[en] Final report for the Columbia Non-neutral Torus. This details the results from the design, construction and initial operation of the Columbia Non-neutral Torus. During the duration of this grant, I designed, built, and operated the Columbia Nonneutral Torus, the world's lowest aspect ratio stellarator, and arguably, the world's simplest stellarator. This demonstrates the ease and robustness of the chosen stellarator design and allowed us to commence the investigation of the physics of non-neutral plasmas confined on magnetic surfaces. These plasmas are unique in many ways and had not previously been studied in a stellarator. Our first results showed that it is possible to confine and study a relatively cold pure electron plasma in a stellarator. We confirmed that the plasma is stable, and that the plasma is reasonably well confined in a stellarator configuration. These results were published in Physics of Plasmas (2006) and Physical Review Letters (2006). They enabled the existing program which is resolving the underlying transport processes in a classical stellarator with intense self-electric fields and enable the next phase of operation, electron-positron plasma physics. During the period of this grant, two students were trained in experimental plasma physics and both received their PhD degrees shortly after the grant terminated. One student is now employed in the financial services industry, the other is a postdoctoral associate at Los Alamos National Laboratory. The chief goals were to build and begin operation of the Columbia Non-neutral Torus. These goals were achieved in the third year of funding. The development of diagnostic methods and the confirmation of stable equilibria were also achieved during the grant period. In summary, the main scientific goals were all met. The main educational goals were also met, as the experiment became the training ground not only for the two aforementioned graduate students but also for a number of undergraduate students. Several of these have gone on to graduate school, some in plasma physics, others in related areas. We have had significant outreach activity, including visits to nearby elementary schools (PS 163 in Manhattan), and high school students and high school teachers volunteering in the laboratory.

[en] The physics of non-neutral plasmas confined on magnetic surfaces is discussed. The Columbia Non-neutral Torus (CNT), a table-top ultrahigh vacuum stellarator being constructed at Columbia University, is being built to systematically study non-neutral plasmas confined on magnetic surfaces. The experimental design is discussed in the context of relevant physics parameters, such as the number of Debye lengths in the device, and the parallel versus perpendicular time scales

[en] Two-dimensional solutions to the equilibrium equation for finite temperature, low density pure electron plasmas confined on magnetic surfaces [T. S. Pedersen and A. H. Boozer, Phys. Rev. Lett. 88, 205002 (2002)] are presented for the first time. These equilibria are not maximum energy states, in contrast to Penning trap equilibria [J. Notte et al., Phys. Rev. Lett. 69, 3056 (1992)]. By varying the number of Debye lengths in the plasma, a/λ_D, from 0.1 to 10, we explore both relatively warm and relatively cold plasma equilibria. The effects of different boundary conditions and the implications for collisional transport rates are discussed

[en] Measurements of the equilibria of plasmas created by emission from a biased filament located off the magnetic axis in the Columbia Non-neutral Torus (CNT) [T. S. Pedersen, J. P. Kremer, R. G. Lefrancois et al., Fusion Sci. Technol. 50, 372 (2006)] show that such plasmas have equilibrium properties consistent with the inner surfaces being in a state of cross-surface thermal equilibrium. Numerical solutions to the equilibrium equation were used to fit the experimental data and demonstrate consistency with cross-surface thermal equilibrium. Previous experiments in CNT showed that constant temperatures across magnetic surfaces are characteristic of CNT plasmas, implying thermal confinement times much less than particle confinement times. These results show that when emitting off axis there is a volume of inner surfaces where diffusion into that region is balanced by outward transport, producing a Boltzmann distribution of electrons. When combined with the low thermal energy confinement time this is a cross-surface thermal equilibrium.

