Solitary and Shock Structures Induced by Poloidal Flow in Tokamaks

It is shown that solitary and shock structures can appear in tokamaks, when a poloidal flow velocity becomes close to ε c s , where c s is a sound velocity and ε is a small inverse aspect ratio. To describe asymptotic behavior of the flow velocity v p , a KdV (Korteweg de Vries)-Burgers equation with a sinusoidal force term is derived from the two-fluid MHD equations with small resistivity and parallel viscosity. A solitary flow velocity structure appears inside of the torus (at the poloidal angle θ=π) in the non-dissipative, dispersive case. The supersonic flow ( v p > ε c s ) parallel to the poloidal magnetic field and the subsonic anti-parallel flow ( v p < ε c s ) are stable. In both cases the solitary density perturbation is negative. For the non-dispersive, dissipative case or the one-fluid MHD limit the forced Burgers equation becomes appropriate to describe the flow dynamics. This case corresponds to an appearance of shock structure. By solving an initial value problem it is shown that the shock position moves from θ≃0 to θ≃π with the variation of | v p - ε c s |.