Magnetic cloud of April 22, 2001. Observations (5-min averages) are plotted by the red lines, B, B_x, B_y, and B_z are the magnetic field magnitude and the field components in the GSE coordinates, V, N, and T are the solar wind velocity, proton number density, and proton temperature, respectively. Estimated cloud boundaries are drawn by the blue vertical lines. The thick green lines are fits by cylindrical models, namely a) the (spatially) constant-α force-free field (the Lundquist solution) with expansion, and b) (spatially) uniform-twist field (the Gold-Hoyle tube) with expansion.