# Scaling of up-down asymmetric turbulent momentum flux with poloidal shaping mode number in tokamaks

Breaking the up-down symmetry of tokamaks removes a constraint limiting intrinsic momentum transport, and hence toroidal rotation, to be small. Using gyrokinetic theory, we study the effect of different up-down asymmetric flux surface shapes on the turbulent transport of momentum. This is done by perturbatively expanding the gyrokinetic equation in large flux surface shaping mode number. It is found that the momentum flux generated by shaping that lacks mirror symmetry (which is necessarily up-down asymmetric) has a power law scaling with the shaping mode number. However, the momentum flux generated by mirror symmetric flux surface shaping (even if it is up-down asymmetric) decays exponentially with large shaping mode number. These scalings are consistent with nonlinear local gyrokinetic simulations and indicate that low mode number shaping effects (e.g. elongation, triangularity) are optimal for creating rotation. Additionally it suggests that breaking the mirror symmetry of flux surfaces may generate significantly more toroidal rotation.

**Comments:**39 pages, 4 figures

## Similar Publications

The collisionless axisymmetric zonal flow residual calculation for a tokamak plasma is generalized to include electromagnetic perturbations. We formulate and solve the complete initial value zonal flow problem by retaining the fully self-consistent axisymmetric spatial perturbations in the electric and magnetic fields. Simple expressions for the electrostatic, shear- and compressional magnetic residual responses are derived that provide a fully electromagnetic test of the zonal flow residual in gyrokinetic codes. Read More

Conventionally, space-charge (SC) limited current is defined as the maximal current allowed to traverse a diode under a DC voltage when a time-invariant current is injected from cathode. In this work, we study the SC limited current under the time-varying injection for both classical and relativistic regimes and determine the maximal amount of limited current under certain conditions. Our simulations show that it is unlikely that a time-varying injection current emitted from cathode exceeds the known SC limits, in either classical or relativistic regime. Read More

We study the Bose-Einstein condensation of photons in a plasma, where we include the cases of both transverse photons and plasmons. We consider four-wave mixing processes of photon and plasmon modes in a relativistic isotropic plasma to determine the coupling constant to lowest order. We further show that photon condensation is possible in an unbounded plasma because, in contrast with other optical media, plasmas introduce an effective photon mass. Read More

The motion of energetic particles in magnetic turbulence across a mean magnetic field is explored analytically. The approach presented here allows for a full time-dependent description of the transport, including compound sub-diffusion. The first time it is shown systematically that as soon as there is transverse structure of the turbulence, diffusion is restored even if no Coulomb collisions are invoked. Read More

The two-dimensional Terry-Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth-Hinton states. This phenomena persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. Analytic progress on the truncated system is reported, focused on determining the growth rates of zonal flows and calculating the upper bound of the Dimits shift. Read More

This letter presents the results of an advanced parametrization of the solar wind electron temperature anisotropy and the instabilities resulting from the interplay of the (bi-)Maxwellian core and (bi-)Kappa halo populations in the slow solar wind. A large set of observational data (from the Ulysses, Helios and Cluster missions) is used to parametrize these components and establish their correlations. The instabilities are significantly stimulated in the presence of suprathermals, and the instability thresholds shape the limits of the temperature anisotropy for both the core and halo populations re-stating the incontestable role that the selfgenerated instabilities can play in constraining the electron anisotropy. Read More

We perform first-principles path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of LiF. Our simulations cover a wide density-temperature range of $2.08-15. Read More

Existing theoretical and observational constraints on the abundance of magnetic monopoles are limited. Here we demonstrate that an ensemble of monopoles forms a plasma whose properties are well determined and whose collective effects place new tight constraints on the cosmological abundance of monopoles. In particular, the existence of micro-Gauss magnetic fields in galaxy clusters and radio relics implies that the scales of these structures are below the Debye screening length, thus setting an upper limit on the cosmological density parameter of monopoles, $\Omega_M\lesssim3\times10^{-4}$, which precludes them from being the dark matter. Read More

The long-standing challenge to describing charged particle dynamics in strong classical electromagnetic fields is how to incorporate classical radiation, classical radiation reaction and quantized photon emission into a consistent unified framework. The current, semiclassical methods to describe dynamics of quantum particles in strong classical fields also provide the theoretical framework for fundamental questions in gravity and hadron-hadron collisions, including Hawking radiation, cosmological particle production and thermalization of particles created in heavy-ion collisions. However, as we show, these methods break down for highly relativistic particles propagating in strong fields. Read More

We obtain analytic solutions of a generalised Grad-Shafranov equation describing steady states with incompressible plasma flow of arbitrary direction, toroidal current reversal and either nested or non-nested magnetic surfaces. It turns out that the component of the flow velocity non parallel to the magnetic field can result in normal equilibria with central current-reversal, i.e. Read More