Invariant Measure and Turbulent Pinch in Tokamaks

Anomalous pinch of turbulent plasmas driven by the magnetic-drift-induced Lorentz force through the Stokes-Einstein relation

“…(33, 34) are also applicable for passing particles. Therefore, the present theory clearly predicts a passing particle pinch, which is absent in previous fluid theory [3] and kinetic theory [4,6]. It should be noted that in a more recent fluid theory and simulation work [20], particle pinch of impurity ions was identified, which is independent of the trapping fraction, as is different from the earlier fluid theory [3]; however, it is not clear in Ref.…”

“…Note that the previous trapped electron pinch [4,6] is included in Eq. (33) (the effect of ∇B drift).…”

“…Eq. (4) indicates that the perpendicular mean electric field does not drive a particle pinch through the Stokes-Einstein relation, due to the cancelation between eE and eV E×B × B, therefore, the anomalous particle pinch must be auto-ambipolar. (4) The physical picture of parallel momentum pinch described in this paper is related to the Stokes-Einstein flux driven by the Lorentz force generated by the magnetic drift, which is different from the previous understanding by invoking the Coriolis force [8][9][10][11].…”

Perturbative studies of toroidal momentum transport using neutral beam injection modulation in the Joint European Torus: Experimental results, analysis methodology, and first principles modeling

“…Furthermore, the drift in the electrostatic potential perturbations accelerates the particles and also leads to the generation of parallel velocity fluctuations and consequently to a momentum flux. Although no complete expression for the flux has been derived for the laboratory frame, the latter effect is related to the turbulent equipartition (TEP [40]) theory and has recently been worked out in Ref. [8].…”

Orbit-averaged quantities, the classical Hellmann-Feynman theorem, and the magnetic flux enclosed by gyro-motion

“…Applications of guiding center theory are diverse and range from particle confinement in the Earth's magnetosphere 2 and in solar coronal loops 3 to the pinch effect in tokamaks. [4][5][6][7][8] Even for non-adiabatic phenomena, such as large energy transfer to particles interacting with electromagnetic waves, 9-11 the introduction of the action integral and its conjugate angle variable is extremely useful, and applications also exist beyond particle motion, such as in conservation laws for waves, including interactions between discrete and continuum modes. 12 Use of the action integral typically implies that the system has been averaged over the fast variation, and this feature of the action integral is born out in the adaptation of the Hellmann-Feynman theorem for classical mechanics 13,14 (see Ref.…”