University of California, San Diego Institute of Pure and Applied Physical Sciences La Jolla, CA 92093

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2 University of California, San Diego Institute of Pure and Applied Physical Sciences La Jolla, CA Final Technical Report Transport in Non-Neutral Plasmas Supported by Office of Naval Research ONR N Principal Investigators: Prof. C.F. Driscoll Prof. T.M. O Neil Prof. D.H.E. Dubin Other Scientific Staff: Dr. F. Anderegg *Dr. A.C. Cass *Dr. J.R. Danielson Dr. K.S. Fine *Dr. T.J. Hilsabeck *Dr. E.M. Hollmann Dr. X.-P. Huang *Dr. D.-Z. Jin Dr. A.A. Kabantsev *Dr. J.M. Kriesel *Dr. S.G. Kuzmin *Dr. D.A. Schecter *Dr. N. Shiga *Dr. J.H. Yu Mr. E.M. Bass *Ph.D. completed during project.

3 1 Transport in Non-neutral Plasmas, ONR support has enabled a highly productive program of experiments and theory on transport, equilibration, and waves in single-species plasmas. These single species plasmas are unique in that they can relax to global thermal equilibrium while confined in a simple cylindrical trap. In practice, this means that incisive quantitative measurements can be made on a variety of fundamental plasma processes, for direct comparison to theory. Significantly, most anti-matter production techniques use similar single-species traps, and the ONR research has had direct and fundamental impact on this nascent field. Under ONR support, two sophisticated apparatuses were developed: the laser-diagnosed ion plasma apparatus, called IV, which allows quantitative measurement of test particle transport; and the camera-diagnosed electron apparatus, CamV, which gives high resolution images of 2D cross-field flows. Additionally, experiments were continued on the existing electron plasma containment apparatus EV. Theory work developed fundamental ideas of waves, transport, and equilibrium in these systems, and supported the experiments. In general, we have sought to obtain tests of plasma theory under the simplest possible circumstances we can devise; and, when the theory is inadequate, to develop it further. The wide range of parameters available in these systems has allowed us to understand which processes dominate in various parameter regimes, and to make connections to the unusual cryogenic regimes found in atomic physics and anti-matter experiments. This led to the entirely new paradigm of long-range collisional transport, which causes strong particle diffusion, heat flow, and viscous relaxation across the magnetic field; and this paradigm is closely coupled to the work on 2D vortex dynamics. Separately, experiments on asymmetryinduced transport have led to a broad perspective on trapped-particle modes and trapped-particlemediated transport. Perhaps most significantly, the entirely unanticipated rotating wall technique allows infinite-time confinement of particles, and has been adopted in labs worldwide. The scientific results are fully described in the 84 published journal articles and 10 Ph.D. theses. Much of this work was also partially supported by the NSF. Here we give a brief overview and reference to the papers, organized by major research topic, with the newer topics discussed first. Anti-Matter and Recombination. Antihydrogen formation in strongly magnetized plasmas is generally preceded by three-body recombination into weakly-bound guiding-center drift atoms, first described by Glinsky and O Neil [Phys. Plasmas 1991]. These weakly-bound states are well described by classical guiding-center drift theory, and represent a significant barrier on the path to the desired ground state antihydrogen. Recent analysis suggests that these weaklybound states offer explanation for the spectrum of binding energies observed in the ATRAP antihydrogen experiment [8]. Recent theory work analyzed plasma effects which drive the antihydrogen towards more deeply bound states [13], correcting some prior misconceptions.

4 2 Moreover, new theory on guiding center atoms has characterized the unusual energy levels to be expected, the cross-field motions which occur, and offers the exciting possibility of polarization trapping of the neutral atoms [10,11,12,93]. Further work on polarization effects may enable confinement of significant quantities of neutral atoms. The recent theory work also described important dynamical effects (including re-ionization) which occur when the guiding center atom moves across the magnetic field. Recent theory has also characterized the novel guiding center ion states which could not exist without the strong magnetic field [9]. For example, a second positron may bind weakly to deeply-bound neutral antihydrogen, and this suggests further diagnostic techniques for antihydrogen production. Recent theory has also characterized three possible minimum-b neutral atom traps which do not have the problematical large-scale magnetic field asymmetries of standard designs [1,3]. In two designs, the field minimum is cylindrically symmetric; in a third design the field asymmetry rotates, providing magnetic rotating wall confinement. These rotating magnetic fields are technically similar to those used in atomic physics and fusion applications, but significant development will be required before the traps are practical. Most recently, experiments have characterized the diocotron instabilities in electron plasmas which result from transiting positive ions [7]. The experimental results are entirely different from the previous ion resonance theory perspective, and the instability is more virulent. This suggests that control of these instabilities will be necessary for significant antihydrogen production by the usual technique of antiprotons transiting through positron plasmas. Recombination in ultracold plasmas with no magnetic field has also been analyzed, using a novel molecular-dynamics simulation [2,5,6,99]. Recent UCSD theory and simulations have established that strong particle correlations do not develop in experiments (in other laboratories) where ultracold neutral plasma clouds are produced by laser ionization. Contrary to earlier speculation, the initial particle interactions necessarily heat the electrons, keeping the temperature high enough that only modest particle correlations exist. The theory also establishes that the three-body recombination rate is in close agreement with the traditional formula, clarifying prior confusion due to incorrect temperature presumptions. Experimental Techniques. The UCSD-developed rotating wall technique for infinite-time containment of single species plasmas continues to find important applications in laboratories world-wide, with important applications in anti-matter production and containment. The technique was first developed for Mg + ions on the IV apparatus, then extended to electron plasmas on the IV and CamV apparatuses [14,17,18,19,20]. At low amplitudes, the rotating wall drive is observed to couple resonantly to discrete Trivelpiece-Gould plasma modes; but at larger amplitudes the coupling becomes broader and significantly modified by plasma heating. Nonetheless, it allows infinite-time confinement of charged particles over a wide parameter range.

