Structure of the<b><i>n</i></b>= 1 mode responsible for relaxation and current drive during sustainment of the SPHEX spheromak

Duck, R C; Browning, Philippa; Cunningham, G.; Gee, S J; al-Karkhy, A; Martin, R.C.; Rusbridge, M G

doi:10.1088/0741-3335/39/5/004

Cited by 53 publications

(72 citation statements)

References 35 publications

(74 reference statements)

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“…Toroidal current is successfully sustained against resistive decay with the n = 1 oscillations. In the current drive phase, a helical distortion of a central open flux column, rotating toroidally, which is in good agreement with SPHEX observations [4], can be observed. We found that an asymmetric plasmoid is generated by the distortion on the gun side, and that the current is periodically fed from it, as shown in Fig.…”

supporting

confidence: 87%

MHD Simulation of Current Drive by Repetitive Plasmoid Injection in Helicity-Driven Spheromaks.

Kagei

Nagata

Suzuki³

et al. 2003

J. Plasma Fusion Res.

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The dynamics of spheromak plasmas in coaxial helicity injection (CHI) systems has been investigated using three-dimensional magnetohydrodynamic (MHD) numerical simulations. It was found that toroidal current is driven by repetitive asymmetric plasmoid injection, which is related to the n = 1 oscillations. In addition, we propose that multiple pulse operation of the helicity injection is effective for improving confinement because it reduces the n = 1 fluctuations. Keywords:coaxial helicity injection, spheromaks, repetitive plasmoid injection, MHD, simulation author's e-mail: skagei@elct.eng.himeji-tech.ac.jp Coaxial helicity injection (CHI) has demonstrated the ability to form and sustain spheromak and spherical tokamak (ST) plasmas on several devices [1,2]. In these experiments, magnetic field fluctuations with toroidal mode number n = 1 are observed during sustainment, and these fluctuations are considered responsible for the current drive. However, the detailed physical mechanism understanding this phenomenon is not yet well understood. Sovinec et al. demonstrated numerical simulations of helicity-driven spheromaks [3], but the detailed dynamics of toroidal current generation in the gun-driven-system was not clearly revealed. In order to reveal this, 3-D magnetohydrodynamic (MHD) numerical simulations for spheromak plasmas were executed.The simulation region consists of two cylinders, each with a center post: one is a gun region (0.175 ≤ r ≤ 0.65 and 0 ≤ z ≤ 0.5), the other a confinement region (0.15 ≤ r ≤ 1.0 and 0.5 ≤ z ≤ 2.0), as shown in Fig. 1. Grid sizes (N r × N θ × N z ) are (39 × 64 × 40) and (69 × 64 × 121) in the direction of the gun and the confinement regions, respectively. Bias magnetic flux penetrates electrodes at the inner and outer boundaries of the gun region. Boundaries of the confinement region are assumed to be perfectly conducting walls. The initial spheromak configuration is given by numerically solving ∇ × B = λ B (λ is the force-free parameter) under these boundary conditions. The governing equations are one-fluid MHD equations, as follows:In this simulation, the mass density is spatially and temporally constant for simplicity. All physical quantities are normalized by initial mass density ρ 0 , typical Alfvén speed V A , and maximum length of the cylinder radius L 0 . The conductivity κ , the resistivity η, and the viscosity ν are fixed to 1 × 10 -3 , 2 × 10 -4 , and 1 × 10 -3 in the normalized units (γ -1) -1 k n 0 L 0 V A , µ 0 L 0 V A , and ρ 0 L 0 V A , respectively. The simulation starts with the application of a toroidally symmetric radial electric field (E inj ) across a gap between two electrodes.The parameters used in this simulation are λ = 4.95

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confidence: 87%

MHD Simulation of Current Drive by Repetitive Plasmoid Injection in Helicity-Driven Spheromaks.

Kagei

Nagata

Suzuki³

et al. 2003

J. Plasma Fusion Res.

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“…Helically distorted structures also are found in numerical simulations (e.g. Gerrard et al 2001) and are observed in experiment (Duck et al 1997). The minimum energy state is the cylindrical Bessel function field if αR < 3.11 but if the normalised helicity exceeds some critical value, then the field with lowest energy has the fixed value αR ≈ 3.11 and is a combination of the axisymmetric and first helical modes…”

Section: Calculation Of Energy Releasementioning

confidence: 54%

Solar coronal heating by relaxation events

Browning¹,

Linden²

2003

A&A

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Abstract.A coronal heating model is proposed which predicts heating by a series of discrete events of various energies, analogous to the observed range of events from large scale flares through various transient brightening phenomena down to the often discussed "nanoflares". We suggest that an energy release event occurs when a field becomes linearly unstable to ideal MHD modes, with dissipation during the nonlinear phase of such an instability due to reconnection in fine-scale structures such as current sheets. The energy release during this complex dynamic period can be evaluated by assuming the field relaxes to a minimum energy state subject to the constraint of helicity conservation. A model problem is studied: a cylindrical coronal loop, with a current profile generated by slow twisting of the photospheric footpoints parameterised by two values of α (the ratio of current density to field strength). Different initial α profiles, corresponding to different footpoint twisting profiles, lead to energy release events of a wide range of magnitudes, but our model predicts an observationally realistic minimum size for these events.

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“…This is not the first reporting of cross-field current in supposedly force-free spheromaks. The SPHEX group reported that up 50 % of the gun current went into the outer wall but only 10% of the gun flux diffused into it 5 is predominantly parallel to the wall, i.e. current perpendicular to surfaces is negligible.…”

Section: Data Analysis and Resultsmentioning

confidence: 99%

“…The toroidal angle is φ and ω is referred to as 'the n=1 frequency'. The Spheromak Experiment (SPHEX) 5,6 made internal floating potential, magnetic probe, and Rogowksi (current) probe measurements all the way to the symmetry axis of the equatorial plane of a spheromak while this "n=1 mode" was active. The n=1 mode was the n=1 mode dominates the spheromak during sustainement, and is believed to be responsible for relaxation current drive.…”

Section: Introductionmentioning

confidence: 99%

Sustained spheromak coaxial gun operation in the presence of an n=1 magnetic distortion

et al. 2006

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The Sustained Spheromak Physics Experiment (SSPX) uses a magnetized coaxial gun to form and sustain spheromaks by helicity injection. Internal probes give the magnetic profile within the gun. Analysis of these data show that a number of commonly applied assumptions are not completely correct, and some previously unrecognized processes may be at work. Specifically, the fraction of the available vacuum flux spanning the gun that is stretched out of the gun is variable and not usually 100%. The n=1 mode that is present during sustained discharges has its largest value of δB/B within the gun, so that instantaneously B within the gun is not axisymmetric. By applying a rigid-rotor model to account for the mode, the instantaneous field and current structure within the gun are determined. The current density is also highly non-axisymmetric and the local value of λ≡µ 0 j || /B is not constant, although the global value λ g ≡µ 0 I g /ψ g closely matches that expected by axisymmetric models. The current distribution near the gun muzzle suggests cross-field current exists, and this is explained as a line-tying reaction to plasma rotation.

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Structure of then= 1 mode responsible for relaxation and current drive during sustainment of the SPHEX spheromak

Cited by 53 publications

References 35 publications

MHD Simulation of Current Drive by Repetitive Plasmoid Injection in Helicity-Driven Spheromaks.

MHD Simulation of Current Drive by Repetitive Plasmoid Injection in Helicity-Driven Spheromaks.

Solar coronal heating by relaxation events

Sustained spheromak coaxial gun operation in the presence of an n=1 magnetic distortion

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