J. Phys. B: At. Mol. Phys. 20 (1987) 1031-1038. Printed in the UK A theoretical determination of the diffusion-like ionisation time of Rydberg atoms " .v._ B Kaulakys and A Ciziunas Institute of Physics of the Academy of Sciences of the Lithuanian SSR, 232600 Vilnius, USSR Received 6 January 1986, in final form 1 July 1986 Abstract. The non-stationary multistep (diffusion-like) ionisation of Rydberg atoms is considered theoretically. The investigation is based on the time-dependent Fokker-Planck equation and is related to collisional and microwave ionisation of Rydberg atoms. Analyti- cal expressions for the mean time and the higher moments of the distribution of the diffusive ionisation times are derived. The conditions for the occurrence of diffusive ionisation are obtained. The relation of the present study to stationary diffusive ionisation and the experimental investigation of the ionisation of Rydberg atoms is discussed. 1. Introduction Considerable attention is devoted at present to the multistep transitions between the Rydberg states of atoms (see e.g. Biberman et a1 1982, Delone et al1978,1983, Kaulakys et a1 1984, Jensen 1984, Bayfield and Pinnaduwage 1985a, b, van Leeuwen e? al 1985). In such a process the change of the energy of a Rydberg atom in each elementary event (the absorption or stimulated emission of a low-frequency photon or the collision of a Rydberg atom with an atomic particle) is small in comparison with the binding energy of the Rydberg electron. The ionisation of the Rydberg atom and the recombina- tion of the electron occur as a result of a great number of elementary events and are described by the Fokker-Planck equation (see Pitayevsky 1962, Lifshitz and Pitayevsky 1979, Biberman e? a1 1982, Kaulakys e? a1 1984). Until now a great deal of attention has been devoted to the theoretical investigation of the kinetics of Rydberg state occupation numbers, the ionisation rates of Rydberg atoms and the recombination of electrons in slightly ionised plasmas in stationary conditions only. Under the impulsive excitation of an atom to a high Rydberg state, as is the case in the experiments on the microwave ionisation of highly excited hydrogen atoms (Bayfield and Pinnaduwage 1985a, b, van Leeuwen et a1 1985), the rate of diffusive ionisation of the Rydberg atom is defined by the solution of the non-stationary Fokker-Planck equation with specified initial and boundary conditions. In general, the non-stationary Fokker-Planck equation, in the case when the diffusion and drift coefficients are dependent on the energy, cannot be solved analytically, and one must be satisfied with the estimation of the order of the mean time of the diffusive ionisation only (Delone et a1 1978, 1983). The purpose of the present work is to obtain analytical expressions for the mean time and higher moments of the distribution of the diffusive ionisation times of the Rydberg atoms. In addition, the conditions for the occurrence of diffusive ionisation will be obtained and the relation between stationary diffusive ionisation and the 0022-3700/87/051031+ 08$02.50 @ 1987 IOP Publishing Ltd 1031