Spectroscopic Flow and Ion Temperature Studies of a Large s FRC

The Swarthmore Spheromak Experiment (SSX) produces a large s FRC by merging counter-helicity spheromaks within a cylindrical flux conserver. Past results have shown that the toroidal fields in each spheromak do not annihilate even after the poloidal flux appears to have completely reconnected. This would suggest a radially directed current density at the midplane, and therefore a radially sheared azimuthal component of J × B. In contrast, fast high resolution spectroscopic measurements indicate that flow at the midplane is small (u < < v _A ) and there is little shear.     

Novel Dipole Trapped Spheromak Configuration

We report the observation and characterization of a spheromak formed in the Swarthmore Spheromak Experiment (SSX) and trapped in a simple dipole magnetic field. The spheromak is studied in the prolate (tilt unstable) 0.4 m diameter, L = 0.6 m length copper flux conserver in SSX. This configuration is stable to the tilt, despite the prolate flux conserver. The spheromak is characterized by a suite of magnetic probe arrays for magnetic structure B(r,t), ion Doppler spectroscopy for T _i and flow, interferometry for n _e , and soft X-ray analysis for T _e . Three dimensional MHD simulations of this configuration verify its gross stability.     

Experimental Results for an Acoustic Driver for MTF

General Fusion is planning to form an FRC or spheromak of 10¹⁷ cm⁻³, 100 eV, 40 cm diameter by merging two spheromaks with reverse or co-helicity. This target will be further compressed in a 3 m diameter tank filled with liquid PbLi with the plasma in the center. The tank is surrounded with pneumatically powered impact pistons that will send a convergent shock wave in the liquid to compress the plasma to 10²⁰ cm⁻³, 10 keV, 4 cm diameter for 7 μs. General Fusion has built a 500 kJ, 80 μs, 6 GW pneumatic impact piston capable of developing 2 GPa (300 kpsi). In this paper we will present the performances achieved to date.     

Extended MHD Simulations of the Compression and Stability of Spheromaks for Current Drive

We examine the compression and stability of spheromaks for magnetic field generation and heating by use of the 3D extended MHD code, NIMROD [C.R. Sovinec, et al., J. Comp. Phys. 195, 355 (2004)]. The formation of compact tori (CT) plasmas with strong magnetic fields by use of repetitive CT injection is being investigated experimentally and serves as impetus for this computational study. To reach high fields, the injected CT will require compression before injection. Stability of the spheromak to tilt and shift modes is examined during compression, as is the amplification of flux during co-helicity spheromak merging.     

Recent Advances in the SPIRIT (Self-organized Plasma with Induction, Reconnection, and Injection Techniques) Concept

Since its inception at the 1997 Innovative Confinement Concept meeting, the Self-organized Plasma with Induction, Reconnection, and Injection Techniques (SPIRIT) concept has been continuously advanced both theoretically and experimentally. The main features of this concept are: (1) formation of large-flux Field Reversed Configuration (FRC) plasmas by merging two spheromaks with opposite helicities; (2) flexibility to assess FRC stability by varying the plasma shape and kinetic parameter, by using passive stabilizers, and by injecting energetic ions; (3) sustainment of the FRC for a time significantly longer than the energy confinement time using an ohmic transformer and/or neutral beam injection. Experiments carried out in TS-3/4 and SSX and more recently in Magnetic Reconnection Experiment (MRX) have further verified the effectiveness of this formation scheme for large-flux FRCs. An improved understanding of FRC stability over plasma shape and kinetic parameter has been obtained in MRX. New numerical simulations showed that FRC plasmas can be globally stabilized by injecting energetic ions. Many of these aspects of the SPIRIT concept can be further studied in the current MRX device.     

Compression, Heating and Fusion of Colliding Plasmoids by a Z-theta Driven Plasma Liner

A potentially promising approach to fusion employs a plasma shell to radially compress two colliding plasmoids. The presence of the magnetic field in the target plasma suppresses the thermal transport to the confining shell, thus lowering the imploding power needed to compress the target to fusion conditions. With the momentum flux being delivered by an imploding plasma shell, many of the difficulties encountered in imploding a solid metal liner are eliminated or minimized. The best plasma for the target in this approach is the FRC. It has demonstrated both high β, and robustness in translation and compression that is demanded for the target plasma. A high density compressed plasmoid is formed by a staged axial and radial compression of two colliding/merging FRCs where the energy that is required for the implosion compression and heating of the magnetized target plasmoid is stored in the kinetic energy of the plasmas used to compress it. An experimental apparatus is being constructed for the demonstration of both the target plasmoid formation as well as the compression of the plasmoid by a plasma liner. It is believed that with the confinement properties and the high β nature of the FRC, combined with the unique approach to be taken, that an nτ_E T _i triple product ∼5 × 10¹⁷ m⁻³ s keV can be achieved.     

