We demonstrate kinematically complete measurements on frustrated double ionization of argon atoms in strong laser fields with a reaction microscope. We found that the electron trapping probability after strong field double ionization is much higher than that after strong field single ionization, especially in case of high laser intensity. The retrieved electron momentum distributions of frustrated double ionization show a clear transition from the nonsequential to the sequential regime, similar to those of strong field double ionization. The dependence of electron momentum width on the laser intensity further indicates that the second released electron has a dominant contribution to frustrated double ionization in the sequential regime. PACS numbers: 33.80.Rv, 42.50.Hz, 82.50.Nd When an atom or a molecule is exposed to a strong laser field it may become singly or multiply ionized [1,2]. After the strong field interaction, a fraction of the ionized electron wave packets with near-zero kinetic energies can be trapped into high-lying Rydberg states, a process also known as frustrated field ionization [3][4][5][6][7][8][9][10][11]. Frustrated double ionization (electron trapping after double ionization) has been experimentally studied for small molecules, including H 2 and argon dimers, using Coulomb explosion imaging [4][5][6][12][13][14] and theoretically using the classical trajectory Monte Carlo method [15,16]. In these experiments the trapping process is identified by the kinetic energy released (KER) during the Coulomb explosion of the molecules. Since an electron trapped in high-lying Rydberg states does not fully shield the nuclear charge, the KER for a molecule with an electron in Rydberg states is higher than that for a nonexcited molecule. Since this method is based on the measurement of KER from molecules undergoing Coulomb explosion, it is applicable to neither atomic targets nor molecules that do not fragment.In this paper, using an alternative method developed in our previous work [10], we report on kinematically complete experiments of electron trapping processes during strong field double ionization of argon atoms. Strong field double ionization may happen sequentially, where the two electrons are removed one after another by the laser field, or non-sequentially, where the second electron is released during the recollision of the first electron with the parent ion [17][18][19]. We show that the trapping probability is strongly enhanced in the sequential ionization regime. Based on our experimental data we explain the electron dynamics underlying these observations.In our experiments we employed a reaction microscope [20,21] for three-body coincidence detection of two electrons and their parent ion created during the interaction of argon atoms with strong laser pulses ( Fig. 1(a)). Laser pulses linearly polarized along the spectrometer axis (z-direction) were provided by a home-built Titanium:sapphire laser amplifier system. The pulses had a center wavelength of 790 nm, a pulse duration of 25 fs an...