Session G15: Sherwood I

From Fundamental Science to Fusion Energy -- the First 50 Years of Fusion Theory

With ITER, fusion energy research will reach the long anticipated goal of a stable, long-duration burning plasma -- one that is largely sustained by fusion reactions. The history of progress towards this goal is intricately entwined with the development of the fundamental physics of plasmas and nonlinear systems. I will examine this history through three examples that highlight the role of theory and the Sherwood meeting. In the first example, I will discuss the development of stability theory. I will begin with the magnetohydrodynamic energy principle calculations of the 1950s and trace advances to the recent sophisticated kinetic calculations of ITER's stability to alpha particle driven modes. The development and application of chaos theory in fusion research will be my second example. I will trace its growth from field-line tracing for the first stellarators to the design of the ELM mitigation coils in ITER. In the final example I will examine the development of plasma turbulence theory to describe the transport of plasma heat and particles in fusion experiments. My (abbreviated) history of plasma turbulence will begin with Bohm's curious formula for turbulent transport and finish with the latest gyro-kinetic simulation of ITER like plasmas.   

Energetic Particle-induced Geodesic Acoustic Mode

A new n=0 Energetic Particle-induced Geodesic Acoustic Modes (EGAM) is shown to exist based on analytic theory and numerical simulation [1]. Unlike the conventional GAMs driven nonlinearly by plasma micro-turbulence, the new mode is found to be linearly driven by energetic particles with free energy associated with anisotropic particle distribution function. An integral differential equation is derived for EGAM including the non-perturbative effects of energetic particles with finite orbit width. Analysis shows that when the energetic particle pressure is comparable to the thermal pressure, the frequency of EGAM is substantially lower than the local GAM frequency associated with thermal species. Furthermore, the new mode has a global radial structure with the mode width determined by the energetic particle drift orbit width. For typical experimental parameters in reversed shear plasmas, the mode width can be quite large. Nonlinear simulation results show initial saturation due to the flattening of particle distribution function in velocity space. A bursting feature of the mode amplitude is found following the initial saturation. These results are consistent with the recent experimental results of the beam-driven GAM-like n=0 mode in DIII-D [2]. In particular, the calculated mode frequency and the global radial structure agree well with the experimental observations. [1] G. Y. Fu, Phys. Rev. Letts. 101, 185001 (2008) [2] R. Nazikian et al., Phys. Rev. Letts. 101, 185001 (2008).   

Flow stabilization of the ideal MHD resistive wall mode$^1$

We demonstrate for the first time in a numerical calculation that for a typical circular cylindrical equilibrium, the ideal MHD resistive wall mode (RWM) can be completely stabilized by bulk equilibrium plasma flow, $\mathbf {V}$, for a window of wall locations \emph{without} introducing additional dissipation into the system. The stabilization is due to a resonance between the RWM and the Doppler shifted ideal MHD sound continuum. Our numerical approach introduces$^2$ $\mathbf {u}=\omega\xi + i\mathbf{V} \cdot\nabla \xi$ and the perturbed wall current$^3$ as variables, such that the eigenvalue, $\omega$, only appears linearly in the linearized stability equations, which allows for the use of standard eigenvalue solvers. The wall current is related to the plasma displacement at the boundary by a Green's function. With the introduction of the resistive wall, we find that it is essential that the finite element grid be highly localized around the resonance radius where the parallel displacement, $\xi_\parallel$, becomes singular. We present numerical convergence studies demonstrating that this singular behavior can be approached in a limiting sense. We also report on progress toward extending this calculation to an axisymmetric toroidal geometry. $^1$Work supported by a DOE FES fellowship through ORISE and ORAU. $^2$L.Guazzotto, J.P Freidberg, and R. Betti, Phys.Plasmas 15, 072503 (2008). $^3$S.P. Smith and S. C. Jardin, Phys. Plasmas 15, 080701 (2008).