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It is suggested that electron-positron (e+ e-) plasma can be accelerated using the concept of cyclotron autoresonance between the particles and a linearly polarized laser radiation propagating along an axial magnetic field (Bz). This scheme can also be applied for other plasmas with oppositely charged particles of equal Â¿qÂ¿/m (e.g., positive and negative ions). An e+ e- plasma can be accelerated to about 2 GeV in the first meter along a 100-kG guide magnetic field by using an Nd: glass laser (Â¿0 = 1 Â¿m) with intensity I0 = 1018 W/cm2. The acceleration scales asymptotically as (Bz, I0 Â¿0 Z2)1/3, where z is the axial distance.