Magnetohydrodynamic simulations of direct current helicity injection for current drive in tokamaks

Sovinec, C. R.; Prager, S. C.

doi:10.1063/1.871759

Cited by 14 publications

(11 citation statements)

References 11 publications

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“…However, we should note that there are presently discussions of whether good poloidal flux surfaces in a ST can be created by CHI. 19,20 For the purpose of revealing the generation of closed flux surfaces and equilibrium configurations of helicity-driven ST plasmas in the operational regime between spheromak and tokamak, we have intensively carried out internal magnetic probe measurements.…”

Section: Introductionmentioning

confidence: 99%

The internal magnetic field structures and current density profiles in the Helicity Injected Spherical Torus plasma driven by coaxial helicity injection

et al. 2003

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In the Helicity Injected Spherical Torus device [Nagata et al., Proceedings of the 17th International Atomic Energy Agency Fusion Energy Conference, Yokohama, 1998 (International Atomic Energy Agency, Vienna, 1998) CD-ROM, EXP4/10], internal magnetic field and current density structures of spherical torus (ST) plasmas sustained by coaxial helicity injection (CHI) have been revealed via intensive internal magnetic measurements. The internal magnetic configuration of the ST plasma formed by CHI is in good agreement with the results of numerical equilibrium fitting calculations. The generation of closed poloidal flux of ST has been verified by varying the external toroidal field strength in the same device. Interestingly, the transition of the current profile from hollow to peaked has been observed during the sustainment phase, which could be explained by inductive effects of currents on open field lines winding the central conductor.

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Section: Introductionmentioning

confidence: 99%

The internal magnetic field structures and current density profiles in the Helicity Injected Spherical Torus plasma driven by coaxial helicity injection

et al. 2003

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“…In contrast, in the numerical simulations of tokamaks found in Ref. 3 there was little drive for magnetic fluctuations in the center of the cylinder and any m ¼ 1 mode activity was radially localized near the plasma boundary, in the vicinity of the parallel current distribution j gradient. Thus, using the assumption of a uniform hyper-resistivity K profile, our cylindrical tokamak model will actually predict the minimum dynamo power that is required for efficient steady-state CHI current drive, in other words, the minimum value for the characteristic length D of the ansatz equation (30), which is precisely what we seek to determine.…”

Section: Tokamak Plasmasmentioning

confidence: 66%

“…Again, the plasma resistivity is gðw; tÞ and the hyper-resistivity is Kðw; tÞ: In this work, we will use the mean-field differential equation (3) to show that on-axis current drive does in fact occur in our tokamak steady-state CHI model, if a hyperresistivity K exists at the magnetic axis. Third, an issue was raised concerning the scaling of CHI physics with the Lundquist number S s g =s A ; which is the ratio of the resistive diffusion time to the Alfven time.…”

Section: Introductionmentioning

confidence: 99%

Analytic model for coaxial helicity injection in tokamak plasmas

Weening

2011

Physics of Plasmas

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Using a partial differential equation for the time evolution of the mean-field poloidal magnetic flux that incorporates resistivity g and hyper-resistivity K terms, an exact analytic solution is obtained for steady-state coaxial helicity injection (CHI) in force-free large aspect ratio tokamaks. The analytic mean-field Ohm's law model allows for calculation of the tokamak CHI current drive efficiency and the plasma inductances at arbitrary levels of magnetic fluctuations, or dynamo activity. The results of the mean-field model suggest that CHI approaching Ohmic efficiency is only possible in tokamaks when the size of the effective current drive boundary layer, d ðK=gÞ 1=2 ; becomes greater than half the size of the plasma, d > a=2; with a the plasma minor radius. The electron thermal diffusivity due to magnetic fluctuation induced transport is obtained from the expression v e ¼ K=l 0 d 2 e ; with l 0 the permeability of free space and d e the electron skin depth, which for typical tokamak fusion plasma parameters is on the order of a millimeter. Thus, the ratio of the energy confinement time to the resistive diffusion time in a tokamak plasma driven by steady-state CHI approaching Ohmic efficiency is shown to be constrained by the relation s E =s g < ðd e =aÞ 2 % 10 À6 :The mean-field model suggests that steady-state CHI can be viewed most simply as a boundary layer of stochastically wandering magnetic field lines.

