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An analytical calculation of the magnetic field of a cylindrical permanent magnet linear generator is presented. The generator utilises a discrete Halbach permanent magnet array as magnetic field source. The array is constructed of permanent magnets that have a non-uniform length. To solve the governing equations, a direct solution method is used. The flux distributions in the air gap, inside the permanent magnet and in the shaft are calculated. Solutions that are derived using this method are compared with that obtained from the finite element analysis simulation method. Another method is also used in the field calculation, and the result is presented for comparison.