Online and FREE access to plasma physics experiments

Plasma is a difficult medium to handle and diagnose due to its very high natural temperature. Only refractory metals can be in direct contact with relatively cold plasmas allowing for direct readings of their properties. Conversely, most plasma diagnostics entail the only possibility of indirect measurements, either by emitted radiation or by the use of external sources. Based on this fact, e-lab presents two plasma experiments exemplifying this paradigm: (i) a Langmuir probe [1] where the voltage/current I(V) characteristic is obtained with an immersive diagnostic and (ii) an electromagnetic (EM) cavity [2] that captures the EM properties of plasma in a non-invasive way.

Recently, e-lab [3] evolved to a web-based platform and these two experiments were the test beds within the advanced remote-controlled laboratory. This platform, the framework for remote experiments in education (FREE) [4], is being offered as open-source code and a plan is in place to migrate all e-lab laboratories to this new technology. Although a completely new underlying technology was used, the foundations and previous knowledge from the earlier e-lab developments were implemented following the same user approach.

This paper brings up an overview of the FREE framework and is followed by a description of how those two experiments were deployed in the e-lab advanced laboratory. We concluded with a brief report on the main results that can be obtained from these two experiments and how they compare between them.

The architecture of FREE is illustrated in Fig. 1, which is composed of a user interface (UI) that is presented as a webpage on a browser. The server implements a portal with a list of different experiments that the provider has and will provide access to them. The Experiment control is deployed on a computer close to the Experiment apparatus, like a simple Raspberry Pi.

Fig. 1.

After the decision to replace the remote experiment controller (ReC) platform and an evaluation of existing alternatives, a new remote laboratory supporting platform was designed and developed. All existing platforms [4] exhibit some limitations, which can be tackled and solved using modern and more suitable technologies and approaches. FREE [4] was written in Python and Django and uses REST API [5] for all the communication between the UI (on a regular browser) and the physical experiment controller.

The project is developed and committed to a structured organization on GitHub, e-lab [6], where the code for the main server of FREE is published on the repository FREE_Web [7] and the Experiment controller is on the repository RPi_Proxy [8]. All code is open-source and, can be freely extended and integrated with existing experiments.

UI

When a user logs into e-lab [9], a list of all the experiments that are connected is presented, showing their corresponding status (offline or online), as shown in Fig. 2. If an apparatus can be used to do different experiments by selecting adequate experimental parameters, it is defined as a protocol. In this manner, the same apparatus can have different configurations and perform a variety of studies.

Fig. 2.

After choosing the desired Apparatus type and the Protocol, the FREE presents the user with a description of the Apparatus type, Apparatus, and Protocol containing the basic knowledge to understand the experiment (on the “Description” tab). Figure 3 presents an example of the page of the EM cavity.

Fig. 3.

On the “Configuration” tab, one can customize and save an execution by inputting the desired values into the box of the execution parameter (the box inside the blue square in Fig. 3a) and then pressing “Save”. By confirming the parameters, the execution can be inserted into a queue list of that Apparatus by pressing “Submit”.

Pressing the “Submit” button will move the webpage to the “Results” tab where, in real-time, the data collected from the experiment is displayed in a graph and on a table. It is also possible to observe the experiment in a window displaying a live video of the experiment (as shown in block of Fig. 3b).

Plasma has a very high temperature (generally >50 000 K), making it a difficult medium to accurately measure and characterize. Usually, this can be achieved by indirect measurements, based on its radiated light or its EM properties.

The Langmuir probe [12] is one of the few direct methods of plasma diagnostics and a simple one that allows for measuring some of these characteristics. The probe consists of a thin conductive wire immersed in the plasma. In a cold plasma, this perturbing object will collect mostly electrons, due to their higher mobility concerning ions, and become negatively charged, attaining a floating potential (V_f) if left floating. Usually, it will collect more electrons due to their mobility until it is sufficiently negatively biased for a null current flow due to electron repulsion.

