© V. Martinez et al., published by EDP Sciences, 2025

1 Introduction

A plasma is a gas made of electrically charged particles and may be generated by more or less sophisticated means [1]. One of them consists in submitting a material to microwaves which in turn creates a plasma [1–5]. Once created, the plasma is attested to last at least 1 min [2] while some [3] claim that the lifetime could have no upper limit. To explain this phenomenon, it has been proposed that the electromagnetic field enables electrons of the material to collide with the surrounding gas which become ionised and thus constitutes the plasma [1]. We will refer to this theory as the breakdown theory. It has also been proposed that the electromagnetic field locally heats the material to such an extent that some of it is ejected and therefore constitutes the plasma [2,3,6]. We will refer to this theory as the Localised Microwave-Heating effect (LMH).

However, it remains unclear which mechanism is effectively responsible for the emergence of the microwave-induced plasma. Here we show that the plasma is made of the heated material, that an increased heating of the material is linked to an easier creation of the plasma and that no upper limit for the plasma lifetime has been found. These findings demonstrate that breakdown cannot account for the creation of plasma and thus support the LMH theory. These results also agree with the theoretical infinite lifetime. It is interesting to note that it is possible to generate plasma without any material to eject from, if enough power [7]. The creation of plasma from some material may be used for material identification by atomic emission spectroscopy [6], ignition of thermal reactions, microwave enhanced combustion processes [8], metal treatments for surface hardening and substrate deposition [2].

This paper is organised as follows. In Section 2, we first introduce our experimental setup. In Section 3, we present the measurements of the plasma lifetime and of its composition. In Section 4, we discuss those results in relation with both the breakdown and the LMH theories. Finally, in Section 5, we describe an experiment that did not lead to any substantial result.

2 Experimental method

Various techniques may be used to foster ionisation and thus plasma creation, from an electrode that touches the material and directs microwaves on it [2,8] to a radioactive element creating a discharge [1]. The materials used are as different as grape [4], glass [3,6], concrete, ceramic, polymers [6], basalt [3,6], silicon [3,6,8], titanium [2], alumina, germanium, [3] or even polydimethylsiloxane [1]. Here, we will use a simple technique to create a microwave-induced plasma using common materials.

2.1 Microwave setup

To create the plasma, we used a commercial micro-wave which imposes a frequency f = 2.45 GHz that corresponds to a wavelength λ = c/f = 12.2 cm and a power ranging from 150 W to 900 W [1–6,8]. The main results presented in the following were obtained at 300 W. Previous experiments used a power from 100 W to 1000 W [2,3,5,6,8].

In our experiment, the microwave is operated without the rotating plate.

In the present study, only one material has been considered: a pencil lead (brand: BIC, type: HB), made of 68% graphite, 26% clay and 5% wax, is used to generate the plasma. It is inserted into a cylindrical support (radius 3.5 cm) made of duraluminium, unless otherwise indicated, that has been drilled to hold the lead. The support enables us to control the position of the lead. Experimentally, an angle of 45° with the base allows the generation of a plasma, whereas 0° and 90° don’t. Therefore a 45° angle is chosen in the following. We tested different lengths for the lead (1 cm to 10 cm) and different diameters (0.5 mm to 2 mm) and each time succeeded in producing a plasma.

The support and the lead are covered by a bowl to confine the plasma, as depicted in Figure 1. Since the temperature of the plasma is expected to reach a temperature as high as 1000°C [2,5,8], we chose a bowl made of borosilicate glass because of its high melting temperature of 1, 650 °C.

Fig. 1 Experimental set up: in a microwave oven are inserted a bowl, a support and a graphite lead. The plasma is schematically shown by the yellow cloud.

2.2 Microwaves cartography

According to both breakdown [1] and LMH theories [6], the material will receive energy from the electromagnetic wave which will create in turn a plasma. Assuming that the microwave is a cavity in the steady-state regime, we can determine the locations of maximum microwave power from the wave antinodes. In order to locate them, we placed chocolate bars in the microwave oven and located the antinodes at the places where the chocolate melts after a few seconds of operation [9]. The distance between two adjacent antinodes is found to be of the order of 6 cm, which is consistent with the expected value λ/2 ~ c/2f ~ 6 cm.

