A model of A model of toroidal rotation reversal ... - Florin Spineanu

A model of toroidal rotation reversal rotation reversal based on inverse based on inverse ... taken on the same time scale by the time-variation of the electric field:.
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A model of toroidal rotation reversal based on inverse Ranque Ranque--Hilsch effect

Florin Spineanu and Madalina Vlad Association EURATOM – MEdC Romania National Institute of Laser, Plasma and Radiation Physics, Bucharest, Romania

Spineanu Oxford 2011

What is the Ranque – Hilsch effect (and why its inverse is interesting for tokamak) A VORTEX TUBE is a cylinder where air Is injected tangentially at high pressure pressure. There are two ouput locations: - At the circumference (the other side) - On the axis (the same side as the input) It separates the temperatures: - At the tangential output air is HOT - At the axial output air is COLD p as that. You can buyy one,, but As simple still we do not understand how it works.

Spineanu Oxford 2011

One of the hypothesis: Colgate and Lovelace Formation of planets in accretion disks: - Loss of azimuthal symmetry by generation of convection cells

Three coupled components: 1. Poloidal rotation 1 2. Convection cells breaking the azimuthal symmetry 3. gradient of temperature

Inverse RH:

1. Gradient of temperature 2. Convection cells breaking azimuthal symmetry 3. Poloidal rotation Spineanu Oxford 2011

Convection cells: not quite conventional

1 ∂T uθ = c eB ∂r

The equilibrium poloidal rotation

C=1 1.17 17 = - 0.5 = - 2.1

banana plateau Pfirsch-Schluter

Transformation of sheared poloidal rotation into a chain of rolls with the same sign of the vorticity

Spineanu Oxford 2011

ITG

Alternative approach: V ill ti Vacillation

streamers t

roll-up ll d tto baroclinic due b li i term t

∂ω 1 ~ 2 ∇ρ × ∇p ∂t ρ Baroclinic term Spineanu Oxford 2011

The poloidal velocity is directly sustained by the gradient of pressure via the baroclinic term The peripheric velocity of the chain of rolls Generates an envelope which is the poloidal velocity Fast time variation of the poloidal velocity can only be taken on the same time scale by the time-variation of the electric field:

∂vθ ∂Er →− ∂t ∂t

Spineanu Oxford 2011

2 c ⎛ ∂Er ⎞ 3/ 2 jr = ε ⎟ 2 ⎜ ∂t ⎠ v Aθ ⎝ ∂t

Every bounce the precession of the banana is accelerated with a small velocity increase

1 ∂Er (t3 − t1 ) u3 − u1 = Bθ ∂t

Spineanu Oxford 2011