Spheromak formation by steady inductive helicity injection

A spheromak is formed for the first time using a new steady state inductive helicity injection method. Using two inductive injectors with odd symmetry and oscillating at 5.8 kHz, a steady state spheromak with even symmetry is formed and sustained through nonlinear relaxation. A spheromak with about 13 kA of toroidal current is formed and sustained using about 3 MW of power. This is a much lower power threshold for spheromak production than required for electrode-based helicity injection. Internal magnetic probe data, including oscillations driven by the injectors, agree with the plasma being in the Taylor state. The agreement is remarkable considering the only fitting parameter is the amplitude of the spheromak component of the state.     

New mode of operating a magnetized coaxial plasma gun for injecting magnetic helicity into a spheromak

By operating a magnetized coaxial plasma gun continuously with just sufficient current to enable plasma ejection, large gun-voltage spikes (approximately 1 kV) are produced, giving the highest sustained voltage approximately 500 V and highest sustained helicity injection rate observed in the Sustained Spheromak Physics Experiment. The spheromak magnetic field increases monotonically with time, exhibiting the lowest fluctuation levels observed during formation of any spheromak (B/B>/=2%). The results suggest an important mechanism for field generation by helicity injection, namely, the merging of helicity-carrying filaments.     

Experimental identification of the kink instability as a poloidal flux amplification mechanism for coaxial gun spheromak formation

The magnetohydrodynamic kink instability is observed and identified experimentally as a poloidal flux amplification mechanism for coaxial gun spheromak formation. Plasmas in this experiment fall into three distinct regimes which depend on the peak gun current to magnetic flux ratio, with (I) low values resulting in a straight plasma column with helical magnetic field, (II) intermediate values leading to kinking of the column axis, and (III) high values leading immediately to a detached plasma. Onset of column kinking agrees quantitatively with the Kruskal-Shafranov limit, and the kink acts as a dynamo which converts toroidal to poloidal flux. Regime II clearly leads to both poloidal flux amplification and the development of a spheromak configuration.     

用变分法近似计算椭球马克中的倾斜模不稳定性

本文利用变分法的基本概念,提出了一种在任意边界形状的情况下近似求解偏微分方程的方法。把求解偏微分方程的问题近似地化为求解常微分方程组的问题。尤其是当边界形状较为复杂时,其优越性更为显著。作者采用这种方法,对大椭圆度的球形马克(Spheromak)中的倾斜模(Tilting Mode)不稳定性进行了研究。得到的结论是:在扁椭球马克中,不会出现倾斜模不稳定性。 关键词：     

Experimental Studies on the Sustainment of Splieromak Plasmas by an Inductive Drive of the Toroidal Current

Sustainment of spheromak plasmas produced in an external equilibrium field has been demonstrated with a center current transformer (ohmic heating (OH) coil) which is used to inductively drive the toroidal current of the plasma. The OH coil is covered by a cylindrical metal liner. It provides the stability against the tilt and shift motions of spheromaks at the expense of the simple connection of its geometry. Since the spheromak is characterized by the elimination of external toroidal fields in association with nonconservation of a toroidal flux during magnetic relaxation, the metal liner was made electrically disconnected from the main vacuum vessel (spheromak mode). In the experiments, existense of the dynamo effect, meaning automatic generation of toroidal flux similar to that of a reversed field pinch (RFP), is observed. Measured MHD activity consists of multihelicity helical modes with toroidal mode numbers N = 1-3. In order to investigate the difference between spheromaks and RFP's in the MHD activity during sustainment, experiments have also been made with the metal liner of the OH coil connected with the vessel (RFP mode). The dynamics of the MHD activities observed are compared with those obtained from the three-dimensional MHD simulations by Katayama and Katsurai [18], and their implication in the dynamo effect is discussed.     

Suppression of MHD fluctuations leading to improved confinement in a gun-driven spheromak

Magnetic fluctuations have been reduced to approximately 1% during discharges on the Sustained Spheromak Physics Experiment by shaping the spatial distribution of the bias magnetic flux in the device. In the resulting quiescent regime, the safety factor profile is nearly flat in the plasma and the dominant ideal and resistive MHD modes are greatly reduced. During this period, the temperature profile is peaked at the magnetic axis and maps onto magnetic flux contours. Energy confinement time is improved over previous reports in a driven spheromak.     