To be sustained, the plasma receives energy from the electromagnetic field and therefore the plasma will be located in the vicinity of an antinode. The horizontal position of the antinodes may depend on the height, but we were only able to determine them at the base of the oven. We assumed that the dependence of the antinodes location on the height is negligible. Moreover, we neglected the fact that the plasma may perturb the wave and modify the electromagnetic field configuration. We found that the size of the plasma is actually similar to the distance between two antinodes. Therefore, the plasma is anyway located near antinodes.

3 Results

3.1 Plasma lifetime

The typical steps leading to the plasma creation are depicted in Figure 2. When the microwaves are turned on, sparks are emitted at the extremity of the lead that is in the air (Fig. 2a). After typically 1 s, a flash is emitted from the lead (Fig. 2b), the plasma is created and ascends to the top of the bowl in a few seconds (Fig. 2c) where it is contained until the microwaves are switched off (Fig. 2d). Note that, during the latter stage, the plasma which is at the top of the bowl does not touch the lead and the lead extremity is usually extinguished.

Once the power is turned off and the plasma has vanished, we observed that the lead, from which plasma was emitted, has been eroded. Both the bowl and the lead are hot. The bowl even melted during one of the experiments (see inset of Fig. 2d), which shows that the plasma reached a temperature larger than the borosilicate melting temperature of 1, 650 C, which is consistent with previous experiments [2,5,6,8]. With our setup, we managed to maintain a plasma for 90 min, almost two orders of magnitude longer than the 1 min already observed [2]. The plasma was extinguished only when the microwaves were switched off.

For comparison, we determined the characteristic electronic times in the plasma, the inverse respectively of the cyclotron pulsation, of the plasma pulsation and of the frequency of collisions [10]:

$$\begin{array}{l}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}1/{\omega }_c=\frac{m_e}{eB}=6\times {10}^{-8}\hspace{0.17em}\text{s}\hfill \\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}1/{\omega }_p=\sqrt{\frac{m_e{\epsilon }_0}{n_e{e}^2}}=2\times {10}^{-10}\hspace{0.17em}\text{s}\hfill \\ 1/v_{coll}=\frac{4\pi n_e{\lambda }_D^3}{{\omega }_p}\frac{1}{\ln \hspace{0.17em}4\pi n_e{\lambda }_D^3}=3\times {10}^{-8}\hspace{0.17em}\text{s}\hfill \end{array}$$

with the Debye length ${\lambda }_D=\sqrt{\frac{{\epsilon }_0{k}_B{T}_e}{n_e{e}^2}}$, ε₀ the electric permittivity, k_B the Boltzmann constant, e the elementary charge, m_e the electron mass, B the magnetic field created by the oven taken to be 9.2 × 10⁻⁵ T [11], n_e the electron density in the plasma of the order of 10¹⁶m⁻³ [6] and T_e the electron temperature of the order of 1000 K. Each of these time scales measures the duration of one phenomenon: the time for an electric charge to perform a turn around the magnetic field it is submitted to, the oscillation of electric charges or the time between two collisions. Since the obtained lifetime (90 min) of the plasma is at least 10 orders of magnitude larger than any of these characteristic timescales, a great number of occurrences of these effects are happening within the plasma. Our result is consistent with the theoretically predicted infinite lifetime [3].

Fig. 2 Steps of plasma creation and corresponding times. (a) Sparks and fumes from the lead (t = 0 s). (b) Creation of the plasma (t = 1 s). (c) Detachment from the lead and elevation (t = 2–4 s). (d) The plasma is maintained, confined by the bowl while the lead is extinguished (t ≥ 4 s). Inset: photograph of the borosilicate bowl that melted due to prolonged contact with the plasma.

