Session NI2: MHD, Strongly Coupled and Low Temperature Plasmas

Ion Heating During Reconnection in the Madison Symmetric Torus

New spatially and temporally resolved measurements of ion temperature in MST provide new insight into the long observed ion heating associated with reconnection, and strong constraints on possible theories for the heating. Ion heating in MST is a strong effect, with a transient heating power of up to 50 MW during large reconnection events, resulting in ion temperatures $>$ 2 keV in high current plasmas. Recently, such ion heating has been used to good effect: to produce high ion temperatures that are then sustained during plasma periods with improved confinement. The heating power during a reconnection event derives from a drop in global stored magnetic energy. Two diagnostic neutral beams are used to make fast localized measurements of impurity ions (via fast charge exchange recombination spectroscopy) and majority ions (via Rutherford scattering). Spatial profiles of the heating show a link between where reconnection occurs and where heating occurs. During large reconnection events involving many coupled reconnection sites, a broadly distributed heating profile is observed. Conversely, heating is localized to the edge in smaller reconnection events involving only edge resonant modes. Impurities are heated more strongly than bulk deuterium ions in deuterium plasmas (by about a factor of 2). This suggests a dependence on mass or charge. Many potential ion heating theories have been advanced but all fail to capture all of the observed features. Recent calculations evaluate viscous and cyclotron damping. Viscous damping of tearing mode flows could be important if strong, localized flow gradients are present, encouraging a search for such flows. A cascade of fluctuation power to ion gyroradius scales appears too weak for direct bulk heating, but could be important for impurity heating. Magnetic pumping can be important during plasma startup but should be less so during the discharge flattop where strong heating is still observed. Work supported by U.S.D.O.E. and N.S.F.   

Measurements and Simulations of Fluctuation-Driven Magnetic Fields in Flowing Liquid Metal

The Madison Dynamo Experiment is designed to self-generate magnetic fields from flows of liquid sodium in a simply-connected spherical geometry. A velocity field is produced in the experiment by two counter-rotating impellers. The flow is very turbulent, with a fluid Reynolds number greater than $10^6$. The role of turbulent velocity and magnetic field fluctuations in magnetic field generation is explored by applying an external magnetic field to the flowing sodium, and measuring the resulting magnetic field. An external dipole moment is measured which the mean axisymmetric velocity field is incapable of generating. Since the external induced magnetic field is axisymmetric, the dipole moment must be generated by fluctuations. The experimental approach to understanding these fluctuations involves measurement of the axisymmetric magnetic field in the sodium experiment, measurement of the velocity field in a dimensionally identical water experiment, and the calculation of the axisymmetric magnetic fields induced by both the mean flow and by fluctuations. The presence of a strong diamagnetic field, generated by fluctuations, is identified and its spatial structure presented. Such a fluctuation-driven magnetic field is also found in simulations of the experiment, which are used to elucidate the nature of the fluctuations, and how they induce the diamagnetic field.   

A Fully-Relaxed Helicity Balance Model for the HIT-SI Spheromak

A fully relaxed Taylor-state model is shown to agree with HIT-SI surface and internal magnetic profile measurements. Helicity balance predicts the peak magnitude of toroidal spheromak current and the threshold for spheromak formation. The model also accurately predicts the division of the applied injector loop voltage between the injector and spheromak regions. The Taylor state for HIT-SI can be thought of as a linear superposition of three Taylor states: One for each injector with the injector flux as a boundary condition, and one for the spheromak equilibrium itself. [T.R. Jarboe, W.T. Hamp, G.J. Marklin, B.A. Nelson, R.G. O'Neill, A.J. Redd, P.E. Sieck, R.J. Smith, and J.S. Wrobel, \textit{Phys. Rev. Lett.}, v 97, p 115003, (2006)] The Taylor states are calculated directly from the machine geometry, and the magnitudes of the injector states are determined by the measured injector currents. Both the surface fields and internal field profile agree to within 10{\%} of the fields measured in the experiment, using only the spheromak current as the fitting parameter. By assuming helicity is injected at a rate 2V$\Psi $, and only decays through resistivity the equilibrium is predicted with no fitting parameters, demonstrating helicity balance in a sustained spheromak for the first time without the large uncertainty of sheath drops. Spitzer resistivity (using Z=2) is assumed with the electron temperature measured by Langmuir probe. Although the experimental results suggest a higher effective resistivity by a factor of 1.5 compared to the Spitzer value the prediction is still within the uncertainties in the measured parameters. The voltage division between injector and spheromak regions is measured with internal electrostatic probes and agrees with the model to within 20{\%}. HIT-SI produces 1 m diameter spheromaks with toroidal currents of up to 30 kA. FIR density data will also be presented.   