5 3 This technique has been productively adopted by Cliff Surko and the ATHENA group at CERN for infinite-time confinement of positrons, with the goal of high densities and large total number. Obviously, the technique is especially useful in experiments with expensive antimatter particles such as antiprotons. The recent research on thermally excited modes [21,22,23,92] has both practical diagnostic applications and connections to fundamental theory. As a diagnostic, the passively received modes can characterize the plasma temperature, density and size, with demonstrated temperature operation down to well below the temperature of the electronic receiver. Again, this may be useful as a diagnostic for antimatter. From a basic physics perspective, these modes have now been characterized from thermal amplitudes to nonlinear amplitudes where BGK equilibria are observed [24,90]. Collisional Transport. The experiments and theory established a new paradigm for collisional cross-field transport: long-range E B drift collisions can dominate over classical velocityscattering collisions when r c << λ D. These collisions result in the radial diffusion of individual particles; in the radial conduction of heat; and in viscous forces which cause bulk particle transport towards the (confined) thermal equilibrium state. The experiments and theory have characterized these long-range collisions in both the 3D regime and the bounce-averaged 2D regime. The first IV experiments on test particle diffusion showed enhanced diffusion compared to classical theory, but at a rate 3 times larger than predicted by initial calculations of long-range collisions [28,29]. Deeper theory analysis found that the standard technique of integration along unperturbed orbits fails due to a novel (and subtle) velocity caging effect; and the more complete theory agrees quantitatively with the experiments [31]. The transport coefficients of heat and viscosity have also been integrated into this picture. Experiments on laser-diagnosed ion plasmas have accurately measured the heat transport due to long-range collisions, verifying the surprising theoretical prediction that the heat flow does not decrease as the magnetic field increases [30,88]. This result also applies to neutral plasmas in low-density, high field regimes found in tokamak scrape-off layers. Other experiments on electron plasmas measured viscous particle transport in the 2D and 3D regimes. Here, the measured viscosity was 10 to 10,000 larger than predicted for classical transport. These experiments demonstrate a simple scaling with the background flow shear which is not yet incorporated into current theories treating finite length plasma columns [41,87]. Other experiments measured the asymmetry-driven transport from compressional viscosity, which is also called second viscosity [25,27]. This compressional viscosity also gives rise to losses in toroidal systems [26]. The theory and experiments have elucidated the differences in transport between the fully 3D kinetic regime and the 2D bounce-averaged regime. Experiments clearly identified diffusion and viscosity increasing with the number N b of times a particle bounces axially before it is

6 4 separated from neighboring particles by radial shear in the rotation velocity. From the 2D perspective, this is called shear-reduction of transport [44]. A major theory effort has now fully described the diffusion of bounce-averaged rods of charge (i.e. point vortices) in the presence of background shear [35,42,43,45] in a thermodynamic system. This work extends the shear-free analysis of Taylor-McNamara and Dawson-Okuda, and is the only analytically rigorous treatment of shear-reduction of transport. The transport arises from thermally excited convective cells, which are non-diffusive and non-markovian, so the theory links transport concepts (like diffusion) to fluid concepts (like eddies). Trapped Particle Modes. In the area of external asymmetry-induced transport, recent experiments discovered a novel trapped-particle asymmetry mode, and the damping of this mode is found to be directly proportional to the observed plasma expansion. The experiments have fully characterized the damping of the mode versus all plasma parameters, and the (rather subtle) theory analysis shows fair (50%) agreement [46,47,51,52,91]. Experiments are able to directly probe the velocity-space trapping separatrix, providing detailed data to clarify the analysis [49]. Experiments have now also established that externally-applied asymmetries produce particle transport which is quantitatively proportional to the damping rate of the trapped-particle mode [48,50,53]. Essentially, collisional dissipation at the trapping separatrix causes both mode damping and particle transport. This may explain the ubiquitous background transport which is observed in many apparatuses, and is now being related to prior results on transport regimes depending on the plasma rigidity [37,41]. Establishing these transport regimes helps place prior experiments in perspective, and makes connections to the theoretical 2D bounce-averaged regime. These experiments pose direct challenges to the developing theory, suggesting that deep insights into particle transport may result. This work has stimulated wide interest in the trapping community, and wide-ranging theory simulation and experimental collaborations are envisioned. 2D Fluid Dynamics and Turbulence. At high magnetic fields, electron plasmas evolve as nearideal incompressible 2D Euler fluids, with effective Reynolds number of about Experiments discovered that novel vortex crystal equilibria can spontaneously emerge from turbulent initial conditions. Related experiments and theory clarified the nature of continuum modes and algebraic decay of perturbations on a single vortex. Experiments on 2D vortex surface waves have established that end shapes significantly affect the instability or damping of the waves, partially answering a ten-year-old enigma of unexpected instability. Theory work has elucidated these results through a powerful eigenmode analysis and a separate three-dimensional mode solution including realistic plasma shapes at low temperature [61,85,89]. Significant theory work has been motivated by the surprising experimental observation of vortex crystals [65,66,67,69,86]. The analysis has characterized the types of turbulence flows

