Plasma heating by spatial resonance of Alfvén wave

Abstract

Heating of a collisionless plasma by utilizing the spatial resonance of shear Alfvén waves is proposed and application to toroidal plasmas is discussed. The resonance exists due to the nonuniform Alfvén speed. This heating scheme is analyzed in one dimension including the effects of a shear magnetic field and plasma compressibility. For plasmas with smooth nonuniformities (${\mathrm{|\hspace{0.17em}k}}_{\perp }{\text{l\hspace{0.17em}|\hspace{0.17em}≫\hspace{0.17em}1,\hspace{0.17em}k}}_{\perp }$ is the wavenumber prependicular to the ambient magnetic field and the nonuniformity direction, and $l$ is the scale length of the nonuniformity), the energy absorbed per unit surface area per driving cycle is ${\mathrm{[b}}_0^2{\mathrm{(\mu }}_0{k}_{\perp }{)}^{\text{−1}}]$ . Here, $b_0$ is the flux density of the driving magnetic field evaluated at the resonant point. With sharp nonuniformities ${\mathrm{(|\hspace{0.17em}k}}_{\perp }\text{l\hspace{0.17em}|\hspace{0.17em}≪\hspace{0.17em}1)}$ , absorption is large if the surface eigenmode is excited. The corresponding value is ${\mathrm{[b}}_0^2{\mathrm{(\mu }}_0{k}_{\perp }{)}^{\text{−1}}{\mathrm{(k}}_{\perp }{\mathrm{l)}}^{\text{−1}}]$ . Otherwise, it is ${\mathrm{[b}}_0^2{\mathrm{(\mu }}_0{k}_{\perp }{)}^{\text{−1}}{\mathrm{(k}}_{\perp }\mathrm{l)]}$ .