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The Classical Motion of the Neutral Particles in the Ioffe Trap

Author: LiuXiaoLiang
Tutor: ZengGaoJian
School: Hunan Normal University
Course: Theoretical Physics
Keywords: Neutral particles Captivity Ioffe trap Mathieu equation WKBJ Method Perturbation approximation Fuluo open solutions
CLC: O413.1
Type: Master's thesis
Year: 2003
Downloads: 22
Quote: 0
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Abstract


The magnetic confinement of the neutral particles is an important subject of study in recent years , neutral particles having a magnetic moment due to the biasing force of the field , it can be achieved under certain conditions captivity . We first discuss several of the basic structure of the static magnetic trap , the accurate calculation of the field , and in paraxial conditions , the use of the series expansion method derived approximate expression of the field , this approximation is conducive to the classic and quantum orbital symmetry . On the Ioffe well , because of its neutral particles stable imprisoned become a closely watched magnetic trap . If only to discuss the area of the well near the origin , the magnetic field in the trap can render a concise form , people called it the ideal Ioffe trap . The neutral particle magnetic moment mu anti- parallel to the magnetic field interacts with the magnetic field in the well by means of the interaction potential , can be obtained classical equations of motion of particles in the well . In a certain approximation , we can use the method of successive approximation , the simplified equations , in which the three components of the formula is easy to solve the equation z , x, y equation evolution we are familiar with Mathieu equation form . If the trap parameters set so that the conditions the lambda gt ; GT ; q > 0 set up , we can take advantage of traditional WKBJ of methods approximate solving Mathieu equation . As a new attempt , this paper also uses the Fourier series expansion approach to solve the Mathieu equation , resulting in the classic law of motion of neutral particles in the well . In the Ioffe trap neutral particles captivity , in fact, we are more interested Mathieu equation periodic solution , in order to obtain the solution of this cycle , lambda and q must meet certain relationship , that must be selected well specific parameters and particle - specific initial conditions on this issue , we conducted a study of the attempt .

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CLC: > Mathematical sciences and chemical > Physics > Theoretical Physics > Quantum theory > Quantum mechanics ( wave mechanics,matrix mechanics )
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