7 5 which can relax to vortex crystals, by comparing the dynamical rate of vortex merger [54,55] to the as yet only partially understood rate of cooling due to vortex/background interactions [56,70]. Along similar lines, simulations have clearly established limits to global entropy and enstrophy theories by demonstrating the importance of initial conditions and dynamics [68,71]. Experiments on 2D vortex surface waves have now characterized the novel diocotron wave echo [63,64,94], establishing the non-dissipative nature of spatial Landau damping [58] and the close analogy between non-neutral plasmas and 2D fluids. Theoretical analysis closely coupled to experiments is now quantitatively determining the subtle effects of interparticle collisions in destroying the late-time behavior of the echo. Other experiments on the dynamics of strong electron vortices moving in a weaker background vorticity gradient have shown close agreement with prior UCSD simulations and analytic theory [57,59,60,62]. This work clarifies the important (but little discussed) distinction between prograde and retrograde vortices, due to the effectively infinite trapping distance for prograde vortices. This 2D inviscid fluids work is intimately connected to the long-range collisional transport research, and may help to clarify enigmas such as the anti-diffusive behavior observed in 2D plasmas. Correlated Ion Plasmas. The theory of crystalline states in cold ion plasmas and dusty plasmas continues in close collaboration with the experiments at NIST Boulder and at U. Iowa. Theory work on Mach cones in dusty plasma crystals established that the measured experimental characteristics can be used to diagnose the plasma parameters of screening length and dust grain charge [72,75,76,82]. This theory reinterprets the observed wakes as a superposition of linear dispersive waves in analogy with the wake behind ships, and in contrast to the shock wave behind supersonic jets. The theory of crystalline states in ultra-cold pure ion plasmas continues in close collaboration with the experiments at NIST Boulder [77-81]. The theory work done at UCSD enabled an investigation of the Mach cone wakes created by intense laser beam absorption in a rotating ion crystal. These NIST experiments have now extended to the drumhead modes of pancakeshaped ion crystals, the theory of which was also developed at UCSD. Another area of research is the experimental and theoretical investigation of stick-slip motion of the ion crystal when it is subjected to a weak external shearing force. Power-law behavior of the slip frequency vs. slip magnitude is observed, similar to that observed in systems exhibiting self-organized criticality. General Theory. A general thermodynamic theory of trapped non-neutral plasmas was formulated [83,84], describing plasmas that evolve slowly through a sequence of thermal equilibrium states. This greatly simplified description has already proven useful in describing asymmetry-induced torques and laser cooling.

8 6 Anti-Matter and Recombination PUBLICATIONS LIST, ONR N [available at 1. Daniel H.E. Dubin, Three Designs for a Magnetic Trap that will Simultaneously Confine Neutral Atoms and a Non-Neutral Plasma, Phys. Plasmas 8, (2001). 2. S. Kuzmin and T.M. O Neil, Numerical Simulation of Ultracold Plasmas, Non-Neutral Plasma Physics IV, (edited by F. Anderegg et al.), New York: American Institute of Physics (2002). 3. Dan Dubin, A Magnetic Trap For Simultaneous Confinement of Neutral Atoms and a Non-Neutral Plasma, Non-Neutral Plasma Physics IV, (edited by F. Anderegg et al.), New York: American Institute of Physics (2002). 4. S.J. Gilbert, Daniel H.E. Dubin, R.G. Greaves, and C.M. Surko, An electron-positron beam-plasma instability, Phys. Plasmas 8, (2001). 5. S.G. Kuzmin and T.M. O'Neil, Numerical Simulation of Ultracold Plasmas (How Rapid Intrinsic Heating Limits the Development of Correlation), Phys. Rev. Lett. 88, (2002). 6. S.G. Kuzmin and T.M. O'Neil, Numerical Simulation of Ultracold Plasmas, Phys. Plasmas 9, (2002). 7. A.A. Kabantsev and C.F. Driscoll, Diocotron Instabilities in an Electron Column Induced by a Small Fraction of Transient Positive Ions, Non-Neutral Plasma Physics V, (edited by M. Schauer, T. Mitchell and R. Nebel), New York: American Institute of Physics (2003). 8. C.F. Driscoll, Comment on Driven Production of Cold Antihydrogen and the First Measured Distribution of Antihydrogen States, Phys. Rev. Lett. 92, (2004). 9. D.H.E. Dubin, Electronic and Positronic Guiding Center Ions, Phys. Rev. Lett. 92, (2004). 10. S.G. Kuzmin and T.M. O'Neil, Polarization and Trapping of Weakly Bound Atoms in Penning Trap Fields, Phys. Rev. Lett. 92, (2004). 11. S.G. Kuzmin, T.M. O Neil and M.E. Glinsky, Guiding Center Drift Atoms, Phys. Plasmas 11, (2004). 12. S.G. Kuzmin and T.M. O'Neil, Motion of guiding center drift atoms in the electric and magnetic field of a Penning trap, submitted to Phys. Plasmas (2004). 13. Eric M. Bass and Daniel H.E. Dubin, Energy Loss Rate for Guiding Center Antihydrogen Atoms, Phys. Plasmas 11, (2004).

