Cyclotron instability of trapped α-particles in a tokamak with elliptic cross-section

Cyclotron excitation of fast magnetosonic waves by trapped α-particles produced by thermonuclear fusion in a tokamak with elliptic cross-section is studied. Earlier, this phenomenon was studied for a tokamak with circular cross-section. It is shown that ellipticity of the tokamak cross-section considerably affects the growth rate of oscillations when A ≡ (ℓ 1 /R) (e 2η −1)/q 2 ≥ 1 where R is the radius of curvature of the magnetic axis, q is the tokamak safety factor, and , where ℓ 1 , ℓ 2 are the minor and major axes of the ellipse, respectively. General expressions for the growth rate of the oscillations are obtained at arbitrary values of the parameter A and are analysed in a limiting case when the wave frequency is close to the cyclotron harmonics of strongly trapped particles. It is shown that the growth rate of oscillations excited by strongly trapped α-particles is considerably smaller at large ellipticity of the tokamak cross-section, A ≥ 1, than in the case of a tokamak with circular cross-section.