If we bias the probe with a certain voltage (V_s), concerning the ground, we can either attract or repel the electrons in the plasma. By measuring the probe, I–V characteristic, that is, the relationship between the biasing voltage and the respective current going through the probe, one can extrapolate the electron temperature and density of the plasma.

If the biasing of the probe is negative enough, all the electrons will be repelled and the ion flux to the probe is almost independent of the applied potential. This is what we call the ion saturation current (isat+)$\left( {i_{sat}^ + } \right)$ and it is described by Eq. (1) [being the current the total charge flow (jsat+)$\left( {j_{sat}^ + } \right)$ into the collection area of the probe (A_S)],

1 isat+=jsat+As≈12encsAs,withcs=kTeM $i_{sat}^ + = j_{sat}^ + A_s \approx {1 \over 2}enc_s A_s ,{\rm{ }}with{\rm{ }}c_s = \sqrt {{{kT_e } \over M}} $

where the flow of charge by the plasma density (n) times the plasma’s speed of sound (c_S), being k the Boltzmann constant, T_e is the electron temperature and M is the ion mass.

There is a dependence between the collecting current and the biasing of the probe, as given by Eq. (2).

2 i+=isat+[1−α(Vs−Vf)] $i^ + = i_{sat}^ + \left[ {1 - \alpha \left( {V_s - V_f } \right)} \right]$

This is due to an expansion of the sheath caused by increasing bias voltage. In such cases, the probe’s electrical field is stronger and penetrates deeply into the plasma leading to an increased effective collection area. This dependence is almost linear and is taken into account by the α factor.

When decreasing the biasing voltage at some point, the electrons start reaching the probe (due to a reduction of sheath shielding), reducing the current. This singularity, where the characteristic detaches from the linear saturation current, gives the point where we observe an exponential behavior. The collected current is reduced by the emerging electron current. This can happen even <0 V because of the electron’s thermal energy.

Accounting for this balance we can retrieve the exponential behavior of the electrons due to their temperature, Eq. (3),

3 i+=isat+(1−eekTe(vs−vf)) $$\matrix{ {{i^ + } = i_{sat}^ + \left( {1 - {e^{{e \over {k{T_e}}}({v_s} - {v_f})}}} \right)} \cr } $$

this expression assumes that there is only one probe and that it is non-perturbative.

After a steep increase in the electron current, the plasma cannot continuously supply this avalanche of electrons. Then, we enter into the electron saturation current regime. This regime is not dictated by the electron temperature anymore, becoming almost linear, as in the ion case, but much steeper due to the electrons’ mobility.

Experiment setup

The Langmuir probe used at the e-lab advanced laboratory is composed of the main chamber at the bottom of it. There is a modified ion gauge head from Edwards Vacuum that has two parallel plates, a thin tungsten filament, and a coil, as shown in Fig. 4.

Fig. 4.

The two parallel plates are connected to a high voltage (HV) radio frequency (RF) generator of approximately 50 kHz, which will generate the plasma. The thin tungsten filament is our Langmuir probe, which has 10 mm in length and a diameter of 0.2 mm, and the coil is used as a local ground.

To generate a vacuum there is a vacuum pump connected to the main chamber and to generate different types of plasma there are three gas cylinders (helium, argon, and xenon) connected to a gas injection system that is also connected to the main chamber. These two components are common to the EM cavity, as shown in Fig. 5. In particular, to reduce the flow of the gas valves a hollow needle was inserted into the valve connectors, as can be seen in Fig. 6. With this modification, we can have better control over the quantity of gas injected into the chambers of the experiments.

Fig. 5.

Fig. 6.

The reading of the pressure inside the main chamber is done by a Pirani Gauge (PPT100) which is connected to a board that controls all experiments.

To function, the Langmuir probe needs a sweeping bias voltage. For this end, a message is sent with the frequency, peak-to-peak voltage (Vpp), and the type of wave (in this case a triangle wave), to the function generator (AD9850). In conjunction with an amplifier, driving an output transformer is to generate the bias voltage. To measure the probe characteristic, we use a PIC based custom-made board [1] with ADCs, and the corresponding electronics are used to provide offset adjustments and signal filtering.

