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Non-neutral Plasmas

In the late eighties I got interested in the physics of dense clouds of electrons confined in electromagnetic traps. They exhibit collective effects like waves, instabilities and self-organization and hence are plasma like. They are called non-neutral plasmas because they are made of single charge species. John Malmberg and his co-workers in the University of California in San Diego had pioneered studies on the basic properties of linear columns of electron plasmas like equilibrium, instabilities, transport, vortex dynamics, relaxation to thermal equilibrium, cryogenic transition to Coulomb crystals etc.

We found that no work on the physics of ring shaped non-neutral plasma trapped in toroidal devices had been reported. A torus is a cylinder bent into the shape of a ring. If the radius of the cylinder and that of the ring become comparable, strong toroidal effects should occur. This was our speculation and being a virgin territory, we exploited this opportunity to do novel experiments. We built a device where a central conductor was inserted into a cylinder along its axis. Current carried by the central conductor created a ring like magnetic field. Electron injected into this and trapped exhibited collective properties. My student 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. Incidentally, this was 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 the work 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 in 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 which used time varying magnetic fields to transport particles and to form toroidal clouds, we were able to access the inward-shifted toroidal equilibria in steady state. 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 was a fundamental difference from the near-equilibrium placement in the Malmberg trap. 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. Some theoreticians believed that there would be no equilibrium. We, the experimentalists, believed otherwise.

Sambaran Pahari built this device. A single 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 placed 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. Thereafter, 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 have led to observation of several novel features of toroidal electron plasmas. In the limit of small aspect ratio these plasmas are seen to have intrinsic confinement properties and unique mode structure. 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. The confinement time, to the best of our knowledge, is the longest reported so far in the absence of any external electric field. In the limit of small aspect ratio, due to strong toroidicity, 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. The compressibility of fluid in the presence of strong inhomogeneous B brings is an entirely new perspective; all of this may bring in a paradigm shift in the investigations of toroidal electron plasmas. In particular, the amplitude saturation and frequency evolution warrants further understanding of the evolution of the vortex.

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

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