Guiding-Center Drifts
The slow, systematic motions of a gyrating particle's center caused by fields, gradients, and curvature.
Averaging out the gyration
A charged particle spirals rapidly around a field line, but the center of that spiral, the guiding center, drifts slowly under various forces. Separating the fast gyration from the slow drift is the foundation of magnetized-plasma theory. The main drifts are:
text
v_ExB = (E x B) / B^2
v_gradB = (m v_perp^2 / 2qB) (B x grad B) / B^2
v_curv = (m v_parallel^2 / qB) (R_c x B) / (R_c^2 B)The E cross B drift moves all particles together regardless of charge or mass. The grad-B and curvature drifts depend on charge, so they separate ions and electrons and drive currents and charge separation.
Consequences in a torus
In a torus, the grad-B and curvature drifts point vertically and in opposite directions for ions and electrons, creating a charge separation and a vertical electric field. That field, crossed with the toroidal field, would drive the plasma outward, which is why a poloidal field (rotational transform) is essential: it short-circuits the charge separation.
How drifts are used
- Guiding-center equations of motion replace the full Lorentz orbit for slow-timescale studies
- Drift orbits explain banana orbits, neoclassical transport, and the bootstrap current
- The E cross B drift and its shear govern turbulence suppression
Numerical and design relevance
Orbit-following codes integrate the guiding-center drift equations to model fast-ion confinement, heating deposition, and losses. Understanding drift orbits is essential for designing the field geometry of any confinement device, including the low-aspect-ratio Hyperion breeder, where drift orbits are relatively wide.