Data collection and analysis

The data collected is grabbed in an elastic buffer. Initially, the sample rate is 1 sample/s and after reaching the preselected pressure, it is changed up to 1 k sample/s during the experiment.

The data collected by the Langmuir probe can be cumbersome and noisy (Fig. 7) due to the initial transient. A visual inspection of the data must be done to determine the relevant time interval to analyze.

Fig. 7.

The points corresponding to each half-period are identified and separated based on the direction of the sweep to verify the symmetry and hysteresis of the plasma response.

Parameters setting

In this experiment, the user can change the following parameters: sweeping voltage, period of the sweeping signal, number of samples per period, number of periods, background pressure, gas type, and injection time.

To generate plasma, it is important to have a low amount of gas in the chamber to allow for the plasma’s existence; it is recommended to set a background pressure of <15 Pa and set the injection time to open the valve for 25 ms to inject a suitable amount of gas. The density of neutrals achieved is an important factor and must be balanced between the critical points where the RF discharge can be sustained and the desired plasma density achieved. In RF or magnetron discharges a relatively high pressure needs to exist to allow the coupling between the EM energy and the molecular collisions that will ignite the plasma. As such the injection time window must be precise according (i) to the desired final pressure at which the experiment is to be performed and (ii) the gas used.

The other parameters are more related to the probe itself and the desired characteristic which relates to the acquisition procedure. These parameters are intended to allow various waveform and data sampling strategies according to the envisaged data analysis studies. Typically, for a well-defined I(V) curve, the highest value for the points per period and a low frequency for the sweep signal should be chosen.

Because of the nature of the exponential region, a single sweep will lack data points.

Data analysis

By reducing the time window and plotting the data, it exhibits a clear lack of symmetry. Following its nature, the plasma will adapt to different spatial charges due to the probe potential, leading to an offset in the sensed potential. This result has a different characteristic according to the sweep direction, introducing a hysteresis effect which is clearly seen in Fig. 8.

Fig. 8.

We can also observe noise in the signal created by the intrinsic nature of the plasma RF generator. This induced noise can be mitigated by doing a proper average. Since we collected all the half-periods, we averaged the currents for a given voltage window.

As discussed earlier, we can identify the ion current region, fit it linearly and remove it from the data to simplify the characteristic, as shown in Fig. 9.

Fig. 9.

No netheless, the last points before the detachment correspond to the minimum sheath and are the ones that should be taken as the ion saturation current used to calculate the density, as displayed in Table 1.

Table 1.

Parameters obtained after the fitting shown in Fig. 9, the ion saturation current

Slope	α(1/V)	Vf (V)	isat+(μA)$i_{sat}^ + {\rm{ }}\left( {{\rm{\mu A}}} \right)$
1	0.96	12.38	−17.2
−1	0.49	35.33	−17.6

Due to the exponential behavior that prompts us to perform a logarithmic scale transformation to identify the correct exponential window, as shown in Fig. 10.

Fig. 10.

On a logarithmic scale, we can see the detachment of the electron saturation current but be aware that log scales are very tricky to fool the eye and even more to the numerical fitting.

Despite the existing hysteresis, the calculated temperatures retrieved from the data yield similar values as expected.

Taking the calculated electron temperatures, it is now possible to determine the sound speed, in which M is the mass of the ions, in this case, argon, so it gives us a sound speed of 3297 m/s allowing the determination of the density, using Eq. (1), which is about n ≈ 10.4 × 10¹⁵ m⁻³.

Results overview

It presented some results of execution done with the Langmuir probe, where the only parameter that was changed was the amount of neutral gas injected into the chamber, as shown in Table 2.

Table 2.

