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Experiments with Electron Plasmas

In the late eighties, while struggling with erecting and commissioning ADITYA, India’s first tokamak, I found relaxation in thinking about the behaviour of dense clouds of electrons confined in electromagnetic traps. They exhibit collective effects like waves, instabilities and self-organization and are plasma-like. John Malmberg and his co-workers at the University of California in San Diego pioneered studies on the fundamental properties of linear columns of electron plasmas like equilibrium, instabilities, transport, vortex dynamics, relaxation to thermal equilibrium, cryogenic transition to Coulomb crystals etc. I found their work fascinating, in the simplicity of the experimental device and the elegence of the experiments.

We found no reported work on the physics of non-neutral plasma rings trapped in toroidal devices. A torus is a cylinder bent into the shape of a hollow ring. We speculated that strong toroidal effects should occur if the radius of the cylinder and the ring become comparable. This appeared to be a virgin territory, with opportunity to do novel experiments. We built a device with a central conductor inserted into a cylinder along its axis. The current carried by the central conductor created a ring-like magnetic field. Electrons were injected into into this by rapidly raising the toroidal magnetic field. The trapped electron cloud exhibited collective properties. Purvi Zaveri presented the first results on the formation and existence of equilibrium of a very low aspect ratio non-neutral plasma ring in the International Conference in Plasma Physics held in Delhi in 1989.

The first paper on the equilibrium features came out in the prestigious Physical Review Letters in 1992, the first paper in experimental plasma physics from India to appear in that journal. Interesting complementarity between charged non-neutral plasmas and current-carrying neutral plasmas, like the capacitive effects replacing inductive effects etc., are discussed in the paper.

I remember two incidents connected with talks I gave on non-neutral plasmas. The first one happened in Indore when I gave a talk at the Annual Conference of the Plasma Science Society of India in the Centre for Advanced Technology in Indore in 1991. The Hindi newspapers from Indore promptly reported that “Scientists had discovered unnatural plasma”. The other incident relates to an invited talk I presented at the 1992 International Conference in Plasma Physics in Innsbruck. Among the audience was Prof. John Malmberg, the pioneer of non-neutral plasma research, who complimented me on the novelty of our approach.

In Sameer Khirwadkar’s work, we invented a method of plasma formation based on the modification of the vertical drifts into closed diocotron drift trajectories by combining the self-consistent space-charge electric field with an externally applied radial electric field. Unlike earlier experiments that used time-varying magnetic fields to transport particles and form toroidal clouds, we could access the inward-shifted toroidal equilibria in steady state. Furthermore, finite resistivity of the wall may also play a role in the formation of the cloud through this mechanism which is essentially the capacitive analogue of the trapping of current-carrying electron beams in toroidal cavities due to magnetic energy loss. These results also appeared in a paper in the Physical Review Letters in 1993.

The turbulent birth of toroidal non-neutral plasmas by cross-field transport in a rising magnetic field was a fundamental difference from the near-equilibrium placement in the Malmberg trap. This method also limited the number of electrons injected into the trap. Therefore, we speculated that the plasma formed by injection parallel to the magnetic field would be more quiescent. However, to do this in a torus, the filaments would have to be placed inside the drift space; the torus would no longer be closed. As a result, some theoreticians believed that there would be no equilibrium. We, the experimentalists, thought otherwise.

Sambaran Pahari built this device. A circular tungsten filament loop placed on a poloidal cross-section emits thermionic electrons when heated. A negatively biased grid placed in front of the filament is pulsed positive to extract electrons parallel to the minor axis. Another grid collector set behind the filament in the poloidal cross-section is biased negative. As the toroidal magnetic field, established by pulsing a current through a multi-turn coil, reaches its flat top, the injector grid is pulsed positive with respect to filament to extract electrons along the field lines. After that, the grid reverts to negative bias, stopping further fuelling. The injected electrons are now trapped toroidally between the negatively biased injector grid and collector grid.

Experiments in SMARTEX-C (Small Aspect Ratio Toroidal EXperiment-C shaped) have led to observing several novel features of toroidal electron plasmas. These plasmas have intrinsic confinement properties and unique mode structures in the limit of a small aspect ratio. The experiments and their interpretation by Sambaran and Hari Ramachandran demonstrate that rotational transform due to self-electric fields and a purely toroidal magnetic field can lead to significant confinement in toroidal geometries. To the best of our knowledge, the confinement time is the longest reported so far in the absence of an external electric field. In the limit of small aspect ratio, due to strong toroidicity, the self-consistent electric field induced on the inner wall is sufficiently strong to make any external force field redundant.

SMARTEX-C has brought to the forefront several novel properties and, with it, the urgent need to further address these issues with new experiments and theory (1). The compressibility of fluid in the presence of strong inhomogeneous magnetic field brings is an entirely new perspective. All of this may bring a paradigm shift in the investigations of toroidal electron plasmas. In particular, the amplitude saturation and frequency evolution warrant a further understanding of the evolution of the vortex. Efforts to confine toroidal electron plasmas have stood the test of time and made significant strides in the last decade. With the recent results on confinement, the traditional transport theories have been put to the test.

Interestingly, the confinement time is independent of magnetic field strength suggesting that transport occurring could be due to magnetic pumping. But the confinement time scales far exceed that suggested by the transport theory for a typically 1–10 eV plasma even after accounting for the low aspect ratio of the trap. These confinement times are the longest reported and have breached the previous record by orders of magnitude. The device is being presently upgraded with a 500 sec steady state magnetic field, and additional getter pumps to consolidate the results. Additional diagnostics for temperature measurement are being developed.

Interestingly, a series of large aspect ratio toroidal traps have also emerged in the last decade. A similar trap that strives to confine the plasmas on open field lines have succeeded up to 1 second, close to theoretical limit set by the transport theory. A stellarator has succeeded in holding the plasma for 100 ms on nested flux surfaces, while one that employs dipole fields has achieved more than 100 sec. Much of the recent motivation and interest in toroidal traps seem to follow from the possibility of creating electron-positron pair plasmas [2] due to the expected lack of instabilities in such plasmas and because of their relevance to astrophysical objects. Amidst all this SMARTEX-C has a unique role to play as the assumed incompressible nature of the fluid is expected to break down in the presence of strong toroidicity. With recent advancements and promising results, it remains to be seen if thermal equilibrium can also be achieved in toroidal traps as in cylindrical geometries.

Non-neutral plasma experiments were conceptually simple but required high technological skills and support to make them work. The persistent commitment over the years and exceptional skill shown by Purvi Zaveri, Sameer Khirwadkar, Sambaran Pahari, and Lavkech Lachwani contributed much to the success of the experiments. In addition, the perceptive understanding of the electron cloud dynamics developed by Predhiman Kaw, Avinash Khare, Hari Ramachandran and Ganesh based on their deep knowledge of plasma physics played a crucial role in creating a coherent account of the physics of non-neutral electron clouds trapped in toroidal traps. Studies of toroidal non-neutral plasmas continue at IPR.

(1) Sambaran Pahari, Prof John@80, Unpublished Report (2) H. Saitoh, et al. J. Phys. Conf. Ser. 505, 012045 2014.

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