Overview of the Helicity Injected Torus (HIT) Program

The Helicity Injected Torus with Steady Inductive Helicity Injection (HIT-SI) consists of a “bowtie”-shaped axisymmetric confinement region, with two half-torus helicity injectors mounted on each side of the axisymmetric flux conserver [Sieck et al, IEEE Trans. Plasma Sci., v.33, p.723 (2005); Jarboe, Fusion Technology, v.36, p.85 (1999)]. Current and flux are driven sinusoidally with time in each injector, with the goal of generating and sustaining an axisymmetric spheromak in the main confinement region. Improvements in machine conditioning have enabled systematic study of HIT-SI discharges with significant toroidal current I_TOR, including cases in which this current I_TOR switches sign one or more times during the discharge. Statistical studies of all HIT-SI discharges to date demonstrate a minimum injected power to form significant I_TOR, and that the maximum I_TOR scales approximately linearly with the total injected power.     

Internal Fields in Helicity Injected Torus with Steady Inductive Helicity Injection (HIT-SI) Discharges

The Helicity Injected Torus with Steady Inductive Helicity Injection (HIT-SI) consists of an axisymmetric flux conserver and two half-torus magnetic helicity injectors, mounted on either side of the axisymmetric confinement region (Jarboe et al., 2006, Phys. Rev. Lett., 97, 115003). Current and flux are driven sinusoidally with time in each injector, injecting both power and magnetic helicity into the HIT-SI device, with the goal of forming and sustaining a spheromak in the confinement region. Recent HIT-SI results include formation of discharges with toroidal spheromak current 1.5 times the injector current amplitude, development of a Taylor-state model for the magnetic fields in HIT-SI discharges, and direct measurement of the portion of the induced injector electric field that drives current in the confinement region.     

Internal Magnetic Field Measurements in the TCSU RMF Current Drive Experiment

Detailed magnetic measurements of Field-reversed configurations (FRC) from the Translation Confinement Sustainment Upgrade (TCSU) experiment are presented. A two-axis probe inserted transversely at the axial midplane provides 24 independent measurements of B _z (r) and B _x (r). Two single-axis 29 channel probes provide axial profiles at the plasma edge. The B _x (r) field profiles, oriented to measure B_θ from the rotating magnetic field (RMF), provide details about RMF penetration into the FRC. B _z (r) profiles, when combined with the high beta nature of the FRC, interferometric density measurements, and assuming uniform temperature, yield radial density and pressure profiles. Time evolution of these profiles gives insight into plasma dynamics and the n = 1 (wobble) and n = 2 instabilities. Data from 123 and 172 kHz RMF frequencies is presented.     

Theoretical and Experimental Approach in Poloidal Beta and Internal Inductance Measurement on IR-T1 Tokamak

Measurements of poloidal beta β _p and internal inductance l _i are essential in tokamak plasma research. Much more plasma parameters such as the plasma current density profile, magnetohydrodynamics instability, and plasma energy confinement time are determined by using these parameters. Discrete poloidal magnetic probes along with the diamagnetic loop can be utilized in measurement of the plasma poloidal beta β _p and internal inductance l _i . In this paper, theoretical and experimental results in determining β _p and l _i are presented and discussed.     

High-Beta Steady-State FRC Plasma Sustained by Rotating Magnetic Field with Spatial High-Harmonic Components

Field-reversed configurations (FRCs) driven by rotating magnetic fields (RMFs) with spatial high-harmonic components have been studied in the metal flux conserver of the FRC injection experiment (FIX). The high-harmonic RMF method has some unique features; (1) field lines of the RMF do not penetrate or cross the vessel wall, (2) selective penetration/exclusion of the fundamental/high-harmonic RMF component will result in a generation of effective magnetic pressure near the separatrix, which helps to keep the separatrix away from the vessel wall, (3) strong azimuthal non-uniformity of the RMF will cause the n = 4 deformation of the core FRC plasma, which will eliminate the destructive modes caused by the rotation of the plasma column. The RMF method with high harmonics will provide quasi-steady current drive of high-beta FRC plasmas without destructive n = 2 rotational mode and will be helpful in reducing the particle loss and thermal load when applied to the fusion core plasma.     

