Power flow in a gun-injected spheromak plasma

Browning, P. K.; Cunningham, G.; Sj, Gee; Kj, Gibson; al-Karkhy, A; Da, Kitson; Martin, R.C.; Mg, Rusbridge

doi:10.1103/physrevlett.68.1718

Cited by 42 publications

(60 citation statements)

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“…Two hypotheses were proposed to explain the mode: (1) development of a q = 1 surface in the closed-flux region [13,15] or equivalently a magnetic axis kink, and (2) current-driven instability of the central column [16,17] or equivalently a geometric axis kink. Additionally, the mode was shown to couple power from the central column to the spheromak [14]. The present work offers a significant new result in that a nonlinear n = 1 geometric axis kink is directly observed to produce the dynamo and poloidal flux amplification leading to spheromak formation.…”

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Experimental Identification of the Kink Instability as a Poloidal Flux Amplification Mechanism for Coaxial Gun Spheromak Formation

2003

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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.PACS numbers: 52.55. Ip,52.35.Py,52.30.Cv The spheromak [1, 2] is a simply-connected plasma configuration in which the magnetic fields are largely determined by dynamo-driven plasma currents. Because of its topological simplicity and ease of formation, the spheromak is of interest as a magnetic fusion confinement scheme [3]. Spheromak formation has traditionally been explained by Taylor's hypothesis [4] that a turbulent magnetohydrodynamic (MHD) system relaxes to a state of minimum magnetic energy subject to the constraint of constant magnetic helicity. While this hypothesis has successfully explained the existence and many equilibrium properties of spheromaks, it says nothing about the actual 3D dynamics underlying the relaxation process, e.g., for coaxial gun spheromaks, the dynamo mechanism which converts injected toroidal flux into required poloidal flux [5]. The dynamics must be 3D because Cowling's theorem [6] shows that purely axisymmetric processes cannot accomplish this. This Letter experimentally identifies the MHD kink instability [7] as a 3D mechanism which converts toroidal to poloidal flux in a coaxial gun system, thereby leading to spheromak formation. This mechanism should also be of fundamental importance to coaxial helicity injection in spherical tori [8], relaxation in reversed-field pinches [4], solar coronal plasma instabilities [9], and astrophysical jets [10].Plasmas in this experiment fall into three regimes depending on peak λ gun = µ 0 I gun /ψ gun (where I gun is the gun current and ψ gun is the bias poloidal magnetic flux intercepting the inner gun electrode), with (I) low values resulting in a straight plasma column with helical magnetic field along the symmetry axis, (II) intermediate values leading to kinking of the column axis, and (III) high values leading immediately to a detached plasma with B tor ≫ B pol . Onset of column kinking agrees quantitatively with the Kruskal-Shafranov limit [7], and the kink acts as a dynamo which converts toroidal to poloidal flux. Regime II clearly leads to both poloidal flux amplification * Now at: Los Alamos National Laboratory, Los Alamos, NM 87545 and magnetic field profiles consistent with spheromak formation. These results are qualitatively consistent with recent time-dependent resistive MHD nu...

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“…More recently, toroidal mode number n = 1 central column instabilities in coaxial gun experiments were reported by several spheromak research groups [13,14,15,16,17]. Typically, the observations were based on edge magnetic measurements, and the mode was studied in the context of relaxation during sustainment.…”

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Experimental Identification of the Kink Instability as a Poloidal Flux Amplification Mechanism for Coaxial Gun Spheromak Formation

2003

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“…Analysis of Langmuir and magnetic probe measurements showed that the SPHEX spheromak (and perhaps all gun-sustained spheromaks) had a high electric field central column (600 V/m) and a low electric field annulus [42]. Most of the current from the inner electrode of the gun was found to return through the copper flux conserver (90%) rather than through plasma (10%) thereby producing a net toroidal field at the wall.…”

