Control fusion plasma | microwave | live formula | algebra | function plot
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 … Read more
Tired of wrestling with complex polynomial equations and curious about their hidden structure or the nature of their roots? Step into a world of mathematical clarity with our brand new Web Polynomial Analyzer, your interactive gateway to exploring the fascinating realm of polynomials directly from your browser. We’ve designed this tool with no downloads or … Read more
1. Introduction: Modeling High-Power Electromagnetic Beams The precise generation, transmission, and manipulation of high-power microwave (HPM) and millimeter-wave (MMW) beams are critical for a range of advanced scientific and industrial applications. These include plasma heating in fusion energy research (like Electron Cyclotron Resonance Heating – ECRH), directed energy systems, high-resolution radar, industrial material processing, and … Read more
Our world is alive with waves – from the gentle ripples on a pond to the invisible carriers of sound and light. When these waves meet, they don’t simply pass by; they interact in a mesmerizing dance of reinforcement and cancellation, a phenomenon known as interference. This principle is fundamental, shaping how we perceive sound, … Read more
In modern software development, deploying applications consistently across different environments (development, testing, production) is crucial. Differences in operating systems, system libraries, or installed package versions can lead to the infamous “it works on my machine” problem. Docker solves this by allowing you to package your application, along with all its dependencies and required system configurations, … Read more
The Smith Chart, a cornerstone of RF and microwave engineering, offers a powerful graphical language for understanding and manipulating complex impedance. It’s essential for tasks ranging from antenna analysis to transmission line troubleshooting and, crucially, designing impedance matching networks. While its theoretical elegance is undeniable, translating designs onto the chart or exploring variations manually can … Read more
The detailed proofs of the key properties of Bessel functions of the first kind \( J_n(x) \) and the second kind \( Y_n(x) \). We’ll focus on:ODE derivationSeries expansion derivation for \( J_n(x) \)Parity proofRecurrence relationsDifferentiation identitiesAsymptotic behaviorDefinition and properties of \( Y_n(x) \) Bessel’s Differential EquationWe start from the ODE:\[x^2 y” + x y’ … Read more
Bessel functions are fundamental in many physics and engineering problems described in cylindrical/polar coordinates. While math.js is extensible, it doesn’t include them by default. Here is how to extend it.
Electromagnetic waves confined within waveguides are fundamental to microwave engineering, telecommunications, and particle accelerators, yet visualizing the invisible fields and understanding how different modes combine within the guide can be challenging. To bridge this gap, we introduce the Waveguide Pattern Visualizer, an interactive web application designed specifically to simulate and display the power distribution across … Read more
Typing French Accents on Canadian Multilingual Standard Direct Input Keys Character Key Combination ç ] Ç Shift + ] à \ À Shift + \ é / É Shift + / è ‘ È Shift + ‘ ù Right Alt + [ then u Ù Right Alt + [ then U Dead Keys for Accents … Read more