  The linear stability of a magnetized plasma accompanying temperature gradient
was reexamined by using plasma kinetic theory. The anisotropic velocity
distribution function was decomposed into two components. One is proportional
to the temperature gradient parallel to and the other is proportional to the
temperature gradient perpendicular to the back ground magnetic field. Since the
amplitude of the anisotropic velocity distribution function is proportional to
the heat conductivity and the heat conductivities perpendicular to the magnetic
field is strongly reduced, the first component of the anisotropic velocity
distribution function is predominant. The anisotropic velocity distribution
function induced by the temperature gradient along the back ground magnetic
field drives plasma kinetic instability and the circular polarized magnetic
plasma waves are excited. The instability is almost identical to Weibel
instability in weakly magnetized plasma. However, depending on whether wave
vectors of modes are parallel to or antiparallel to the back ground magnetic
field, the growth rate is suppressed or enhanced due to back ground magnetic
field. In the strongly magnetized plasma, one mode is stabilized and only one
of the modes remains unstable.
  The Jitter radiation spectrum formulae emitted by relativistic electrons when
they travel through the magnetized plasma with the plasma waves driven by the
instability, are deduced at the first time. The synchrotron emission and the
Jitter radiation are simultaneously emitted from the same relativistic
electron. The Jitter radiation is expected to be circularly polarized but with
a very small polarization degree since almost the same amount of left and right
handed circular polarized magnetic waves are excited by the instability.