Section: Appendix 2 Recent Results From the Sphex Experimentsmentioning

confidence: 99%

The Spheromak path to fusion energy

Hooper¹,

Barnes²,

Bellan³

1998

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The spheromak is a simple and robust magnetofluid configuration with several attractive reactor attributes including compact geometry, no material center post, high engineering p, and sustained steady state operation through helicity injection. Spheromak physics was extensively studied in the US program and abroad (especially Japan) in the 1980's with work continuing into the 1990s in Japan and the UK. Scientific results included demonstration of self-organization at constant helicity, control of the tilt and shift modes by shaped flux conservers, elucidation of the role of magnetic reconnection in the magnetic dynamo, and sustainment of a spheromak by helicity injection.Several groups attained electron temperatures above 100 eV in decaying plasmas, with CTX reaching 400 eV. This experiment had high magnetic field (>l T on the edge and -3 T near the symmetry axis) and good confinement. More recently, analysis of CTX found the energy confinement in the plasma core to be consistent with Rechester-Rosenbluth transport in a fluctuating magnetic field, potentially scaling to good confinement at higher electron temperatures. The SPHEX group developed an understanding of the dynamo in sustained spheromaks but in a relatively cold device. These and other physics results provide a foundation for a new "concept exploration" experiment to study the physics of a hot, sustained spheromak.If successful, this work leads to a next generation, proof-of-principle program.The new SSPX experiment will address the physics of a large-scale sustained spheromak in a national laboratory (LLNL) setting. The key issue in near term spheromak research will be to explore the possibly deleterious effects of sustainment on confinement.Other important issues include exploring the P scaling of confinement, scaling with Lundquist number S, and determining the need for active current-profile control. Collaborators from universities and other national laboratories are contributing experience from previous work, diagnostics, and physics support. Experiments at PPPL and Swarthmore are being conducted on the physics of magnetic reconnection, yielding physics results which should help advance the confinement work.A spheromak reactor will require steady state operation with the equilibrium fully supported by external coils. Although the present generation of experiments can provide data on the initial stages of the transition from short-pulsed operation, sustainment longer than the wall resistance time will be addressed in the proof-of-principle experiments.-lContents

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“…Since relaxation operates on a shorter time scale, the spheromak configuration is maintained regardless of the details of the specific helicity injection mechanism. Some particular examples are the coaxial helicity injection method (CHI) [4][5][6], the merging of helicitycarrying filaments (MHF) [7] and the helicity injected torus with steady inductive helicity injection (HIT-SI) [8].In this Letter we report the first evidence coming from nonlinear, resistive, 3D MHD numerical simulations that demonstrate the possibility of forming and sustaining a spheromak by forcing tangential flows at the plasma boundary. The method can by explained in terms of helicity injection and differs from other helicity injection methods employed in the past (CHI, MHF and HIT-SI).…”

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Spheromak formation and sustainment by tangential boundary flows

García-Martínez

Farengo

2010

Physics of Plasmas

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The nonlinear, resistive, 3D magnetohydrodynamic equations are solved numerically to demonstrate the possibility of forming and sustaining a spheromak by forcing tangential flows at the plasma boundary. The method can by explained in terms of helicity injection and differs from other helicity injection methods employed in the past. Several features which were also observed in previous dc helicity injection experiments are identified and discussed.Spheromak plasmas have been formed using several different techniques [1,2]. The existence of multiple formation methods clearly shows that the spheromak is a preferred (lowest energy) state toward which a magnetohydrodynamic (MHD) system naturally evolves when the appropriate boundary conditions are imposed. The physical process responsible for the formation is magnetic relaxation: on the time scale of MHD instabilities the plasma relaxes to the minimum energy state compatible with its magnetic helicity content (which remains approximately constant) [3]. Once formed, the spheromak will decay in a resistive time scale because resistivity does dissipate magnetic helicity. For this reason, the sustainment of the configuration during times longer than the resistive decay time requires some helicity injection method. Since relaxation operates on a shorter time scale, the spheromak configuration is maintained regardless of the details of the specific helicity injection mechanism. Some particular examples are the coaxial helicity injection method (CHI) [4][5][6], the merging of helicitycarrying filaments (MHF) [7] and the helicity injected torus with steady inductive helicity injection (HIT-SI) [8].In this Letter we report the first evidence coming from nonlinear, resistive, 3D MHD numerical simulations that demonstrate the possibility of forming and sustaining a spheromak by forcing tangential flows at the plasma boundary. The method can by explained in terms of helicity injection and differs from other helicity injection methods employed in the past (CHI, MHF and HIT-SI).An enhanced helicity injection mode was recently reported in spheromak experiments with large plasma rotation [9]. Althought not analyzed in terms of boundary flows, this observation could support the feasibility of the mechanism proposed and studied in this Letter.We model the plasma using the resistive MHD equations with finite viscosity and zero β. The evolution equations for u and B are:where E = −u × B + ηJ and Π = (∇u + ∇u T ) − (2/3) × (∇·u) (see Ref.[10] for further details). These equations are normalized with a (chamber radius), ψ G (imposed flux) and c A (Alfvèn speed). In addition, B and J are scaled with √ µ 0 . Time is expressed in units of the Alfvèn time τ A = a/c A . The normalized resistivity η and the kinematic viscosity ν are set to 5 × 10 −5 . With these values the resistive time is τ r ∼ 800 (defined as in Ref.[11]). The resulting system is solved with the Versatile Advection Code [12].The domain is a cylinder of elongation h/a = 1, with perfectly conducting wall conditions (B · n = 0 ...

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Power flow in a gun-injected spheromak plasma

Cited by 42 publications

References 5 publications

Experimental Identification of the Kink Instability as a Poloidal Flux Amplification Mechanism for Coaxial Gun Spheromak Formation

Experimental Identification of the Kink Instability as a Poloidal Flux Amplification Mechanism for Coaxial Gun Spheromak Formation

The Spheromak path to fusion energy

Spheromak formation and sustainment by tangential boundary flows

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