3.2 Determination of the plasma composition

The different theories put forward to explain the present phenomenon do not agree on the nature of the plasma ions. The breakdown theory suggests that these ions come from the surrounding gas, ambient air in our case, whereas the LMH theory predicts that the ions are extracted from the material that initiated the plasma. To discriminate between these two theories, we determined the composition of the plasma by measuring the visible - near infra-red spectrum within the oven. To do so, a hole in the oven has been made, to tightly insert an optical fibre connected to a spectrophotometer (bandwidth = 200 nm – 1100 nm, resolution = 2 nm, [12]). We took special care to make sure that the microwave oven was leak-tight for safety reasons. We introduced different gases (nitrogen, argon) in the oven by releasing the gas from bottles linked to the oven by a tube before starting the experiment, and in all the cases, a plasma was created. The different spectra obtained are displayed on Figure 3.

Fig. 3 Plasma emission spectra for different configurations. The basic configuration is a support made of aluminium that holds the pencil lead and a surrounding which is air. Only one parameter is changed in each experiment: the material of the support becomes wood or the gas inserted in the microwave oven which can be nitrogen or argon. As a reference, the spectrum without plasma and with the microwave oven on is also given.

3.2.1 General features of the spectra

All spectra in Figure 3 are composed of a continuous background and of some spectral peaks. The continuous bell-shaped background corresponds to a black body emission due to the burning of the lead at the beginning of the process, to some bremsstrahlung due to the deceleration of charged particles in the plasma (320-550 nm) and to ion recombination (550-700 nm) [13]. The black body emission may be stronger for some support materials like wood because the support itself was heated. We will focus on the three spectral peaks of higher intensity experimentally found at 588 nm, 766 nm and 769 nm. They can correspond to excited molecules or ions [13]. They appear when the plasma is present and disappear when the plasma is extinguished, and this, whatever the situation in Figure 3. The spectral peaks can therefore be attributed to the plasma.

3.2.2 Influence of the support and the bowl

We changed the material of the support (wood, plastic, aluminum or just the lead without any support) and of the bowl (glass, plastic, borosilicate, no bowl). Whatever material was used for the support, a plasma was created which produced the same spectral peaks, as shown in Figure 3. Therefore the plasma come neither from the support nor from the bowl.

3.2.3 Influence of the gas

If the lead is removed, no plasma emerges and, as can be seen in Figure 2, the plasma initially appears close to the lead before rising to the top of the bowl. This is a first indication that the the plasma is created from the lead.

The spectra in Figure 3 all share the same spectral peaks regardless of the surrounding gas. As a consequence, the spectral peaks that appear during the plasma phase can be attributed to the material that has been ignited and not to the surrounding gas, as predicted by the LMH theory and at odds from predictions of Breakdown theory. The wavelength of the lines are consistent with those of carbon transitions (more details in Appendix A).

It is therefore very likely that the main element responsible for the emission from the plasma is carbon, as suggested by the LMH theory.

3.3 Impact of the parameters of the lead

Now that we have identified the origin of the plasma, we would like to know the impact of the pencil lead parameters on the plasma. Different lengths (1 cm to 10 cm) and diameters (0.5 mm to 2 mm) have been tested and in each case, a plasma was obtained. However, we noticed that the thicker the lead i), the larger the sparks, ii) the hotter the pencil lead and iii) the easier the plasma creation.

4 Discussion

We now turn to the discussion concerning the mechanisms for both the creation and the maintenance of the plasma, in relation with our experimental results.

To our knowledge, as previously mentioned, there are two theories to explain the plasma creation: the breakdown theory and the LMH theory. According to the breakdown theory [1], the plasma could originate from the air excited by electrons coming from the material. Since our experiments show the same spectral peaks whatever gas is inserted inside the oven, the breakdown theory is unlikely to apply in our case. On the other hand, according to LMH theory, the electromagnetic field in the oven locally heats the lead proportionally to the square of the electromagnetic field and to the dielectric permittivity [6]. Moreover, the permittivity of the lead increases locally with temperature. This dependence creates a self-reinforcing loop, called the Localised Microwave-Heating effect, between the local heating and the dielectric permittivity. The temperature locally increases until the sublimation temperature, T_s = 3652° C for graphite [14], is reached, and material ejection begins, creating the plasma [2,3]. This process is illustrated in Figure 4. This theory is consistent with our observation that the plasma originates from the pencil lead and with the fact that increased heating results in a faster plasma generation.

