Boris N. Breizman

Chapter 5: Physics of energetic ions

This chapter reviews the progress accomplished since the redaction of the first ITER Physics Basis (1999 Nucl. Fusion 39 2137-664) in the field of energetic ion physics and its possible impact on burning plasma regimes. New schemes to create energetic ions simulating the fusion-produced alphas are introduced, accessing experimental conditions of direct relevance for burning plasmas, in terms of the Alfvenic Mach number and of the normalised pressure gradient of the energetic ions, though orbit characteristics and size cannot always match those of ITER. Based on the experimental and theoretical knowledge of the effects of the toroidal magnetic field ripple on direct fast ion losses, ferritic inserts in ITER are expected to provide a significant reduction of ripple alpha losses in reversed shear configurations. The nonlinear fast ion interaction with kink and tearing modes is qualitatively understood, but quantitative predictions are missing, particularly for the stabilisation of sawteeth by fast particles that can trigger neoclassical tearing modes. A large database on the linear stability properties of the modes interacting with energetic ions, such as the Alfven eigenmode has been constructed. Comparisons between theoretical predictions and experimental measurements of mode structures and drive/damping rates approach a satisfactory degree of consistency, though systematic measurements and theory comparisons of damping and drive of intermediate and high mode numbers, the most relevant for ITER, still need to be performed. The nonlinear behaviour of Alfven eigenmodes close to marginal stability is well characterized theoretically and experimentally, which gives the opportunity to extract some information on the particle phase space distribution from the measured instability spectral features. Much less data exists for strongly unstable scenarios, characterised by nonlinear dynamical processes leading to energetic ion redistribution and losses, and identified in nonlinear numerical simulations of Alfven eigenmodes and energetic particle modes. Comparisons with theoretical and numerical analyses are needed to assess the potential implications of these regimes on burning plasma scenarios, including in the presence of a large number of modes simultaneously driven unstable by the fast ions.

Magnetohydrodynamic scenario of plasma detachment in a magnetic nozzle

Some plasma propulsion concepts rely on a strong magnetic field to guide the plasma flow through the thruster nozzle. The question then arises of how the magnetically confined plasma can detach from the spacecraft. This work presents a magnetohydrodynamic (MHD) detachment scenario in which the plasma flow stretches the magnetic field lines to infinity. Detachment takes place after the energy density of the expanding magnetic field drops below the kinetic energy density of the plasma. As plasma flows along the magnetic field lines, the originally sub-Alfvenic flow becomes super-Alfvenic; this transition is similar to what occurs in the solar wind. In order to describe the detachment quantitatively, the ideal MHD equations have been solved for a cold plasma flow in a slowly diverging nozzle. The solution exhibits a well-behaved transition from sub- to super-Alfvenic flow inside the nozzle and a rarefaction wave at the edge of the outgoing flow. It is shown that efficient detachment is feasible if the nozzle...

Theoretical components of the VASIMR plasma propulsion concept

The ongoing development of the Variable Specific Impulse Magnetoplasma Rocket (VASIMR) involves basic physics analysis of its three major components: helicon plasma source, ion cyclotron-resonance heating module, and magnetic nozzle. This paper presents an overview of recent theoretical efforts associated with the project. It includes (1) a first-principle model for helicon plasma source, (2) a nonlinear theory for the deposition of rf-power at the ion cyclotron frequency into plasma flow, and (3) a discussion of the plasma detachment mechanism relevant to VASIMR.

Spontaneous hole-clump pair creation in weakly unstable plasmas

A numerical simulation of a kinetic instability near threshold shows how a hole and clump spontaneously appear in the particle distribution function. The hole and clump support a pair of Bernstein, Greene, Kruskal (BGK) nonlinear waves that last much longer than the inverse linear damping rate while they are upshifting and downshifting in frequency. The frequency shifting allows a balance between the power nonlinearly extracted from the resonant particles and the power dissipated into the background plasma. These waves eventually decay due to phase space gradient smoothing caused by collisionality.

The HAGIS self-consistent nonlinear wave-particle interaction model

Abstract The problem of modelling the self-consistent interaction of an energetic particle ensemble with a wave spectrum specific to magnetically confined plasmas in a torus is discussed. Particle motion in a magnetic field coordinate system, whose surfaces are perturbed by a spectrum of finite amplitude magnetohydrodynamical (MHD) waves, is described using a Hamiltonian formulation. Employing the δƒ method enables the simulation particles to only represent the change in the total particle distribution function and consequently possesses significant computational advantages over standard techniques. Changes to the particle distribution function subsequently affect the wave spectrum through wave-particle interactions. The model is validated using large aspect-ratio asymptotic limits as well as through a comparison with other numerical work. A consideration of the Kinetic Toroidal Alfven Eigenmode instability driven by fusion born α -particles in a D-T JET plasma illustrates a use of the code and demonstrates nonlinear saturation of the instability, together with the resultant redistribution of particles both in energy and across the plasma cross section.