Spheromak Formation and Current Sustainment Using a Repetitively Pulsed Source

By repeated injection of magnetic helicity (K = 2φψ) on time-scales short compared with the dissipation time (τ_inj << τ _K ), it is possible to produce toroidal currents relevant to POP-level experiments. Here we discuss an effective injection rate, due to the expansion of a series of current sheets and their subsequent reconnection to form spheromaks and compression into a copper flux-conserving chamber. The benefits of repeated injection are that the usual limits to current amplification can be exceeded, and an efficient quasi-steady sustainment scenario is possible (within minimum impact on confinement). A new experiment designed to address the physics of pulsed formation and sustainment is described.     

Magnetic Reconnection in the Spheromak: Physics and Consequences

Magnetic reconnection in the spheromak changes magnetic topology by conversion of injected toroidal flux into poloidal flux and by magnetic surface closure (or opening) in a slowly decaying spheromak. Results from the Sustained Spheromak Physics Experiment, SSPX, are compared with resistive MHD simulations using the NIMROD code. Voltage spikes on the SSPX gun during spheromak formation are interpreted as reconnection across a negative-current layer close to the mean-field x-point. Field lines are chaotic during these events, resulting in rapid electron energy loss to the walls and the low T _e < 50 eV seen in experiment and simulation during strong helicity injection. Closure of flux sufaces (and high T _e ) can occur between voltage spikes if they are sufficiently far apart in time; these topology changes are not reflected in the impedance of the axisymmetric gun. Possible future experimental scenarios in SSPX are examined in the presence of the constraints imposed by reconnection physics. Work performed under the auspices of the U. S. DOE by U. California LLNL under contract No. W-7405-Eng-48.     

Antisymmetric RMF Current Drive in FRCs

A major concern for Rotating Magnetic Field (RMF) current drive of an FRC is that a transverse magnetic field tends to open the field lines, thus compromising confinement. In recent FRC current drive experiments it was found that thermal confinement is much improved when an antisymmetric RMF is applied, rather than the usual symmetric RMF. A field line tracking analysis showed that with a combination of partial penetration and antisymmetric RMF, the field lines remain closed for larger ratios of B _ω/B _e than was previously thought. In this paper the analysis is extended to more fully understand the boundaries of when and where the field lines are expected to remain closed when antisymmetric RMF current drive is applied to an FRC.     

Confinement & Current Drive Measurements for Steady-State FRCs

Detailed measurements in the TCS Rotating Magnetic Field (RMF) driven FRC device display a highly non-uniform resistivity profile, highly peaked near the separatrix where the ratio of electron drift velocity v _de to ion sound speed v _s is large. The RMF parameters determine the plasma density. The plasma temperatures are governed by power balance, and higher temperatures result in higher diamagnetic currents, mostly inside the magnetic field null, and higher magnetic fields, with surprisingly little increase in absorbed power. The results are well modeled by a ‘Chodura’ type resistivity scaling with electron collision frequency scaling as ν_ch∼ω_pi(1− exp[−v _de/v _s]).     

Formation of a Stable Field Reversed Configuration through Merging

The Inductive Plasma Accelerator (IPA) Field Reversed Configuration (FRC) experiment is a plasmoid accelerator/interaction experiment designed to explore the acceleration, reconnection and compression of high beta compact toroids. The IPA experiment is designed to be able to form, accelerate, and merge two FRCs having a mass of 0.1–0.2 mg at velocities ranging from 150 km/s to 250 km/s in a centrally located interaction/compression chamber. The interaction/compression chamber magnetic fields are arranged in a mirror configuration to trap and allow the FRCs to merge. The merged FRCs are then magnetically compressed to high density and temperature. After compression, ion temperatures are predicted to exceed several kV at densities greater than 10²² m⁻³. The experimental device now in operation will be discussed. Initial results of FRC merging will be presented, as well as results from 2D numerical calculations based on the current experiment.     

