Collisionless dissipation wavenumber: Linear theory

<jats:p>The collisionless dissipation wavenumber <jats:italic>k<jats:sub>d</jats:sub></jats:italic> of a plasma fluctuation may be defined as the minimum value of wavenumber at which damping becomes significant. Linear Vlasov theory is used to determine <jats:italic>k<jats:sub>d</jats:sub></jats:italic> for both magnetosonic and Alfvén fluctuations in a spatially homogeneous, collisionless plasma with Maxwellian velocity distributions. Alfvén mode properties at maximum dissipation are independent of <jats:italic>T<jats:sub>e</jats:sub></jats:italic>/<jats:italic>T<jats:sub>p</jats:sub></jats:italic>, and the corresponding magnetosonic mode properties are weakly dependent on this temperature ratio, so theory predicts that the proton beta β<jats:sub><jats:italic>p</jats:italic></jats:sub> is the primary parameter determining <jats:italic>k<jats:sub>d</jats:sub></jats:italic>. Theory yields <jats:italic>k<jats:sub>d</jats:sub></jats:italic>c/ω<jats:italic>p</jats:italic> = <jats:italic>S<jats:sub>k</jats:sub></jats:italic>/β<jats:sub><jats:italic>p</jats:italic></jats:sub><jats:sup>α<jats:italic>k</jats:italic></jats:sup>, where ω<jats:sub><jats:italic>p</jats:italic></jats:sub> is the proton plasma frequency and <jats:italic>S<jats:sub>k</jats:sub></jats:italic> and α<jats:italic><jats:sub>k</jats:sub></jats:italic> are fitting parameters; for the Alfvén mode α<jats:italic><jats:sub>k</jats:sub></jats:italic> ≃ 0.3, whereas for the magnetosonic mode α<jats:italic><jats:sub>k</jats:sub></jats:italic> ≃ 0.8. This implies that Alfvén fluctuations are the more likely source of collisionless dissipation for long wavelength magnetic turbulence cascading to shorter wavelengths at β<jats:sub><jats:italic>p</jats:italic></jats:sub> ≲ 1, and magnetosonic fluctuations are more likely to dissipate such turbulence at β<jats:sub><jats:italic>p</jats:italic></jats:sub> ≳ 1.</jats:p>