Dynamics of whistler spheromaks in magnetized plasmas

Recent laboratory experiments [Stenzel et al., Phys. Rev. Lett. 96, 095004 (2006)10.1103/PhysRevLett.96.095004] have demonstrated interesting phenomena of propagating nonlinear whistler structures (spheromaks) and stationary field-reversed configurations, whose magnetic fields exceed the ambient magnetic field strength. Our objective here is to present simulation studies for these nonlinear whistler structures based on the three-dimensional nonlinear electron magnetohydrodynamic equations. The robustness and longevity of the propagating whistler spheromaks found in the experiments are confirmed numerically. Varying the toroidal field of the spheromak in the initial conditions, we find that the polarity and the amplitude of the toroidal field determine the propagation direction and speed of the spheromak. Our simulation results are in excellent agreement with those observed in the laboratory experiments.     

Torus instability

The expansion instability of a toroidal current ring in low-beta magnetized plasma is investigated. Qualitative agreement is obtained with experiments on spheromak expansion and with essential properties of solar coronal mass ejections, unifying the two apparently disparate classes of fast and slow coronal mass ejections.     

New Approaches and Solutions of Nonlinear Force-Free Magnetic Field

Some new approaches for nonlinear force-free magnetic field are presented and new exact solutions are found analytically. Examples are given and some implications of results to astrophysical solar plasmas as well as tokamak or/and spheromak plasmas are discussed.     

Effect of ion skin depth on relaxation of merging spheromaks to a field-reversed configuration

The effect of ion skin depth on the relaxation of merging spheromaks to a field-reversed configuration (FRC) is studied experimentally for a wide range of size parameter S* (ratio of minor radius to ion skin depth) from 1 to 7. The two merging spheromaks are observed to relax to an FRC or a new spheromak depending on whether the initial poloidal eigenvalue is smaller or larger than a threshold value. The bifurcation value is found to increase with decreasing size parameter S*, indicating that the low-S* condition provides a wide bifurcated range of relaxation to an FRC. The FRC-style relaxation under the low-S* conditions was accompanied by the suppression of the low-n modes (n is the toroidal mode number) activity. The fast rotations of the modes were followed by suppression of the low-n modes.     

Force-free magnetic relaxation in driven plasmas

Taylor relaxation in a driven plasma with normal magnetic field intercepting the boundary is described by the Jensen-Chu theory, which predicts infinite energy and helicity barriers that constrain the accessible relaxed states to system scale. For a partially relaxed force-free (j=kB) plasma where k is a field line constant, nonlinearity regularizes the Jensen-Chu singularities and new branches of relaxed state become accessible, such as the flipped spheromak and other high k states.     

New Approaches and Solutions of Nonlinear Force-Free Magnetic Field

Some new approaches for nonlinear force-free magnetic field are presented and new exact solutions are found analytically. Examples are given and some implications of results to astrophysical solar plasmas as well as tokamak or/and spheromak plasmas are discussed.PACS numbers: 52.30.Cv, 52.55.-s, 95.30.Qd     

Chaotic scattering and self-organization in spheromak sustainment

Flux core spheromak sustainment by electrostatic helicity injection is studied in resistive MHD. The geometry has magnetized electrodes at the ends held at a potential difference V. For V>V(c) the central current column is kink unstable. The nonlinear state with V just above V(c) has a large volume of flux surfaces, with rotational transform provided by the helical kinking of the column. As V increases the kink becomes stronger, the tori are destroyed, and the field lines exhibit chaotic scattering. The distribution of field line lengths L, related to confinement and parallel current density, is studied. At larger V or larger Lundquist number S, a limit cycle appears.     

Evidence for separatrix formation and sustainment with steady inductive helicity injection

The first sustainment of toroidal plasma current of 50 kA at up to 3 times the injected currents, added in quadrature, using steady inductive helicity injection is described. Separatrix currents-currents not linking the helicity injectors-are sustained up to 40 kA. Decreases in the n=1 toroidal mode of the poloidal magnetic field at higher current amplifications indicate more quiescent, direct toroidal current drive. Results are achieved in HIT-SI (with a spheromak of major radius 0.3 m) during deuterium operations immediately after helium operation. These results represent a breakthrough in the development of this new current drive method for magnetic confinement fusion.     

Whistler modes with wave magnetic fields exceeding the ambient field

Whistler-mode wave packets with fields exceeding the ambient dc magnetic field have been excited in a large, high electron-beta plasma. The waves are induced with a loop antenna with dipole moment either along or opposite to the dc field. In the latter case the excited wave packets have the topology of a spheromak but are propagating in the whistler mode along and opposite to the dc magnetic field. Field-reversed configurations with net zero helicity have also been produced. The electron magnetohydrodynamics fields are force free, have wave energy density exceeding the particle energy density, and propagate stably at subelectron thermal velocities through a nearly uniform stationary ion density background.     

