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Experiments with Plasmas: Cross-field Instabilities



(Adapted from the e-Book: Experiments with Plasmas)

Plasma Physics in India began in Allahabad in 1920 with Saha’s fundamental theoretical investigations of ionization rates in thermal equilibrium plasmas. In 1938, Saha moved to the University of Calcutta to establish the Institute for Nuclear Physics. With the setting up of the first cyclotron, experiments with the duoplasmatron ion source started. A toroidal pinch experiment had operated at the Tata Institute of Fundamental Research in the early 1960s. However, with the failure of the ZETA experiment in Harwell in England, this work was stopped.

Sarabhai Plan

Vikram Sarabhai picked up the threads again when he assembled a group in the Physical Research Laboratory (PRL) in Ahmedabad in the early 1970s. In Abhijit Sen’s words (1), “The year was 1970, and a faculty meeting was in progress in the committee room of the PRL. In the middle of that meeting, Sarabhai suddenly rose and went to the blackboard to announce his plans to start an experimental plasma physics programme in PRL that would act as a seed programme for a future fusion research programme in the country. He then briefly explained why it was important to do so for the present needs of PRL and the country’s future energy needs.”

The long-term plan was to establish an experimental programme in basic plasma physics with a strong orientation towards the simulation of space plasma phenomena. However, there was a clear purpose of eventually gaining the skills necessary for fusion research. Leaving my faculty position at the Aligarh Muslim University, | joined PRL in 1972 and was assigned to set up the programme. Yogesh Saxena, who had worked on Cosmic Ray Physics, was an early collaborator.

Ionospheric Plasma Instabilities

Prof. Satyaprakash’s rocket experiments from PRL had observed instabilities in the Equatorial electrojet region of the ionosphere at about 100 km height. This region can be characterized as a low density, weakly ionized plasma region where the electrons are magnetised, and collisions with neutral molecules dominate the ions. It has an east-west electron current, vertical density gradient and a vertical polarization electric field and is immersed in the geomagnetic field. The currents and the density gradients in this collisional plasma act as free energy sources and can drive instabilities in the plasma. Radar backscatter and the PRL rocket experiments revealed primarily two types of instabilities in the electrojet region. One is a long wavelength instability excited in the regions where electric fields and density gradients are in the same direction and are now accepted as the high-frequency analogue of the Simon-Hoh or cross-field instability. The other is a short wavelength instability caused by the relative streaming of electrons past the essentially stationary ions with speed exceeding the local ion acoustic velocity and is called the Farley-Buneman or two-stream instability. The ionosphere observations have revealed many discrepancies with the existing theoretical analysis. This, as well as the fact that a laboratory experiment is amenable to close control over the relevant parameters, has been the primary motivation for the present study.

The Experiment

In setting up the experiment, we put priority on spectral and nonlinear dispersion characteristics, of interest in theoretical work related to the instabilities. Modern digitally implemented statistical signal analysis techniques have rendered these measurements feasible, and our diagnostics were based greatly on these techniques.

An important component of the experiment was the pair of magnetic field coils to produce a uniform magnetic field in the Helmholtz configuration (The large circular objects in the picture). The hollow rectangular copper windings used with very high currents used in the US laboratories was a luxury for us because of import restrictions. We decided to use small gauge insulated copper wires to wind the large magnets. In the absence of a lathe of the required size to hold the large fabricated Aluminum bobbins, we had to rent this in a workshop in the industrial area of Ahmedabad. Winding the magnets was a logistic nightmare, as we had to transport the very expensive wires in many bundles and keep them in safe storage. An expert mechanic from the workshop, Rambhai was the winding specialist. It took a few months before the magnets were finished. Transporting the huge coils to the laboratory was another major issue.

Another critical requirement of this experiment was to have a plasma region with a variable density gradient. The original plan was to create a plasma by photoionization of Caesium vapour by Ultraviolet light from Mercury discharge lamps. Such a source would have uniform plasma production within the volume because of the transparency of the plasma to the ultraviolet light. However, I realized that this source would have a diffusion-controlled density gradient which would not be externally variable.

