Understanding the physics of tokamak boundary [edge and scrape-off-layer (SOL)] plasmas continues to be an active and important area of fusion research. It is widely recognized that the edge plasma can control global confinement and provides a crucial and as yet poorly understood boundary condition for core transport. Turbulent transport in the SOL is thought to set the SOL width, and is therefore important when considering divertor heat exhaust issues. Thus the physics of boundary plasma stability, turbulence and transport has received increasing attention in the fusion community.
The boundary plasma in a typical L-mode diverted tokamak discharge is unstable to a class of modes called resistive X-point (RX) modes.[1] The RX mode is a type of resistive ballooning mode that exploits a synergism between resistivity and the magnetic geometry of the X-point region. RX modes are shown to give robust instabilities at moderate mode numbers, and therefore are expected to be the dominant contributors to turbulent diffusion in the boundary plasma of a diverted tokamak. Work at Lodestar, in collaboration with LLNL, has elucidated the properties of the RX mode and compared the stability of the edge and SOL in diverted (limited) plasmas where the RX mode is (is not) present.[2] The role of a separatrix and X-point on wave propagation and on MHD and fluid instabilities at the plasma edge have been reviewed from a general point of view in a recent paper.[3]
These, and other ongoing studies are focused on gaining further physical insight into the exciting simulation results from the nonlinear BOUT turbulence code, which has shown the importance of X-point effects in fixed profile[4] and dynamical[5],[6] simulations of L-H transition physics. From these advances, the possibility of employing 3D turbulence codes for routine modeling of boundary plasmas for comparison and interpretation of experimental data is emerging.[7]
One physics theme that has arisen from this work is the competition between drift and curvature drive in boundary plasma instabilities. In the limit of resistive MHD, the curvature-driven RX modes display a scaling with q and B that is similar to the Carreras-Diamond modes.[8] Recent work has elucidated the importance of divertor geometry for resistive and electron-inertial drift-driven instabilities in the edge plasma.[9] It has been shown that the pure (with curvature drives suppressed) drift-Alfvén-wave is unstable in divertor geometry while it is well known[10] to be stable in an equivalent circular flux surface geometry (with sufficiently weak radial variation of w*). The results, seen in both the linear codes BAL, MBAL (a matrix-method eigenvalue code that generalizes BAL) and the BOUT turbulence code, were ultimately understood in terms of simple models which illustrated the role of wave reflection from the localized regions of strong magnetic shear near the X-points. Thus X-point effects are significant for both curvature and drift-wave branches in the edge plasma. The crucial effects of geometry suggest the existence of a new dimensionless parameter governing edge stability, which has yet to be fully characterized.
[1] J.R. Myra, D.A. D’Ippolito, X.Q. Xu and R.H. Cohen, Phys. Plasmas 7, 2290 (2000).
[2] J.R. Myra, D.A. D’Ippolito, X.Q. Xu and R.H. Cohen, Phys. Plasmas 7, 4622 (2000).
[3] J.R. Myra, D.A. D’Ippolito, X.Q. Xu and R.H. Cohen, Contrib. Plasma Phys. 40, 352 (2000).
[4] X.Q. Xu, R. H. Cohen, G.D. Porter, T.D. Rognlien, D.D. Ryutov, J.R. Myra. D.A. D'Ippolito and R. Moyer, Nucl. Fusion 40 Yokohama Special Issue 3, 731 (2000).
[5] X.Q. Xu, R.H. Cohen, T.D. Rognlien and J.R. Myra, Phys. Plasmas 7, 1951 (2000).
[6] X.Q. Xu, R.H. Cohen, W.M. Nevins, G.D. Porter, M.E. Rensink, T.D. Rognlien, J.R. Myra, D.A. D’Ippolito, R.A. Moyer, P.B. Snyder and T.N. Carlstrom, Nucl. Fusion 42, 21 (2002).
[7] X.Q. Xu, W.M. Nevins, R.H. Cohen, J.R. Myra and P.B. Snyder, New Journal of Physics 4, 53 (2002).
[8] T.C. Hender et al., Phys. Fluids 27, 1439 (1984).
[9] J.R. Myra, D.A. D'Ippolito and X.Q. Xu, Phys. Plasmas 9, 1637 (2002).
[10] P.N. Guzdar, L. Chen, P.K. Kaw and C. Oberman, Phys. Rev. Lett 40, 1566 (1978).