9 7 Invited Talks Daniel H.E. Dubin, Magnetic traps that can simultaneously confine neutral atoms and a nonneutral plasma in thermal equilibrium, Workshop on Cold Antimatter, Boston (2002). T.M. O Neil, Numerical Simulation of Ultracold Plasmas, Intl. Conf. on Strongly Coupled Coulomb Systems, Santa Fe (2002). S.G. Kuzmin and T.M. O Neil, Guiding Center Drift Atoms, Workshop on Non-Neutral Plasmas 2003, Santa Fe (2003). Thomas M. O Neil, Guiding Center Drift Atoms, APS Div. Plasma Physics Mtg., Albuquerque (2003). Bull. Am. Phys. Soc. 48, 244 (2003). Experimental Techniques 14. X.-P. Huang, F. Anderegg, E.M. Hollmann, C.F. Driscoll and T.M. O'Neil, Steady-State Confinement of Non-Neutral Plasmas by Rotating Electric Fields, Phys. Rev. Lett. 78, (1997). 15. J.M. Kriesel and C.F. Driscoll, Electron Plasma Profiles from a Cathode with an r 2 Potential Variation, Phys. Plasmas 5, (1998). 16. B.P. Cluggish, J.R. Danielson, and C.F. Driscoll, Resonant Particle Heating of an Electron Plasma by Oscillating Sheaths, Phys. Rev. Lett. 81, (1998). 17. F. Anderegg, E.M. Hollmann, and C.F. Driscoll, Steady-State Confinement of Non-Neutral Plasmas Using Trivelpiece-Gould Modes Excited by Rotating Wall, in Trapped Charged Particles and Fundamental Physics, (D.H.E. Dubin and D. Schneider, eds.), American Institute of Physics (1999). 18. F. Anderegg, E.M. Hollmann, and C.F. Driscoll, Rotating Field Confinement of Pure Electron Plasmas Using Trivelpiece-Gould Modes, Phys. Rev. Lett. 81, (1998). 19. F. Anderegg, E.M. Hollmann, and C.F. Driscoll, Steady-State Confinement of Non-neutral Plasmas Using Trivelpiece-Gould Modes Excited by a Rotating Wall, in Non-Neutral Plasma Physics III, pp (J.J. Bollinger, R.L. Spencer, and R.C. Davidson, eds.), New York: American Institute of Physics (1999). 20. E.M. Hollmann, F. Anderegg, and C.F. Driscoll, Confinement and Manipulation of Nonneutral Plasmas using Rotating Wall Electric Fields, Phys. Plasmas 7, (2000). 21. F. Anderegg, N. Shiga, J.R. Danielson, D.H.E. Dubin, C.F. Driscoll, and R.W. Gould, Thermal Excitation of Trivelpiece-Gould Modes in a Pure Electron Plasma, Non-Neutral Plasma Physics IV, (edited by F. Anderegg et al.), New York: American Institute of Physics (2002). 22. F. Anderegg, N. Shiga, D.H.E. Dubin and C.F. Driscoll, Thermally Excited Trivelpiece-Gould Modes as a Pure Electron Plasma Temperature Diagnostic, Phys. Plasmas 10, (2003).

10 8 23. F. Anderegg, N. Shiga, J.R. Danielson, D.H.E. Dubin, and C.F. Driscoll, Thermally Excited Modes in a Pure Electron Plasma, Phys. Rev. Lett. 90, (2003). 24. J.R. Danielson, F. Anderegg and C.F. Driscoll, Measurement of Landau Damping and the Evolution to a BGK Equilibrium, Phys. Rev. Lett. 92, :1-4 (2004). Invited Talks F. Anderegg, Steady-State Confinement of Non-Neutral Plasmas Using Trivelpiece-Gould Modes Excited by Rotating Wall, Conference on Trapped Charged Particles and Fundamental Physics, Monterey (1998). F. Anderegg, E.M. Hollmann, and C.F. Driscoll, Steady-State Confinement of Non-neutral Plasmas Using Trivelpiece-Gould Modes Excited by a Rotating Wall, Non-Neutral Plasma Physics Workshop, Princeton, New Jersey (1999). F. Anderegg, N. Shiga, J.R. Danielson, D.H.E. Dubin, C.F. Driscoll, and R.W. Gould, Thermal Excitation of Trivelpiece-Gould Modes in a Pure Electron Plasma, Non-Neutral Plasma Physics Workshop, San Diego (2001). Francois Anderegg, Observation of Thermally Excited Trivelpiece-Gould Modes in Trapped Pure Electron Plasmas, Bull. Am. Phys. Soc. 47, (2002). N. Shiga, F. Anderegg, and C.F. Driscoll, Observation of Resonant and Non-Resonant Thermal Fluctuations in Pure Electron Plasmas, Workshop on Non-Neutral Plasmas 2003, Santa Fe (2003). Collisional Transport 25. B.P. Cluggish and C.F. Driscoll, Transport and Sawtooth Oscillations from Rotational Pumping of a Magnetized Electron Plasma, Phys. Plasmas 3, (1996). 26. S. M. Crooks and T. M. O'Neil, Transport in a Toroidally Confined Pure Electron Plasma, Phys. Plasmas 3, 2533 (1996). 27. B.P. Cluggish, C.F. Driscoll, and K. Avinash, Sawtooth Oscillations in a Damped/driven Cryogenic Electron Plasma: Experiment and Theory, Phys. Plasmas 4, (1997). 28. F. Anderegg, X.-P. Huang, C.F. Driscoll, E.M. Hollmann, T.M. O'Neil, and D.H.E. Dubin, Test Particle Transport due to Long Range Interactions, Phys. Rev. Lett. 78, (1997). 29. F. Anderegg, X.-P. Huang, E.M. Hollmann, C.F. Driscoll, T.M. O'Neil, and D.H.E. Dubin, Test Particle Transport from Long Range Collisions, Phys. Plasmas 4, (1997). 30. D.H.E. Dubin and T.M. O'Neil, Cross-Magnetic Field Heat Conduction in Nonneutral Plasmas, Phys. Rev. Lett. 78, (1997). 31. D.H.E. Dubin, Test Particle Diffusion and the Failure of Integration along Unperturbed Orbits, Phys. Rev. Lett. 79, (1997).