In the literature, different techniques have been be used to direct the electromagnetic field on the material [1,2,8]. In our case, we simply localised the maximum power of the electromagnetic field and placed the free extremity of the pencil lead at this location. Since the lead is conducting and given its shape, we think that the lightning rod effect [15] is responsible for the accumulation of charges and thus a stronger electromagnetic field at the tip of the lead. This is consistent with sparks appearing at the tip of the lead in the beginning of the process. The plasma being hot, it is less dense than the surrounding air and thus rises, until it reaches the bowl.

A possible mechanism for the plasma maintenance is provided by the Townsend discharge [16]. Electrons accelerated by the electric field collide with particles of the surrounding plasma and create an avalanche of collisions that can last as long as the production of electrons by ionisation remains more important than the loss of electrons by diffusion or absorption by neutral particles [16]. This explanation is consistent with an infinite lifetime, as predicted by [3], and consistent with our experimental observations.

Fig. 4 Sum-up of the ignition mechanism.

5 Dead-end

Since a plasma is made of electrically charged particles, we wanted to investigate the effect of a magnetic field on the properties of the plasma. To this end, we placed a magnet (magnetic flux density ≈0.01 T) on the outer surface of the bowl. We did not place the magnet inside the bowl because the plasma temperature (1,500 °C at least as shown before) could have demagnetised the magnet. We expected it to influence the equilibrium position of the plasma. Our experiment did not however result is any visible effect on the position of the plasma. This may be due to the weakness of magnetic field, not intense enough to have a meaningful effect.

6 Conclusion

We investigated the mechanism that leads to the formation of a plasma when placing a graphite lead in a microwave oven. We discarded the breakdown theory as a possible explanation for the ignition of the plasma. We found on the contrary that the Localised Microwave-Heating theory, which explains the ejection of material through the local heating of the material, was consistent with our observations. We showed that the plasma reached at least a temperature of 1500 C. We found that a plasma could be created with a very simple apparatus and last 90 min, two orders of magnitude larger than the 1 min found in the literature.

It remains to understand why a thicker lead becomes hotter when submitted to an electromagnetic wave. One could study the impact of the length, the diameter and the angle of the lead on the plasma. One could investigate the dependence of the ignition time on the wavelength of the electromagnetic field and look for an hypothetical optimal wavelength. One could also study the evolution of the wave antinodes inside the microwave oven in the presence of the plasma. Since it may be expected to observe CO spectral peaks that are not present in our experiment, one could investigate the reason for such an absence. This may be due to a too weak quantity of carbon to form CO, which would contradict other results in this paper. It may result from other reactions that may take place and may be more favoured than the reaction forming CO from carbon, or the conditions for the reaction from carbon to CO are not completely gathered to take place sufficiently to be detectable, or also, the CO is consumed by other reactions before it is detected. Finally, one could investigate what change in the parameters can stop light emission from the plasma.

Acknowledgements

We would like to thank the French Physicists’ Tournament for organising the 2023 competition and for this subject, the Master de Physique Fondamentale (Universite Paris-Saclay) who organised our time table to let us study those subjects one day per week and we want to thank in particular our supervisors, Claire-Marrache Kikuchi, Louis Heitz, Philippe Gondret, Jean-Marie Fischbach and Bertrand Pilette for their advice, their dedication and for having let us live this tournament the way we wanted to. This work was partially supported by the Investissements d’Avenir of the LabEx PALM (ANR-10-LABX-0039-PALM).

References

Appendix A Atomic optical transitions at wavelengths λ = 588,670,766,769 nm

Table A.1 presents a summary of the known carbon optical transitions around the measured wavelength in the present work: 588 nm, 766 nm and 769 nm (±1 nm), the element involved in the transition as well as the initial and final configurations and their term symbol ^2S+1L_J [17]. Carbon C I and its ionisations C II and C III are represented at each wavelength. Even though the emission energy of carbon of about 11 eV makes the ionisations C II and C III unlikely to occur, carbon C I remains present at each wavelength of interest.

