****************************************************** PR # 12019 Geminga is a rotation-powered,radio-quiet pulsar with period$P=0.237$ ~s and spin-down age $3.4 \times 10^5$ yr.Geminga affords the most de tailed look so far at the surface and environment of a neutron star,& how they are affected by the particle accelerator which is reponsible for the $\gamma$-rays.Although it is a strong soft X-ray and $\gamma$ -ray source,Geminga has not yet been studied in the 2--10 keV window. The $ASCA$ spectrum & pulse profile will reveal whether the hardX-ray component is thermal emission from the hot polar caps,or synchrotron emission from the inner magnetosphere. In conjunction with $ROSAT$, $EUVE$, and $EGRET$,the $ASCA$ data will be used to develop a consist ent model of the magnetosphere accelerator, surface magnetic field geometry,and polar cap heating ******************************************************