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 Incoming links: Past exam of the collisionless plasma physics course of the University of Oxford / 2025 / 1 / a

Past exam of the collisionless plasma physics course of the University of Oxford / 2025 / 1 / f / Solution 2026-10-25

For the ordinary plasma wave, choose

k = k \hat{x}

and

δ E = E_{z} \hat{z}

. The equations in a give

u_{x s} = u_{ys} = 0

and

u_{zs} = \frac{i q _{s}}{m _{s} ω} E_{z} .

The driven particle motion is entirely parallel to

B_{0}

: the parallel Lorentz force has no magnetic contribution. Nevertheless, the ordinary plasma wave is electromagnetic, since

δ E ⊥ k

and the Faraday law gives

δ B = - \frac{c k}{ω} E_{z} \hat{y} \neq = 0.

An electrostatic plasma wave instead has

δ E ∥ k

and zero perturbed magnetic field. Alignment with the equilibrium magnetic field does not make a wave electrostatic. At the exact plasma wave cutoff

k = 0

, this propagating-wave distinction becomes degenerate.

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