Force-free magnetic field in a cylindrical flux rope without a constant alpha

It is generally assumed that magnetic fields inside interplanetary magnetic clouds and flux ropes in the solar photosphere are force-free. In order to model such fields, the solution of rot B = αB is commonly used where α = const. But comparisons of this solutions with observations show significant difference. To treat this problem,we examine the solutions with α=α0/(1+r/r0)3/2.