The wavelengths are also consistent with those of N, O or Si, as shown in Table A.2 [17]. Those elements could come from ambient air made of 78% dinitrogen 20% dioxygen or from the bowl made of borosilicate (composition: 70–80% SiO₂, 7–13% B₂O₃, 4-8% Al₂O₃ [18]).

However, as mentioned in 3.2.2, the plasma and the spectral peaks of highest intensity at 588 nm, 766 nm and 769 nm appear whatever the composition of the bowl or even, without a bowl. The bowl cannot therefore account the composition of the plasma. Also, as detailed in 3.2.3, the plasma and the spectral peaks of highest intensity appear whatever the gas inside the oven. Then, the gases of the air cannot neither account for the composition of the plasma.

In order to check more in details the results suggested by the analysis of the spectral peaks of highest intensity, we next analyse a secondary peak and look for spectral peaks that are characteristic of some element that are relevant to look for, given our setup. In Figure 3, a secondary peak is visible at λ = 670 nm in the case when the introduced gas is Argon or Nitrogen. In Table A.3, we show the possible elements that could correspond to this peak and that are relevant with our setup [17]. Indeed, in addition to oxygen, only Argon and Nitrogen are relevant gases emitting at this range of wavelength, which is consistent with the gas introduced inside the oven.

To test the presence of nitrogen, we feature the N₂ First Positive System in Figure A.1 and Second Positive System in Figure A.2 [19]. The intensity at wavelength 670.48 nm could correspond to such an emission, but this is the only remarkable one. Dinitrogen is then another possibility to account for the emission at this wavelength. However, since once again we changed the gas inside the oven and nitrogen was hence removed, nitrogen cannot account for the main composition of the emitting gas.

To test the presence of C₂ in the plasma, we present the Swan bands in Figure A.3 that are characteristic of C₂ emissions [20]. In our case, only the Swan band at the wavelength 550 nm could possibly match some peak of the measured intensity. However, all others do not match any peak whatever the support and the gas inside the oven. This could mean that the density in C₂ of our plasma is low or that the power used in our experiment is not high enough to foster the formation of C₂.

To better examine the presence of oxygen into the plasma, we look at some characteristic spectral lines at wavelengths 777 nm and 845 nm in Figure A.4 [17,21], Given the precision of 1 nm, there is no doubt that the peaks in intensity in the spectrum do not correspond to these spectral lines. Then these lines are unlikely to correspond to oxygen and this reinforces the rejection of oxygen as a relevant component of the plasma.

Fig. A.1 Plasma emission spectra for different configurations and with the N2 First Positive System emission. The basic configuration is a support made of aluminium that holds the pencil lead and a surrounding which is air. Only one parameter is changed in each experiment: the material of the support becomes wood or the gas inserted in the microwave oven which can be nitrogen or argon. As a reference, the spectrum without plasma and with the microwave oven on is also given. The N2 FPS are situated respectively at wavelength 632 nm, 639 nm, 647 nm, 654 nm, 662 nm, 670 nm, 679 nm, 687 nm, 716 nm.

Fig. A.2 Plasma emission spectra for different configurations and with the N2 Second Positive System emission. The basic configuration is a support made of aluminium that holds the pencil lead and a surrounding which is air. Only one parameter is changed in each experiment: the material of the support becomes wood or the gas inserted in the microwave oven which can be nitrogen or argon. As a reference, the spectrum without plasma and with the microwave oven on is also given.

Fig. A.3 Plasma emission spectra for different configurations and with the Swan bands. The basic configuration is a support made of aluminium that holds the pencil lead and a surrounding which is air. Only one parameter is changed in each experiment: the material of the support becomes wood or the gas inserted in the microwave oven which can be nitrogen or argon. As a reference, the spectrum without plasma and with the microwave oven on is also given. The Swan band are situated respectively at wavelength 437 nm, 470 nm, 505 nm, 550 nm, 600 nm and 660 nm.

