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Register a new userAvailable energy of magnetically confined plasmas
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Per Helander
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The concept of available energy of a collisionless plasma is discussed in the context of magnetic confinement. The available energy quantifies how much of the plasma energy can be converted into fluctuations (including nonlinear ones) and is thus a measure of plasma stability, which can be used to derive linear and nonlinear stability criteria without solving an eigenvalue problem. In a magnetically confined plasma, the available energy is determined by the density and temperature profiles as well as the magnetic geometry. It also depends on what constraints limit the possible forms of plasma motion, such as the conservation of adiabatic invariants and the requirement that the transport be ambipolar. A general method based on Lagrange multipliers is devised to incorporate such constraints in the calculation of the available energy, and several particular cases are discussed. In particular, it is shown that it is impossible to confine a plasma in a Maxwellian ground state relative to perturbations with frequencies exceeding the ion bounce frequency.
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The energy budget of a collisionless plasma subject to electrostatic fluctuations is considered, and the excess of thermal energy over the minimum accessible to it under various constraints that limit the possible forms of plasma motion is calculated. This excess measures how much thermal energy is available for conversion into plasma instabilities, and therefore constitutes a nonlinear measure of plasma stability. A distribution function with zero available energy defines a ground state in the sense that its energy cannot decrease by any linear or nonlinear plasma motion. In a Vlasov plasma with small density and temperature fluctuations, the available energy is proportional to the mean square of these quantities, and exceeds the corresponding energy in ideal or resistive magnetohydrodynamics. If the first or second adiabatic invariant is conserved, ground states generally have inhomogeneous density and temperature. Magnetically confined plasmas are usually not in any ground state, but certain types of stellarator plasmas are so with respect to fluctuations that conserve both these adiabatic invariants, making the plasma linearly and nonlinearly stable to such fluctuations. Similar stability properties can also be enjoyed by plasmas confined by a dipole magnetic field.
We present Aurora, an open-source package for particle transport, neutrals and radiation modeling in magnetic confinement fusion plasmas. Auroras modern multi-language interface enables simulations of 1.5D impurity transport within high-performance computing frameworks, particularly for the inference of particle transport coefficients. A user-friendly Python library allows simple interaction with atomic rates from the Atomic Data and Atomic Structure database as well as other sources. This enables a range of radiation predictions, both for power balance and spectroscopic analysis. We discuss here the superstaging approximation for complex ions, as a way to group charge states and reduce computational cost, demonstrating its wide applicability within the Aurora forward model and beyond. Aurora also facilitates neutral particle analysis, both from experimental spectroscopic data and other simulation codes. Leveraging Auroras capabilities to interface SOLPS-ITER results, we demonstrate that charge exchange is unlikely to affect the total radiated power from the ITER core during high performance operation. Finally, we describe the ImpRad module in the OMFIT framework, developed to enable experimental analysis and transport inferences on multiple devices using Aurora.
The electromagnetic theory of the strongly driven ion-temperature-gradient (ITG) instability in magnetically confined toroidal plasmas is developed. Stabilizing and destabilizing effects are identified, and a critical $beta_{e}$ (the ratio of the electron to magnetic pressure) for stabilization of the toroidal branch of the mode is calculated for magnetic equilibria independent of the coordinate along the magnetic field. Its scaling is $beta_{e}sim L_{Te}/R,$ where $L_{Te}$ is the characteristic electron temperature gradient length, and $R$ the major radius of the torus. We conjecture that a fast particle population can cause a similar stabilization due to its contribution to the equilibrium pressure gradient. For sheared equilibria, the boundary of marginal stability of the electromagnetic correction to the electrostatic mode is also given. For a general magnetic equilibrium, we find a critical length (for electromagnetic stabilization) of the extent of the unfavourable curvature along the magnetic field. This is a decreasing function of the local magnetic shear.
A first-principles method to calculate the critical temperature gradient for the onset of the ion-temperature-gradient mode (ITG) in linear gyrokinetics is presented. We find that conventional notions of the connection length previously invoked in tokamak research should be revised and replaced by a generalized correlation length to explain this onset in stellarators. Simple numerical experiments and gyrokinetic theory show that localized spikes in shear, a hallmark of stellarator geometry, are generally insufficient to constrain the parallel correlation length of the mode. ITG modes that localize within bad drift curvature wells that have a critical gradient set by peak drift curvature are also observed. A case study of nearly helical stellarators of increasing field period demonstrates that the critical gradient can indeed be controlled by manipulating magnetic geometry, but underscores the need for a general framework to evaluate the critical gradient. We conclude that average curvature and global shear set the correlation length of resonant ITG modes near the absolute critical gradient, the physics of which is included through direct solution of the gyrokinetic equation. Our method, which handles general geometry and is more efficient than conventional gyrokinetic solvers, could be applied to future studies of stellarator ITG turbulence optimization.
we report the identification of a localised current structure inside the JET plasma. It is a field aligned closed helical ribbon, carrying current in the same direction as the background current profile (co-current), rotating toroidally with the ion velocity (co-rotating). It appears to be located at a flat spot in the plasma pressure profile, at the top of the pedestal. The structure appears spontaneously in low density, high rotation plasmas, and can last up to 1.4 s, a time comparable to a local resistive time. It considerably delays the appearance of the first ELM.
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