4. Mg islands, electric fields, plasma rotation Tokamak Physics Jan Mlynář 4. Mg islands, electric fields, plasma rotation Magnetic islands, periodicity, resistivity, loop voltage, Ware pinch, poloidal electric field, radial electric fields, toroidal and poloidal plasma rotations, grad B effect, plasma current direction, fast particle losses, rotation and B x grad B Fyzika tokamaků 1: Úvod, opakování

Magnetic islands Magnetic field lines: outside islands: OK, lines complete full q inside islands: lines form double helics, flattening the pressure profile overlapping islands: too bad for transport, field lines become chaotic (stochastic) Tokamak Physics 3: Tokamak field equilibrium

Magnetic field periodicity Top view: Top view: Similarly, top view: Watch out! Something to think of: Is the direction of the main toroidal field of any importance? Next lecture: grad B drift, plasma rotation, electric field, main plasma parameters i.e. 3 poloidal cross-sections will be identical Tokamak Physics 3: Tokamak field equilibrium

Plasma resistivity (singly charged ions) Plasma physics: + e-e collisions (Spitzer): e.g. equivalent of Cu conductivity @ 1.4 keV Tokamak Physics 3: Tokamak field equilibrium

Resistivity in special cases Resistivity perpendicular to mg. field: Hydrogen plasma with impurities: Plasma with a charge Z: Neoclassical resistivity: For e << 1 : Tokamak Physics 3: Tokamak field equilibrium

Electric fields in a tokamak ULOOP starts at high levels in order to get plasma breakdown IP penetrates to the centre from the edge - diffusion - drift complicated transition due to (Te) Steady - state: frame-dependent Sum of all species: quasineutrality  frame-independent Tokamak Physics 3: Tokamak field equilibrium

Ware pinch Conservation of the angular momentum: Guiding centre orbit: & banana: Tokamak Physics 3: Tokamak field equilibrium

Poloidal and radial el. field Due to Pfirsch-Schlüter In fact the vertical electrical field is a relict of B polarisation due to finite h Substantial in transport sutdies (causes poloidal rotation via the drift) ~ ambipolar field Tokamak Physics 3: Tokamak field equilibrium

Plasma rotation toroidal poloidal centrifugal force electric potential induced rotation (neutral beams, … ) spontaneous rotation Important consequence (?) of the radial electric fields Change in poloidal rotation tears turbulences  transport barriers Tokamak Physics 3: Tokamak field equilibrium

Plasma rotation Spinning up the plasma by neutral beams Rotation throws heavy impurities to the outboard of the plasma due to centrifugal force Typical rotation profile Tokamak Physics 3: Tokamak field equilibrium

grad-B effect H-mode power threshold is 2-3x lower in “forward” field configuration (divertor at bottom) “forward” or “clockwise” field “reversed” or “anti-clockwise” field Qualitative explanation: Tokamak Physics 3: Tokamak field equilibrium

H-mode power threshold Ohmic H-mode possible at low B(T) (low densities) and forward field Tokamak Physics 3: Tokamak field equilibrium

Direction of the plasma current Ip & Bf defines helicity FORWARD REVERSED Change in helicity can be troublesome For example at JET’s tiles: Tokamak Physics 3: Tokamak field equilibrium

Fast particle losses co-current counter-current beam beam Fast particle loss: In co-current, units of percent In counter-current, tens of percent Due to banana orbits : in forward field: co-current counter-current in reversed field: Tokamak Physics 3: Tokamak field equilibrium

Toroidal rotation & grad B effect Alcator-C: Up-down symmetry tested and, indeed... Tokamak Physics 3: Tokamak field equilibrium

Title ...the spontaneous rotation depends on the poloidal direction of ions in the Scrape-Off Layer ! Tokamak Physics 3: Tokamak field equilibrium