Ever wondered how tiny charged particles like electrons behave when they encounter powerful electric and magnetic fields? Imagine being able to not just read about it, but to see it happen, to tweak the conditions, and to observe the intricate dance in real-time. Our new interactive web application, the Electron Cyclotron Motion Simulator, lets you do just that! This browser-based tool is designed for students, educators, and physics enthusiasts to gain a deeper, intuitive understanding of fundamental electromagnetic principles and particle dynamics, including those relevant to devices like gyrotrons.
At its heart, the simulator solves the motion of electrons governed by the Lorentz force: F = q(E + v x B), where q is the electron’s charge, E is the electric field, v is its velocity, and B is the magnetic field. You get to control these fields and observe the outcome! Key physical concepts you can explore include Cyclotron Motion, where you can see electrons gyrate in circles when a magnetic field (B_z) is applied perpendicular to their motion. The app automatically calculates the initial transverse velocity needed for an electron to orbit the origin based on its starting position and the B-field strength. You can also investigate Electric Field Interaction by applying various types of electric fields in the plane of motion, controlling their magnitude and frequency , and choosing from Linear (X or Y axis), Circular Clockwise (CW), or Circular Counter-Clockwise (CCW) polarization. For high-energy electrons, where classical physics isn’t enough, you can toggle Relativistic Effects ON to see how an electron’s mass increases with velocity, impacting its trajectory and cyclotron frequency (f_c). This is crucial for understanding high-power devices. Furthermore, explore the Axial Velocity & Alpha Ratio; since electrons in many devices also have a velocity component (v_z) along the magnetic field, you can set the ratio alpha = v_⊥ / v_z to initialize electrons with both transverse and axial motion, observing how this combined velocity influences their total energy, relativistic gamma factor, and subsequently their cyclotron frequency.
Our simulator is packed with features to make your exploration insightful and customizable. Interactive Controls with intuitive input fields allow you to precisely set the Magnetic Field Strength (Bz), Electric Field Magnitude & Frequency, E-Field Polarization, the Velocity Ratio (α) for axial motion, and the Physics Time Step (dt) for numerical accuracy. The Flexible Electron Setup allows you to define initial electron transverse positions via a textarea (x,y in mm or r@angle in mm), with the simulator calculating the necessary orbital velocity. Alternatively, use Pick Mode to simply click on the canvas to add an electron, or utilize the Batch Circle Add modal dialog to place multiple electrons arranged in a circle, specifying the number, radius, phase offset, and whether to append or replace existing electrons – great for visualizing bunches or beams. You have full Real-Time Simulation Control with Start/Pause, Reset Time (reverting to initial states), and Load/Reload from Text to refresh based on the textarea. The motion is calculated using a robust 4th Order Runge-Kutta (RK4) numerical integration method, providing greater accuracy than simpler Euler methods, especially for orbital motion and energy conservation over time.
The right-hand panel brings the simulation to life with Rich Visualizations. Observe Real-Time Electron Animation as electrons trace their paths. Their Energy-Based Coloring (from blue for low, through yellow, to red for high energy) provides an immediate visual cue for energy changes. Electric Force Arrows on each electron indicate the direction and relative magnitude of the electric force it’s currently experiencing. Clear X and Y Coordinate Axes and an Orbit Guide (a faint circle indicating the initial intended orbit of the first electron) help visualize deviations. For Circularly Polarized Clockwise (CW) E-fields, you can enable visualization of Accel/Decel Sections: two 30-degree rotating, semi-transparent red and green regions highlighting where electrons are expected to be maximally decelerated or accelerated based on the E-field’s phase. The bottom-left of the animation panel displays critical On-Canvas Information: the Total Kinetic Energy of all electrons, the Current Cyclotron Frequency of the first electron, and the Simulation Time expressed in units of the electric field’s period (TE). The control panel also provides key calculated values in the Detailed Simulation Information section, including current simulation time (in ns), canvas scale (px/mm), calculated initial Kinetic Energy of the first electron, and the calculated E-Field Period (TE) and initial Cyclotron Period (Tc) and Frequency (fc) for the first electron, considering its total gamma factor.
This simulator isn’t just for watching particles move; it’s a sandbox for learning. You can Visualize the Lorentz Force directly, Understand Cyclotron Orbits and see how B, radius, and energy/velocity are related, and observe how f_c changes with relativistic gamma. Witness Relativistic Mass Increase and see how it prevents particles from exceeding light speed and affects their gyration. With an E-field, observe electrons Energy Exchange, visualized by color changes and KE displays – try to achieve resonance! The CW E-field, alpha ratio, and accel/decel sections provide a simplified glimpse into Gyrotron Concepts and energy extraction. Finally, appreciate the role of dt and the Numerical Methods used to handle complex motion.
Getting started is easy: no installation is needed! Simply open the index.html file in a modern web browser. Configure your desired field parameters, set the velocity ratio, define initial electron positions, click “Start,” and watch the physics unfold! While already a powerful tool, future enhancements could include more complex magnetic field geometries, different particle types, radiation damping effects, or data export. The Electron Cyclotron Motion Simulator offers an engaging and interactive way to explore the fascinating world of charged particle dynamics. By providing real-time visual feedback and extensive control, it aims to transform abstract physical concepts into tangible, understandable phenomena. Dive in, experiment, and see the dance of electrons for yourself!