lowercase Greek letter: $\sigma$, $\pi$, $\delta$, ... Molecular multi-electron wave functions are constructed from a set of molecular orbitals. The ground state of I₂ is written as:

$$ (\sigma_g 5s)^2 (\sigma_u 5s)^2 (\sigma_g 5p)^2 (\pi_u 5p)^4 (\pi_g 5p)^4, \quad ^1\Sigma_g^+. \qquad (61) $$

A given electronic configuration gives rise to different energy levels characterized by the total angular momentum vectors, $\vec{L}$, $\vec{S}$, and $\vec{J}$. However, the motion of the electrons occurs within the framework of a cylindrical symmetry defined by the internuclear axis of the molecule. Generally, the spin-orbit coupling of each individual electron is weak compared to other couplings, leading to a consideration of the orbital momentum of all the electrons on one hand and the resulting spin on the other.

Regarding the total orbital momentum, only the projection onto the internuclear axis of the molecule is a constant of motion. The component of the orbital angular momentum of all electrons on the molecular axis is $M_L \times \hbar$, where the quantum number $M_L$ can take positive, negative, or zero integer values. The value of $\Lambda = |M_L|$ for the molecule is symbolized by a capital Greek letter: $\Sigma$, $\Pi$, $\Delta$, etc depending on whether $\Lambda = 0, 1, 2, 3, ...$

The ensemble of electron spins has a resultant characterized by a quantum number $\vec{S}$, whose component also has a quantized value on the internuclear axis because the orbital motion of the electrons creates a magnetic field whose average direction is that of the molecular axis. The quantum number $\Sigma$, characterizing the projection of the resultant spin, can take $2S + 1$ different values between $-S$ and $+S$. The total electronic momentum $\Omega$ along the internuclear axis for all the electrons of the molecule is in units of $\hbar$: $\Omega = |\Lambda + \Sigma|$. For each electronic energy state corresponding to a value of $\Lambda$ and a determined value of $S$, $\Omega$ can take $2S + 1$ different values, which correspond to $2S + 1$ sub-energy levels. The quantity $2S + 1$ is the multiplicity of the considered state. A molecular term is therefore represented by the symbol

$$ ^{2S+1}\Lambda_{\Omega}. \qquad (62) $$

For a homonuclear molecule, the electron probability density must always be symmetric with respect to the midpoint between the nuclei, but the wave function itself can be symmetric ‘gerade’ or antisymmetric ‘ungerade’. This symmetry is indicated by the subscript $g$ or $u$. For any given $\Sigma$ state, a $^+$ or $^-$ index is used to denote the symmetry with respect to reflection in any plane passing through the two nuclei.

Traditionally, the electronic states of diatomic molecules are distinguished by different uppercase and lowercase letters: X is reserved for the ground state, A, B, C, etc are used to denote excited states in order of increasing energy characterized by the same multiplicity ($2S + 1$), and the lowercase letters a, b, c, etc are used for a different multiplicity. This convention is not always followed, as in our case for I₂, but also for N₂, where the ground state is $X \Sigma_g^+$ and the triplet electronic states are denoted $B \, ^3\Pi_g$ and $C \, ^3\Pi_u$.

Note that nuclear rotation is denoted by $\vec{R}$ and the total angular momentum is $\vec{J} = \vec{R} + \vec{\Omega}$, with the quantum number $J = R + \Omega$. In figure 5, we represent the different electronic states for the first four levels of I₂ using the notation explained above and summarized in table 23, with the shape of the potentials approximated by an empirical expression (the Morse potential). The values of the potential curve parameters for I₂ (i.e. the electronic energy ($T_e$), the vibrational constant ($\omega_e$), the unharmonicity ($\omega_e x_e$), the rotational constant for the $v=0$ vibrational level ($B_e$), the equilibrium internuclear distance ($R_e$) and the dissociation energy for the $v=0$ vibrational level ($D_0$)) can be found, for instance, in Lukashov’s book *The Iodine Molecule* [61].