11 9 32. D.H.E. Dubin, Two-Dimensional Bounce-Averaged Collisional Particle Transport in a Single- Species Non-Neutral Plasma, Phys. Plasmas 5, (1998). 33. D.H.E. Dubin, Collisional Transport in Nonneutral Plasmas, Phys. Plasmas 5, (1998). 34. E.M. Hollmann, F. Anderegg, and C.F. Driscoll, Measurement of Cross-Magnetic-Field Heat Transport in a Pure Ion Plasma, Phys. Rev. Lett. 82, (1999). 35. Daniel H.E. Dubin and D. Jin, 2D Collisional Diffusion of Rods in a Magnetized Plasma Column with Finite E x B Shear, in Non-Neutral Plasma Physics III, pp (J.J. Bollinger, R.L. Spencer, and R.C. Davidson, eds.), New York: American Institute of Physics (1999). 36. E.M. Hollmann, F. Anderegg, and C.F. Driscoll, Measurement of Cross-Magnetic-Field Heat Transport due to Long Range Collisions, in Non-Neutral Plasma Physics III, pp (J.J. Bollinger, R.L. Spencer, and R.C. Davidson, eds.), pp New York: American Institute of Physics (1999). 37. J.M. Kriesel and C.F. Driscoll, Two Experimental Regimes of Asymmetry-Induced Transport, in Non-Neutral Plasma Physics III, pp (J.J. Bollinger, R.L. Spencer, and R.C. Davidson, eds.), New York: American Institute of Physics (1999). 38. D.L. Eggleston and T.M. O'Neil, Theory of asymmetry-induced transport in a non-neutral plasma, Phys. Plasmas 6, (1999). 39. E.M. Hollmann, F. Anderegg, and C.F. Driscoll, Measurement of Cross-Magnetic-Field Heat Transport due to Long-Range Collisions, Phys. Plasmas 7, (2000). 40. J.M. Kriesel and C.F. Driscoll, Two Regimes of Asymmetry-Induced Transport in Non-neutral Plasmas, Phys. Rev. Lett. 85, (2000). 41. J.M. Kriesel and C.F. Driscoll, Measurements of Viscosity in Pure-Electron Plasmas, Phys. Rev. Lett. 87, (2001). 42. Daniel H.E. Dubin and Dezhe Z. Jin, Collisional Diffusion in a 2-Dimensional Point Vortex Gas, Phys. Letters A 284, (2001). 43. Dan Dubin, Shear Reduction of 2D Point Vortex Diffusion, Non-Neutral Plasma Physics IV, (edited by F. Anderegg et al.), New York: American Institute of Physics (2002). 44. C.F. Driscoll, F. Anderegg, D.H.E. Dubin, D.-Z. Jin, J.M. Kriesel, E.M. Hollmann, and T.M. O'Neil, Shear Reduction of Collisional Transport: Experiments and Theory, Phys. Plasmas 9, (2002). 45. Daniel H.E. Dubin, Collisional Diffusion in a 2-Dimensional Point Vortex Gas or a 2-Dimensional Plasma, Phys. Plasmas 10, (2003). Invited Talks F. Anderegg, Test Particle Transport due to Long Range Interactions, UC Berkeley (1996); UCLA (1997).

12 10 F. Anderegg, Test Particle Transport from Long-Range Collisions, Bull. Am. Phys. Soc. 41, 1477 (1996). D.H.E. Dubin, Collisional Transport in Nonneutral Plasmas, Conference on Strongly Coupled Coulomb Systems, Boston (1997). D.H.E. Dubin, Collisional Transport in Nonneutral Plasmas, Bull. Am. Phys. Soc. 42, 1876 (1997). Daniel H.E. Dubin, Collisional Transport in Nonneutral Plasmas, IAEA meeting, Japan (1998). Daniel H.E. Dubin, 2D Collisional Diffusion of Rods in a Magnetized Plasma Column with Finite E x B Shear, Non-Neutral Plasma Physics Workshop, Princeton, New Jersey (1999). E.M. Hollmann, Measurement of Cross-Magnetic-Field Heat Transport due to Long Range Collisions, Non-Neutral Plasma Physics Workshop, Princeton, New Jersey (1999). J.M. Kriesel, Two Experimental Regimes of Asymmetry-Induced Transport, Non-Neutral Plasma Physics Workshop, Princeton, New Jersey (1999). E.M. Hollmann, Heat Transport due to Long-Range Collisions, Bull. Am. Phys. Soc. 44, 290 (1999). Dan Dubin, Shear Reduction of 2D Vortex Diffusion: Theory, Simulation and Experiments, Non- Neutral Plasma Physics Workshop, San Diego (2001). C. Fred Driscoll, Shear-Limited Diffusion and Viscosity: Experiments and Theory, Bull. Am. Phys. Soc. 46, 22 (2001). Dan Dubin, Cross-Magnetic Field Transport: Theory and Experiments with Nonneutral Plasmas, ICPP meeting, Sydney, Australia (2002). C.F. Driscoll, Cross-Magnetic Field Transport due to Long-Range Collisions, for Intl. Symposium: Plasmas in the Laboratory and in the University, Como, Italy (2003). C.F. Driscoll, "Shear Reduction of Collisional Diffusion: Experiments and Theory," Workshop on Self- Organization and Structures in Plasmas, UCSD (2003). T.M. O Neil, Collisional Transport in Plasmas with Small Cyclotron Radius Theory and Experiment, 13 th Intl. Toki Conf. on Plasma Physics, Nagoya, Japan (2003). Trapped Particle Modes 46. A.A. Kabantsev, C.F. Driscoll, T.J. Hilsabeck, T.M. O'Neil, and J.H. Yu, Trapped-Particle Asymmetry Modes in Single Species Plasmas, Phys. Rev. Lett. 87, (2001). [Erratum (2002)]. 47. A.A. Kabantsev, C.F. Driscoll, T.J. Hilsabeck, T.M. O'Neil, and J.H. Yu, Trapped Particle Asymmetry Modes in Non-Neutral Plasmas, Non-Neutral Plasma Physics IV, (edited by F. Anderegg et al.), New York: American Institute of Physics (2002).