Results of multiple executions with different neutral gas pressure (Ar) and results for the ion saturation current, and the respective calculation of the speed of sound and the density

Pressure (Pa)	(μgA)isat+$$\mathop {\left( {{\rm{\mu gA}}} \right)}\limits^{i_{{\rm{sat}}}^ + } $$	Te (eV)	Cs (m/s)	n (×1015 m−3)
64	−15.2	4.8	3405	8.9
100	−14.2	6.3	3901	7.2
150	−12.7	5.7	3711	6.8

Evaluating the data, we can observe that in this region when we increase the pressure of neutral gas the density and the ion saturation current decrease and the electron temperature (and the speed of sound) stays approximately the same. With this, a conclusion can be made that the ion flux is reducing. This observation is expected and can be explained, and by increasing the pressure, we are reducing the mean free path of the particles, so a loss of energy due to the increase in the collision and consequent recombination of ion-electron pairs is expected.

An EM cavity can be seen as a portion of a waveguide and so the EM waveguide theory applies [13]. In a cylindrical cavity filled with a homogeneous and isotropic medium, the resonant frequencies of the transversal magnetic (TM) modes are given by Eq. (4).

4 fnml=c2πμrεr(Pnma)2+(lπd)2 $f_{nml} = {c \over {2{\rm{\pi }}\sqrt {{\rm{\mu }}_r \varepsilon _r } }}\sqrt {\left( {{{P_{nm} } \over a}} \right)^2 + \left( {{{l{\rm{\pi }}} \over d}} \right)^2 } $

The chosen mode to make this study was the TM₀₁₀ due to no dependence on the z direction. Also, the electric field of this mode is parallel to the axial direction, while the magnetic field is parallel to the azimuthal direction, Fig. 11. Because of this, it is easily excitable by a loop antenna (magnetic antenna) with its axis in the azimuthal direction, instead of using a linear antenna that needs to be 1/4 of the wavelength and placed inside the plasma jeopardizing it. Note that the objective of this plasma diagnostic is to be a non-intrusive tool to measure the plasma parameter [14].

Fig. 11.

Since the EM cavity has a 32 mm radius the resonant frequency (f₀₁₀) is around 3586 MHz.

Plasma is an atmosphere of electrons and ions immersed in a neutral gas; therefore, it is an electrically conductive medium due to the presence of charged particles.

Since there are free charges, the propagation characteristics of the EM radiation change, and as such the solution of the wave equation yields the dispersion relation in the form of the Appleton–Hartree formula [15].

5 N2=1−2X (1-X)2(1-X)−Y2sin⁡2θ±ZZ=Y4sin⁡4θ+4Y2(1−X)2cos⁡2θ $\matrix{ {N^2 = 1 - {{{\rm{2}}X{\rm{ (1 - }}X{\rm{)}}} \over {{\rm{2}}\left( {{\rm{1 - }}X} \right) - Y^2 \sin ^2 {\rm{\theta }} \pm {\rm{Z}}}}} \cr {Z = \sqrt {Y^4 \sin ^4 {\rm{\theta + 4}}Y^2 \left( {1 - X} \right)^2 \cos ^2 \theta } } \cr } $

Here, N represents the refraction index, and as a dependence on the plasma frequency (X = (ω_pe/ω)²) and the cyclotronic frequency (Y = ω_c/ω with ω_c = eB₀/m_e) and θ is the angle between wave vector k and the external magnetic field B₀. Moreover, the dielectric tensor can be simplified if the magnetic field is assumed to exist only in the ZZ axis, making the angle θ zero.

In the experimental setup, it is possible to change the plasma frequency and the cyclotronic frequency by changing the pressure and the intensity of the external field, respectively. There will always be a cross effect, as increasing the magnetic field alters the plasma density by capturing the electrons in the field lines, confining it, so a direct linear relationship cannot be expected.

A great simplification occurs if there is no external magnetic field, making the Appleton–Hartree to appear in the following form:

6 N2=1−(ωpeω)2 $N^2 = 1 - \left( {{{{\rm{\omega }}_{pe} } \over {\rm{\omega }}}} \right)^2 $

When the cavity is filled with a neutral gas, it has a resonant frequency of f₀. This resonant frequency is shifted, from Δf to a new frequency f when the cavity is filled with a dielectric medium (plasma).

