正电子面沟道辐射的非线性特征

经典物理学指出,在电磁场中作加速运动的带电粒子将不断向外辐射能量.在晶体沟道中运动的带电粒子也不例外,晶格场可以使带电粒子的辐射能量达到很高.对于10MeV的正电子,辐射能量可达keV量级.粒子在沟道中的运动行为决定于粒子晶体的相互作用势,常用的相互作用势有Lindhard势、Moliere势和正弦平方势.由于粒子在沟道中的运动行为十分类似于震荡器中运动的自由电子,可望把沟道辐射改造为Χ射线激光或γ射线激光.从Lindhard势出发,将其展开到四次项,在经典力学框架内,粒子的运动方程可以化为含立方项的二阶非线性微分方程,并利用Jacobian椭圆函数和第一类全椭圆积分解析地表示了系统的解和粒子运动周期,导出了正电子面沟道辐射的瞬时辐射强度、平均辐射强度和最大辐射频率,指出了利用沟道辐射作为γ激光的可能性.

Nonlinear Properties for the Planar Channelling Radiation of a Positrons

A charged particle moving along the direction of the low crystal face index can penetrates through the crystal as easily as it does through a channel. This phenomenon is so-called channeling effect. The classical physics points out that an accelerated charged particle radiates energy continuously when moving in an electromagnetic field. The analogous situation occurs in crystal channel. When a charged particle moves in an accelerated way through a lattice field, the radiation energy can be produced. It is such an extremely strong lattice field that results in the rather higher radiation energy. For a positron with the energy of 10MeV, the radiation energy can reach keV in order of magnitude. The motion behavior of the channeling particle is governed by the interaction potential between the particle and the crystal. The potential, which we generally use, is Lindhard potential, Moliere potential, and sine-squared potential. Because the motion behavior of the channeling particle is most similar with that of a free electron moving in a Wiggler, it is expected that the channeling radiation can be changed as X-laser or γ-laser to pretend new high energy laser source. In 4^th-order Lindhard potential approximation, the particle motion equation can be reduced to a second order nonlinear differential equation with a cubic term under the frame of the classical mechanics. By employing both the Jaco-bian ell iptic function and the first kind complete elliptic integral, the solution of the equation is derived and the channeling radiation frequency is obtained in an analytical expression. Besides, the instantaneous radiation intensity, the average radiation intensity and the maximum radiation frequency of positrons are also obtained. As an application of channeling radiation of positrons, the average intensity and the maximum frequency of single crystal silicon are calculated. The results indicate that it is possible to make channeling radiation as γ-laser.