We study the evaporative cooling of magnetically trapped atomic hydrogen on the basis of the kinetic theory of a Bose gas. The dynamics of trapped atoms is described by the coupled differential equations, considering both the evaporation and dipolar spin relaxation processes. The numerical time-evolution calculations quantitatively agree with the recent experiment of Bose-Einstein condensation with atomic hydrogen. It is demonstrated that the balance between evaporative cooling and heating due to dipolar relaxation limits the number of condensates to $9\ifmmode\times\else\texttimes\fi{}{10}^{8}$ and the corresponding condensate fraction to a small value of 4% as observed experimentally.
We have confined over 5\ifmmode\times\else\texttimes\fi{}
1012 atoms of hydrogen in a static magnetic trap. The atoms are loaded into the trap by precooling with a dilution refrigerator. At operating densities near 1\ifmmode\times\else\texttimes\fi{}
1013 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ the gas is observed to be electron and nuclear polarized in the uppermost hyperfine state. The long lifetime of the trapped gas (over 20 min) suggests that it is thermally decoupled from the wall and has evaporatively cooled to a temperature of about 40 mK. The residual decay of the gas density is consistent with spin relaxation induced by dipolar interactions between atoms.