我們討論一高轉速中子星磁場球內的粒子加速連鎖反應；因整體電流導致的電荷缺乏產生延著磁力線的強大電場，正負電子經由此電場加速幅射出gamma射線，某些gamma射線與中子星表面放出的X射線碰撞產生正負電子對，這些帶電粒子屏蔽了部分原來的電場，所有這些物理過程都須同時考慮。此篇論文中，我們首次討論粒子加速的時間演化性質，藉由同時解 Poisson equation 與正負電子及光子的 non-stationary Boltzmann equations。將此方法應用至毫秒脈衝星上，我們發現對於一定範圍的毫秒脈衝星參數，解會收斂為穩定解，粒子加速連鎖反應藉由磁極冠的熱輻射維持。檢驗一加速區是否能自我維持，我們可訂出毫秒脈衝星在週期-週期微分圖上對於不同磁傾角的deathlines。 我們討論一高轉速中子星磁場球內的粒子加速。

We investigate a pair creation cascade in the magnetosphere of a rapidly rotating neutron star. The charge depletion due to global flows of charged particles causes a large electricfield along the magnetic field lines. Electrons and positrons are accelerated by this field to radiate gamma-rays via curvature process. Some of the gamma-rays collide with the X-rays emitted from the stellar surface to materialize as pairs in the gap. The replenished charges partially screen the original electric field. To take in to account of these physical processes self-consistently, we must solve the set of the Poisson equation for the electro-static potential and the Boltzmann equations for electrons, positrons, and gamma-ray photons simultaneously. In this thesis, we first examine the time-dependent nature of particle accelerators by solving the non-stationary Boltzmann equations on the twodimensional poloidal plane in which both the rotational and magnetic axes reside. Evaluating the temperature of the heated polar cap surface, which is located near the magnetic pole, by the bombardment of gap-accelerated particles, and applying the scheme to millisecond pulsar parameters, we demonstrate that the solution converges to a stationary solution of which pair-creation cascade is maintained by the heated polar-cap emission, in a wide range of three-dimensional parameter space (period, period derivative, magnetic inclination angle). We also examine the criterion for such a self-sustained particle accelerator to be maintained, and present the deathlines of millisecond pulsars on the (period, period derivative) plane for a few representative inclination angles.

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