帶電粒子在空間中緩慢變化的磁場中的運動

The motion of a charged particle in a slow-varying magnetic field in the space

柳銘哲(Ming-Tse Liu)

《加馬》 46期 (2015/07) Pp. 37-46

摘要

所謂核融合（核聚變）是指兩個或更多個原子核聚在一起，以高速相撞然後融在一起形成新的原子核的一種作用。為了讓反應順利進行，這些荷電的原子核應該盡可能的聚在某處，磁場是一個好方法。均勻的磁場無法鎖住這些荷電的原子核，但是某種軸對稱且在空間是緩慢變化的磁場卻辦得到。我們的方法是分別置放兩個磁偶極子在z=±a處，它們將產生兩端很強、中間較弱的磁場。奠基在單粒子理論，帶電粒子的運動是遵守勞侖茲力定律的。透過理論分析和數值模擬，滿足某些條件的粒子將在磁瓶裡駐留。Matlab軟體用來將計算結果可視化，除此之外，我們的討論中暫且忽略了相對論效應和加速帶電粒子的輻射效應。

關鍵字

磁鏡 ； 磁約束 ； 數值計算 ； 可視化 ； 勞侖茲力

並列摘要

Nuclear fusion is a nuclear reaction in which two or more atomic nuclei come very close and then collide at a very high speed and join to form a new type of atomic nucleus. In order to proceed smoothly, these charged nuclei should stay at somewhere as long as possible. Magnetic field is a good method. Uniform magnetic field cannot lock these charged nuclei, yet some kind of slow-varying magnetic field with axial symmetry in the space can afford it. Our treatment is to place two magnetic dipoles at z=±a respectively. They will produce a magnetic field with strength stronger on both sides and weaker in the middle. Based on single-particle theory, the motion of a charged particles is to follow the Lorentz force law. Through theoretical analysis and numerical simulation, we found some particles satisfied to some conditions could be stationary in the magnetic bottle. The Matlab software is used to visualize the calculated results. In addition, we ignore the relativistic effect and the radiative effect of a charged particle under acceleration in all of our discussions.

並列關鍵字

magnetic mirror ； magnetic confinement field ； numerical calculation ； visualization ； Lorentz force