13 A.A. Kabantsev and C.F. Driscoll, Trapped-Particle Modes and Asymmetry-Induced Transport in Single-Species Plasmas, Phys. Rev. Lett. 89, (2002). 49. Andrey A. Kabantsev and C. Fred Driscoll, Diagnosing the Velocity-Space Separatrix of Trapped Particle Modes, Rev. Sci. Instrum. 74, (2003). 50. A.A. Kabantsev, J.H. Yu, R. Lynch, and C.F. Driscoll, Trapped Particles and Asymmetry-Induced Transport, Phys. Plasmas 10, (2003). 51. T.J. Hilsabeck, A.A. Kabantsev, C.F. Driscoll, and T.M. O'Neil, Damping of the Trapped-Particle Diocotron Mode, Phys. Rev. Lett. 90, (2003). 52. T.J. Hilsabeck and T.M. O Neil, Trapped-Particle Diocotron Modes, Phys. Plasmas 10, 3402 (2003). 53. C.F. Driscoll, A.A. Kabantsev, T.J. Hilsabeck and T.M. O Neil, Trapped-Particle-Mediated Damping and Transport, Non-Neutral Plasma Physics V, 3-14 (edited by M. Schauer, T. Mitchell and R. Nebel), New York: American Institute of Physics (2003). Invited Talks A.A. Kabantsev, C.F. Driscoll, T.J. Hilsabeck, T.M. O'Neil, and J.H. Yu, Trapped Particle Asymmetry Modes in Non-Neutral Plasmas, Non-Neutral Plasma Physics Workshop, San Diego (2001). T.M. O'Neil, Trapped Particle Mode in a Nonneutral Plasma Column, ICPP meeting, Sydney, Australia (2002). Andrey A. Kabantsev, Diagnosing the Velocity-Space Separatrix of Trapped Particle Modes, 14th Topical Conference on High Temperature Plasma Diagnostic, Madison, Wisconsin (2002). Andrey A. Kabantsev, Trapped-Particle Modes and Asymmetry-Induced Transport, Bull. Am. Phys. Soc. 47, 250 (2002). C. Fred Driscoll and Andrey A. Kabantsev, Trapped Particle Effects: Results, Implications, Open Questions, Workshop on Non-Neutral Plasmas, Santa Fe (2003). 2D Fluid Dynamics 54. T.B. Mitchell and C.F. Driscoll, Electron Vortex Orbits and Merger, Phys. Fluids 8, (1996). 55. I.M. Lansky, T.M. O'Neil, and D.A. Schecter, A Theory of Vortex Merger, Phys. Rev. Lett. 79, (1997). 56. D.A. Schecter, D.H.E. Dubin, K.S. Fine, and C.F. Driscoll, Vortex Crystals from 2D Euler Flow: Experiment and Simulation, Phys. Fluids 11, (1999). 57. D.A. Schecter and Daniel H.E. Dubin, Vortex motion driven by a background vorticity gradient, Phys. Rev. Lett. 83, (1999).

