Helicity-Flux-Driven $\alpha$ Effect in Laboratory and Astrophysical Plasmas

The constraint imposed by magnetic helicity conservation on the $\alpha$ effect is considered for both magnetically and flow dominated self-organizing plasmas. Direct numerical simulations are presented for a dominant contribution to the $\alpha$ effect, which can be cast in the functional form of a total divergence of an averaged helicity flux, called the helicity-flux-driven $\alpha$ ($\mathrm{H}\alpha$) effect. Direct numerical simulations of the $\mathrm{H}\alpha$ effect are presented for two examples—the magnetically dominated toroidal plasma unstable to tearing modes, and the flow-dominated accretion disk.

Figure 1

The radial structure of hyper-resistivity ${\kappa }^2$ for a single tearing mode with $S={10}^6$. The solid line denotes the analytical result, while the dashed line shows the numerical result in the vicinity of the reconnecting surface where linear theory is applicable. The reconnecting surface is shown at $r=r_s$ with the vertical line.

Figure 2

Dynamo term ${ϵ}_{\mathrm{emf}}·\overline{\mathbf{B}}$, total divergence form of fluctuation-induced helicity flux given in Eq. (4) $-\nabla ·⟨{\mathrm{\Gamma }}_k⟩/2$, and the divergence form of helicity flux given by Vishniac and Cho, during $m=1$ MRI mode nonlinear saturation.

Figure 3

Magnetic energy $W_{m,n}=\frac{1}{2}\int {\tilde{B}}_{r(m,n}{)}^{2}d{r}^3$ vs time for different MRI modes for fully nonlinear computations.

Figure 4

The radial profiles of (a) $\mathrm{H}\alpha$ for all the MRI modes. (b) Large-scale mean azimuthal magnetic field generated, averaged over three points in time ($t/{\tau }_R=0.006$, 0.0062, 0.0065).