The evolution of a spherical single-mass star cluster is followed in detail up to core collapse by numerically solving the orbit-averaged two-dimensional Fokker-Planck equation in energy-angular momentum space .
Velocity anisotropy is allowed in the two-dimensional Fokker-Planck model .
Using improved numerical codes , the evolution has been followed until the central density increased by a factor of 10 ^ { 14 } with high numerical accuracy .
The numerical results clearly show self-similar evolution of the core during the late stages of the core collapse .
In the self-similar region between the isothermal core and the outer halo , the density profile is characterized by a power law \rho ( r ) \propto r ^ { -2.23 } and the ratio of the one-dimensional tangential velocity dispersion to the radial one is \sigma _ { t } ^ { 2 } / \sigma _ { r } ^ { 2 } = 0.92 .
As the core collapse proceeds , the collapse rate \xi \equiv t _ { r } ( 0 ) d \ln \rho ( 0 ) / dt tends to the limiting value of \xi = 2.9 \times 10 ^ { -3 } , which is 19 % smaller than the value for isotropic clusters .
When Plummer ’ s model is chosen as the initial condition , the collapse time is about 17.6 times the initial half-mass relaxation time .
As the result of strong relaxation in the core , the halo becomes to be dominated by radial orbits .
The degree of anisotropy monotonically increases as the radius increases .
In the outer halo , the profiles of the density are approximated by \rho \propto r ^ { -3.5 } .
This work confirms that the generation of velocity anisotropy is an important process in collisional stellar systems .

Key words : Clusters : globular — Fokker-Planck equation — Numerical methods — Stars : stellar dynamics