14 D.A. Schecter, D.H.E. Dubin, A.C. Cass, C.F. Driscoll, I.M. Lansky, and T.M. O'Neil, Inviscid Damping of Asymmetries on a Two-dimensional Vortex. Phys. Fluids 12, (2000). 59. D.A. Schecter and D.H.E. Dubin, Theory and simulations of 2D vortex motion driven by a background vorticity gradient, Phys. Fluids 13, (2001). 60. Dezhe Z. Jin and Daniel H.E. Dubin, Point Vortex Dynamics within a Background Vorticity Patch, Phys. Fluids 13, (2001). 61. T.J. Hilsabeck and T.M. O'Neil, Finite Length Diocotron Modes, Phys. Plasmas 8, (2001). 62. Andrey A. Kabantsev and C. Fred Driscoll, Generation and Instability of Spiral Wakes in Sheared Electron Flows, IEEE Trans. on Plasma Science 30, (2002). 63. Jonathan H. Yu and C.F. Driscoll, Diocotron Wave Echoes in a Pure Electron Plasma, IEEE Trans. On Plasma Science 30, (2002). 64. J.H. Yu and C.F. Driscoll, Experimental Observation of Fluid Echoes in a Non-Neutral Plasma, Non- Neutral Plasma Physics IV, (edited by F. Anderegg et al.), New York: American Institute of Physics (2002). 65. C.F. Driscoll, D.Z. Jin, D.A. Schecter, and D.H.E. Dubin, Vortex Dynamics of 2D Electron Plasmas. Physica C 369, (2002). 66. C.F. Driscoll, D.A. Schecter, D.Z. Jin, D.H.E. Dubin, K.S. Fine, and A.C. Cass, Relaxation of 2D Turbulence to Vortex Crystals, in Statistical Physics: Invited Papers from STATPHYS 20, pp (A. Gervois et al., editors), North-Holland (1999). Reprinted from Physica A 263, (1999). 67. C.F. Driscoll, D.Z. Jin, D.A. Schecter, E.J. Moreau and D.H.E. Dubin, Dynamics, Statistics and Vortex Crystals in the Relaxation of 2D Turbulence, in Proceedings of the 5th Experimental Chaos Conference, pp (M. Ding, W. Ditto, L.M. Pecora and M.L. Spano, editors), Singapore: World Scientific (2001). 68. D.Z. Jin and D.H.E. Dubin, Characteristics of 2D Turbulence that Self-Organizes into Vortex Crystals, in Non-Neutral Plasma Physics III, pp (J.J. Bollinger, R.L. Spencer, and R.C. Davidson, eds.), New York: American Institute of Physics (1999). 69. C.F. Driscoll, D.Z. Jin, D.A. Schecter, E.J. Moreau and D.H.E. Dubin, Dynamics, Statistics and Vortex Crystals in the Relaxation of 2D Turbulence, Physica Scripta T84, (2000). 70. Dezhe Z. Jin and Daniel H.E. Dubin, Theory of Vortex Crystal Formation in Two-dimensional Turbulence, Phys. Plasmas 7, (2000). 71. Dezhe Z. Jin and Daniel H.E. Dubin, Characteristics of Two-Dimensional Turbulence that Self- Organizes into Vortex Crystals, Phys. Rev. Lett. 84, (2000). Invited Talks T.M. O'Neil, Recent Theory and Experiment for Plasmas with a Single Sign of Charge (From Coulomb Crystals to 2D Turbulence and Vortex Crystals), Bull. Am. Phys. Soc. 42, 899 (1997).

15 13 K.S. Fine, Observations of Vortex Crystals in 2D Turbulence, Conf. on Strongly Coupled Coulomb Systems, Boston (1997). C.F. Driscoll, Electron Plasmas as 2D Fluids, CECAM Workshop on Nonlinear Processes in Nonlinear Plasmas and in Fluids, Lyon (1998). C.F. Driscoll, Observation of Vortex Crystals in Freely Relaxing 2D Turbulence, Bull. Am. Phys. Soc. 43, 64 (1998). T.M. O'Neil, Recent Theory and Experiment for Plasmas with a Single Sign of Charge (From Coulomb Crystals to 2D Turbulence and Vortex Crystals), ITC-9 Conference, Toki City, Japan (1998). C.F. Driscoll, Relaxation of 2D Turbulence to Vortex Crystals, 20th IUPAP Intl. Conf. on Statistical Physics STATPHYS 20, Paris (1998). C.F. Driscoll, Relaxation of 2D Turbulence to Vortex Crystals, Bull. Am. Phys. Soc. 44, 644 (1999). C.F. Driscoll, Dynamics, Statistics and Vortex Crystals in the Relaxation of 2D Turbulence, 5th Experimental Chaos Conference, Orlando, Florida (1999). D.Z. Jin, Characteristics of 2D Turbulence that Self-Organizes into Vortex Crystals, Non-Neutral Plasma Physics Workshop, Princeton, New Jersey (1999). D.Z. Jin, Theory of Vortex Crystal Formation in Two-Dimensional Turbulence, Bull. Am. Phys. Soc. 44, (1999). C.F. Driscoll, Relaxation of 2D Turbulence to Vortex Crystals, Intl. Topical Conference on Plasma Physics: New Frontiers of Nonlinear Sciences, Faro, Portugal (1999). David A. Schecter, Gradient-Driven Vortex Motion in Nonneutral Plasmas and Ideal 2D Fluids, Bull. Am. Phys. Soc. 45, 215 (2000). T.M. O'Neil, Recent Theory and Experiment for Plasmas with a Single Sign of Charge (From Coulomb Crystals to 2D Turbulence and Vortex Crystals), Danish Physical Society meeting, Nyborg, Denmark (2000). C.F. Driscoll, Vortex Dynamics of 2D Electron Plasmas, 2nd European Conference on Vortex Matters in Superconductors, Crete (2001). Daniel H.E. Dubin, Vortex Dynamics in 2-D Fluid Turbulence: Theory and Experiments Using Non- Neutral Plasmas, Bull. Am. Phys. Soc. 46, 134 (2001). J.H. Yu and C.F. Driscoll, Experiments with Fluid Echoes in a Non-Neutral Plasma, Workshop on Non-Neutral Plasmas 2003, Santa Fe (2003). Correlated Ion Plasmas 72. D.H.E. Dubin, Nonlinear Debye Shielding of a Dusty Plasma, Proc. of the 6th Workshop on the Physics of Dusty Plasmas,15-21 (P.K. Shukla, D.A. Mendis, and V.W. Chow, editors), Singapore: World Scientific (1996).