Modeling Nuclear Fusion with an Ultracold Nonneutral Plasma

In the hot dense interiors of stars and giant planets, nuclear fusion reactions are predicted to occur at rates that are greatly enhanced compared to rates at low densities. The enhancement is caused by plasma screening of the repulsive Coulomb potential between nuclei, which increases the probability of the close collisions that are responsible for fusion.\footnote{E. E. Salpeter and H. van Horn, {\it Astrophys. J.} {\bf 155}, 183 (1969).} This screening enhancement is a small but measurable effect in the Sun;\footnote{J. N. Bachall L.S.Brown, A.Gruzinov, and R. F. Sawyer., {\it A\&A} {\bf 383}, 291-295 (2002).} and is predicted to be much larger in dense objects such as white dwarf stars and giant planet interiors where the plasma is strongly coupled (i.e., where the Debye screening length is smaller than the mean interparticle spacing). However, these strongly enhanced fusion reaction rates have never been definitively observed in the laboratory. This talk discusses a method for observing the enhancement using an analogy between nuclear energy and cyclotron energy in a cold nonneutral plasma in a strong magnetic field. In such a plasma, the cyclotron frequency is higher than other dynamical frequencies, so the kinetic energy of cyclotron motion is an adiabatic invariant. This energy is not shared with other degrees of freedom except through close collisions that break the invariant and couple the cyclotron motion to the other degrees of freedom. Thus, the cyclotron energy of an ion, like nuclear energy, can be considered to be an internal degree of freedom that is accessible only via close collisions. Furthermore, the rate of release of cyclotron energy is enhanced through plasma screening by precisely the same factor as that for the release of nuclear energy, because both processes rely on the same plasma screening of close collisions.\footnote{D. Dubin, {\it Phys. Rev. Lett.} {\bf 94}, 025002 (2005); M. J. Jensen, T. Hasegawa, J. J. Bollinger, and D.H.E. Dubin, {\it Phys. Rev. Lett.} {\bf 94}, 025001 (2005).} Simulations and experiments measuring large screening enhancements in strongly-coupled plasmas will be discussed, along with the possibility of exciting and studying ``burn fronts.''   