7 N2=f02f2=ω02ω2 $N^2 = {{f_0^2 } \over {f^2 }} = {{{\rm{\omega }}_{\rm{0}}^{\rm{2}} } \over {{\rm{\omega }}^{\rm{2}} }}$

By replacing this last result in Eq. (6),

ne=ε0me(ω2−ω02)e2=4π2ε0mee2(f2−f02)=4π2ε0mee2((f0+Δf)2−f02) $\matrix{ {n_e = {{{\rm{\varepsilon }}_{\rm{0}} m_e \left( {{\rm{\omega }}^{\rm{2}} - {\rm{\omega }}_{\rm{0}}^{\rm{2}} } \right)} \over {e^2 }} = {{4{\rm{\pi }}^{\rm{2}} {\rm{\varepsilon }}_{\rm{0}} m_e } \over {e^2 }}\left( {f^2 - f_0^2 } \right)} \cr { = {{4{\rm{\pi }}^{\rm{2}} {\rm{\varepsilon }}_{\rm{0}} m_e } \over {e^2 }}\left( {\left( {f_0 + \Delta f} \right)^2 - f_0^2 } \right)} \cr } $

we get the equation that relates the shift of the resonance frequency with the plasma density, Eq. (8)

8 ne=8π2ε0mee2f0Δf $n_e = {{8{\rm{\pi }}^{\rm{2}} {\rm{\varepsilon }}_{\rm{0}} m_e } \over {e^2 }}f_0 \Delta f$

Experimental setup

As mentioned before the vacuum system and the gas injection are shared with the Langmuir probe.

The main chamber is a cavity made from a nickel-plated copper body to protect it against corrosion, with a width of 64 mm in diameter and 50 mm in length, Fig. 12c. A cold cathode fluorescent light (CCFL) inverter serves as a current source to generate a Penning discharge inside the cavity. The HV inverter converts a ~12 V DC source to ~1 kV/50 kHz AC output which is applied between both electrodes inside the cavity.

Fig. 12.

These electrodes are copper-plated meshes, as shown in Fig. 12d, and are electrically insulated from the cylinder’s lateral surface and close to the extremes of the cylinder seen in the figure. This configuration ensures that the discharge permeates the entire cavity uniformly.

The CCFL inverter managed to sustain discharges with working gas pressures between ~10 Pa and ~300 Pa. The whole cavity lies between two Helmholtz coils that generate a magnetic field of up to 25 mT, with a given ~1.4 mT/A on the coils.

Two loop antennas lie in the middle of the cylinder wall opposing each other. The antennas have a ~4 mm radius with their axis coincident with the magnetic field line of highest intensity, the TM₀₁₀ mode. One of the antennas injects the microwaves into the cavity, and the other antenna collects the propagated signal. An observed resonance is expected to be close to a frequency of 3560 MHz.

The main component of the diagnostic is shown in Fig. 12a, the spectrum analyzer (ARINST SSA-TG R2) allows scans in the range of 35–4500 MHz with a precision of 100 kHz.

Data collection and analysis

If we consider the spectrum analyzer that is being used, a broad-span scan done without plasma, Fig. 13, allows us to identify the main peak of the TM₀₁₀ mode.

During the experiment we can see a slight pressure variation after the plasma ignition because some power is deposited on the neutral gas, leading to its heating and a corresponding neutral pressure increase.

Fig. 13.

By doing a broad span scan without plasma we can identify the main peak of the transverse magnetic mode 010.

Parameters setting

Users are allowed to configure the following parameters of the experiment: starting, ending, and step frequency of the acquisition of the spectrum; the number of spectrums to be collected; the background pressure; the injection time; and the type of gas that is injected; the intensity of the external magnetic field which activates the generation of the discharge (this allows the users to measure the resonant frequency of the cavity with no plasma).

It is important to (i) use enough large window of frequencies to observe the frequency shift and (ii) a sufficiently smaller frequency step to get more data points although this will reflect in a greater acquisition time.

To change the density of the plasma it is possible to increase/decrease the time that the gas injection valve is open (ranging between 0 ms and 250 ms). It is important to know that the injection time is not linearly correlated to the pressure measured, so it is advisable to do a calibration set of experiments.

