# Item

ITEM ACTIONSEXPORT

Released

Journal Article

#### On axisymmetric resistive magnetohydrodynamic equilibria with flow free of Pfirsch–Schlüter diffusion

##### External Resource

No external resources are shared

##### Fulltext (restricted access)

There are currently no full texts shared for your IP range.

##### Fulltext (public)

There are no public fulltexts stored in PuRe

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Throumoulopoulos, G. N., & Tasso, H. (2003). On axisymmetric resistive magnetohydrodynamic
equilibria with flow free of Pfirsch–Schlüter diffusion.* Physics of Plasmas,* *10*(6),
2382-2388. doi:10.1063/1.1571542.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0027-3AAB-1

##### Abstract

The equilibrium of an axisymmetric magnetically confined plasma with anisotropic resistivity and incompressible flows parallel to the magnetic field is investigated within the framework of the magnetohydrodynamic (MHD) theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order elliptic partial differential equation for the poloidal magnetic flux function ψ along with a decoupled Bernoulli equation for the pressure identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the resistivities η

_{║}and η_{│}parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic resistivity and parallel flows [G. N. Throumoulopoulos and H. Tasso, J. Plasma Phys. 64, 601 (2000)] the equilibrium is compatible with nonvanishing poloidal current densities. Also, although exactly Spitzer resistivities either η_{║}(ψ) or η_{│}(ψ) are not allowed, exact solutions with vanishing poloidal electric fields can be constructed with η_{║}and η_{│}profiles compatible with roughly collisional resistivity profiles, i.e., profiles having a minimum close to the magnetic axis, taking very large values on the boundary and such that η_{│}> η_{║}. For equilibria with vanishing flows satisfying the relation (dP/dψ)(dI²/dψ)>0, where P and I are the pressure and the poloidal current functions, the difference η_{│}–η_{║}for the reversed-field pinch scaling, B_{p}≈ B_{t}, is nearly two times larger than that for the tokamak scaling, B_{p}≈ 0.1B_{t}(B_{p}and B_{t}are the poloidal and toroidal magnetic-field components). The particular resistive equilibrium solutions obtained in the present work, inherently free of—but not inconsistent with—Pfirsch–Schlüter diffusion, indicate that parallel lows might result in a reduction of the diffusion observed in magnetically confined plasmas.