On an electron in a nonuniform axial magnetic field in a uniformly rotating frame

2019 ◽  
Vol 34 (33) ◽  
pp. 1950229
Author(s):  
K. Bakke ◽  
R. F. Ribeiro ◽  
C. Salvador
Keyword(s):  
Magnetic Field ◽  
Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Symmetry Axis ◽  
Axial Magnetic Field ◽  
Radial Distance ◽  
Nonuniform Magnetic Field ◽  
Rotating Frame ◽  
The Magnetic Field

The interaction of an electron with a nonuniform axial magnetic field is analyzed in a uniformly rotating frame. In particular, the magnetic field is proportional to the square of the radial distance from the symmetry axis. Then, in search of analytical solutions to the Schrödinger equation, it is shown that these solutions are possible if the nonuniform magnetic field possesses a discrete set of values.

scholarly journals Simultaneous determination of the magnetic field and the electric potential in the Schrödinger equation by a finite number of boundary observations

2018 ◽  
Vol 26 (2) ◽  
pp. 201-209 ◽  
Author(s):  
Ibtissem Ben Aïcha ◽  
Youssef Mejri
Keyword(s):  
Magnetic Field ◽  
Schrödinger Equation ◽  
Finite Number ◽  
Electric Potential ◽  
Schrodinger Equation ◽  
Initial Conditions ◽  
Stability Estimate ◽  
Lipschitz Stability ◽  
The Magnetic Field

AbstractWe study the inverse problem of determining the magnetic field and the electric potential appearing in the magnetic Schrödinger equation from the knowledge of a finite number of lateral observations of the solution. We prove a Lipschitz stability estimate for both coefficients simultaneously by choosing the “initial” conditions suitably.

Nonlinear evolution of a wave packet propagating along a hot magnetoplasma column

1987 ◽  
Vol 37 (1) ◽  
pp. 107-115
Author(s):  
B. Ghosh ◽  
K. P. Das
Keyword(s):  
Magnetic Field ◽  
Multiple Scales ◽  
Nonlinear Evolution ◽  
Axial Magnetic Field ◽  
Modulational Instability ◽  
Wave Train ◽  
Dielectric Medium ◽  
Ion Effects ◽  
The Magnetic Field ◽  
Uniform Plasma

The method of multiple scales is used to derive a nonlinear Schrödinger equation, which describes the nonlinear evolution of electron plasma ‘slow waves’ propagating along a hot cylindrical plasma column, surrounded by a dielectric medium and immersed in an essentially infinite axial magnetic field. The temperature is included as well as mobile ion effects for ail possible modes of propagation along the magnetic field. From this equation the condition for modulational instability for a uniform plasma wave train is determined.

scholarly journals DC Glow Discharge in Axial Magnetic Field at Low Pressures

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Shen Gao ◽  
Shixiu Chen ◽  
Zengchao Ji ◽  
Wei Tian ◽  
Jun Chen
Keyword(s):  
Magnetic Field ◽  
Glow Discharge ◽  
Differential Equations ◽  
Axial Magnetic Field ◽  
Glow Discharge Plasma ◽  
Dc Glow Discharge ◽  
Fluid Approximation ◽  
Low Pressures ◽  
Physical Quantities ◽  
The Magnetic Field

On the basis of fluid approximation, an improved version of the model for the description of dc glow discharge plasma in the axial magnetic field was successfully developed. The model has yielded a set of analytic formulas for the physical quantities concerned from the electron and ion fluids equations and Poisson equation. The calculated results satisfy the practical boundary conditions. Results obtained from the model reveal that although the differential equations under the condition of axial magnetic field are consistent with the differential equations without considering the magnetic field, the solution of the equations is not completely consistent. The results show that the stronger the magnetic field, the greater the plasma density.

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