Finally, it should be mentioned that the various moments associated with the electron spin, the orbital momentum, and the momentum associated with rotation can be coupled in different ways depending on the internuclear distance. These different couplings are referred to as Hund’s cases, distinguished by the letters (a), (b), (c), (d), and (e). These couplings are obtained by comparing the relative importance of electrostatic interactions, spin-orbit interactions, and spin-rotation coupling. The
description of the states previously described corresponds to Hund's case (a), where the vectors $\vec{L}$ and $\vec{S}$ are decoupled by the electrostatic field of the nuclei and precess independently along the internuclear axis. The rotation does not disturb the coupling of the electronic motion to the internuclear axis, so $\Omega$ remains well-defined. $\vec{R}$ precesses around $\vec{J}$, and the molecule, as a whole, rotates around $\vec{J}$. The significant quantum numbers are $S, \Lambda, \Sigma, \Omega$, and $J$.

For heavy nuclei, such as $I_2$, the spin-orbit interaction is significant enough that $\vec{L}$ and $\vec{S}$ are not decoupled by the field generated by the nuclei. This is Hund's case (c), and one then defines $\vec{J}_a = \vec{L} + \vec{S}$ and $\hbar\Omega$ as the projection of $\vec{J}_a$ onto the internuclear axis. The molecule rotates around $\vec{J}$ such that $\vec{J} = \vec{\Omega} + \vec{R}$. The significant quantum numbers are $S, \Omega$, and $J$ (but not $\Lambda$ and $\Sigma$), and states are noted, for example, as $^3\Omega_u$ where 0 designates $\Omega$. However, if coupling (c) is not strictly satisfied, $\Sigma, \Pi, \Delta$, etc are also applied, which is why, in the case of $I_2$, we find notations such as $^3\Pi(0_u^+)$, $^3\Pi(1_u)$, $^3\Pi(2_u)$, etc.

## Electronic spectrum—transition rules

Electronic transitions are primarily of the electric dipole type. The selection rules are as follows if Hund's coupling case (a) is satisfied:

1. $\Delta\Lambda = 0, \pm 1$.

2. $\Delta S = 0$. As with atoms, this selection rule no longer applies when the nuclear charge increases.

3. $\Delta\Sigma = 0; \Delta\Omega = 0, \pm 1$. For transitions between multiplet components.

4. $+ \leftrightarrow +; - \leftrightarrow -; + \leftrightarrow -$. This applies only to $\Sigma - \Sigma$ transitions, so only $\Sigma^+ - \Sigma^+$ and $\Sigma^- - \Sigma^-$ transitions are allowed.

5. $g \leftrightarrow u; g \leftrightarrow g; u \leftrightarrow u$.

For Hund's coupling case (c):

1. $\Delta S = 0$ which, as in case (a), is approximate.

2. $\Delta\Omega = 0, \pm 1$.

3. $0^+ \leftrightarrow 0^+; 0^- \leftrightarrow 0^-$; $0^+ \leftrightarrow 0^-$ with 0 the $\Omega$ value.

4. $g \leftrightarrow u; g \leftrightarrow g; u \leftrightarrow u$.

## Molecular ions

The same reasoning applies for homonuclear ions such as $I_2^+$ and $I_2^-$, whose electronic configuration are respectively given by

$$ (\sigma_g 5s)^2 (\sigma_u 5s)^2 (\sigma_g 5p)^2 (\pi_u 5p)^4 (\pi_g 5p)^3, \quad ^2\Pi_{u;3/2}, \qquad (63) $$

and

$$ (\sigma_g 5s)^2 (\sigma_u 5s)^2 (\sigma_g 5p)^2 (\pi_u 5p)^4 (\pi_g 5p)^3 (\sigma_u 5p)^2, \quad ^2\Sigma_{u;1/2}^+. \qquad (64) $$

