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Magnetron: Particle Trajectory
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The trajectory of an electron in a magnetron can be determined from the magnetic and electric fields present in the space between the cathode and the anode. In this application, the electric and magnetic fields are perpendicular to each other. As the electron starts moving from the cathode to the anode, it is forced to travel on a path that is bent due to the magnetic field.
The geometry of the magnetron is shown. The inside conductor is the cathode and the cylindrical shell on the outside is the anode. A coil is wrapped around the tube so that a magnetic field that is parallel to the axis of the tube is produced.
In the analysis performed for this example, the electric and magnetic field strengths are adjusted so that the electron does not reach the anode and forms a cyclic trajectory.
METHODS and RESULTS
Electric Field Simulation
The voltage source is DC and is connected in series with the cathode and the anode terminals. By controlling the voltage level, the electric field strength in the cavity can be adjusted. To obtain the electric field, the electrostatic solver in ElecNet is used.
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Magnetic Field Simulation
The outside coil, made of several turns, is connected in series with a DC current source so that a constant magnetic field is generated in the cavity. To obtain the magnetic field, the magnetostatic solver in MagNet is used.
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Particle Trajectory Calculation
The particle trajectory is obtained from the Trajectory Evaluator Assistant. This program uses the magnetic and electric fields and calculates the trajectory of a particle based on some input data from the user. The input data from the user is the charge on the particle, its mass and initial position, as well as the travel time.
In this example, the particle is an electron and is placed at a point near the cathode. The Trajectory Evaluator Assistant then calculates the path that the electron takes over the time specified by the user. The path, which proceeds counter-clockwise, is shown in magenta.
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Particle Position, Velocity and Acceleration
The Trajectory Evaluator Assistant produces the coordinates of the particle, as well as its velocity and acceleration over time. These results can be viewed as graphs within the Trajectory Evaluator Assistant and are available in a form that can be imported to other programs (e.g., Microsoft Excel).
In this example, a graph illustrating Position vs Time, only the x and y-components of the quantities are examined as the electron travels on the xy plane only.
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Velocity vs. Time
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