Trapping Instabilities in a Slightly Inhomogeneous Plasma

Abstract

The stability of an infinite collisionless plasma with a small density gradient in the x direction (using the collisionless Boltzmann equation and Maxwell's equations) confined by a static magnetic field in the z direction, is studied. Unstable modes are found at frequencies near multiples of the ion‐cyclotron frequency Ω_i. These modes are electrostatic oscillations transverse to the magnetic field, and have very short wavelengths λ ∼ v_d/Ω_i, where v_d is the (small) drift occasioned by the magnetic‐field inhomogeneity. The phase velocity of the wave is comparable to v_d, and resonant interaction leads to the growth. Typical growth rates are large, α ∼ (m_e/m_i) Ω_i, but the effect of the instability is minimized by the extremely short wavelength.