Guiding-Center Drifts
The slow motion of a particle's gyration center across field lines under crossed forces and field gradients.
The Guiding-Center Picture
A charged particle in a strong magnetic field executes fast circular gyration around a slowly moving center, the guiding center. Averaging over the fast gyration reduces the motion to the drift of this center. Any force perpendicular to B, or any spatial variation of B, causes the guiding center to drift across field lines at a velocity much smaller than the thermal speed but crucial for confinement.
The Main Drifts
- E-cross-B drift: v = E x B / B^2; independent of charge, mass, and energy, so all species drift together with no current.
- Grad-B drift: v proportional to (perpendicular energy) grad B x B / B^3; charge-dependent, so ions and electrons drift oppositely, driving a current.
- Curvature drift: from the centrifugal force along curved field lines; also charge-dependent and, in a torus, adds to the grad-B drift.
- Polarization drift: a transient drift responding to a time-changing electric field, proportional to dE/dt.
Consequences in a Torus
In a torus the grad-B and curvature drifts are vertical and oppositely directed for ions and electrons, so they separate charge and would destroy confinement in a purely toroidal field. The helical twist of the field, produced by the plasma current, short-circuits this charge separation along field lines. This is the fundamental reason a tokamak needs a poloidal field, not just a toroidal one.
Relevance
Guiding-center drifts underlie neoclassical transport, the physics of trapped-particle banana orbits, and the E-cross-B shear that suppresses turbulence. For the Hyperion breeder concept, drift orbits set neoclassical transport and fast-ion confinement in design-stage modeling; the analysis is computational for a machine in simulation.