Potential vorticity transport in weakly and strongly magnetized plasmas

Abstract

Tangled magnetic fields, often coexisting with an ordered mean field, have a major impact on turbulence and momentum transport in many plasmas, including those found in the solar tachocline and magnetic confinement devices. We present a novel mean field theory of potential vorticity mixing in β -plane magnetohydrodynamic (MHD) and drift wave turbulence. Our results show that mean-square stochastic fields strongly reduce Reynolds stress coherence. This decoherence of potential vorticity flux due to stochastic field scattering leads to suppression of momentum transport and zonal flow formation. A simple calculation suggests that the breaking of the shear-eddy tilting feedback loop by stochastic fields is the key underlying physics mechanism. A dimensionless parameter that quantifies the increment in power threshold is identified and used to assess the impact of stochastic field on the L-H transition. We discuss a model of stochastic fields as a resisto-elastic network.

Ion Heat and Parallel Momentum Transport by Stochastic Magnetic Fields and Turbulence

“…Here, we construct a model for the evolution of density and parallel flow in presence of stochastic fields in Cartesian (slab) coordinates used in Chen et al [35]x is radial, y is poloidal, and z is toroidal direction, in which the mean toroidal field lies (Figure 3). In this 3D…”

“…Notice that both the Reynolds stress u x u z and Kinetic stress p b r /ρ in Equation ( 31) are affected by stochastic magnetic fields. Chen et al [35] discussed magnetic stochasticity effects on Reynolds stress. Also, the RHS of Equation ( 32) contains the compressive energy flux…”

“…Note that this analysis is, in some sense, 'dual' to that of Chen et al [35]. There, the vorticity response δU/δ u r was calculated in the presence of a prescribed ensemble of b 2 and used to calculate the Reynolds stress, where U = ∇ 2 ⊥ φ/B 0 is the E × B vorticity and φ denotes the electrical potential.…”

Synergy of Turbulent Momentum Drive and Magnetic Braking

“…The other main symmetry breaking mechanism is turbulence in presence of a background E × B shear, which has also been extensively studied [7,[31][32][33][34][35][36][37][38][39][40][41][42][43]. Yet, the possible competing and/or synergetic effects of extrinsic (ripple) versus self-generated (turbulence) asymmetries on rotation has drawn little [44] attention so far. Consequences are of prime importance, since any modification of mean flows impacts the radial electric field, and therefore also the transition toward improved confinement regimes [45].…”

Feynman rules for forced wave turbulence

“…A 3. This includes: elastic plate wave turbulence[8][9][10][11][12][13][14], turbulence in surface gravity waves[15][16][17][18][19], in gravitational waves[20][21][22][23], acoustic turbulence[24], planetary Rossby waves[25], waves on bubbles[26], emergent hydrodynamics[27], in a diatomic chain[28], in plasmas[29,30], optical waves[31][32][33], and rotating waves[34,35], and in FPUT chains[36].…”