In the summer of 1974, I visited the Plasma Physics laboratory of the University of California Los Angeles campus, which was a significant centre of plasma physics, working in frontier areas like parametric instabilities and building large volume uniform plasma sources using the McKenzie technique of surface magnetic condiment. The giant devices referred to as machines were a revelation to me, familiar with small experiments in the corner of a room. This was a great learning experience as it liberated me from being constrained to think small because of resource limitations to being comfortable with the idea of big devices. My colleague Prof Kaw also happened to be visiting UCLA at this time, and we had many opportunities to discuss the physics of the ongoing experiments. In addition, we discussed ideas of what we could do back in India to try to be at the forefront of experimental work.

On my return, we discarded the photoionized Caesium plasma approach in favour of a more elegant method of using an axial plasma column at the centre produced by capacitively coupled RF power. The magnetic field along the axis ensures that the density along the axis is uniform. Radial diffusion from a magnetised central column produces a radial density gradient uniform. As a result, plasma diffuses out radially to fill the chamber and the radial density gradient is controlled by the density of the central column, which was variable with the RF power. The critical requirement of the radial electric field was realized by having the plasma end on concentric metal rings on which a variable potential gradient was imposed. The parallel conductivity of the plasma ensured that this end wall potential distribution would be replicated within the plasma.

Raising the potential gradient or the magnetic field, which steepened the density gradient, triggered the instability, which could be detected using Langmuir probes which can pick up both density and potential fluctuations.

Farley-Buneman instability is triggered when electrons stream with a velocity exceeding the ion sound speed. The cross-field instability is a flute-like instability which arises because of a density gradient parallel to the electric field. Seeing the distorted density perturbations picked up by Langmuir probes on the oscilloscope screen gave us an incredible thrill.

My colleague Yogesh Saxena used cross-correlation techniques on the data stored on an analogue recorder to get the dispersion relation. This differed significantly from the linear theory predictions showing the contributions from nonlinear effects. Dispersion characteristics of the instabilities got experimentally for different values of the applied electric field show a good agreement with linear theory for small values of the electric field. Still, they diverge significantly from the theoretical predictions for large values of electric fields. We observed a nonlinear frequency shift from linear theory predictions.

The data storage technique was strongly influenced by the collaborators from the rocket experiments group, for whom the duration of a single transient rocket flight was all the time they had to collect the data. The situation in a laboratory experiment is quite different, where we can get instability data every time, we turn on the plasma. Therefore, the data could have been more conveniently analyzed using spectrum analyzers.

Conclusions

We had great fun discussing the experimental data with the theoreticians. The oscilloscope photographs of observed waves were non-sinusoidal. This triggered an explosion of questions on the experimental process. A delightful part of these discussions was that they generated a lot of ideas on how to interpret the results, how they differed from the predictions of the linear theory etc. The first publication was on the nature of the spectrum of high-frequency instability. More publications (2–4) followed on the nonlinear aspects of the cross-field instabilities.

Thus began the revival of experimental plasma physics in India. The Electrojet Instability experiment and later experiments broadened our understanding of the behaviour of different types of plasmas. Plasma theory came alive when we could experimentally realize the predictions made in theory. In comparing our experimental results with theoretical predictions, we learned what was needed to improve the theory. This was the best way to learn plasma physics.

References

[1] Abhijit Sen, Current Science, Vol. 118, №8, 25 April 2020

[2] P I John and Y C Saxena: Laboratory observations of Farley-Buneman instability: Proc. 12th Conference, Phenomena in lonized Gases, Eindhoven 1,302, 1975

[3] PI John and Y C Saxena: Observation of Farley-Buneman Instability in laboratory plasmas: Geophys. Res. Letters, 2,251, 1975.

[4] Y C Saxena and P I John, Dispersion, and spectral characteristics of cross-field instability in collisional magnetoplasmas: Pramana, 8,123, 1977.

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