Anisotropic cyclotron instability in an inhomogeneous magnetic field

Anisotropy in the energy distribution of ions leads to the build-up of oscillations with frequencies near the cyclotron resonance frequencies, ω ≈ nωi. Oscillations with ω nωi are damped, even in a non-equilibrium plasma. If the magnetic field is inhomogeneous, a region of oscillation build-up can coexist with a region of oscillation damping. In an inhomogeneous magnetic field, therefore, anisotropic cyclotron instability is possible only when the influence of the region of oscillation build-up, where ωi > ω/n, is predominant. If the magnetic field varies monotonically, this requires fulfilment of the condition (ηn/ω'i n0)' > 0. The prime in this expression denotes the derivative in the direction of the magnetic field, n0 is the plasma density and is the transverse velocity distribution function of the ions, k⊥ is the transverse component of the wave vector and Jn is a Bessel function with index n. If the magnetic field has a minimum, there is no damping region for oscillations with ω = nωi min and these oscillations therefore build up at the highest rate.