[en] Cold pure electron plasmas confined in Penning-Malmberg traps with mirror fields are known to exhibit density variations along field lines, such that the density is roughly proportional to the magnetic field strength, n∼B. The Columbia Nonneutral Torus (CNT) is the first stellarator designed to study pure electron plasmas, and exhibits substantial mirroring, with B_max≅1.8B_min. However, results of a three-dimensional equilibrium solver, presented in this Letter, predict a factor of 5.3 increase in density from the minimum-field cross section to the maximum-field cross section along the magnetic axis, for a 1.5 cm Debye length plasma (a≅15 cm for CNT). In this Letter, it is shown that the density variation of electron plasmas in mirror traps can be significantly enhanced in a device that has a cross section that varies from cylinder-like to slab-like, such as the CNT. A simple analytic expression is derived that describes the axial density variation in such a device, and it is found to agree well with the computational predictions for CNT

[en] The confinement of a nonneutral plasma in a magnetic-surface, or stellarator, configuration is explored. The fluid equilibrium equations are derived and are found to be fundamentally different from previous results. Diocotron modes are predicted to be stable. The collisional confinement time can be very long. Possible applications include positron trapping and confinement of positron-electron plasmas. The basic physics can be addressed experimentally in the simple tabletop stellarator planned for construction at Columbia University

[en] A retractable electron emitter has been constructed for the creation of unperturbed pure electron plasmas on magnetic surfaces in the Columbia Non-neutral Torus stellarator. The previous method of electron emission using emitters mounted on stationary rods limited the confinement time to 20 ms. A pneumatically driven system that can retract from the magnetic axis to the last closed flux surface in less than 20 ms while filling the surfaces with electrons was designed. The motion of the retractable emitter was modeled with a system of dynamical equations. The measured position versus time of the emitter agrees well with the model and the fastest axis-to-edge retraction was measured to be 20 ms with 40 psig helium gas driving the pneumatic piston

[en] Significant variations in the density and potential along the axis of a pure electron plasma in the Columbia Non-neutral Torus (CNT) stellarator have now been measured. Large variations along the magnetic field are predicted by three-dimensional equilibrium reconstructions of CNT plasmas and by simple electrostatic and geometric arguments [Lefrancois and Pedersen, Phys. Plasmas 13, 120702 (2006)]. The density variation, n_{axis,φ=0deg.}/n_{axis,φ=90deg.}, is measured directly for several different plasma equilibria, and has a median value of 7.8, consistent with the predicted density variation of 4.4, because the error bars are large. The associated variation in potential predicted from the Boltzmann relation, eΔΦ/T_e=ln(4.4)=1.5, was also measured experimentally. The median measured, eΔΦ/T_e, was 1.1, which is of the predicted sign and in rough agreement with the measurements, but smaller than predicted. The difference is statistically significant, but might be related to the imperfect numerical modeling of the complicated electrostatic boundary conditions in CNT. The measured variations reconfirm that the Debye lengths of these plasmas are small

[en] The equilibrium, stability, and transport of pure electron plasmas confined on magnetic surfaces is reviewed. The prospects for creation of partly neutralized plasmas and electron-positron plasmas confined in a stellarator are discussed. The Columbia Non-neutral Torus, a small ultrahigh vacuum stellarator being constructed at Columbia University, is being built to systematically study non-neutral plasmas confined on magnetic surfaces. The experimental design is discussed in the context of relevant physics parameters, and the initial experimental plans for creation and diagnosis of pure electron plasmas are discussed

[en] Accumulation of ions can alter and may destabilize the equilibrium of an electron plasma confined on magnetic surfaces. An analysis of ion sources and ion content in the Columbia Non-neutral Torus (CNT) [T.S. Pedersen, J.P. Kremer, R.G. Lefrancois, Q. Marksteiner, N. Pomphrey, W. Reiersen, F. Dahlgreen, and X. Sarasola, Fusion Sci. Technol. 50, 372 (2006)] is presented. In CNT ions are created preferentially at locations of high electron temperature, near the outer magnetic surfaces. A volumetric integral of n_eν_iz gives an ion creation rate of 2.8x10¹¹ ions/s. This rate of accumulation would cause neutralization of a plasma with 10¹¹ electrons in about half a second. This is not observed experimentally, however, because currently in CNT ions are lost through recombination on insulated rods. From a steady-state balance between the calculated ion creation and loss rates, the equilibrium ion density in a 2x10^-8 Torr neutral pressure, 7.5x10¹¹ m^-3 electron density plasma in CNT is calculated to be n_i=6.2x10⁹ m^-3, or 0.8%. The ion density is experimentally measured through the measurement of the ion saturation current on a large area probe to be about 6.0x10⁹ m^-3 for these plasmas, which is in good agreement with the predicted value