The Landau problem of a charged particle in a plane with a uniform perpendicular magnetic field is analysed in two oscillator modes. The coherent states for the problem have been found out using a general definition of displaced states. The time evolution and the associated nonadiabatic geometric phase for both initially displaced and non-displaced wave packets have been studied. The path integral is derived in a simple way through the calculation of Gaussian integrals via the concept of coherent state wavefunctions.
± of the quadratic Hamiltonian are analyzed numerically in both the normal and reversed-field configurations for different values of the ratio
w/
0. The electron trajectories are thus discussed. It is found that pseudo-circular and elliptic trajectories are characterizing both group-I and reversed-field group-II modes while the motion in the normal group-II mode is much more complicated.]]>
Electron beam dynamics in a helical-wiggler free-electron laser (FEL) with a uniform axial guide magnetic field are studied using a three-dimensional Hamiltonian approach. The basic feature of the analysis is the definition of a rotational variable,ĥ, that plays the primordial role in lowering to the half the dimension of the quadratic Hamiltonian as a system of two uncoupled oscillators with definite frequencies and amplitudes. It is through applying this variable in the vicinity of a fixed point that the Heisenberg picture of the dynamics of the particles comes to light, leading thus to the association of the steady-state ideal helical trajectories with arbitrary trajectories. The approach recognized the usual two constants of motion, one being the total energy while the other is the canonical axial angular momentum, P z . If the value of the latter is such that a fixed point exists, the Hamiltonian is expanded about the fixed point up to second order. The so-obtained oscillator characteristic frequencies allowed one to study the different modes of propagation and to identify, and then avoid the problematic operating conditions of the FEL concerned. On the other hand, the amplitudes of the oscillations, which do depend on the frequencies, are fortunately found to be constants of motion and then controlled by the boundary conditions (initial conditions). PACS Nos.: 52.40-w, 52.60+h, 42.55.Tb, 52.75MsRésumé : Utilisant une approche hamiltonienne en 3-D, nous étudions la dynamique d'un faisceau d'électrons dans l'onduleur hélicoïdal d'un laser à électron libres (FEL) avec un guide constitué d'un champ magnétique axial uniforme. L'outil de base de notre analyse est la définition d'une variable rotationnelle qui joue un rôle premier en diminuant de moitié la dimension du Hamiltonien quadratique sous la forme de deux oscillateurs découplés avec fréquences et amplitudes définies. L'utilisation de cette variable dans le voisinage d'un point fixe fait apparaître la dynamique de la particule dans la représentation de Heisenberg, menant à une association entre les trajectoires hélicoïdales idéales et les trajectoires arbitraires. L'approche reconnaît les deux constantes habituelles du mouvement, l'énergie totale et la composante axiale du moment cinétique canonique. Si la valeur de ce dernier permet l'existence de points fixes, nous y centrons une expansion au deuxième ordre pour le Hamiltonien. Les
A model for steady state neutral atom transport in a finite thickness, one dimensional plasma slab with a source of neutrals and molecules at the edge, is formulated. A computer code OMID is developed for computational analysis. The analysis shows that the cold neutral particle density is maximum near the wall, the total fuelling profile peaks in the vicinity of the wall for a molecular source more than for an atomic one, energetic neutrals formed in successive charge exchange collisions carry energy to the wall and sputter impurity atoms back 'to the plasma. For low edge temperatures where molecular hydrogen is dissociated, mostly atomic hydrogen is produced, the ionization profile shifts towards the wall as the edge temperature is raised and more ions are created directly from molecular dissociation.The effect of varying the incident neutral particle energy has been investigated.The comparison of the results with the predictions of other codes showed satisfactory agreement for regions close to the wall.
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