We calculate the alignment of inter stellar dust grains with respect to the magnetic field of our galaxy. The alignment is found for several values of magnetic field strength, internal grain temperature, and grain shape. We treat in detail the following processes which affect the alignment: (i) a dissipative magnetic torque due to Davis and Greenstein; (ii) the collisions of the grain with inter stellar hydrogen; (iii) the non-zero internal temperature of the grain.
We obtain a Fokker-Planck equation which takes account of these processes, and the solution of this equation provides the probability distribution of grain orientations. The equation is solved for these cases: (i) spherical grains in all fields; (ii) needles, prolate spheroidal grains, nearly-spherical oblate grains, and disks in strong magnetic fields; (iii) needles and nearly- spherical grains in weak fields. Using the distribution of orientations, we calculate the degrees of alignment.
Our results are in mixed agreement with those of E. M.Purcell and in good agreement with the weak-field calculation of C.R. Miller. We find that for the relatively strong magnetic field10-5 gauss and grain temperature of 10°K, the measures of alignment are smaller than the values obtained from complete orientation of the grains.
