Alfven Waves
Transverse waves that travel along magnetic field lines as if they were tensioned strings.
Waves on field lines
In a magnetized plasma the field lines behave like elastic strings under tension: pluck them and a transverse wave propagates along the field. This is the shear Alfven wave, one of the fundamental MHD waves. Its speed is the Alfven speed:
v_A = B / sqrt(mu0 rho)where rho is the mass density. The wave is incompressible and carries no pressure perturbation; the restoring force is purely magnetic tension.
The MHD wave family
Ideal MHD supports three waves: the shear Alfven wave, and the fast and slow magnetosonic waves, which combine magnetic and thermal pressure. The Alfven speed is the reference velocity for MHD dynamics and sets the timescale for ideal instabilities and for the numerical stiffness of MHD codes.
Alfven eigenmodes and fast ions
- Toroidal geometry creates gaps in the Alfven continuum where discrete eigenmodes live
- Energetic particles (alphas, beam ions) can resonantly drive these modes unstable
- Unstable Alfven eigenmodes can expel fast ions before they deposit their energy
Why it matters for fusion
Fusion-born alpha particles travel near the Alfven speed and can resonantly excite toroidal Alfven eigenmodes, redistributing or ejecting the very particles meant to heat the plasma. Predicting Alfven-eigenmode stability is a key fast-ion analysis for any burning plasma, including the D-T Hyperion breeder.
How it is computed
Ideal and gyrokinetic eigenvalue codes solve for the mode frequencies and structures; the drive from fast ions is evaluated from their distribution and compared against damping. The Alfven speed also fixes the CFL time-step limit that makes explicit MHD simulation stiff.