Verification of rod safety via confidence intervals for a binomial proportion

The probabilistic safety assessed to a set of N fuel rods assembled in one core of a nuclear power reactor is commonly modelled by ∑_i≤N X_i, where X₁, …, X_N are independent Bernoulli random variables (rv) with individual probability p_i = P (X_i = 1) that the ith rod shows no failure during one cycle. This is the probability of the event that the ith rod will not exceed the failure limit during one cycle. The safety standard presently set by the German Reaktor-Sicherheitskommission (Reactor Safety Commission) requires that the expected number of unfailed rods in the core during one cycle is at least N − 1, i.e., E(∑_i≤N X_i) = ∑_i≤N p_i ≥ N − 1, whereby a confidence level of 0.95 for the verification of this condition is demanded. In this paper, we provide an approach, based on the Clopper–Pearson confidence interval for the proportion p of a binomial B(n, p) distribution, how to verify this condition with a confidence level of at least 0.95. We extend our approach to the case, where the set of N fuel rods is arranged in strata, possibly due to different design in each stratum.     

The Search for Reconnection and Helicity During Formation of a Bounded Spheromak

Recent results from investigations using insertable magnetic probes at the Sustained Spheromak Physics Experiment (SSPX) [E. B. Hooper et al., Nucl. Fusion 39, 863 (1999)] are presented. Experiments were carried out during pre-programmed, constant amplitude coaxial gun current pulses, where magnetic field increases stepwise with every pulse, but eventually saturates. Magnetic traces from the probe, which is electrically isolated from the plasma and spans the flux conserver radius, indicate there is a time lag at every pulse between the response to the current rise in the open flux surfaces (intercepting the electrodes) and the closed flux surfaces (linked around the open ones). This is interpreted as the time to buildup enough helicity in the open flux surfaces before reconnecting and merging with the closed ones. Future experimental and diagnostic plans to directly estimate the helicity in the open flux surfaces and measure reconnection are briefly discussed. This work performed under the auspices of the USDOE by LLNL under contract 7405-Eng-48. The authors are grateful to Paul M. Bellan and Caltech for their continued support to SSPX with the high-speed imaging hardware, and to the Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas (CMSO) for their continued financial support.     

Computation of Mass Sweeping Efficiency Factor and Current Efficiency Factor in Z-pinch Devices

In this paper, mass sweeping efficiency factor (f _m ) and current efficiency factor (f _i ) have been computed for Z-pinch devices. We used slug model for analysis of Z-pinch dynamics. Magnetic piston reaps electrons and ions in duration of motion. But only a fraction of plasma mass sweeps with magnetic piston, therefore we should add mass sweeping efficiency factor (f _m ) in equations. Such like alone the fraction of electrical current flows of magnetic piston and remainder of it flows of internal and external radial of magnetic piston, so we should add f _i in equations. In this paper, equations are solved with characteristics of CERN Z-pinch device (its length and radius, resistivity, circuit inductance and capacitanc and plasma inductance) and with values of Boggasch experiments (discharge voltage: 15 kV, initial pressure: 400 pa). Recorded code runs with different values of f _m and f _i and in each section, pinch time and pinch current are compared with Boggasch experimental values. Optimum values for f _m and f _i obtain with Comparing between numerical values and experimental values. These values are f _i  = 0.8 and f _m  = 0.08.     

Energy Confinement Scaling Predictions for the Stabilized Tandem Mirror

The absence of toroidal curvature and the relatively weak internal parallel currents in a tandem mirror gives the system favorable stability and transport properties. GAMMA-10 experiments demonstrate that sheared plasma rotation suppresses turbulent radial losses through control of the radial potential profiles. Recent achievements of the GAMMA-10 include 3 keV ion confinement potentials and T _e ≥ 800 eV. Total energy confinement times for the GAMMA-10 experiment exceed by an order of magnitude the corresponding empirical confinement times in toroidal devices. At the temperatures achieved in the GAMMA-10, the end loss rate τ_p ≃ 100 ms so that radial losses determine τ_E, as intended in tandem mirror reactor designs. Drift-wave results on radial confinement times developed using Bohm, gyro-Bohm, and electron temperature gradient (ETG) scalings imply that the tandem mirror has a qualitatively different form of drift-wave radial transport from that in toroidal devices. Drift-wave eigenmodes for the GAMMA-10 are analyzed for the fluctuating electrostatic potential and magnetic perturbations.