16 D.H.E. Dubin, Minimum Energy State of the 1-D Coulomb Chain, Phys. Rev. E 55, (1997). 74. T.B. Mitchell, J.J. Bollinger, X.-P. Huang, W.M. Itano, and D.H.E. Dubin, Direct Observations of the Structural Phases of Crystallized Ion Plasmas, Phys. Plasmas 6, (1999). 75. Daniel H.E. Dubin, The Phonon Wake Behind a Charge Moving Relative to a Two-Dimensional Plasma Crystal, Phys. Plasmas 7, (2000). 76. Daniel H.E. Dubin, The Phonon Wake Behind a Charge Moving Relative to a 2D Plasma Crystal, Physica Scripta T89, (2001). 77. T.B. Mitchell, J.J. Bollinger, W.M. Itano, and D.H.E. Dubin, Stick-Slip Dynamics of a Stressed Ion Crystal, Phys. Rev. Lett. 87, (2001). 78. T.B. Mitchell, J.J. Bollinger, W.M. Itano, J.M. Kriesel, and D.H.E. Dubin, Doppler Velocimetry of Cryogenic Ion Plasmas, IEEE Trans. on Plasma Science 30, (2002). 79. J.M. Kriesel, J.J. Bollinger, T.B. Mitchell, L.B. King and D.H.E. Dubin, Laser-Induced Wakes in Ion Crystals, Non-Neutral Plasma Physics IV, (edited by F. Anderegg et al.), New York: American Institute of Physics (2002). 80. J.M. Kriesel, J.J. Bollinger, T.B. Mitchell, L.B. King and D.H.E. Dubin, Laser-generated waves and wakes in rotating ion crystals, Phys. Rev. Lett. 88, (2002). 81. J.J. Bollinger, J.M. Kriesel, T.B. Mitchell, L.B. King, M.J. Jensen, W.M. Itano and D.H.E. Dubin, Laser-cooled ion plasmas in Penning traps, J. Phys. B: At. Mol. Opt. Phys. 36, (2003). 82. V. Nosenko, J. Goree, Z.W. Ma (U. Iowa), D.H.E. Dubin (UCSD), and A. Piel (Christian-Albrechts Univ.), Compressional and Shear Wakes in a Two-Dimensional Dusty Plasma Crystal, Phys. Rev. E 68, : 1-15 (2003). Invited Talks D.H.E. Dubin, Nonlinear Debye Shielding of a Dusty Plasma, 6th Workshop on the Physics of Dusty Plasmas (1996). D.H.E. Dubin, Density Functional Theory for 1-D Coulomb Chains, Intl. Workshop on Advances in Strongly Correlated Plasmas, Trento, Italy (1997). D.H.E. Dubin, Simulations of Coulomb Crystals and Vortex Crystals in Nonneutral Plasmas, Bull. Am. Phys. Soc. 42, 1065 (1997). Daniel H.E. Dubin, Mach Cones in a 2D Dusty Plasma Crystal: Shock Wave or Wake?, Bull. Am. Phys. Soc. 45, 215 (2000).

17 15 General Theory 83. T.M. O'Neil and D.H.E. Dubin, Thermal Equilibria and Thermodynamics of Trapped Plasmas with a Single Sign of Charge, Phys. Plasmas 5, (1998). 84. D.H.E. Dubin and T.M. O'Neil, Trapped Nonneutral Plasmas, Liquids, and Crystals (The Thermal Equilibrium States), Rev. Mod. Phys. 71, (1999). Invited Talks T.M. O'Neil, Thermal Equilibria and Thermodynamics of Trapped Nonneutral Plasmas, Bull. Am. Phys. Soc. 41, 1529 (1996). T.M. O'Neil and D.H.E. Dubin, Thermodynamics of Trapped Nonneutral Plasmas, Conference on Trapped Charged Particles and Fundamental Physics, Monterey (1998). T.M. O'Neil and D.H.E. Dubin, Thermodynamics of Trapped Nonneutral Plasmas, CECAM Workshop on Nonlinear Processes in Nonlinear Plasmas and in Fluids, Lyon (1998). T.M. O'Neil, The Wave-Particle Interaction in Plasmas (A Half Century Retrospective), Bull. Am. Phys. Soc. 44, 1402 (1999). Dan Dubin, Basic Plasma Physics with Trapped Nonneutral Plasmas, MIT Dept. of Physics, Boston, Massachusetts (2002). D.H.E. Dubin, Basic Plasma Physics with Trapped Nonneutral Plasmas, at 50th Anniversary Celebration, Princeton (2002). Theses 85. A.C. Cass, Experiments on Vortex Symmetrization in Magnetized Electron Columns, Ph.D. dissertation (1998). 86. Dezhe Jin, Theory of Vortex Crystal Formation in Two-Dimensional Turbulence, Ph.D. dissertation (1999). 87. Jason Kriesel, Experiments on Viscous and Asymmetry-Induced Transport in Magnetized, Pure Electron Plasmas, Ph.D. dissertation (1999). 88. Eric Hollmann, Experimental Studies of Cross-Magnetic-Field Transport in Nonneutral Plasmas, Ph.D. dissertation (1999). 89. D.A. Schecter, On the Dynamics of Inviscid Relaxation in 2D Fluids and Nonneutral Plasmas, Ph.D. dissertation (1999). 90. James R. Danielson, Measurement of Landau Damping of Electron Plasma Waves in the Linear and Trapping Regimes, PhD dissertation (April 2002). 91. Terance Joseph Hilsabeck, Finite Length and Trapped-Particle Diocotron Modes, Ph.D. dissertation (2003).

18 Nobuyasu Shiga, Experimental Studies of Thermal Fluctuations in Electron Plasmas, Ph.D. dissertation (2004). 93. Stanislav G. Kuzmin, Ultracold Plasmas and Guiding Center Drift Atoms, Ph.D. Dissertation (2004). 94. Jonathan H. Yu, The Diocotron Echo and Trapped-Particle Diocotron Mode in Pure Electron Plasmas, Ph.D. Dissertation (2004).