Two-dimensional motion of a parabolically confined charged particle in a perpendicular magnetic field

Open Physics ◽  
2013 ◽  
Vol 11 (2) ◽  
Author(s):  
Orion Ciftja
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Equations Of Motion ◽  
Complex Variables ◽  
Perpendicular Magnetic Field ◽  
Two Dimensional ◽  
Cyclotron Motion ◽  
Lissajous Figures ◽  
Long Time ◽  
Concentric Circles

AbstractThe classical two-dimensional motion of a parabolically confined charged particle in presence of a perpendicular magnetic is studied. The resulting equations of motion are solved exactly by using a mathematical method which is based on the introduction of complex variables. The two-dimensional motion of a parabolically charged particle in a perpendicular magnetic field is strikingly different from either the two-dimensional cyclotron motion, or the oscillator motion. It is found that the trajectory of a parabolically confined charged particle in a perpendicular magnetic field is closed only for particular values of cyclotron and parabolic confining frequencies that satisfy a given commensurability condition. In these cases, the closed paths of the particle resemble Lissajous figures, though significant differences with them do exist. When such commensurability condition is not satisfied, path of particle is open and motion is no longer periodic. In this case, after a sufficiently long time has elapsed, the open paths of the particle fill a whole annulus, a region lying between two concentric circles of different radii.

Motion of a charged particle in superposed Heliotron and biconical cusp fields

1969 ◽  
Vol 3 (2) ◽  
pp. 255-267 ◽  
Author(s):  
M. P. Srivastava ◽  
P. K. Bhat
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Magnetic Moment ◽  
Particle Trajectory ◽  
Three Dimensional ◽  
Equation Of Motion ◽  
Neutral Point ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Hybrid Type

We have studied the behaviour of a charged particle in an axially symmetric magnetic field having a neutral point, so as to find a possibility of confining a charged particle in a thermonuclear device. In order to study the motion we have reduced a three-dimensional motion to a two-dimensional one by introducing a fictitious potential. Following Schmidt we have classified the motion, as an ‘off-axis motion’ and ‘encircling motion’ depending on the behaviour of this potential. We see that the particle performs a hybrid type of motion in the negative z-axis, i.e. at some instant it is in ‘off-axis motion’ while at another instant it is in ‘encircling motion’. We have also solved the equation of motion numerically and the graphs of the particle trajectory verify our analysis. We find that in most of the cases the particle is contained. The magnetic moment is found to be moderately adiabatic.

scholarly journals Superdiffusion of two-dimensional Yukawa liquids due to a perpendicular magnetic field

2014 ◽  
Vol 90 (1) ◽  
Author(s):  
Yan Feng ◽  
J. Goree ◽  
Bin Liu ◽  
T. P. Intrator ◽  
M. S. Murillo
Keyword(s):  
Magnetic Field ◽  
Perpendicular Magnetic Field ◽  
Two Dimensional

Frictional drag between parallel two-dimensional electron gases in a perpendicular magnetic field

1996 ◽  
Vol 8 (39) ◽  
pp. L557-L562 ◽  
Author(s):  
N P R Hill ◽  
J T Nicholls ◽  
E H Linfield ◽  
M Pepper ◽  
D A Ritchie ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Perpendicular Magnetic Field ◽  
Two Dimensional ◽  
Dimensional Electron ◽  
Frictional Drag ◽  
Electron Gases

scholarly journals Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution

2014 ◽  
Vol 29 (29) ◽  
pp. 1450148
Author(s):  
Eva Gevorgyan ◽  
Armen Nersessian ◽  
Vadim Ohanyan ◽  
Evgeny Tolkachev
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Free Particle ◽  
Two Dimensional ◽  
Qualitative Character ◽  
Surface Of Revolution ◽  
Paraboloid Of Revolution ◽  
Kepler System ◽  
The Magnetic Field ◽  
Dimensional Surface

We define the Landau problem on two-dimensional ellipsoid, hyperboloid and paraboloid of revolution. Starting from the two-center McIntosh–Cisneros–Zwanziger (MICZ)–Kepler system and making the reduction into these two-dimensional surfaces, we obtain the Hamiltonians of the charged particle moving on the corresponding surface of revolution in the magnetic field conserving the symmetry of the two-dimensional surface (Landau problem). For each case we figure out the values of parameter for which the qualitative character of the motion coincides with that of a free particle moving on the same two-dimensional surface. For the case of finite trajectories we construct the action-angle variables.

On gyroresonance

1968 ◽  
Vol 2 (1) ◽  
pp. 59-64 ◽  
Author(s):  
M. J. Laird
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Pitch Angle ◽  
Uniform Magnetic Field ◽  
Equations Of Motion ◽  
Circularly Polarized ◽  
Simple Picture

The motion of a charged particle in the field of a plane circularly polarized wave propagating along a uniform magnetic field B0 is investigated. For the wave magnetic field small compared with B0, the equations of motion simplify to those of the pendulum, and a simple picture of what happens for particles near gyro- resonance results. Expressions are found for the amplitude and period of the pitch angle oscillations. Departures from uniformity and possible applications to the magnetosphere are briefly discussed.

scholarly journals Analysis of MHD Flow and Heat Transfer of Casson fluid Flow Between Porous Disks

2021 ◽  
Vol 83 (1) ◽  
pp. 46-60
Author(s):  
B Devaki ◽  
P Pai Nityanand ◽  
Kumar V S Sampath
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Reynolds Number ◽  
Magnetic Parameter ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Mhd Flow ◽  
Thermal Control ◽  
Two Dimensional ◽  
Special Cases

A study is carried out for the two-dimensional Casson flow of conducting fluid in the presence of a magnetic field. The governing non-linear equations of motion are transformed in two dimensional form. A solution is obtained by the homotopy perturbation method and it is valid for moderately large Reynolds numbers for injection at the wall. Also an efficient algorithm based finite difference scheme is developed to solve the reduced coupled ordinary differential equations with necessary boundary conditions. The effects of Reynolds number, the magnetic parameter, pradantl number Casson parameter on flow velocity and temperature distribution is analysed for increasing the non-Newtonian characteristics of the fluid by both the methods and results agree well with previous work for special cases. It is observed that the overall effect of magnetic field is same as Hartmann flow. Further the analysis predicts that the heat transfer at the surface of the disks increases with increase in Reynolds number, magnetic parameter and Prandtl number, shear stress at lower disk also calculated. The study of such phenomenon is beneficial in the industry for thermal control in polymeric processing.

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