  The spatial distribution of electric current under magnetic field and the
resultant orbital magnetism have been studied for two-dimensional electrons
under a harmonic confining potential $V(\vecvar{r})=m \omega_0^2 r^2/2$ in
various regimes of temperature and magnetic field, and the microscopic
conditions for the validity of Landau diamagnetism are clarified. Under a weak
magnetic field $(\omega_c\lsim\omega_0, \omega_c$ being a cyclotron frequency)
and at low temperature $(T\lsim\hbar\omega_0)$, where the orbital magnetic
moment fluctuates as a function of the field, the currents are irregularly
distributed paramagnetically or diamagnetically inside the bulk region. As the
temperature is raised under such a weak field, however, the currents in the
bulk region are immediately reduced and finally there only remains the
diamagnetic current flowing along the edge. At the same time, the usual Landau
diamagnetism results for the total magnetic moment. The origin of this dramatic
temperature dependence is seen to be in the multiple reflection of electron
waves by the boundary confining potential, which becomes important once the
coherence length of electrons gets longer than the system length. Under a
stronger field $(\omega_c\gsim\omega_0)$, on the other hand, the currents in
the bulk region cause de Haas-van Alphen effect at low temperature as
$T\lsim\hbar\omega_c$. As the temperature gets higher $(T\gsim\hbar\omega_c)$
under such a strong field, the bulk currents are reduced and the Landau
diamagnetism by the edge current is recovered.
