The Hall dynamo effect and nonlinear mode coupling during sawtooth magnetic reconnection

Abstract

During magnetic reconnection associated with sawtooth activity in a reversed field pinch, we observe a large fluctuation-induced Hall electromotive force, ͗␦J ϫ ␦B͘ / n e e, which is capable of modifying the equilibrium current. This Hall dynamo effect is determined in the hot plasma core by laser Faraday rotation which measures equilibrium and fluctuating magnetic field and current density. We find that the Hall dynamo is strongest when nonlinear mode coupling between three spatial Fourier modes of the resistive tearing instability is present. Mode coupling alters the phase relation between magnetic and current density fluctuations for individual Fourier modes leading to a finite Hall effect. Detailed measurements of the spatial and temporal dynamics for the dominant core resonant mode under various plasma configurations are described providing evidence regarding the origin of the Hall dynamo.

First-order finite-Larmor-radius fluid modeling of tearing and relaxation in a plasma pinch

“…Laser-polarimetry measurements of the m ¼ 1, n ¼ 6 perturbed magnetic field, where m is the poloidal-mode number and n is the toroidal-mode number, show the Halldynamo emf induced from this mode is significant in the core of 400 kA standard MST plasmas during relaxation. 2,3 Additionally, magnetic probe measurements in 200 kA lowcurrent plasmas demonstrate that Hall dynamo is important near the wall during relaxation. 4 Considerations of linear tearing modes, 8,9 the dominant long-wavelength instability in RFPs, show that the correlation hJ ÂBi vanishes with a single-fluid model.…”

“…[2][3][4] These measurements often focus temporally on relaxation or "sawtooth" events where fluctuations are large. During these events, correlations of fluctuations induce emfs that flatten the current profile by driving poloidal current at r & 0:5a, where a is the minor radius, and reducing the toroidal current in the core.…”

Particle-in-cell simulations of tearing modes in reversed-field-pinch-like plasma

“…They are thought to be responsible for fast reconnection of magnetic fields, relaxation to the Taylor state, and the dynamo effect in reversed field pinch ͑RFP͒. [2][3][4][5][6] It is also believed that the tearing instabilities contribute to the ion heating 7 and the momentum transport 8 in RFPs, observed during internal reconnection events ͑sawtooth crashes͒ [9][10][11][12][13][14][15][16] in these machines. The understanding of the physics of tearing instabilities is important for the understanding of various processes in RFP.…”

Magnetic-Fluctuation-Induced Particle Transport and Density Relaxation in a High-Temperature Plasma

“…This requires measurement of (i) the local density fluctuation and its derivative n, @n=@r, (ii) magnetic field fluctuation b r , and (iii) their correlation. In cylindrical coordinates, the expression r Á À n r;e can be simplified since measurements show that the parallel electron velocity, mean magnetic field, and radial magnetic fluctuation profiles are nearly flat in the core [14]. Therefore, we can write r Á À n r; ¼ 1 r @ @r ðrÀ n r; Þ % 2 V k;e B h @n @r b r i.…”

“…At the magnetic axis, the equilibrium magnetic field strength B $ 0:3-0:4 T, the equilibrium current density J k $ 2 MA=m 2 , and safety factor q $ 1=6, where q describes the rotational transform of a field line in a torus. The mean electron velocity V k;e is inferred from the measured parallel current density and electron density, V k;e % J k =n e e $ 10 6 m=s [14]. MST discharges display a sawtooth cycle in many parameters, and the measured quantities are ensemble (flux-surface) averaged over these reproducible sawtooth events.…”