Current Density Equation in Turbulent Magnetized Plasmas

A turbulent extension of Ohm’s law, derived from the self-consistent action-angle transport theory, is presented. The equation describes the steady-state profile of the current density in axisymmetric magnetized plasmas in the presence of magnetic turbulence. The hyper-resistive, helicity-conserving contribution, usually derived in the framework of magneto-hydro-dynamics, is recovered, and the hyper-resistivity is defined. Additionally, the generalized Ohm’s law contains an anomalous resistivity term, and a term proportional to the current density derivative. For given thermodynamic profiles, the numerical solution of the equation shows that turbulent contributions, besides regularizing the current density profile in the central region, lead to an increase of the total plasma current. This “turbulent bootstrap” effect provides a possible explanation to discrepancies recently observed between experimental current profiles and neoclassical predictions

Turbulent Contributions to Ohm's Law in Axisymmetric Magnetized Plasmas

The effect of magnetic turbulence in shaping the current density in axisymmetric magnetized plasma is analyzed using a turbulent extension of Ohm's law derived from the self-consistent action-angle transport theory. Besides the well-known hyper-resistive (helicity-conserving) contribution, the generalized Ohm's law contains an anomalous resistivity term, and a turbulent bootstrap-like term proportional to the current density derivative. The numerical solution of the equation for equilibrium and turbulence profiles characteristic of conventional and advanced scenarios shows that, trough "turbulent bootstrap" effect and anomalous resistivity turbulence can generate power and parallel current which are a sizable portion (about 20-25%) of the corresponding effects associated with the neoclassical bootstrap effect. The degree of alignment of the turbulence peak and the pressure gradient plays an important role in defining the steady-state regime. In fully bootstrapped tokamak, the hyper-resistivity is essential in overcoming the intrinsic limitation of the hollow current profile.Comment: 19 pages, 6 figures, journal pape

Effect of temperature anisotropy on the dynamics of geodesic acoustic modes

In this work, we revisit the linear gyro-kinetic theory of geodesic acoustic modes (GAMs) and derive a general dispersion relation for an arbitrary equilibrium distribution function of ions. A bi-Maxwellian distribution of ions is then used to study the effects of ion temperature anisotropy on GAM frequency and growth rate. We find that ion temperature anisotropy yields sensible modifications to both the GAM frequency and growth rate as both tend to increase with anisotropy and these results are strongly affected by the electron to ion temperature ratio

Turbulent sources in axisymmetric plasmas

Successful operation of tokamaks and other magnetic confinement schemes of fusion interest rely on the tailoring of the parallel momentum/current density and temperature profiles via resonant absorption of externally injected waves. Similarly, it is to be expected that a turbulent spectrum of waves, internally generated to free the energy stored in the gradients of the equilibrium profiles, could transfer locally momentum and energy to the particle degree of freedom of the plasma. Turbulent sources stem out nicely from the action-angle transport formalism, as a detailed derivation of the general transport law from the collision operator (which includes both the diffusion and the friction coefficients) in action-space shows. The special case of magnetic turbulence is considered, and explicit expressions for the electron parallel momentum and energy sources are presented. An interesting feature of the sources resides in their dependence on the first and second powers of the safety factor derivative, a dependence that is often found in turbulent fluxes as well. One term in the energy source depends, in a determinant way, also on the relative magnitude of the electron and ion temperature. This dependence, an output of the retention of the friction term in the collision operator, leads to an energy flow that is always directed from the hotter to the cooler species, a desirable property that is missed when a quasilinear approach is employed

Self-consistent electron transport in tokamaks.

Electron particle, momentum, and energy fluxes in axisymmetric toroidal devices are derived from a version of the action-angle collision operator that includes both diffusion and drag in action-space [D. A. Hitchcock, R. D. Hazeltine, and S. M. Mahajan, Phys. Fluids 26, 2603 (1983); H. E. Mynick, J. Plasma Phys. 39, 303 (1988)]. A general result of the theory is that any contribution to transport originating directly from the toroidal frequency of the particle motion is constrained to be zero when the electron temperature is equal to the ion temperature. In particular, this constraint applies to those components of the particle and energy fluxes that are proportional to the magnetic shear, independent of the underlying turbulence and of whether the particles are trapped or untrapped. All the total fluxes describing collisionless transport of passing electrons in steady-state magnetic turbulence contain contributions proportional to the conventional thermodynamic drives, which are always outward, and contributions proportional to the magnetic shear, which have both magnitude and sign dependent on the ion-electron temperature ratio. The turbulent generalization of Ohm's law includes a hyper-resistive term, which flattens the current density profile on a fast time scale, and a turbulent electric field, which can have both signs depending on the electron-ion temperature ratio