Fig. A.4 Plasma emission spectra for different configurations and Oxygen characteristic emission. The basic configuration is a support made of aluminium that holds the pencil lead and a surrounding which is air. Only one parameter is changed in each experiment: the material of the support becomes wood or the gas inserted in the microwave oven which can be nitrogen or argon. As a reference, the spectrum without plasma and with the microwave oven on is also given. The Swan band are situated respectively at wavelength 437 nm, 470 nm, 777 nm, 845 nm.

After having examinated the main peaks in the spectra in Figure 3 as we did previously, we would like to focus on the bump at 600 nm. For that, we list in Table A.4 [17] the different elements that could emit at such a wavelength and that are relevant given our setup. We remark that only nitrogen and carbon appear. Yet, once again, since we changed the gas inside the oven and obtained the same spectral bump, nitrogen has to be rejected and only carbon remains. This thus reinforces the possibility of an emitting gas made of carbon.

All Tables

All Figures

	Fig. 1 Experimental set up: in a microwave oven are inserted a bowl, a support and a graphite lead. The plasma is schematically shown by the yellow cloud.
In the text

	Fig. 2 Steps of plasma creation and corresponding times. (a) Sparks and fumes from the lead (t = 0 s). (b) Creation of the plasma (t = 1 s). (c) Detachment from the lead and elevation (t = 2–4 s). (d) The plasma is maintained, confined by the bowl while the lead is extinguished (t ≥ 4 s). Inset: photograph of the borosilicate bowl that melted due to prolonged contact with the plasma.
In the text

Fig. 3 Plasma emission spectra for different configurations. The basic configuration is a support made of aluminium that holds the pencil lead and a surrounding which is air. Only one parameter is changed in each experiment: the material of the support becomes wood or the gas inserted in the microwave oven which can be nitrogen or argon. As a reference, the spectrum without plasma and with the microwave oven on is also given.

In the text

	Fig. 4 Sum-up of the ignition mechanism.
In the text

Fig. A.1 Plasma emission spectra for different configurations and with the N2 First Positive System emission. The basic configuration is a support made of aluminium that holds the pencil lead and a surrounding which is air. Only one parameter is changed in each experiment: the material of the support becomes wood or the gas inserted in the microwave oven which can be nitrogen or argon. As a reference, the spectrum without plasma and with the microwave oven on is also given. The N2 FPS are situated respectively at wavelength 632 nm, 639 nm, 647 nm, 654 nm, 662 nm, 670 nm, 679 nm, 687 nm, 716 nm.

In the text

Fig. A.2 Plasma emission spectra for different configurations and with the N2 Second Positive System emission. The basic configuration is a support made of aluminium that holds the pencil lead and a surrounding which is air. Only one parameter is changed in each experiment: the material of the support becomes wood or the gas inserted in the microwave oven which can be nitrogen or argon. As a reference, the spectrum without plasma and with the microwave oven on is also given.

In the text

Fig. A.3 Plasma emission spectra for different configurations and with the Swan bands. The basic configuration is a support made of aluminium that holds the pencil lead and a surrounding which is air. Only one parameter is changed in each experiment: the material of the support becomes wood or the gas inserted in the microwave oven which can be nitrogen or argon. As a reference, the spectrum without plasma and with the microwave oven on is also given. The Swan band are situated respectively at wavelength 437 nm, 470 nm, 505 nm, 550 nm, 600 nm and 660 nm.

In the text

Fig. A.4 Plasma emission spectra for different configurations and Oxygen characteristic emission. The basic configuration is a support made of aluminium that holds the pencil lead and a surrounding which is air. Only one parameter is changed in each experiment: the material of the support becomes wood or the gas inserted in the microwave oven which can be nitrogen or argon. As a reference, the spectrum without plasma and with the microwave oven on is also given. The Swan band are situated respectively at wavelength 437 nm, 470 nm, 777 nm, 845 nm.

In the text