Energy Efficiency Analysis of the Discharge Circuit of Caltech Spheromak Experiment

The Caltech spheromak experiment uses a size A ignitron in switching a 59-$ muhbox{F}$ capacitor bank (charged up to 8 kV) across an inductive plasma load. Typical power levels in the discharge circuit are $sim$200 MW for a duration of $sim!! 10 muhbox{s}$. This paper describes the setup of the circuit and the measurements of various impedances in the circuit. The combined impedance of the size A ignitron and the cables was found to be significantly larger than the plasma impedance. This causes the circuit to behave like a current source with low energy transfer efficiency. This behavior is expected to be common with other pulsed plasma experiments of similar size that employ an ignitron switch.      

The double of a Jacobian quasi-bialgebra

We show that the construction of the double of a Lie bialgebra can be extended to the case where a vector space is only equipped with the structure of a Jacobian quasi-bialgebra (also called a Lie quasi-bialgebra). In this case, the double is itself a Jacobian quasi-bialgebra and it is quasi-triangular. The more general case of the double of a proto-Lie bialgebra is also discussed. In the first section, the notions of exact, strictly exact, quasi-triangular and triangular Jacobian quasi-bialgebras are defined and their equivalence classes under twisting are studied.     

Experimental estimation of the transmission loss contributions of a sound package placed in a double wall structure

The objective of this paper is to propose a practical impedance tube method to optimize the sound transmission loss of double wall structure by concentrating on the sound package placed inside the structure. In a previous work, the authors derived an expression that breakdown the transmission loss of a double wall structure containing a sound absorbing blanket separated from the panels by air layers in terms of three main contributions; (i) sound transmission loss of the panels, (ii) sound transmission loss of the blanket and (iii) sound absorption due to multiple reflections inside the cavity. The sound transmission loss contributions of the blanket can thus be estimated from three acoustic measurements using impedance tube techniques: two reflection coefficients at the front face and the rear face of the blanket placed in specific positions characteristic of its position inside the double wall structure and its sound transmission coefficient. The method is first validated in the case of a double wall structure filled with a 2 in. foam material. Next, it is applied to investigate (i) the effect of frame compression of a 2 in. fibre glass in an aeronautic-type double wall structure and (ii) the effect of double porosity with or without porous inclusions in a building-type double wall structure.     

Intersubband excitations in single-and double-layer electron systems in a parallel magnetic field

The spectrum of neutral intersubband excitations in single and double quantum wells has been studied by the inelastic light scattering method. It is shown that excitation energies in an external magnetic field have an anisotropic component proportional to the dipole moment of excitations along the growth axis of the quantum wells. Consequently, the measurement of excitation energy in a magnetic field makes it possible to experimentally estimate the quantitative measure of asymmetry of the quantum wells (dipole moment of the intersubband transition). In addition, a parallel magnetic field makes it possible to considerably extend the range of momenta studied since it shifts the dispersion curves in the momentum space by the value of the anisotropic component. A new method is proposed for determining the symmetry of double quantum wells. In asymmetric wells, intersubband excitations appear between the layers and have a large dipole moment along the growth axis. In symmetric wells, the magnetic field itself induces the dipole moment of intersubband excitations so that the excitation spectrum does not change upon magnetic field inversion. Analysis of energy anisotropy in intersubband excitations in double quantum wells makes it possible to determine the symmetry of double wells to a high degree of accuracy.     

Y型微通道内双重乳液流动破裂机理

基于体积分数法建立了Y型微通道中双重乳液流动非稳态理论模型,数值模拟研究了Y型微通道内双重乳液破裂情况,详细分析了双重乳液流经Y型微通道时的流场信息以及双重乳液形变参数演化特性,定量地给出了双重乳液流动破裂的驱动以及阻碍作用,揭示了双重乳液破裂流型的内在机理.研究结果表明:流经Y型微通道时,双重乳液受上游压力驱动产生形变,形变过程中乳液两端界面张力差阻碍双重乳液形变破裂,两者正相关;隧道的出现将减缓双重乳液外液滴颈部收缩速率以及沿流向拉伸的速率,并减缓了内液滴沿流向拉伸的速率,其对于内液滴颈部收缩速率影响不大;隧道破裂和不破裂工况临界线可以采用幂律关系式l~*=βCa~b进行预测,隧道破裂和阻塞破裂工况临界线可以采用线性关系l~*=α描述;与单乳液运动相图相比,双重乳液运动相图各工况的分界线关系式系数α和β均相应增大.