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“…[6][7][8][9] All of these studies find that macroscopic symmetry-breaking MHD modes are driven unstable prior to relaxation, but the stabilizing influence of large toroidal field is evident in the tokamak and ST calculations. To obtain information relevant to startup CHI, our present study applies simplified modeling to conditions in HIT-II discharges that were run without Ohmic drive and did not have strong relaxation.…”

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confidence: 94%

Zero-β modeling of coaxial helicity injection in the HIT-II spherical torus

2011

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Coaxial helicity injection in the HIT-II [A. J. Redd et al., Phys. Plasmas 9, 2006(2002] spherical torus is modeled with time-dependent resistive magnetohydrodynamics computations run to steady state for conditions without strong relaxation. Laboratory and computed results on injector current and plasma current agree reasonably well as toroidal magnetic field and injector flux are scaled. The scalings are consistent with a dimensional estimate from the Grad-Shafranov equation that provides a new perspective on a previously published model based on a current-sheet equilibrium and the magnetic pressure required for the "bubble-burst" criterion. Numerical solutions of the Grad-Shafranov equation with an assumed current profile also indicate large qualitative changes as the predicted criterion is crossed.The strong curvature, shaping, and high normalized pressure (b) of spherical torus (ST) plasmas lead to confinement and stability properties that are distinct from large aspect-ratio tokamaks. Driving plasma current also requires special consideration of the geometric limitations on passing time-dependent magnetic flux through a small central column. The coaxial helicity injection (CHI) method is a direct-current (DC) alternative 1 to conventional inductive loop voltage. CHI biases a pair of toroidally symmetric electrodes that intercept the strike points of open poloidal magnetic field to generate linked poloidal and toroidal magnetic flux. Maintaining an electrostatic bias on the "injector" flux then sustains parallel current density in the presence of resistive dissipation. The CHI method was first tested for STs in the helicity injected torus (HIT) and HIT-II experiments-as the sole source of current drive in the case of HIT and with transition to Ohmic drive in HIT-II. 2,3 When gradients of parallel current density are sufficient to excite symmetry-breaking MHD activity, magnetic relaxation 4 can broaden the parallel current profile. However, when helicity injection is used for startup, relaxation is not required. Startup injection generates a plasma configuration that can be transitioned to inductive or other non-inductive current drive, and closed magnetic flux can be formed transiently without breaking toroidal symmetry. Here, we describe simplified modeling of two HIT-II discharge series that did not produce strong relaxation. Implications of the "bubble-burst" criterion of Ref.5 for the driven current to expand the injector flux beyond the injector region are reconsidered in terms of the Grad-Shafranov (GS) equation and are used to interpret our results.Simplified zero-b resistive MHD modeling of CHI has been applied to reversed-field pinch, straight tokamak, spheromak, and ST configurations to study magnetic relaxation from current-driven activity. 6-9 All of these studies find that macroscopic symmetry-breaking MHD modes are driven unstable prior to relaxation, but the stabilizing influence of large toroidal field is evident in the tokamak and ST calculations. To obtain information relevant to startup CHI...

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Magnetohydrodynamic simulations of direct current helicity injection for current drive in tokamaks

Cited by 14 publications

References 11 publications

The internal magnetic field structures and current density profiles in the Helicity Injected Spherical Torus plasma driven by coaxial helicity injection

The internal magnetic field structures and current density profiles in the Helicity Injected Spherical Torus plasma driven by coaxial helicity injection

Analytic model for coaxial helicity injection in tokamak plasmas

Zero-β modeling of coaxial helicity injection in the HIT-II spherical torus

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