Collisionless power dissipation has been calculated analytically taking into account particle trapping in the wave and electron collisions with neutrals. The approximation of analytical calculations for a decrement of nonlinear Landau damping gives, within an error less than $5\%$, ${\gamma }_{\mathrm{nl}}={\gamma }_l\tanh \left(2\nu {\tau }_r\right),$ where ${\gamma }_l$ is the linear Landau damping, $\nu$ is the total collision frequency, and ${\tau }_r$ is a bounce time of trapped electrons. The theory is applied to the calculation of collisionless heating in a bounded low-pressure glow discharge plasma. It is shown that the difference with previously published results of linear theory on collisionless power dissipation can be as large as 3 orders of magnitude.

• Received 19 August 1998

DOI:https://doi.org/10.1103/PhysRevLett.82.327