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High-voltage laboratory experiments show that discharges in air, generated over a gap of one meter with maximal voltage of 1 MV, may produce X-rays with photon energies up to 1 MeV. It has been suggested that the photons are bremsstrahlung from electrons accelerated by the impulsive, enhanced field during collisions of negative and a positive streamers. To explore this process, we have conducted the first self-consistent particle simulations of streamer encounters. Our simulation model is a 2-D, cylindrically symmetric, particle-in-cell code tracing the electron dynamics and solving the space charge fields, with a Monte Carlo scheme accounting for collisions and ionization. We present the electron density, the electric field, and the velocity distribution as functions of space and time. Assuming a background electric field 1.5 times the breakdown field, we find that the electron density reaches 2·1021 m−3, the size of the encounter region is ∼3·10−12 m3 and that the field enhances to ∼9 times the breakdown field during ∼10−11 s. We further find that the radial component becomes comparable to the parallel component, which together with angular scattering leads to an almost isotropic distribution of electrons. This is consistent with laboratory observations that X-rays are emitted isotropically. However, the maximum energy of electrons reached in the simulation is ∼600 eV, which is well below the energies required to explain observations. The reason is that the encounter region is small in size and duration. For the photon energies observed, the field must be enhanced in a larger region and/or for a longer time.