1. 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

2. 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

3. 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

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

5. 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

6. 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

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

8. 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

9. 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

10. 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

11. 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

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

13. 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

14. 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

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

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