## Appendix C. Principle of detailed balance

For almost all collisional processes discussed in section 3, only forward reaction rate coefficients are known. These have either been computed through integration of an assumed Maxwellian energy distribution function over the relevant cross-sections, or have been taken directly from the literature. However, certain reverse reactions can be important, such as electron impact de-excitation of the $^2\text{P}_{1/2}^\circ$ state. To find reaction coefficients for such processes, we make use of the principle of detailed balance [124], which effectively states that at equilibrium, the reaction rates of all forward and reverse processes are equal. Here, we employ this principle to explicitly establish rate coefficients for both de-excitation and three-body recombination. Consider the electron impact atomic excitation and de-excitation reactions given by

$$ I(i) + e^{-} \leftrightarrow I(j) + e^{-}, \qquad (65) $$

where $j$ and $i$ label upper and lower excited states. At equilibrium, the forward and reverse rates are equal such that

$$ n_e n_i K_{\text{exc},ij} = n_e n_i K_{\text{deexc},ji}, \qquad (66) $$
with $K_{deexc,ji}$ the de-excitation rate coefficient. If atomic iodine is in LTE, then the relative density of excited states can be determined from Boltzmann statistics

$$ \frac{n_i}{n_j} = \frac{g_i}{g_j} \exp \left( \frac{\varepsilon_{exc,j} - \varepsilon_{exc,i}}{k_B T} \right), \qquad (67) $$

where $g_j$ and $g_i$ are the degeneracies of the upper and lower excited states, $\varepsilon_{exc,j}$ and $\varepsilon_{exc,i}$ are the excitation threshold energies, and $T$ is the temperature (see below). Combining equations (66) and (67) we obtain an expression for the reverse rate coefficient

$$ \frac{K_{deexc,ji}}{K_{exc,ij}} = \frac{g_i}{g_j} \exp \left( \frac{\varepsilon_{exc,j} - \varepsilon_{exc,i}}{k_B T} \right). \qquad (68) $$

There is some ambiguity as to what temperature to use when applied to non-equilibrium systems, but as the excitation/de-excitation is due to collisions with electrons, typically $T = T_e$. Consider now the electron impact ionization and three-body recombination reactions given by

$$ I(i) + e^{-} \leftrightarrow I^{+} + 2e^{-}, \qquad (69) $$

where $I^+$ is in the ground state. At LTE, the forward and reverse rates must again be equal such that

$$ n_e n_i K_{iz} = n_e^2 n_{I^+} K_{rec}, \qquad (70) $$

with $K_{rec}$ the recombination rate coefficient and $n_{I^+}$ the positive ion density. Ignoring any molecular iodine species, we can use the Saha equation to express the densities as

$$ \frac{n_e n_{I^+}}{n_i} = \frac{2g_{I^+}}{g_i} \exp \left( \frac{\varepsilon_{exc,i} - \varepsilon_{iz,I^+}}{k_B T} \right). \qquad (71) $$

Combining equations (70) and (71) we then find

$$ \frac{K_{rec}}{K_{iz}} = \frac{g_i}{2g_{I^+}} \exp \left( \frac{\varepsilon_{iz,I^+} - \varepsilon_{exc,i}}{k_B T} \right). \qquad (72) $$

As before, we typically set $T = T_e$.

For some models, cross-sections for the reverse reaction are needed instead of the rate coefficient. Considering reaction (65) as an example, the principle of detailed balance in this case gives [124]

$$ \frac{\sigma_{deexc,ji}(\varepsilon)}{\sigma_{exc,ij}(\varepsilon + \Delta\varepsilon_{ij})} = \frac{g_i}{g_j} \left( \frac{\varepsilon + \Delta\varepsilon_{ij}}{\varepsilon} \right), \qquad (73) $$

where $\varepsilon$ is the electron energy, $\sigma_{exc}(\varepsilon + \Delta\varepsilon_{ij})$ is the energy-dependent excitation cross-section, $\sigma_{deexc}(\varepsilon)$ is the energy-dependent de-excitation cross-section, and $\Delta\varepsilon_{ij} = \varepsilon_{exc,j} - \varepsilon_{exc,i}$.

## ORCID iDs

Trevor Lafleur ID 0000-0002-9926-2187

Benjamin Esteves ID 0000-0002-3724-4899

Cyril Drag ID 0000-0001-9247-3945

Anne Bourdon ID 0000-0003-3662-4651

Pascal Chabert ID 0000-0002-6211-4746

Luca Vialetto ID 0000-0003-3802-8001

Rawoof Shaik ID 0009-0002-4391-9634

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