Data analysis

The simplest data analysis is to average the spectrums to mitigate the noise in the signal created by the RF generator.

With this initial data treatment, it is possible to accurately measure the peak frequency (f) and the width at −3 dB (δf) from where the quality factor is computed (Q = f/δf). It was chosen the reference at −3 dB from the peak’s maximum value because the baseline noise level is never well-defined in RF measurements, and this is the main reason for considering the width at −3 dB instead of the width at half height.

In physics and engineering, the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio between the initial energy stored in the resonator and the energy lost.

Figure 14 shows a proper fitting of the data. In this case, we analyze argon plasma, where we can detect the shift in frequency and the lowering in both the quality factor and the maximum intensity due to increased energy losses. These values can also be read by inspection of the figures. So, after analyzing the experimental data, we concluded that the generated plasma had a density of 9.7 × 10¹⁴ m⁻³ (Δf = 3574.5 – 3563.6 = 10.9 MHz) and a Q factor of about 198 and 190.1, respectively, resulting in a 4.0% reduction (Fig. 14).

Fig. 14.

Of course, a better estimation can be done mathematically by correlating the signals and extracting the frequency lag. Another reading from the correlation function is the similitude in the waveforms, allowing for accounting for the signal attenuation.

Results overview

It is presented with some results of execution done with the EM cavity, where the only parameter that was changed was the amount of neutral gas argon injected into the chamber, as shown in Table 3.

Table 3.

Results of multiple executions with diffrent neutral gas (Ar) pressures and the resultants frequency shift measured

Pressure injection (Pa)	f (MHz)	Δf (MHz)	ne (×1014 m−3)
8	3563.6	–	–
10	3573.6	10.0	8.8
12	3580.8	17.2	15.2
13	3584.8	21.2	18.7
16	3586.4	22.8	20.2
18	3584.4	20.8	18.3
20	3582.5	18.9	16.7
21	3580.0	16.4	14.4
25	3578.4	14.8	13.1
28	3574.5	10.9	9.6
34	3572.8	9.2	8.1
44	3570.0	6.4	5.7
48	3568.8	5.2	4.6
60	3567.2	3.6	3.2
98	3566.8	3.2	2.8
120	3566.8	3.2	2.8

Looking at the data presented in Table 3 the first conclusion is that this experimental setup has a lower limit of 10 Pa for the neutral particles to be ionized corresponding to ≈0.7 mm of mean free path (Fig. 15). Below that point, the CCFL cannot generate any plasma as it corresponds to the usual pressure limit of the Townsend discharge breakdown voltage where the avalanche process can no longer exist. From this point to the maximum plasma density achievable, a constant raising of the electron density is visible, in a window of a few hundred microns, where the maximum relationship exists between the mean free path and the density. Here the density varies by one order of magnitude from the 0.1 mm reference. Then, due to the high pressure and the corresponding increase in the neutrals’ density, the discharge’s electron density is so low that the spectrometer cannot resolve the shift in frequency (0.1 MHz).

Fig. 15.

Both the Langmuir probe and the EM cavity are implementation paradigms of the open-source FREE. These experiments constitute the e-lab plasma advanced laboratory offered to the community by Instituto Superior Técnico (IST). The FREE infrastructure allows both real-time and offline data access to these experiments in a way that users can compare how invasive and non-invasive plasma experiments compare. Both experiments have been designed with a common rail gas injection and pumping system and both are equipped with the same ionizing source to make the experiments similar regarding the plasma source. It can be shown that the plasma density relates linearly with the mean free path between maximum density and the Townsend limits within the discharge existence.

To achieve very low pressures (<20 Pa) initially the vessel needs to be filled with a significant amount of the desired gas before the experiment. Then another execution is performed without gas injection and where the background pressure is used as a reference for the discharge.

Another important indication when doing a pressure sweeping is to do it from high pressures toward lower pressures to ensure less contamination from other gases used in previous experiments.

Overall, the plasma advanced laboratory requires a comprehensive knowledge of data analysis with different techniques and approaches that can be easily extended to other fields in physics.