Theory of Alfvén eigenmodes in shear reversed plasmas

Plasma configurations with shear reversal are prone to the excitation of unusual Alfven eigenmodes by energetic particles. These modes exhibit a quasiperiodic pattern of predominantly upward frequency sweeping (Alfven cascades) as the safety factor q changes in time. This work presents a theory that employs two complementary mechanisms for establishing Alfven cascades: (1) a nonstandard adiabatic response of energetic particles with large orbits and (2) toroidal magnetohydrodynamic effects that are second-order in inverse aspect ratio. The developed theory explains the transition from Alfven cascades to the toroidicity induced Alfven eigenmodes (TAEs), including modifications of the TAEs themselves near the shear reversal point.

Plasma pressure effect on Alfvén cascade eigenmodes

Tokamak plasmas with reversed magnetic shear are prone to the excitation of Alfven cascade (AC) eigenmodes by energetic particles. These modes exhibit a quasiperiodic pattern of predominantly upward frequency sweeping. Observations also reveal that the AC spectral lines sometimes bend at low frequencies, which is a significant deviation from the shear Alfven wave dispersion relation. This paper shows that the underlying reasons for such bending are the finite pressure of the plasma and the geodesic curvature that precludes shear Alfven perturbations from being strictly incompressible. In addition to the geodesic effect, there are two other pressure effects on shear Alfven waves, which are the convection in the presence of an equilibrium pressure gradient and the toroidicity-induced coupling between shear Alfven waves and acoustic modes. An analytical treatment of the problem enables a parametric comparison of all three mechanisms. The key distinction between the geodesic compressibility and the acoustic c...

Spontaneous hole–clump pair creation

Numerical simulations and quantitative theoretical explanations are presented for the spontaneous formation of a hole–clump pair in phase space. The equilibrium is close to the linear threshold for instability and the destabilizing resonant kinetic drive is nearly balanced by either extrinsic dissipation or a second stabilizing resonant kinetic component. The hole and clump, each support a nonlinear wave where the trapping frequency of the particles is comparable to the kinetic linear growth rate from the destabilizing species alone. The power dissipated is balanced by energy extracted by trapped particles locked to the changing wave-phase velocities. With extrinsic dissipation, phase space structures always form just above the linear instability threshold. With a stabilizing kinetic component, an electrostatic interaction is considered with varying mass ratios of the stabilizing and destabilizing species together with collisional effects. With these input parameters, various nonlinear responses arise, on...

Critical nonlinear phenomena for kinetic instabilities near threshold

A universal integral equation has been derived and solved for the nonlinear evolution of collective modes driven by kinetic wave particle resonances just above the threshold for instability. The dominant nonlinearity stems from the dynamics of resonant particles that can be treated perturbatively near the marginal state of the system. With a resonant particle source and classical relaxation processes included, the new equation allows the determination of conditions for a soft nonlinear regime, where the saturation level is proportional to the increment above threshold, or a hard nonlinear regime, characterized by explosive behavior, where the saturation level is independent of the closeness to threshold. In the hard regime, rapid oscillations typically arise that lead to large frequency shifts in a fully developed nonlinear stage. The universality of the approach suggests that the theory applies to many types of resonant particle driven instabilities, and several specific cases, viz. energetic particle dr...

Finite orbit energetic particle linear response to toroidal Alfven eigenmodes

Abstract The linear response of energetic particles of the TAE modes is calculated taking into account their finite orbit excursion from the flux surfaces. The general expression reproduces the previously derived theory for small banana width; when the banana width Δ b is much larger than the mode thickness Δ m , we obtain a new compact expression for the linear power transfer. When Δ m / Δ b ⪡1, the banana orbit effect reduces the power transfer by a factor Δ m / Δ b from that predicted by the narrow orbit theory. A comparison is made of the contribution to the TAE growth rate of energetic particles with a slowing-down distribution arising from an isotropic source, and a balanced-injected beam source when the source speed is close to the Alfven speed. For the same stored energy density, the contribution from the principal resonances (| v ‖ |= v A ) is substantially enhanced in the beam case compared to the isotropic case, while the contribution at the higher sidebands (| v ‖ |= v A /(2 l −1) with l ⩾2) is substantially reduced.