Coulomb crystallization in classical and quantum systems

Coulomb crystallization occurs in one-component plasmas when the average interaction energy exceeds the kinetic energy by about two orders of magnitude. A simple road to reach such strong coupling consists in using external confinement potentials the strength of which controls the density. This has been succsessfully realized with ions in traps and storage rings and also in dusty plasma. Recently a three-dimensional spherical confinement could be created [1] which allows to produce spherical dust crystals containing concentric shells. I will give an overview on our recent results for these ``Yukawa balls'' and compare them to experiments. The shell structure of these systems can be very well explained by using an isotropic statically screened pair interaction. Further, the thermodynamic properties of these systems, such as the radial density distribution are discussed based on an analytical theory [3]. I then will discuss Coulomb crystallization in trapped quantum systems, such as mesoscopic electron and electron hole plasmas in coupled layers [4,5]. These systems show a very rich correlation behavior, including liquid and solid like states and bound states (excitons, biexcitons) and their crystals. On the other hand, also collective quantum and spin effects are observed, including Bose-Einstein condensation and superfluidity of bound electron-hole pairs [4]. Finally, I consider Coulomb crystallization in two-component neutral plasmas in three dimensions. I discuss the necessary conditions for crystals of heavy charges to exist in the presence of a light component which typically is in the Fermi gas or liquid state. It can be shown that their exists a critical ratio of the masses of the species of the order of 80 [5] which is confirmed by Quantum Monte Carlo simulations [6]. Familiar examples are crystals of nuclei in the core of White dwarf stars, but the results also suggest the existence of other crystals, including proton or $\alpha$-particle crystals in dense matter and of hole crystals in semiconductors. \newline [1] O. Arp, D. Block, A. Piel, and A. Melzer, Phys. Rev. Lett. {\bf 93}, 165004 (2004). \newline [2] M. Bonitz, D. Block, O. Arp, V. Golubnychiy, H. Baumgartner, P. Ludwig, A. Piel, and A. Filinov, Phys. Rev. Lett. {\bf 96}, 075001 (2006). \newline [3] C. Henning, H. Baumgartner, A. Piel, P. Ludwig, V. Golubnychiy, M. Bonitz, and D. Block, Phys. Rev. E {\bf 74}, 056403 (2006) and Phys. Rev. E (2007). \newline [4] A. Filinov, M. Bonitz, and Yu. Lozovik, Phys. Rev. Lett. {\bf 86}, 3851 (2001). \newline [5] M. Bonitz, V. Filinov, P. Levashov, V. Fortov, and H. Fehske, Phys. Rev. Lett. {\bf 95}, 235006 (2005) and J. Phys. A: Math. Gen. {\bf 39}, 4717 (2006). \newline [6] {\em Introduction to Computational Methods for Many-Body Systems}, M. Bonitz and D. Semkat (eds.), Rinton Press, Princeton (2006)   

Neutral depletion and transport in low temperature plasmas

Space and laboratory plasmas can be dramatically affected by neutral depletion. We describe the effect of neutral depletion on low temperature laboratory plasmas in which the plasma is either collisional or collisionless and neutrals are either thermalized or move ballistically. In all these cases the total number of neutrals is shown to be the similarity variable that determines the electron temperature. For collisional plasma that is in pressure balance with the neutral gas it has been shown that because of the inherent coupling of ionization and transport, an increase of the energy invested in ionization can nonlinearly enhance the transport process. Such an enhancement of the plasma transport due to neutral depletion was shown to result in an unexpected \textit{decrease }of the plasma density when power is \textit{increased; }despite the \textit{increase }of the flux of generated plasma.$^{1}$ Unexpected steady-state has also been found for collisionless plasma due to neutral depletion. For ballistically-moving neutral-gas the strong ionization results in an expected neutral-gas minimum at the center of the chamber.$^{2}$ However, Raimbault \textit{et al}. have shown that in the case of thermalized neutral-gas (in which the pressure increases with density) a strong ionization results in a maximum of the neutral-gas density surprisingly located at the center of the chamber.$^{3}$ The effects of neutral depletion due to a noticeable neutral gas heating will also be discussed. When collisions with electrons are the dominant source of neutral heating, that heating is larger at the center of the discharge,$^{ 4}$ while when collisions with ions are the dominant source, the heating is larger near the wall. It will be shown that, interestingly, the partitioning of power between plasma and neutral-gas is a function of the electron temperature only and not of the power level. \begin{enumerate} \item A. Fruchtman, G. Makrinich, P. Chabert, and J.-M. Rax, Phys. Rev. Lett. \textbf{95, }115002 (2005). \item A. Fruchtman, ``Neutral depletion and pressure balance in plasma'', 33rd EPS Conference on Plasma Physics, Rome, 19 - 23 June 2006, ECA Vol. \textbf{30I}, D-5.013 (2006). \item J.-L. Raimbault, L. Liard, J.-M. Rax, P. Chabert, A. Fruchtman, and G. Makrinich, Phys. Plasmas \textbf{14}, 013503 (2007). \item L. Liard, J.-L. Raimbault, J.-M. Rax, and P. Chabert, ``Plasma transport under neutral gas depletion conditions'', submitted to J. Phys. D. \end{enumerate}